Performance Studies and Star Tracking for PoGOLite CECILIA MARINI BETTOLO

Transcription

1 Performance Studies and Star Tracking for PoGOLite CECILIA MARINI BETTOLO Doctoral Thesis Stockholm, Sweden 2010

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3 Doctoral Thesis Performance Studies and Star Tracking for PoGOLite Cecilia Marini Bettolo Particle and Astroparticle Physics, Department of Physics, Royal Institute of Technology, SE Stockholm, Sweden Stockholm, Sweden 2010

4 Cover illustration: Crab Nebula composite image. Credits: X-ray: NASA/CXC/ASU/J; Optical: NASA/HST/ ASU/J. Akademisk avhandling som med tillstånd av Kungliga Tekniska Högskolan i Stockholm framlägges till offentlig granskning för avläggande av teknologie doktorsexamen fredagen den 4 juni 2010 kl 13:15 i sal FB52, AlbaNova Universitetscentrum, KTH Partikel- och Astropartikelfysik, Roslagstullsbacken 21, Stockholm. Avhandlingen försvaras på engelska. ISBN TRITA-FYS 2010:24 ISSN X ISRN KTH/FYS/--10:24--SE c Cecilia Marini Bettolo, Maj 2010 Printed by Universitetsservice US AB 2010

5 Abstract PoGOLite is a balloon-borne experiment, which will study polarized soft γ-ray emission from astrophysical targets in the kev energy range by applying well-type phoswich detector technology. Polarized γ-rays are expected from a wide variety of sources including rotation-powered pulsars, accreting black holes and neutron stars, and jet-dominated active galaxies. Polarization measurements provide a powerful probe of the γ-ray emission mechanism and the distribution of magnetic and radiation fields around the source. The polarization is determined using Compton scattering and photoelectric absorption in an array of 217 plastic scintillators. The sensitive detector is surrounded by a segmented Bismuth Germanium Oxide (BGO) anticoincidence shield. The function of this shield is to reduce backgrounds from charged cosmic rays, primary and atmospheric γ-rays, and atmospheric and instrumental neutrons. The anticoincidence shield consists of 427 BGO crystals with three different geometries. The characteristics of the BGO crystals of the bottom anticoincidence shield have been studied with particular focus on the light yield. The maiden flight of PoGOLite will be with a reduced detector volume pathfinder instrument. The flight, lasting about 24 hours, is foreseen from Esrange, Sweden in August The performance of the pathfinder has been studied using computer simulations. The effect of atmospheric attenuation, both on the signal of the astronomical target and on the background, are studied. These allow an observation strategy to be developed for the forthcoming flight. A polarization analysis method is described and applied to an observation example. The method sets an upper limit on the accuracy with which the polarimeter will be able to detect polarization the angle and degree. The PoGOLite polarimeter has a relatively small field of view ( ) which must be kept aligned to objects of interest on the sky. A star tracker forms part of the attitude control system. The star tracker system comprises a CCD camera, a lens, and a baffle system. Preliminary studies of the star identification performance are presented and are found to be compatible with the environment around the Crab, which is the main observational target for the first flight. iii

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7 Contents Abstract Contents iii v Preface 1 1 Introduction Gamma-ray Polarimetry Observations PoGOLite Scientific Objectives Polarization Emission Mechanisms Pulsars Accreting Black Holes Accreting Magnetic Neutron Stars Interaction of Gamma Rays Polarization Mechanisms Polarization Measurement Principle PoGOLite Polarimeter Instrument Overview Polarimeter Telescope Scintillators Phoswich Detector The Anti-Coincidence Shield Bottom Shield Side Anti-coincidence Shield, SAS Data Processing Sources of Background PoGOLite Pathfinder v

8 vi Contents 3 Tests of BGO Scintillators Market Survey Tests of Selected Candidates Acceptance Tests Energy Resolution Energy Resolution Setup for PDC Crystals The Fitting Method Further Studies Spectrum Anomaly Temperature Dependence of BGO Pulsars: Current Status Fermi Pulsar Features Light-Curves Minimum Emission Height Luminosity Spectrum Millisecond Pulsars Polarization Pulsars in a Broader View The Crab Pulsar and Nebula Studies of PoGOLite Pathfinder Performance Observation simulations with Geant Simulation Setup Analysis Steps Performance Studies Determination of M Minimum detectable polarization (MDP) Effects of Air Attenuation Neutron Background Outline of a Polarization Analysis Method Polarization Matrix χ 2 Matrix Background and Air Attenuation Analysis Procedure Case Study Modulation Curve Method Conclusions

9 Contents vii 6 The Star Tracking System Attitude Control System Design Star Tracking Matching System (STM) Star Tracker Design CCD Calibration Star Identification Software Design Tests Simulations Preliminary Sky Observation Tests Conclusions 167 A Minimum Detectable Polarization 169 Acknowledgments 173 List of figures 175 List of tables 179 Bibliography 181

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11 Preface Outline of the thesis This thesis describes three different aspects of the Polarized Gamma-ray Observer (PoGOLite). The first study concerns the performance of BGO crystals used for the bottom anti-coincidence shield. In the second study, the performance of the PoGOLite pathfinder instrument is assessed using computer simulations in preparation for the maiden balloon flight in August The final study addresses a preliminary calibration of a star tracker used in the PoGOLite attitude control system which keeps the PoGOLite instrument aligned to sources during flight. Chapter 1 provides an overview of developments in gamma-ray polarimetry, and describes scientific targets of interest to PoGOLite. The physics of the detection of polarization is also briefly described emphasizing the photon interaction processes on which the experiment relies. The experiment is described in chapter 2, with the polarimeter, anti-coincidence shield, electronics and pointing system described in detail. The PoGOLite pathfinder is introduced. This is a smaller version of PoGOLite which will be used to evaluate the design concept during a test flight foreseen for Chapter 3 presents the laboratory setups used for testing the scintillator crystals and the results of performance studies. In chapter 4, an overview of the current status of pulsar studies in the γ-ray band is given, demonstrating the necessity of polarimetric studies. The performance of the pathfinder are studied through Monte Carlo simulations in chapter 5. A simulation-based polarization analysis methodology is described in the same chapter. The final chapter describes the star tracker system and presents tests made on the CCD camera and star matching software. The author s contribution I started my PhD position in the Particle and Astroparticle Physics group at KTH in My position forms part of the AlbaNova High Energy Astrophysics and 1

12 2 Contents Cosmology (HEAC) Centre, funded as a centre of excellence by the Swedish Research Council. At the start of my PhD studies I was involved mainly in testing the performance of BGO samples which constitute the anti-coincidence shield of the polarimeter. I helped to prepare final specifications for the crystals and designed the prototype of the mechanical support for the anti-coincidence shield. Considering the large number of crystals that were received I set up a MySQL database in order to keep track of the crystal test results. After the testing of the final delivery of 240 crystals I coated the crystal surfaces in order to maximize internal reflections and improve the light collection performance. Then I concentrated my research on the star tracker system of PoGOLite. I tested the CCD camera, the baffle system, and I set up the first prototype of the star tracker computer, including acquisition software for the CCD. I also studied a possible control system for the focusing motor. In order to facilitate the testing of the matching software I prepared simulation software to create sky images. The work of the first years is described in my Licentiate thesis [1], which was presented in April With the forthcoming flight of the PoGOLite pathfinder, I have finally performed performance studies using computer simulations. These are done with the Geant4 toolkit. A mass model of the polarimeter already existed, and I contributed to optimize and update the software. With this final code I have constructed a polarization analysis method based on χ 2 -test and simulation data. Beside PoGOLite, during the early part of my studies, I was involved in the SEASA (Stockholm Educational Air Shower Array) project, especially in building scintillator detectors together with high school students and later in installing the detectors in the schools. The work described in this thesis has been partially presented in the following publications: C. Marini Bettolo et al., The BGO anticoincidence system of the PoGOLite balloon-borne soft gamma-ray polarimeter. Proceedings of 30th International Cosmic Ray Conference, Merida, Mexico. June T. Kamae et al., PoGOLite - A High Sensitivity Balloon-borne Soft Gammaray Polarimeter. Astroparticle Physics, 30 (2008) C. Marini Bettolo, The PoGOLite star tracker system. Proceedings of IEEE Nuclear Science Symposium, Dresden, Germany. October Additionally, publications describing other studies and progress of the PoGOLite development, and are listed below: M. Axelsson et al., Measuring energy dependent polarization in soft gammarays using Compton scattering in PoGOLite. Astroparticle Physics, 28 (2007)

13 Contents 3 T. Mizuno et al., A Monte Carlo method for calculating the energy response of plastic scintillators to polarized photons below 100 kev. Nucl. Instr. and Meth. A 600 (2009) 609. M. Pearce, M. Jackson, et al., PoGOLite - a high sensitivity balloon-borne soft gamma-ray polarimeter. Proceedings of IEEE Nuclear Science Symposium, Orlando, USA, October 2009.

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15 Chapter 1 Introduction When an electromagnetic wave propagates through space the electric field vector oscillates in the plane orthogonal to the direction of propagation. The polarization identifies the position in time of the electric field vector in the plane. Polarization is described by two components: polarization degree and angle. Depending on the rotation in time the polarization vector will describe an ellipse or a circle. If the orientation of the vector is fixed in time, the polarization is linear. The polarization depends on the emission process of the radiation and on the properties of the medium the electromagnetic field travels through. In astronomy polarimetry is a working tool that can be used across the whole electromagnetic spectrum, from the radio to the γ-ray energy band. It often gives information not accessible by other methods. At high energies the study of polarization is not as well advanced as compared to lower energies. In this chapter a summary of previous missions searching for γ-ray polarization is given. Some examples of sources that emit polarized radiation are described. Depending on the energy of the radiation different techniques can be used to detect polarization. At high energies polarization arises under various conditions. For synchrotron radiation, polarization is due to electrons gyrating in ordered magnetic fields. In this case the study of polarization provides information on the characteristics of the magnetic fields around the source. Since the interaction cross-section of the photons propagating through the magnetic field is energy and polarization dependent, it is possible to investigate directly the field close to the source, for example a neutron star or a gamma ray burst (GRB). Polarization can also be observed in Compton scattering of photons in the accretion disks around compact stars and active galactic nuclei. In both cases the orientation of the polarization plane depends on the geometry of the source, including the orientation of the magnetic field and accretion disk. All this makes polarization a powerful diagnostic tool. However, to date, few experiments have measured polarization at hard X-ray/soft γ-ray energies, where most of the power is usually emitted. 5

16 6 Chapter 1. Introduction 1.1 Gamma-ray Polarimetry Since the early 1960s the study of celestial X-ray and gamma-ray sources has dealt with their spectra, time variability and projected image on the sky. This information can probe the nature of different emission mechanisms for sources but in many cases is not enough to model the distribution of magnetic and radiation fields. The parameter space can be restricted if one studies also the polarization, which is described by two parameters: polarization degree and polarization angle. Many sources are expected to exhibit strong polarization: rotation-powered pulsars, accreting black holes, neutron stars and gamma-ray bursts (GRB). Moreover, high energy environments are always interesting for studying mechanisms impossible to reproduce on Earth. In the X-ray/γ-ray band the Crab nebula is the main target of many missions, due to the fact that it is the brightest non-variable source. This is also the reason why it is used as a calibration source, and Crab and millicrab are commonly used as units of flux density: in the kev band 1 Crab corresponds to W/m Observations The first attempt to measure polarization at X-ray energies was made in 1969 with an instrument based on Thomson scattering in lithium [2]. The Crab Nebula was observed with an observation time of 4 minutes. The results stated that the X-ray flux from the Crab nebula was 27% polarized between 5 kev and 22 kev with a confidence level of 99%. In 1971 a larger version of the Thomson scattering polarimeter with an additional Bragg reflection polarimeter were launched on a sounding rocket [3] to observe the Crab Nebula. A polarization degree of (14.7±7.9)% and polarization angle of (155±14) were measured for photon energies in the range of kev. For the range kev, the measurements yielded (24.1±10.2)% for the polarization degree and (155±11) for the polarization angle. In 1975 polarization measurements were made by the two X-ray polarimeters on the Orbiting Solar Observatory 8 (OSO-8). The Crab nebula was viewed at energies of 2.6 kev and 5.2 kev using the Bragg reflection technique (see figure 1.1) [4]. The measured polarization degree and angle of the nebula were (19.2±1.0)% and (156.4±1.4), (19.5±2.8)% and (153.6±4.0), for the two different energies respectively. Most recently, almost three decades after the first measurement, polarization studies were performed on the Crab nebula with the spectrometer SPI and the IBIS imager on the INTEGRAL observatory [6]. The operating mode of SPI is based on multiple Compton scattering events in a 19 hexagonal shaped pixel detector. Even though the instrument was not optimized for polarization measurements it was able to detect a polarization degree of (46±10)% and an angle of (123±11) (see figure 1.2) between 100 kev-1 MeV. The IBIS instrument, with its finely pixilated detectors, is also well suited for polarization measurement between 200 kev and 5 MeV, and confirmed the result of INTEGRAL with lower significance [7].

17 1.1. Gamma-ray Polarimetry 7 Figure 1.1. The polarization vectors for the Crab nebula at (left) 2.6 kev and (right) 5.2 kev as measured by OSO-8 [5]. Surrounding the vectors in order of increasing size are the 67% and 99% confidence contours. The radial scale is the polarization degree in percent.

18 8 Chapter 1. Introduction The polarization measurements of the Crab nebula can be compared with the earlier ones, and with the measurements in the optical band [8]. In the latter case the polarization degree was found to be 33% with an angle of 123. The values determined by INTEGRAL are close to the optical ones [8], in particular the polarization angle values are in agreement. The alignment suggests that the polarization arises under the same conditions in the same region of the nebula. The results of the polarization measurements in the X-ray band are summarized in table 1.1. Figure 1.2. The polarization of the Crab nebula measured by INTEGRAL: the gamma-ray polarization vector is superimposed on the composite image of the Crab observed by Chandra in the x-ray band (blue) and by Hubble Space Telecope in the optical band (red). The alignment suggests that the polarization arises under the same conditions in the same region of the nebula. The polarization vector goes through the pulsar and limits on the direction of the vector are indicated by the grey fan [6]. Another experiment, the PHENEX hard X-ray Compton scattering polarimeter, attempted in 2006 to observe the Crab system in the energy range kev from a balloon-borne platform. The reported degree of polarization [9] (33±26)% is inconclusive. A failure of the attitude control system was reported during the flight. Many new polarimetric instruments have been proposed to investigate the X/γregion. POLAR (5-300 kev) will study polarization arising in GRB through Compton scattering and photoelectric absorption in a plastic scintillator array [10]. GRAPE

19 1.1. Gamma-ray Polarimetry 9 Year Technique Energy Range Result 1969 Thomson 5-22 kev 27% at 99% C.L Thomson + Bragg 7-17 kev (15.7±7.9)% (155±14) 1971 Thomson + Bragg kev (24±10)% (155±11) 1975 Bragg 2.6 kev (19.2±1.0)% (156.4±1.4) 1975 Bragg 5.2 kev (19.5±1.0)% (153.6±4.0) 2008 Compton MeV (46±10)% (123±11) Table 1.1. List of past measurements of X-ray polarization of the Crab. ( kev), also based on Compton scattering with a very precise geometry reconstruction, will focus on polarization produced in solar flares as well as in GRBs [11]. CIPHER is a hard X-ray and soft γ-ray spectroscopic and polarimetric coded mask telescope and will study the Crab pulsar over the energy range 10 kev-1 MeV [12]. POLARIX ( kev) will be a pathfinder for a new technique, the Micropattern Gas Chamber. This method is a good imager and performs simultaneously timing and spectra [13]. IXO (2-6 kev), based on a gas image pixel detector, will study polarization from AGN (Active Galactic Nuclei) and will test strong gravity [14]. GRIPS ( kev) will focus, besides spectroscopy, on polarization mechanisms in GRBs [15]. GEMS (2-10 kev) will investigate polarization by tracking photoelectrons. The observation targets will be black holes, pulsars, neutron stars and supernova remnants [16] PoGOLite In this thesis the PoGOLite (Polarized Gamma-ray Observer - Light weight version) balloon-borne polarimeter is presented [17] [18]. PoGOLite is designed to study polarized emission from point-like sources in the energy band kev. The primary targets for the first flight are the Crab system (pulsar and nebula) and an accreting black hole candidate, Cygnus X-1. The detection of polarization is based on Compton scattering and photo-absorption in a closely packed array of plastic scintillator elements. The full version of PoGOLite comprises 217 such elements. A pathfinder flight of 61 elements instrument, expected to last approximately 24 hours, is foreseen for 2010 from the Esrange facility in the north of Sweden. The primary aim of this flight will be to test PoGOLite systems, evaluate backgrounds, and observe the Crab system. It is also foreseen to enlarge the instrument volume. Long duration flights of several days from Esrange to Western Canada or complete circumpolar flights, lasting about two weeks, are long term goals.

20 10 Chapter 1. Introduction 1.2 Scientific Objectives X-ray astronomy is a relatively new science. X-rays cannot penetrate the Earth s atmosphere so it is impossible to observe X-rays from astronomical sources with ground-based instruments. Detectors must therefore be deployed above the atmosphere. The specific altitude required depends on the energy of the X-rays, for example in order to detect radiation in the range of kev one has to reach 80 km, whereas for 30 kev photons 35 km is sufficient (see figure 1.3). The technology required for instruments above the atmosphere was unavailable until the mid-20 th century. An X-ray quantum has an energy of about 1000 times greater than an optical photon, thus if produced in a thermal process the temperature of the X-ray source has also to be 1000 times greater than the one of the optical source, which usually has a typical temperature of 3000 K. Until the discovery of the first astronomical X-ray emitter, sources with temperatures of millions of degrees had not been predicted. The first extra-solar X-ray source was detected in 1962 by Giacconi using a rocket [19]. The target of the mission was to study the X-ray radiation of the Sun reflected from the Moon. Unexpectedly, besides the two peaks coming from the Sun and the Moon a much brighter source was observed coming from the constellation of Scorpius and was called Sco X-1. The optical counterpart is a hundred times fainter than the faintest star that can be seen by the naked eye. This discovery opened up a new field in astronomy and revealed the presence of high energy phenomena and sources (see figure 1.4). To date, thousands of sources have been classified and the challenge is to understand the mechanism of their emission. One tool is to study the polarization of photons emitted by the source. This can be either intrinsic, if the radiation produced is polarized, or extrinsic, if polarization is induced after emission Polarization Emission Mechanisms Polarization is a characteristic of many emission mechanisms. The polarization degree and the polarization angle depend on the geometry of the source and/or on the magnetic field environment. The principal mechanisms that produce polarization are: synchrotron radiation, curvature radiation and inverse Compton scattering. Synchrotron Emission Synchrotron emission [22] is produced when an electron moves with relativistic velocity v in a magnetic field, B. The electron will experience a force, perpendicular both to the velocity and the magnetic field. Consequently it will move in a helicoidal trajectory along the magnetic field emitting radiation with a typical frequency ν γ 2, where γ is the Lorentz factor of the electron. One feature of synchrotron emission is the polarization, which depends on both the observer s position with respect to the beam and the energy of the emitted photons. The polarization vector determines the direction of the electric field in the plane orthogonal to the direction of propagation. The tip of the polarization vector

21 1.2. Scientific Objectives 11 Figure 1.3. The depth of penetration of different frequencies of light into the Earths atmosphere [20]. Figure 1.4. The HEAO-1 sky survey in galactic coordinates showing 842 X-ray sources. The sizes of the dots are proportional to the log of the intensity, the energy band is kev [21].

22 12 Chapter 1. Introduction describes in the most general case an ellipse. In the case of circular polarization the ellipse becomes a circle, whereas when the ellipse becomes a line, the polarization is linear. In the case of synchrotron radiation, the polarization is elliptical, but will become linear with increasing energy. The polarization vector is orthogonal to the magnetic field. In an astronomical context the energy distribution of the electrons if often assumed to be a power-law: n(e)de = n 0 E p de (1.1) where p is the power-law index, E is the energy of the electron, and n 0 is a normalization constant. The power-law index depends on the acceleration mechanism, and for an astrophysical source has a value between [22]. In the presence of a magnetic field such an electron distribution will emit synchrotron radiation. The photon spectrum will have the following shape [23]: P(E γ )de γ E (p 1)/2 γ de γ (1.2) with E γ the energy of the photon. The upper limit on the polarization degree that can be derived for an astronomical source is also of interest. It can be shown [22] that the upper limit on the degree of linear polarization, Π, for synchrotron radiation can be expressed as: For an astrophysical source Π = 65% 80%. Π = p + 1 p + 7/3. (1.3) Curvature Radiation Curvature radiation is due to the motion of an electron in the presence of a non-uniform magnetic field. The electron will drift in the direction of the field lines with an angular frequency ν γ 3. Thus, the emitted power will be a factor γ greater with respect to the synchrotron emission. The polarization characteristics are similar to those of synchrotron radiation, with the only difference being that the polarization vector is parallel to the magnetic field in this case. Inverse Compton Scattering During inverse Compton scattering a photon gains energy by scattering on a relativistic electron. The outgoing photon will have a typical energy, E: E = γ 2 E 0 (1.4) where E 0 is the initial energy of the photon, and γ is the Lorentz factor of the electron. Thus an optical photon can be boosted up to a gamma-ray photon. The emitted spectrum is similar to the one of previously described mechanisms, however, the polarization pattern is different.

23 1.2. Scientific Objectives Pulsars One of the primary targets for PoGOLite observations are pulsars, which are rapidly rotating, highly magnetized neutron stars. These objects are the final stage of stars with a mass greater than 8 solar masses but less than 20 solar masses. When the star, the progenitor, has finished burning, the gravitational force wins over the thermal pressure, leading to the collapse of the star. The neutron degeneracy pressure stops the collapse. The sudden deceleration sends a shock wave out into the collapsing gas, reversing its direction. This leads to a supernova explosion; the envelope is blown away and the neutron core, or neutron star, remains with a radius of 10 km. This will rotate with a period, P, which can be of few seconds to millisecond, due to conservation of angular momentum. The progenitor with radius 10 5 km was typically rotating with P 10 6 s. The presence of a strong magnetic field is inherited from the progenitor. If the rotation axis and the magnetic field axis are misaligned, magnetic dipole emission will take place. The result will be a pulsed beamed emission. Pulsars were discovered in 1968 by Jocelyn Bell and Anthony Hewish using a radio telescope meant to study scintillation observed when radio waves from quasars pass through the solar wind [24]. The data showed the presence of a source once every sidereal day ( 23 hours and 56 minutes) indicating that the source was outside the solar system. Investigating this signal in more detail, a series of regularly spaced radio pulses seconds apart were observed. Several more sources were quickly found by other radio observatories. To date about 550 pulsars are known, each designed by PSR (Pulsating Source for Radio) followed by the right ascension (RA) and declination (DEC). The pulsar discovered by Bell is for example PSR , identifying the position as RA = 19 h 19 m and DEC = +21. One of the properties of pulsars is that the mean frequency profile is (in most cases) extremely stable. The phase of this profile is very predictable. More recently pulsars have been observed also in γ-rays, see figure 1.5, and at other wavelengths. Another characteristic of pulsar emission is that it is generally thought to be highly polarized, with linear polarization dominating over circular. The polarization is determined by magnetic fields in or above the emission region. The profiles of the polarization degree and polarization phase are very stable within a source. There are currently three main models that describe the high-energy emission: polar cap model, outer gap model and caustic model (figure 1.6). In the polar cap model electrons and positrons are accelerated in the open field line region near the magnetic polar cap of a rotating neutron star. The curvature radiation emitted interacts with the strong magnetic field of the pulsar and produces e ± pairs. These pairs in turn emit synchrotron radiation which also interacts with the strong magnetic field. An electromagnetic cascade results, and the gamma-ray flux seen from the Earth consists of the curvature and synchrotron radiation. The outer gap model describes the emission of particles accelerated in the vacuum gaps formed in the outer regions of the pulsar magnetosphere along the boundary between the closed and open field line zones. In these gaps a high potential

24 14 Chapter 1. Introduction Figure 1.5. All sky γ-ray map seen by Fermi-LAT: 16 new pulsars (yellow) and eight millisecond pulsars (magenta) are shown [25]. drop is formed which accelerates electrons and positrons to high energies. Curvature radiation and inverse Compton photons emitted by these particles interact with low-energy particles to produce secondary pairs of electrons and positrons responsible for the synchrotron and inverse Compton radiation. Finally, the caustic model, a combination of the other two models, predicts that the emission takes place in a region confined to the surface of the last open magnetic field lines but extending between the polar cap and the light cylinder (the radial distance at which the rotational velocity of co-rotating particles equals velocity of light). To date, observations, especially from the Fermi Gamma-ray Space Telescope [26], rule out the polar cap model. The polar cap model can describe radio emission well, but fails in describing high-energy emission. The 2-pole caustic and the outer gap model can describe better, but not completely, the emission. A detailed overview of the current results will be given in chapter 4. All three models predict similar emission features which is why the three models have been working well for a long time. However, the polarization profiles differ depending on the models. Due to the difficulty of measuring polarization at high energy there are no results regarding the polarization pattern yet. The primary target of PoGOLite will be the Crab pulsar and nebula, since it is one of the brightest astronomical objects in the X-ray region.

25 1.2. Scientific Objectives 15 Figure 1.6. Schematic illustration of pulsar acceleration models. The pulsar in the middle rotates with angular velocity Ω around the vertical axis. The magnetic field B forms an angle α with the rotation axis [27]. Three different emission regions are shown: polar cap, slot gap and outer gap. The polar cap emission takes place close to the poles, the outer gap goes from the null surface to the light cylinder, and the slot gap emission arises along the last open magnetic field line.

26 16 Chapter 1. Introduction Accreting Black Holes Another type of object of great interest for PoGOLite are accreting compact objects. A well known object among these is Cygnus X-1 which is a black hole candidate. It is the brightest accreting compact object of X-rays above 20 kev. It is part of an X-ray binary (XRB) system consisting of a super-giant 09-B0 (20-30 M ) and a compact object (7-13 M ). Since the mass of a neutron star cannot exceed 3 M it is believed that the compact object is a black hole. The material flowing from the super-giant to the black hole is predicted to gather in a hot, rapidly rotating accretion disk, hot enough to emit X-rays. The source shows a spectrum which consists of two distinct spectral states (see figure 1.7), the so called hard (low) state and soft (high) state (see figures 1.7, 1.8). Transitions from the hard state to the soft state take place every few years and the source stays in the soft state only for weeks or months. The hard state is primarily due to multiple scattering of blackbody photons from a cold disk by thermal electrons in a hot inner flow. The contribution of nonthermal synchrotron emission is small. Some hard X-rays are Compton reflected on the cold disk, which is truncated and does not reach the innermost stable orbit but overlaps the inner flow. The signature of this secondary component are the 6.4 kev FeK fluorescence line, proof of cold material in the disk, and a broad hump at kev, an indication of Compton reflection by the cool material. The second component is believed to be intrinsically polarized (>50%), depending on the inclination relative to the observer, but since albedo particles contribute with a 30% polarization the resulting polarization is about 15%. Polarization measurements in the energy range of the hump ( kev) can provide constraints on the geometry of the emission. In the soft state X-ray emission arises from Compton up-scattering of non thermal electrons in active regions above the disk surface. In this case polarization could give information about the anisotropy of the non-thermal distribution of electrons.

27 1.2. Scientific Objectives 17 Figure 1.7. Energy spectrum of Cygnus X-1. The solid lines represent the models of emission, the dashed curves represents the model before galactic absorption. The soft state has a higher flux which peaks in the lower energies, whereas the hard state peaks at higher energies. An upper limit for EGRET and a sensitivity for GLAST (now Fermi) are shown. The vertical red lines indicate the energy range of PoGOLite [28].

28 18 Chapter 1. Introduction Figure 1.8. Schematic representation of the two different geometries of Cygnus X-1. Hard spectral state (top): hot inner accretion flow surrounded by optically thick accretion disk. The disk does not reach the minimum stable orbit but overlaps the hot flow. The soft photons emitted by the disk are Compton up-scattered in the hot flow, and the emission from the hot flow is partly Compton-reflected from the disk. In the soft state (bottom) a flares/active region extends on an optically thick accretion disk close to the minimum stable orbit. The soft photons are up-scattered in the flares, and emission from flares is partly Compton-reflected from the disk [29].

29 1.2. Scientific Objectives Accreting Magnetic Neutron Stars The accreting source of an XRB can also be a neutron star with a strong magnetic field (10 13 G) on the surface. The X-ray and γ-ray radiation originates from the accreting material which is flowing along the lines of the magnetic field onto the poles of the neutron star. In the strong magnetic field near the poles the plasma electrons will gyrate in the plane perpendicular to the magnetic field and interact with higher probability with photons that are polarized in the plane orthogonal to the magnetic field. The resulting radiation will also have a net polarization. Since the neutron star is rotating the polarization and degree of linear polarization will be modulated in time. Time resolved polarization measurements can provide information about orientation and magnitude of magnetic field relative to the observer. In a long duration flight PoGOLite will be able to confirm the underlying mechanism responsible for the reflection component, most probably Compton scattering. The first target among these objects will be Hercules X-1, and in addition two bright transient objects, 4U and V , which have been observed to have outbursts lasting several months.

30 20 Chapter 1. Introduction 1.3 Interaction of Gamma Rays When a mono-energetic photon beam of intensity I 0 passes through a material of thickness x, and of mass thickness X = ρx, the intensity of the beam decreases as: I(x) = I 0 e µx = I 0 e (µ/ρ)x (1.5) where µ is the linear mass absorption coefficient, ρ the density and µ/ρ the mass absorption coefficient. This coefficient is related to the cross-section σ by µ = σρ/ua, where A is the atomic number of the material and u is the atomic mass unit. The dominant contributions to the cross-section for photon energies above 10 kev in water 1 are: the photoelectric effect at energies below 10 kev, the Compton effect around energies of 1 MeV and pair production above energies of 2 MeV. The PoGO- Lite determination of polarization is based on the first two interactions: photons Compton scatter and are then photo-absorbed. Photoelectric Absorption In photoelectric absorption a photon is absorbed by an atom, and a photo-electron from an atomic shell (usually the K-shell) is ejected with an energy: E e = hν E b (1.6) where E b represents the binding energy of the photo-electron in its original shell and hν is the energy of the photon. The vacancy in the ionized absorber atom is filled through capture of a free electron from the medium and/or a rearrangement of electrons from the other shells of the atom. The photoelectric effect dominates for γ and X-rays of relatively low energy, and the probability increases with increasing atomic number Z. No analytical equation for the differential cross-section exists, but an approximation is given by: dσ dω = K Zn E 3.5. (1.7) For photon energy, E γ, below 0.5 MeV, K is a constant and n varies between 4 and 5 [30]. For higher energies the differential cross-section becomes: where n is defined as before and K is a new constant. γ dσ dω = K Zn E γ (1.8) Compton Scattering In Compton scattering the γ-ray photon is deflected from the original direction. Part of the energy is transferred to an electron. All scattering angles are possible and the energy of the electron can vary from zero to a large fraction of the photon energy. The probability of Compton scattering depends 1 Water has similar cross section to the plastic scintillators used in the PoGOLite polarimeter.

31 1.4. Polarization Mechanisms 21 on the number of electrons available as scattering targets and therefore increases linearly with Z. It is given by the Klein-Nishina formula [30]: dσ dω = 1 [ ] 1 2 Zr2 eǫ 2 ǫ + ǫ 2 sin2 θ cos 2 η (1.9) where ǫ = E /E = 1/(1 + α(1 cosθ)), α = E/m e c 2, r 0 is the classical electron radius, m e the mass of the electron, θ is the angle between the incident photon direction and the scattered photon direction, and η is the azimuthal scattering angle relative to the plane of the electric field. Pair Production Pair production is possible if the energy of the γ-ray photon exceeds twice the rest-mass of an electron (1.02 MeV). The probability remains very low until the γ-ray energy approaches several MeV. The γ-ray photon interacts in the Coulomb field of a nucleus and is absorbed, and an electron-positron pair appears. The differential cross-section is described by dσ dω = AZ2 (ln E γ B) (1.10) for photon energies 2 MeV E γ < 137/Z 1/3 MeV, A and B are constants, Z is the atomic number. For photon energies E γ 137/Z 1/3 the differential cross-section becomes ( ( ) ) dσ 183 dω = CZ2 ln D (1.11) Z 1/3 where C and D are new constants [30]. 1.4 Polarization Mechanisms The possibility of measuring polarization is given by the fact that the differential cross-section of the radiation interaction depends on the polarization of the incoming photon. Even though PoGOLite is based on Compton scattering, a short overview of the methods used to detect polarization signal in the γ/x-ray regime is given for completeness. The main processes are Bragg reflection, photoelectric absorption, Compton scattering and pair production. Bragg Reflection Photons with wavelength λ undergo Bragg reflection when they reflect off a crystal with lattice constant d and interfere constructively, at different orders n, at an angle θ: nλ = 2d sinθ. (1.12) The component of the electric field, which is parallel to the plane of the crystal, will be totally reflected whereas the orthogonal component will not be reflected.

32 22 Chapter 1. Introduction Thus if the crystal is rotated around the line of sight and the X-rays scatter through 90 the reflected signal will be sinusoidally modulated at twice the rotation frequency. The main disadvantage of this technique is that the polarization will be measured only for specific energies that satisfy equation Usually the values are of the order of a few kev. Moreover since the intensity drops with increasing n, usually only the first orders can be used. A schematic view of the principle of operation of the polarimeter is shown in figure 1.9. The Bragg reflection technique has been used on the OSO-8 satellite [4]. Figure 1.9. Principle of operation of a Bragg crystal polarimeter [22]. Photoelectric Effect For energies below 30 kev the photoelectric effect can be exploited to study polarization, the emitted photoelectron of the K-shell carries the memory of the polarization of the incoming photon. The distribution of the photoelectron is modulated with a cos 2 φ term with φ the angle between the direction of emission and polarization. The differential cross section of the process is: dσ dω sin2 θ cos 2 φ (1 β cosφ) 4 (1.13) with θ the angle between the direction of the photon and the direction of the photoelectron, see figure 1.10.

33 1.4. Polarization Mechanisms 23 Figure Photoelectric effect in a gas. Following the photon conversion in the gas, the photoelectron is ejected with an angle θ respect to the incoming photon. The direction carries a significant memory of the electric field. The azimuth angle φ indicates the angle between direction of emission and polarization vector [31].

34 24 Chapter 1. Introduction The electron undergoes several elastic scatterings which randomize its direction. The challenge in this technique is to reconstruct the track since the information of polarization is in the initial part of the track because the photo-electron undergoes Coulomb diffusion on the nuclei. Compton Scattering The differential polarimetric Compton cross-section is described by the Klein-Nishina formula, already mentioned before. For completeness it is rewritten here: dσ dω = 1 [ ] 1 2 Zr2 e ǫ2 ǫ + ǫ 2 sin2 θ cos 2 η (1.14) The azimuthal angle η is the angle relative to the plane of polarization. When projected on a plane, the angle of scattering will thus be modulated as cos 2 η and the resulting scattering angle depends on the polarization of the photon (see figure 1.11). If the incoming beam has a net linear polarization and the detector is rotating, the distribution of the scattered photons should reveal a cos 2 η shape. This modulation contains the information about the polarization of the source. Photons scattered directly forward (θ = 0 ) or directly backward (θ = 180 ) carry no information about polarization of the incident photon beam. This technique is used between 30 kev and several MeV, whereas in the non-relativistic limit, Thomson scattering is valid for energies below 30 kev. Figure A schematic illustration of Compton scattering. An incoming photon with energy E and electric vector ξ scatters off an electron. The incident and scattered photon form an angle θ and η is the azimuthal angle of the scattered photon with respect to the electric vector of the incident photon [22]. Pair Production At higher energies (above 2 MeV) pair production can be used to make polarization measurements. This process is sensitive to the polarization of the incident photon in that the plane of pair production tends to lie

35 1.5. Polarization Measurement Principle 25 parallel to the incident electric field vector. The cross section for pair production by polarized photons is: σ(φ) = σ 0 2π [1 + PR cos(2(φ φ 0))] (1.15) where φ φ 0 is the angle between the plane containing the electron-positron pair and the direction of the gamma-ray polarization, σ 0 is the total cross section, P is the degree of linear polarization and R 0.1 is the strength of the quadrupole asymmetry for the pair production process [32]. In practice it is very difficult to determine the plane which contains the pair because the azimuthal orientation depends weakly on the polarization, and multiple Compton scattering makes it even more difficult to identify the orientation of the plane. 1.5 Polarization Measurement Principle In the γ/x-ray band the polarization of photons is extracted from the modulation factor M. This quantity describes the asymmetry in the scattering of the photons, which depends on the polarization angle and degree (see figure 1.12). In the specific case of PoGOLite the incoming photon will Compton scatter in the detector. The scattering direction will be determined by locating the photo-absorption site of the outgoing photon. To extract polarization information from a source, the modulation factor M and the average value T are used, defined as: and M = C max C min C max + C min (1.16) T = C max + C min. (1.17) 2 It can be shown [22] that the modulation can be parametrized as f(η) = T(1 + M(cos(2η + 2α))) (1.18) where η is the azimuthal angle (see figure 1.12), and α is the polarization angle of the source. The modulation factor is connected to the polarization degree, P, through the equation P = M M 100 (1.19) where M 100 is the modulation factor for a 100% polarized source. This is determined through simulations or beam test measurements. An important figure of merit is the MDP (Minimum Detectable Polarization) at a certain confidence level, nσ (it is customary to use 99%), which quantifies how statistically well determined a measurement is.

36 26 Chapter 1. Introduction Figure Distribution of scattering angles used to determine the modulation factor [33]. The MDP at 99% confidence level is defined as: MDP nσ = 4.29 M 100 R S [ ] 1/2 RS + R B (1.20) where R S and R B are the source and background rates respectively, and T the observing time. The MDP has to be smaller than the degree of polarization to be measured. The challenge in designing a polarimeter depends first of all on the fact that unpolarized background is added to the sought polarized signal. Moreover the degree of polarization is positively defined, see equation Thus a polarimeter will always measure a degree of polarization and all polarimeters have a detection limit set by the MDP. T

37 Chapter 2 PoGOLite Polarimeter PoGOLite, the Polarized Gamma-ray Observer-Lightweight version, is a balloonborne experiment designed to detect polarization from a 100 mcrab point source in the energy band band kev. The study of point sources is possible due to the small field of view of The measurement of the polarization signal is based on the simultaneous detection of Compton scattering and photoelectric absorption in an array of plastic scintillators. PoGOLite is an international collaboration between several research groups from Sweden 1, the United States 2 and Japan 3. In this chapter the PoGOLite payload is described with particular focus on the polarimeter. In the last section PoGOLite Pathfinder is described. This is a smaller version of PoGOLite which will be used to evaluate the design concept during a test flight foreseen for Instrument Overview The PoGOLite payload, shown in figure 2.1, consists mainly of a polarimeter telescope with a cooling system, a data acquisition system and an attitude control system (ACS). These systems are mounted on a gondola frame which connects to a stratospheric balloon which lifts the apparatus to an altitude of about 40 km. The polarimeter, data acquisition electronics and cooling system are placed in a pressure vessel which is mounted on an elevation pivot. The polarimeter is able to rotate around its longitudinal axis to allow systematic effects to be studied during observations. The ACS, discussed in chapter 6, controls the position of the telescope relative to the gondola platform, and the orientation of the gondola in space. The cooling system is needed to remove the heat generated by the electronics. The heat 1 Royal Institute of Technology and Stockholm University. 2 Stanford Linear Accelerator Center, Kavli Institute for Particle Astrophysics and Cosmology and the University of Hawaii. 3 Tokyo Institute of Technology, Hiroshima University, Yamagata University, Japan Aerospace Exploration Agency. 27

38 28 Chapter 2. PoGOLite Polarimeter can degrade the performance of some parts of the polarimeter, details are found in [34]. Figure 2.1. Overview of the PoGOLite payload. The dimensions of the gondola is 2.9 m 2.9 m and height about 3.5 m Polarimeter Telescope The measurement of polarization is based on Compton scattering and photoelectric absorption. To provide spatial resolution in order to detect the positions of the signals the detector has to be segmented. By connecting the photon scattering and absorption centers the scattering angle is determined, which allows the photon polarization to be measured. The PoGOLite polarimeter consists of a hexagonal close-packed array of 217 phoswich detector cells (PDCs), made from plastic scintillators and BGO (bismuth germanate oxide: Bi 4 Ge 3 O 12 ), surrounded on the side and bottom by an anticoincidence shield made from BGO crystals (see figure 2.2). The assembly is housed in a cylindrical structure (the inner cylinder) which can rotate (see figure 2.3.). The inner cylinder is placed in a second cylinder (the outer cylinder) filled with polyethylene for neutron background reduction [35]. Each PDC unit is composed of a thin-walled tube of slow plastic scintillator (fluorescence decay time 285 ns),

39 2.2. Scintillators 29 a solid rod of fast plastic scintillator (decay time 2 ns) and a short BGO crystal (decay time 300 ns), all read out by a single photomultiplier tube (PMT). The wells serve as active collimators, the fast scintillator rod is where photon detection and scattering take place, and the bottom BGO acts as lower anti-coincidence. More details about the configuration and working operations of the detector are given in section 2.3. The anti-coincidence system comprises an array of BGO crystals which covers the side and bottom of the PoGOLite polarimeter as shown in figures 2.2 and 2.3. The bottom shield consists of an interlocking assembly of crystals with hexagonal cross-section. Each crystal forms part of a PDC unit, and interfaces the PMT to the solid fast scintillator. The side shield is made of 54 elements which each in turn consist of 3 crystals of pentagonal cross-section. Signals from the 217 PDC units and from the 54 SAS elements are read out by PMTs and fed to individual ADCs (Analog to Digital Converters) and digitized to 12 bit accuracy at 24 MHz. From all recorded waveforms only those containing a signal generated only in the fast scintillator are kept for further analysis. The well-type phoswich detector technology was proven to reduce cosmic-ray background by more than one order of magnitude by the WELCOME balloon experiment [36] and the Suzaku Hard X-ray Detector [37], [38]. In the PoGOLite design, the PDCs are used to detect both Compton and photo-absorption of the X-ray radiation of interest. This property allows the detector to be scalable in size, hence the possibility to test the detector at different stages. It also allows the reuse of the detector units in a bigger version of the polarimeter in future missions. A disadvantage of the dual functionality detector units is the fact that the scintillator has to be able both to detect and measure the two interactions. This restricts the choice of the scintillators and lowers the energy resolution. 2.2 Scintillators Two types of scintillators, organic (liquid and plastic) and inorganic (crystals, glass and noble gases) exist. In organic scintillators the production of scintillation light relies on the process of fluorescence which is the transition in the energy level structure of the single organic molecule. Many organic scintillators are based on molecules with a π-electron structure (the structure is illustrated in figure 2.4). Energy absorption can excite the electron to a number of excited singlet states: S 0, S 1, S 2...(spin 0) or T 1, T 2, T 3... (spin 1). The singlets are subdivided into different vibrational states. S 00 represents the lowest vibrational state of the electronic state. A charged particle passing nearby can excite the electron to a higher energy singlet state which then deexcites to the S 10 singlet. The principal scintillation light (prompt fluorescence) is emitted in transitions between S 10 and S 0 states. The intensity of fluorescence at a time t is described by: I = I 0 exp( t/τ) (2.1)

40 30 Chapter 2. PoGOLite Polarimeter Figure 2.2. The PoGOLite polarimeter. The lateral green units are the SAS BGO crystals (not all crystals are shown for clarity), and the purple and orange items are the slow and fast scintillators, respectively. The bottom BGO crystals are also shown in green, and the PMTs are shown in yellow. The total length is about 1 m. The neutron shield is not shown.

41 2.2. Scintillators 31 Figure 2.3. Axial cross section of the PoGOLite polarimeter (not to scale). The inner cylinder holds PDCs, the anti-coincidence shield, PMTs and data acquisition system (not in the picture). The outer cylinder houses the rotation mechanism, the pivot for elevation pointing, and the polyethylene shield [39].

42 32 Chapter 2. PoGOLite Polarimeter Figure 2.4. Energy levels of an organic molecule with π-electron structure [30].

43 2.2. Scintillators 33 where I 0 is the initial intensity and τ the fluorescence decay time. Since the fluorescence energy is less than the total absorbed energy (see figure 2.4), organic scintillators can be transparent to their own fluorescence emission. The organic scintillators PoGOLite uses are plastic, Eljen Technology EJ-204 and Eljen Technology EJ-240 [40]. Plastic scintillators are not ideal absorbers but have good performance for Compton scattering. The performance of the plastic scintillators have been tested and show that a polarization signal is still possible to be detected (see section 2.4.3). The linear attenuation coefficient for a plastic scintillator as function of energy is shown in left panel in figure 2.5. Figure 2.5. Linear attenuation factor for plastic scintillator (left) and BGO (right) [41]. The scintillation mechanism in inorganic scintillators depends on the energy states determined by the crystal lattice. Absorption of energy results in an electron being excited from its ground state in the valence band to the conduction band (figure 2.6). The gap is such that the released energy would be too high to lie in the visible band. To increase the probability of emission of visible photons, impurities (activators) are added. The anti-coincidence shield is made of BGO, its major advantage is the high density (7.13 g/cm 3 ) and the large atomic number (83) of the bismuth component, which results in a very high probability per unit volume for the photoelectric absorption of gamma rays. It is also easy to handle since it is not hygroscopic in

44 34 Chapter 2. PoGOLite Polarimeter Figure 2.6. Energy band structure of an activated crystalline scintillator. comparison to other inorganic scintillator materials. BGO presents a large shift between optical absorption and emission spectra, thus the crystal remains transparent to its own emission over dimensions of many centimeters. The linear attenuation coefficient as a function of energy is shown in the right panel of figure 2.5. The disadvantages of the BGO crystals are the low light yield, the high refractive index (2.15) which makes light collection difficult due to internal reflections, the temperature dependence of the light output and the large weight and cost. The BGO crystals are grown through the Czochralski process, in which a small seed crystal is used to produce a bigger boule [42]. Later the crystals are shaped into the desired shape. This process does not permit, so far, to easily grow big volumes of BGO, in fact in the case of the 600 mm side anti-coincidence shield three different 200 cm long sections are used. 2.3 Phoswich Detector The PDCs combine collimation, detection and anti-coincidence functions in a single unit (see figure 2.7), thus they can be packed closely together to avoid gaps. The dimensions and characteristics of these units are dictated by the physics of photon interactions. The lowest photon energy to which PoGOLite is sensitive puts a limit on the width of the PDC fast scintillator (EJ-204). At 20 kev a significant fraction of the scattered photons are photo-absorbed and stopped within a few cm after the scattering point. Since Compton scattering and photo-absorption have to take place in two different PDCs a width of 2.75 cm has been chosen (see figure 2.8), a lower width would require a finer pixellization and thus more complex mechanics and electronics. The depth of the detection unit has to fulfill two requirements: the volume has to be deep enough for a Compton scattering to take place and shallow enough to limit the photons that remain in it to polar scattering angles about (90 ± 30). A length of 20 cm ensures that in the energy band of kev 95% of the photons will Compton scatter. To improve light collection, the plastic scintillators are wrapped in highly-reflective 3M VM2000 reflector film [43].

45 2.4. The Anti-Coincidence Shield 35 The slow plastic scintillator (EJ-240) serves as a collimator. The efficiency in detecting and vetoing charged particles depends on the thickness of the walls, 2 mm. Each wall is sheathed in a 50 µm thick layer of tin and lead foils to provide passive collimation. The length of 60 cm and its associated passive collimator shell determines the field of view (FOV) of The BGO crystals at the end of the PDC unit are part of the anti-coincidence shield and will be described in the following section. All three sections are joined together with a UV transparent epoxy glue (Hartel Plastics). The entire PDC stack is read out by a single PMT (Hamamatsu R7899EGKNP) (shown in figure 2.9), and the different decay times of the scintillation light (slow plastic: 285 ns, fast plastic: 1.8 ns, and BGO: 300 ns), allows the signal to be separated and thus to trigger the data acquisition. The crystals have to be transparent to their own scintillation light (480 nm) and to the light produced in the slow (435 nm) and fast (408 nm) plastic scintillators. The PMT converts the scintillation light to an electrical pulse which is sampled by a flash ADC (FADC). This photomultiplier is chosen since it has a low noise, which is very important since the energy deposited during Compton scattering is very small. Figure 2.7. Phoswich Detector Cell: (left) schematic drawing and (right) photos of slow, fast and bottom BGO scintillator before being glued together. 2.4 The Anti-Coincidence Shield The PDC assembly is surrounded by a BGO crystal anti-coincidence shield. Three different crystal geometries are used (figure 2.10). The BGO crystals were provided by the Nikolaev Institute of Inorganic Chemistry, Novosibirsk, Russia.

46 36 Chapter 2. PoGOLite Polarimeter Figure 2.8. Cross section of the slow scintillator section (left) and the fast scintillator (right). Figure 2.9. Picture of PMT Hamamatsu R7899EGKNP. The aperture is visible where the cylindrical protrusion of the BGO bottom crystal is seated, the total length is 190 mm. The shield consists of a side and a bottom part, to reduce background from charged cosmic rays, primary and atmospheric gamma-rays, and atmospheric and structure induced neutrons. Signals produced in the BGO crystals will be used to veto background events Bottom Shield The bottom BGO shield consists of 217 identical crystals, of length 4 cm and maximum width of 3 cm, as shown in figure Each crystal has a mass of 160 g. The complex geometry, a hexagonal section which goes to a cylindrical one, arises from its function as a waveguide: it has to couple the hexagonal detector section to the round aperture of the PMT. The length is a compromise for having a high light transmission, a low weight and cost and at the same time for being an efficient anti-coincidence shield. The width is 0.5 mm wider than the plastic well and detector, in order to form a nearly continuous layer with the rest of the PDC unit (the 0.5 mm gap in the upper part is filled by reflection material and passive shield). To improve the light yield and to provide optical isolation between

47 2.4. The Anti-Coincidence Shield 37 Figure Picture of the side and bottom crystals: left the bottom crystal, in the middle the corner unit and right the edge unit. The SAS units are seen from the end that will be connected to the PMT, it is made of three 20 cm long crystals, the height of the bottom BGO is 4 cm. the adjacent units the crystals are coated with a 100 µm thick BaSO 4 loaded resin. The crystals are seated in an aluminum base plate, the hexagonal end is joined to the detector scintillator with the epoxy glue, the cylindrical part fits into the PMT aperture and is attached to the PMTs window through optical grease and a silicone pad. A detailed study of the bottom BGO crystals is described in chapter Side Anti-coincidence Shield, SAS The SAS shield is segmented into 54 units, each of them has a BGO mass of 4.5 kg, is 600 mm long and is built of three crystals. The SAS units together with the PDC hexagonal array form a bigger hexagonal assembly (see figure 2.11). The resulting geometry for the BGO crystals is of two types. This configuration is scalable and in a future bigger version of the detector the crystals can be reused.

48 38 Chapter 2. PoGOLite Polarimeter Figure Cross section of 217 PDC cells (red) and 54 SAS units (orange). The total width is approximately 60 cm.

49 Figure Drawing of the two types of crystal used in the SAS shield: the crystal type used for the 6 sides of the shield (left), the crystal used for the 6 corners (right). The dimensions are in mm The Anti-Coincidence Shield 39

50 Figure D drawing of the two types of crystal used in the SAS shield and which connect to PMT: the crystal type used for the 6 sides of the shield (left), the crystal used for the 6 corners (right). The dimensions are in mm. 40 Chapter 2. PoGOLite Polarimeter

51 2.4. The Anti-Coincidence Shield 41 The SAS shield covers two thirds of the length of the PDC elements, this length is enough for covering the acceptance of the fast scintillators and saves weight and cost. Each unit of a given type is built of two upper crystals with flat ends (see figure 2.12) and one piece which has a cylindrical protrusion on one end (see figure 2.13), 23 mm in diameter, which interfaces to a PMT (the same type that is used for the PDC units). The three crystals within one unit are joined together with UV-transparent epoxy glue (EpoTek 301-2). All BGO surfaces, except optical interfaces, are coated with the same BaSO 4 -loaded resin layer as the bottom crystals to improve light yield and to optically separate adjacent crystals. The SAS crystals are located around the PDC array with a mechanical support system. The design of this must allow for the significant acceleration experienced at the end of the flight (parachute opening, landing). The segmentation of the SAS shield makes it possible to correlate SAS and PDC events, thus reducing the risk of rejecting valid events Data Processing Signals from all 217 PDCs and 54 SAS PMTs are sent to the 38 FADC boards. Each board is equipped with a FPGA (Field Programmable Gate Array) which checks for signals compatible with energy deposits in the fast scintillator between 15 kev and 200 kev. If the FPGAs detect a signal above the discrimination level or with a slow rise-time due to the slow plastic scintillator or to the BGO, a veto signal is produced, whereas if the signal is clean a trigger is issued and the digitized waveforms of all PMTs are stored for a period of 1.6 µs starting 0.4 µs earlier than the trigger. This allows to correct for possible baseline offset from preceding signals. Only PDC data with a transient greater than 0.5 kev will be stored in the buffer of the FADC. The trigger rate is expected to be about 0.5 khz and the data-rate about 240 kb/s with no zero suppression. The waveforms and hit pattern are stored on an onboard computer, the Space Cube, and are processed [44]. A valid event is one that travels through the slow plastic scintillator without hitting the walls, reaches the fast scintillator where it Compton scatters, and then is photo-absorbed or manages to escape from the active detector (see figure 2.14). The selection of the PDC where the photo-absorption takes place is done by choosing the highest energy compatible with being a clean fast signal in the fast scintillator (see figure 2.15). Figure 2.16 shows how well γ-ray signals from 241 Am (59.5 kev) can be selected in the fast scintillator while embedded in a background environment created by 90 Sr electrons in the slow scintillator. The diagonal concentration of dots between the two dashed lines corresponds to clean fast signals in the fast scintillator. A strong concentration of recorded events can be found around the dominant line of 60 kev. The signals from all neighboring PDCs, up to two rings or 18 PDCs, around the identified photo-absorption site are searched for a Compton scattering signal. For valid events the distribution of the sum of the energy depositions, at the photo-absorption site and at the Compton scattering site, is plotted versus the

52 42 Chapter 2. PoGOLite Polarimeter Figure Schematic cross section of PoGOLite detector (not to scale) showing valid and background photon interactions. Also possible background events are shown. Figure An example of waveforms of PoGOLite charge sensitive amplifier output signal. The rise time (negative polarity) is shorter for the fast plastic scintillator, whereas slow plastic and BGO scintillator have a longer rise time [44].

53 2.4. The Anti-Coincidence Shield Figure Selection of clean gamma-ray hits from 241 Am on the fast scintillator while the slow scintillator is irradiated with electrons from 90 Sr. Each dot corresponds to one triggered event. The horizontal and vertical coordinates are the charges integrated over the fast ( 120 ns) and slow ( 1µs) component of the pulse. A crude energy scale for gamma-rays detected in the fast scintillator has been added [39]. 43

54 44 Chapter 2. PoGOLite Polarimeter Sum of deposited energies [kev] distribution of the energy deposition at the Compton scattering site. Such a distribution, obtained at the test beam at KEK Photon Factory, Japan, in 2007, is shown in figure The bound region identifies the events for which both Compton scattering and photo-absorption have taken place. For these events the azimuthal angle is then calculated and it is possible to plot the modulation curve. The arrangement of the corresponding PDCs is shown in the bottom panel of figure The top panel in figure 2.18 shows the modulation curve for three pairs of PDCs. On the x-axis the rotation angle of the detector relative to the plane of the polarized beam is shown. The energy of the beam is 25 kev and has a polarization degree of (90±1)%. The measured modulation factor is (33±0.7)% Energy deposit in the center PDC [kev] Figure Selection of Compton scattered events for data taken in a 25 kev 90% polarized beam at KEK. The dashed box shows valid Compton scattering events [39] Sources of Background Several backgrounds can affect the polarization measurement at a typical balloon flight altitude of 40 km: γ-rays within the field of view, gamma-rays and charged particles that penetrate through the SAS and the bottom BGO shield, and neutrons produced as secondary particles in the atmosphere and in the gondola. The fluxes of the different backgrounds depend on the thickness of the residual atmospheric layer (above and below) on the solar activity and on the latitude where the observations take place.

55 2.4. The Anti-Coincidence Shield 45 Counting rate (relative) Ch.1 and Ch.4 Ch.2 and Ch.5 Ch.3 and Ch Rotation Angle [degree] Figure Modulation measured in a polarized 25 kev pencil beam at KEK (top) [39], (bottom) arrangement of 7 PDCs, the polarized beam hits the center of the PDC 0 and is scattered. Photo-absorption is recorded in the 6 peripheral units. The setup is rotated in azimuth by 15 steps.

56 46 Chapter 2. PoGOLite Polarimeter Background photons are produced both outside and within the atmosphere. They behave like X-rays from the sources of interest but are not polarized on average. The contribution of these is only 20 mcrab [33], [35]. The bottom BGO shield, the side anti-coincidence shield (SAS), the slow plastic scintillators and the lead/tin foils around the tubes efficiently suppress the gamma-ray background. For high latitude flights auroral X-ray emission is also a potential source of background. This type of radiation is due to the Bremsstrahlung emission of electrons entering the Earth s magnetic field at an altitude of km. Most of the emission is at energies below PoGOLite sensitivity, but a few spikes exceeding 100 mcrab are expected above 20 kev [45]. The emission will take place, in the worst case, 5-10% of the flight time. To keep track of the events PoGOLite will be equipped with auroral monitoring instruments. The data acquired during high auroral activity will be used to study the polarization of the auroral emission. Neutrons are produced as secondary particles by high energy charged particles, originating from the Sun and other sources, hitting the atmosphere. Neutrons do not carry charge, thus they can travel through different parts of the detector before they interact and deposit an amount of energy similar to that deposited by the photons from astronomical targets [46]. The flux of neutrons for PoGOLite altitude is not isotropic, 80% is coming from the lower hemisphere because most of the neutrons are produced in the atmosphere below 40 km [47]. Also charged particles can produce secondary neutrons in the structure of the detector. The neutron background is suppressed by the thick polyethylene shield. Background rates have been calculated using Geant4 simulations [48], the total background rate is shown in figure The expected total background is equivalent to a mcrab source between 30 and 50 kev. Of the total background, 60-70% is produced by albedo neutrons. The expected performance characteristics of PoGOLite is reported in table 2.1.

57 2.4. The Anti-Coincidence Shield ) -1 kev cm Signal Rate (c s Crab 100 mcrab total background neutron background gamma-ray background Energy [kev] Figure Expected background rates at an atmospheric overburden of 4 g/cm 2 compared to expected signal rates expected for a Crab source (thick solid histogram) and 100 mcrab source (thin solid histogram). Filled circles denote the total background; open circles the neutron background; and filled squares gamma-ray background.

58 Energy 25 kev 30 kev 50 kev 80 kev Total Field of view 1.25 msr Geometric area 994 cm 2 Effective area for polarization 93 cm cm cm cm 2 measurement Signal rate for a 100 mcrab source at 4 g/cm /s/keV 0.044/s/keV 0.025/s/keV /s/keV 1.52/s effective overburden Background rate 0.043/s/keV 0.041/s/keV 0.029/s/keV 0.018/s/keV 1.77/s Modulation for 100% polarized beam with Crab spectrum 33% 29% 27% 40% 33% Table 2.1. Instrument performance characteristics for a 6 hour flight at 4 g/cm 2 overburden for a 100 mcrab source. 48 Chapter 2. PoGOLite Polarimeter

59 2.5. PoGOLite Pathfinder PoGOLite Pathfinder The maiden flight of PoGOLite will be with a reduced detector volume pathfinder instrument and is planned to take place in August 2010 from Esrange Space Center in Sweden. It consists of 61 PDC units (instead of 217) and is meant to test the principle of detection of the polarimeter. At the same time it will test the functionality of the ACS (Attitude Control System) and of the cooling system. Although the sensitive volume is reduced it will still be able to measure the polarization of a 1 Crab source with a MDP of 8.5 % in a six hours flight. The performance characteristics are summarized in table 2.2 and the expected background rate is shown in figure The measurement of the background will be very important, since at the altitude of 40 km and at the high latitude of Esrange, 67.8, it has never been studied in detail. This flight is expected to be followed by other 6-24 hour long flights from Esrange. In the future a full volume polarimeter will be developed with which it will be possible to study many more targets. A long term goal is a long duration balloon flight from Sweden to Canada (about 5 days) and a complete circumnavigation of the Northern pole. The pathfinder is under construction. To date (May 2010) the polarimeter is completed (see figures 2.21 and 2.22), the PDCs are in place, the pressure vessel containing the polarimeter has been put in the rotating frame (see figure 2.23). The polyethylene shield is not yet in place. The cooling system has been integrated, except for the radiator. The gondola is being manufactured. The attitude control system is in the last phase of development and will soon be ready to be integrated with other components.

60 Energy 25 kev 30 kev 50 kev 80 kev Total Field of view 1.25 msr Geometric area 280 cm 2 Effective area for polarization 21 cm 2 36 cm 2 39 cm 2 25 cm 2 measurement Signal rate for a 1 Crab source at 5 g/cm /s/keV 0.066/s/keV 0.040/s/keV /s/keV 2.39/s effective overburden Background rate 0.037/s/keV 0.032/s/keV 0.019/s/keV 0.017/s/keV 1.44/s Modulation for 100% polarized 33% 29% 27% 40% 33% beam with Crab spectrum Table 2.2. Instrument performance characteristics for a 6 hour flight at 5 g/cm 2 overburden for a 1 Crab source. 50 Chapter 2. PoGOLite Polarimeter

61 2.5. PoGOLite Pathfinder 51 /kev) 2 flux (c/s/cm Crab (20-80) kev Crab (80-200) kev Neutrons (20-80) kev Neutrons (80-200) kev energy (kev) Figure Expected neutron background rate between kev (blue line) and kev (magenta line) at an atmospheric overburden of 5 g/cm 2 compared to expected signal rates expected for a Crab source between kev (red line) and kev (green line).

62 52 Chapter 2. PoGOLite Polarimeter Figure PoGOLite pathfinder PDCs assembly, (left panel) view from the top of the PDCs, (right panel) view of the PMTs and cabling. The diameter is about 45 cm.

63 Figure PoGOLite pathfinder polarimeter before integration. On the left the PDCs assembly, in the middle the pressure vessel and on the right the rotation frame PoGOLite Pathfinder 53

64 54 Chapter 2. PoGOLite Polarimeter Figure Integrated PoGOLite Pathfinder, the height is 175 cm, including the electronic box. The rotation frame is painted white in order to maximize radiative emission and minimize absorption.

65 Chapter 3 Tests of BGO Scintillators In this chapter the tests performed on the BGO crystals are described. The procedure starts from small samples used to determine the characteristics of the BGO crystals available on the market. Tests were then performed on prototypes from two suppliers, which presented the best characteristics, after the first screening. After having refined the performance specifications, a tendering procedure was completed and the final crystals ordered. The final crystals have been tested to check if they matched the requirements listed in the procurement contract. Further tests have also been performed to complete the characterization studies. 3.1 Market Survey In 2003 the evaluation of four potential suppliers for BGO crystals started. Both technical and commercial aspects had to be evaluated. To establish the quality of the crystals the absolute light yield and light transmission of cubic samples of side 10 mm were studied. Light yield is an absolute measurement and can be used to assess the quality of the BGO. Light transmission is measured to check if the crystal is transparent to its own scintillation light (480 nm) and to the scintillation light of the plastic scintillators (408 nm and 425 nm). For the light yield measurement a 137 Cs source is used. 137 Cs β -decays to an excited state of 137 Ba. Upon its deexcitation, a γ-photon with energy 662 kev is emitted. The γ-photon is detected by Compton scattering or photo-absorption in the scintillators. The photo-peak will be used to determine the energy resolution. Figure 3.1 shows the spectrum recorded using a multichannel analyzer (MCA), the channel number on the x-axis is proportional to energy, and on the y-axis the number of counts is shown. 55

66 56 Chapter 3. Tests of BGO Scintillators The absolute light yield is defined as N ph [photons/mev] = 1 1 E( 137 Cs) q.e. N peak N sph G 2 G 1 (3.1) where E( 137 Cs) is the energy of the photopeak of MeV, q.e is the quantum efficiency of the PMT, N peak is the channel number of the photopeak position, N sph is the channel number of the position of the single photoelectron peak, G 1 and G 2 the gain used to measure N peak and N sph respectively. In the setup at KTH, G 1 is set equal to 10 and G 2 equal to 500. The value of G 2 is 50 times higher in order to be able to distinguish the single photoelectron peak from the background level, caused by noise in the electronics. A threshold is set around channel number 400 in order to reduce the dead time. The threshold is set to zero when measuring the single photoelectron peak. The single photoelectron peak is due to the spontaneous electron emission from the photocathode of the PMT and is a characteristic that depends only on the PMT. It is needed in order to calibrate the measurement. The measurement of this peak is performed without source and choosing a high gain G 2 since the signal is weak (see figure 3.2). Figure 3.1. Typical energy spectrum of 137 Cs acquired with the Tukan-8k MCA [49]. The x-axis shows the channel number which is proportional to the energy, on the y-axis the counts are shown. The photopeak at about channel number 1300 is due to photoeffect of the emitted 137 Cs γ-line (662 kev). During tests all BGO crystal surfaces, except the one that will be connected to the PMT, are covered with Teflon tape and black tape to maximize reflectivity and

67 3.1. Market Survey 57 Counts Channel number Figure 3.2. Single photoelectron peak.

68 58 Chapter 3. Tests of BGO Scintillators shield from light respectively. The crystal is then connected with the free surface, which is also polished, through optical grease to a Philips XP2020/Q PMT. The whole assembly is covered in black paper and irradiated with a 370 kbq 137 Cs radioactive source. The results from tests of the first samples are listed in table 3.1, the light-yield values were found to agree with other published values [50]. The light transmission is measured with a UV-spectrometer and the value of transmission at 425 nm is given, which is the wavelength of the emission of BGO. This measurement is not absolute since many effects are not considered, e.g reflections from crystal surfaces and instrument calibration. ] id Sample Size Light yield ( 137 Cs) Transmission Cost for 1 (at 425 nm) bottom BGO (2004) 1 10x10x10 mm (3) 3650 photons/mev 48% 460 USD (polished) 2 10x10x10 mm 5900 photons/mev 72% 450 USD (ground-polished) 3 10x10x10 mm (2) 6300 photons/mev 73 % 200 USD (ground-polished) 4 10x10x10 mm 5160 photons/mev 74 % 550 USD (ground-polished) Table 3.1. Results from mm samples for four different suppliers. Some had four ground and two opposite polished surfaces and others presented a polished surfaces on all 6 sides. The first column contains the identity number of the supplier, the second the size and number of crystals tested, third the light yield value and the fourth the transmission in percent evaluated at 425 nm which is the wavelength of maximum emission from the fast plastic scintillator. The transmission measurement was not calibrated and should not be considered as absolute. From the results of these measurements 10 bottom PDC crystals (shown in figure 3.3) were acquired from supplier 2 and supplier Tests of Selected Candidates The candidate PDC crystals were tested in 2005 with the same setup except for the PMT, which was now of type Photonis XP5202/B. The crystal is coupled to the PMT through optical grease applied to the cylindrical end. The results are plotted in figure 3.4. The two suppliers are almost equivalent regarding quality. These prototypes were subsequently used in the PDC units constructed for test beams.

69 3.2. Tests of Selected Candidates 59 Figure 3.3. Drawing of bottom BGO crystal, this is the final design which will be used in flight. The dimensions are in mm.

70 60 Chapter 3. Tests of BGO Scintillators After these tests the final geometry of the BGO crystals was decided, and drawings of both the bottom BGO and the side anticoincidence shield final were produced. The final version of PoGOLite needs 217 bottom BGO crystals and 54 SAS units, each consisting of three different crystals. When purchasing for high cost a tender has to be issued to which different suppliers can reply. The specifications of the tender have to be unambiguous and easy to check. The tender was issued in June 2006, the winner was the Nikolaev Institute of Inorganic Chemistry, Novosibirsk, Russia. The tender requirements were: dimensions and tolerances must be met, the crystals have to be transparent with no visible grain boundaries when viewed under strong lighting, surfaces have to have a fine mirror-like polish, the light yield must exceed a certain level, and there should be no dramatic degradation in the light yield due to radiation damage. Light Yield [γ/mev] supplier 2 supplier crystal id Figure 3.4. Comparison between light yield of the crystals of supplier 3 (square) and of the crystals of supplier 2 (dots). The error bars, of the order of 1%, are too small to be plotted. 3.3 Acceptance Tests The final crystals were delivered in a series of shipments during Each shipment contained alternately PDC BGO crystals and SAS crystals. The testing of the SAS crystals is described elsewhere [51]. Before assembling the anticoincidence system, each crystal undergoes acceptance testing. This consists of visual inspection and measurement of energy resolution using a 662 kev photopeak from a 137 Cs

71 3.3. Acceptance Tests 61 radioactive source. The crystals are produced in large rods and a number of samples are cut out of one rod and then machined. One rod is not enough to provide all the crystals needed for the detector, thus the crystals originate from different boules. Small cylindrical samples are also archived for each boule, to allow boule parameters to be monitored independently of the cut crystals. The characteristics of the crystal depends on the crystalline structure that can vary from boule to boule and also within the same boule. For each shipment the relative transmission is also tested for four PDC BGO crystals, a typical plot of the transmission is shown in figure 3.5. Figure 3.5. Plot of relative transmission of four PDC BGO crystals, between nm, range in which the PDC scintillators emit fluorescence light, the transmission is about %. The measurement is not absolute, but shows little variation between crystals Energy Resolution For the measurement setup for the relative energy resolution of the bottom BGO crystals an energy spectrum is sampled and the 662 kev line of 137 Cs is used to determine the relative energy resolution. The parameter that more accurately characterizes the crystal is the absolute light yield but it is difficult to isolate contributions coming from the PMT and electronics and thus it is not easy to compare values obtained with two different setups, the KTH setup and that of the manufacturer in Novosibirsk. Moreover in this case we are interested in tracking the relative

72 62 Chapter 3. Tests of BGO Scintillators changes within different crystals coming from the same source. The relative energy resolution is defined as: R = E (3.2) E where E is the position of the photo-peak and E is the corresponding full width at half maximum value (see figure 3.8). The energy resolution measured with a scintillator coupled to a photodetector can be written as ( ) 2 E = (δ sc) 2 + (δ st) 2 + (δ n ) 2 (3.3) E where δ sc is the intrinsic resolution of the crystal, δ st is the statistical contribution, and δ n is the dark noise contribution to the resolution [52]. The intrinsic resolution is associated with the non-proportional response of the scintillator, inhomogeneities in the scintillator and non uniform reflectivity of the crystal covering, and it depends on the energy. In our measurement the energy is constant, thus this term will be constant. The dark noise contribution in the case of measurements with PMTs is negligible. The statistical uncertainty is described as ( ) σ (δ st ) 2 = (1 + ǫ) (3.4) N and since it is a Poisson distribution and σ = N ( (δ st ) ) 2 ( ) 2 N 2.35 = (1 + ǫ) = (1 + ǫ) (3.5) N N where N is the number of photoelectrons and ǫ is the variance of the electron multiplier gain ( 0.1 from data-sheet). N is a measure of the light yield, so by measuring the energy resolution we evaluate indirectly the light yield. The resolution is enhanced if the light yield is high. Good resolution is defined by small values of R Energy Resolution Setup for PDC Crystals The setup for the measurement of the energy resolution is similar to the one described in section 3.1, but has been redesigned so that the measurement is reproducible. For the energy resolution measurement, the BGO crystal is placed in a 5 mm thick reflective Teflon cup to maximize light collection. The cylindrical portion of the crystal is connected to the PMT (Photonis XP5202/B) with a thin layer of optical grease. The spectral sensitivity of this PMT goes from 270 nm to 650 nm with a peak at 420 nm, this range is identical to the one of the PMT Hamamatsu R7899 that will be used in the flight configuration. The entire assembly is

73 3.3. Acceptance Tests 63 made light-tight with a black PVC cup that covers the Teflon and PMT window. A collimated 137 Cs source is directed toward the hexagonal face of the crystal directly opposite to the PMT as shown in figure 3.6. The PMT is operated at V, the output of the PMT is connected to a preamplifier and a shaping amplifier with a time constant set to 2 µs, this is connected to a multichannel analyzer, Tukan 8k USB, connected to a PC (figure 3.7). An energy spectrum is acquired for 5 minutes, at constant temperature of 23 C, for each crystal. Figure 3.6. Setup for energy resolution measurement: a collimated source (1+2), (2) is a block of lead with a hole in the center, irradiates a BGO crystal covered in Teflon and PVC (3), and attached to a PMT (4). The PMT signal is amplified and read out by a multichannel analyzer The Fitting Method With each measurement of 8192 channels a histogram with 1024 bins is filled. The peak position is determined which corresponds to the 137 Cs photopeak. The data

74 64 Chapter 3. Tests of BGO Scintillators BGO HV = 1500 V PMT Photonis XP 5202 preamplifier amplifier t= 2 micro s G = 10 Tukan MCA 8k t= 300s Figure 3.7. Schematic diagram of the data acquisition chain. The preamplifier has a time constant of t = 2µs, and the gain G of the amplifier is set to 10. Figure 3.8. A typical energy spectrum of a 137 Cs source measured using a bottom BGO crystal. The vertical line indicates the peak position E, and the horizontal line indicates the FWHM. The spike at channel number 500 is due to binning effects and the bump on the right side of the peak is due to the geometry of the crystal (see section 3.4). are fitted with a Gaussian peak on a symmetrical range of about 200 channels around the peak:

75 3.3. Acceptance Tests 65 f(x) = Ae (x m)2 2σ 2 (3.6) The parameters A, m and σ are determined by χ 2 fitting. A is the number of counts in the bin of the fitted peak, m is the position of the peak and σ, the standard deviation, is proportional to the full width at half maximum (FWHM) of the Gaussian peak. The background is not fitted since only the peak is fitted to avoid the bump on the right side of the peak which will be discussed later. The parameters that determine the energy resolution are m and σ: R = E E = FWHM m = 2.35σ m (3.7) This procedure is done for each crystal and at the end it is possible to fill a histogram with the 240 energy resolution values ( spares) as shown in figure 3.9. The energy resolution values obtained have a mean value of (12.75±0.20)%, whereas the value obtained at the Nikolaev Institute of Inorganic Chemistry is (11.83±0.86)%. The two measurements are compatible within one standard deviation. The KTH results are more reproducible, possibly because a more sophisticated fitting technique is used. The value obtained is lower than 16%, which is the value stated in the tender requirement. Counts Resolution (%) Figure 3.9. Distribution of energy resolution values for 240 bottom BGO crystals, the dotted histogram represents the values measured by Novosibirsk and has a mean value of (11.83±0.86)%; the shaded histogram represents the value measured at KTH and has a mean value of (12.75±0.20)%.

76 66 Chapter 3. Tests of BGO Scintillators In order to study if the energy resolution depends on the boule of origin the results have been grouped for each boule. The mean value and the standard deviation of the energy resolution value from each crystal belonging to one boule has been calculated. This has been performed for all 23 different boules and plotted in figure There is no significant difference in the boule characteristics. Resolution (%) boule id Figure The mean value of the energy resolution of the crystals belonging to each boule are plotted versus the boule identity number.

77 3.4. Further Studies Further Studies Spectrum Anomaly After accepting the crystals further studies took place. As can be seen from the spectrum, next to the photo emission peak, at higher energies, a bump is visible which is possible to fit with a second Gaussian peak (figure 3.11). Different hypotheses were made regarding the origin of this bump : contribution of background, effect of electronics and multichannel analyzer, geometry of the crystal. The first two were rejected, the bump is obtained also when changing PMT, MCA and electronics, and the background due to intrinsic radioactivity (measured in a low background laboratory with a Germanium detector) is not significant. Testing a cylindrical BGO boule sample like the one shown in figure 3.12, the bump is not observed (see figure 3.13) thus indications that the origin of it could be the crystal geometry were studied in more detail. Counts χ 2 / ndf / 94 p e+04 ± 98 Peak 1 Channel# 2004 ± 0.4 p ± 0.4 p ± 44.8 Peak 2 Channel# 2251 ± 8.1 p ± Channel number Figure Energy spectrum of a BGO PDC crystal, the first peak is the photo emission peak that is used to calculate the relative energy resolution, the second peak is fitting the bump. The first three fitted parameters are the amplitude, the mean value and the standard deviation of the first peak, the other parameters correspond to the second peak. A crystal was irradiated from the side in two different positions with a more collimated source. A spectrum (the peak on the left in figure 3.14) with the source closer to the hexagonal upper part of the crystal has been recorded and the bump is visible. A second spectrum (the peak on the right in figure 3.14) was taken when

78 68 Chapter 3. Tests of BGO Scintillators Figure PDC BGO crystal and sample BGO crystal. The PDC crystal is 4 cm tall and has a maximum width of 3 cm. The cylindrical sample is 1.5 cm tall, and the diameter is about 0.8 cm. Counts BGO PDC BGO sample Channel number Figure Spectra for PDC BGO crystal (black continuous) and BGO sample crystal (red dotted), the peaks have moved because of the use of higher gain. the source was placed closer to the cylindrical end of the BGO and the bump is more pronounced. In both cases the PMT is attached to the cylindrical protrusion. It is concluded that the bottom BGO crystal consisting of two different parts contributes in different ways to the light yield. The hexagonal part is bigger so the probability to have photoabsorption is high which gives a greater amplitude but

79 3.4. Further Studies 69 the light gets partly reflected and trapped when passing through the cylindrical protrusion resulting in a lower light yield (peak at lower channel number). The cylindrical part has low counting rate but the light that is produced inside it can travel mostly undisturbed to the PMT resulting in a high light yield. Counts 2 10 position1 position Channel number Figure Energy spectra of 137 Cs for PDC BGO crystal for two different positions: (green left) close to the hexagonal part and (black right) close to the cylindrical part.

80 70 Chapter 3. Tests of BGO Scintillators Temperature Dependence of BGO As in many scintillation materials the light yield is a function of temperature. The reason for this is that the probability for radiative transitions is temperature dependent. The radiative transitions are responsible for the production of scintillation light and they dominate at low temperatures. The light output as a function of temperature for BGO and other inorganic scintillators is shown in figure Contrary to other scintillators, BGO has the disadvantage of a strong and negative-slope temperature dependence. The temperature could vary depending on the float altitude, position of the sun, and pointing direction, the goal of the cooling system is to keep the temperature inside the pressure vessel below 10 C, but the light yield has been studied over a wide temperature range: -20 C to 60 C. The temperature has an influence on the counting rate of the the SAS crystals, and on the veto efficiency of the PDC, whereas for the PDC the counting rate will remain the same since here the BGO is only a waveguide. Figure Temperature response of various inorganic scintillation materials [30]. The temperature affects both scintillation decay time and light output. The decay time increases whereas the light output decreases with increasing temperature. The scintillation decay time can be described by the function f(t) which consists of several components f(t) = r 1 e t/τ1 + r 2 e t/τ2 + r 3 e t/τ3 (3.8) where t is the time, r 1,2,3 are constants of order unity, and τ 1,2,3 are decay time constants. The contribution of each exponential term depends on the temperature

81 3.4. Further Studies 71 [53]. The decay time can be studied by means of the delayed coincidence method. As can be seen in [53] the scintillation decay time also above room temperature will remain higher than the typical decay time of the fast scintillators, thus the pulse shape discrimination described in section is not affected. The light output has been measured for one sample crystal for different values of temperature from (-20 to 60) C. The temperature values below 0 C have been obtained with dry ice and the values above room temperature with a programmable oven. In figure 3.16 the energy spectra for some temperature values are shown ((20, 40, 50) C). The position of the energy peak moves to higher energies with decreasing temperature as expected. The peaks are fitted with the same procedure as for the relative energy resolution. For each temperature the single photoelectron peak has been measured, the position of this does not vary with temperature, thus the absolute light yield is proportional to the energy of the photopeak. The peak positions are plotted as a function of the respective temperature in figure 3.17, and fitted with a linear function. For comparison and completeness also the light yield values obtained in a second setup, the measurement described in [53], have been plotted after a calibration with the data obtained at KTH. The calibration has been performed by calculating the ratio between the light yield values at 20 C obtained by both setups: E KTH (20 C)/E 2 (20 C) = K (3.9) E KTH (20 C) is the light yield value obtained at KTH, whereas E 2 (20 C) is the value obtained by the second setup, K is the calibration constant. By multiplying the data obtained in the other setup it is possible to compare the data and fit with the same function. The data are fitted with a linear function, a+b T, the value of the fitted parameters relating to channel number are a = (2456 ± 12) (3.10) b = ( 27.2 ± 0.5) C 1 (3.11) The BGO behaves as expected and it will be possible to correct the polarimeter data once information about the temperature profile during flight is available.

82 72 Chapter 3. Tests of BGO Scintillators Counts C 40 C 50 C Channel number Figure Energy spectrum of 137 Cs depending on temperature: the peak position moves to higher energies with decreasing temperature. peak energy [ch] data1 fit data temperature [ C] Figure Peak position versus temperature: data1 (green square) are the KTH data, data2 (blue dots) are the data taken from [53]. All points are fitted linearly (continuous line).

83 Chapter 4 Pulsars: Current Status Studies of pulsars in γ-rays began with balloon-borne experiments [54] detecting the Crab pulsar in The results were confirmed by the satellite experiment SAS-2 [55] in 1972, which additionally found γ-ray pulsations from the Vela pulsar. In 1975, COS-B [56] found the same results with the additional information that the Vela radio emission was not in phase with the γ emission. In 1991 the Energetic Gamma Ray Experiment Telescope (EGRET) on the Compton Gamma Ray Observatory (CGRO) satellite observed the full sky above 50 MeV for the first time. It observed 300 γ-ray sources, of which only one third could be identified, many of them are pulsars. Since the launch in June 2008, the Large Area Telescope (LAT) aboard the Fermi Gamma-ray Space Telescope, is providing a clearer picture of the γ-ray sky. Here, the results which concern pulsars are summarized. These observations, though carried out in the γ-ray energy band, give insight into the emission models which involve a broad part of the energy spectrum. However, as it will be seen, this information alone is still not enough to model the pulsar emission. Polarization measurements will hopefully disentangle the problem. Pulsars have been proposed to explain other astrophysical phenomena, as described in the last section. 4.1 Fermi The Fermi satellite was launched into low-earth orbit on June 11 th The LAT is a pair production telescope (silicon tracker) sensitive to energies from 20 MeV up to 300 GeV. With a geometric area of 8000 cm 2, a field of view of 2.4 sr and a low-earth orbit the telescope is able to cover the entire sky every three hours. The LAT measures the direction, the energy and the time of arrival of the gamma-rays. The direction is recorded in the tracker: a gamma-ray undergoes pair production in a tungsten foil, the passage of the resulting e + e is recorded by the planes of the silicon detectors. This information is used to reconstruct the direction of the incoming photons [57]. The energy is measured in the CsI calorimeter where 73

84 74 Chapter 4. Pulsars: Current Status electromagnetic showers resulting from the e + e pairs are produced. Charged particles are rejected by a segmented plastic scintillator anti-coincidence shield. The timing of the photons has been shown to be accurate to better than 1 µs. With these high performance properties the LAT could already after six months of data acquisition report the detection of 46 gamma-ray pulsars (see figure 4.1). Of these, six had previously been detected in gamma rays, 24 were previously known from radio observations, and the remaining 16 were new detections. The observations performed in all the three groups enable the study of light-curves, spectra and luminosities, which help in differentiating between the different emission models.

85 Figure 4.1. Pulsars catalog in galactic coordinates [26]. Gray dots: all known pulsars from the ATNF catalog [58]. The 46 pulsars detected by Fermi LAT: (black dots) pulsars discovered using radio ephemerides, (red triangles) millisecond pulsars, (blue squares) gamma-ray pulsars detected through blind search and (green circles) radio loud γ-ray pulsars Fermi 75

86 76 Chapter 4. Pulsars: Current Status 4.2 Pulsar Features Light-Curves The pulsars observed by Fermi can be classified according to their light-curves. The light-curve is the intensity of the pulsar, for a fixed energy range, as function of the revolution period of the pulsar. One revolution period corresponds to one phase. One class shows two narrow peaks, separated by in phase, and the first γ-peak lagging the radio peak by in phase. The second class is characterized by having two peaks with small separation, almost blending into one. The last class consists of a single component, which may or may not be two components merged together. It has been observed that pulsars with close peaks, while the class with distinct separation can have any value of Ė [59]. One example of each class will be discussed, underlining the features that point to the type of emission model. or a single peak have lower values of the spin down luminosity Ė = de dt Class I : Two widely spaced peaks The light-curve of J (figure 4.2) consists of two γ peaks with phases 0.200±0.003 and 0.661±0.007 with respect to the radio peak. The pulsar has been observed in four different γ-energy ranges, MeV, 300 MeV-1 GeV, 1-3 GeV and > 3 GeV. The integrated light-curve is shown in figure 4.2. Pulsations are detected up to an energy of 4 GeV. The difference in phase between the radio peak and the γ-peaks and the fact that the peaks in the higher energy band cover a wide range of phases are a hint that the γ-ray emission beam covers a large fraction of the solid angle. This suggests that the emission takes place in the outer magnetosphere, as described by the outer gap, OG [60], and slot gap model, SG [61], shown schematically in figure 4.3. Class II : Two closely spaced peaks Doubled-peaked curves with small separation, with correct phase shift relative to the radio peak are in agreement with the two pole caustic model and outer-gap model, if the observer s line of sight is crossing tangentially the edge of the outer magnetosphere cone. If the peaks are narrow (figure 4.4) the emission occurs for a magnetic inclination angle α and viewing angle ξ (see figure 4.5) assuming the outer-gap model, for α and ξ in the case of the two-pole caustic model. Wider peaks (figure 4.6) are obtained for a larger range both for α and ξ, up to 80 in the outer-gap picture. These peaks are more difficult to create with the two-pole caustic model [59]. Class III : Single peaked If the peak is actually the convolution of two peaks the description is the same as the second class. If the peak is genuinely single (see figure 4.7), a magnetic geometry with α and viewing angle ξ is

87 4.2. Pulsar Features >0.1 GeV J Counts >1.0 GeV 40 Counts Counts Counts GeV GeV Radio Flux (au) Parkes 1.4 GHz Pulsar Phase Figure 4.2. Light-curves for PSR J with period P = 91.4 ms [26].

88 78 Chapter 4. Pulsars: Current Status Figure 4.3. Sky map of pulsed beams and pulse profiles of the Vela pulsar according to the outer gap model. In the top panel: pulsar emission as a function of phase and viewing angle. Depending on the viewing angle ξ the line-of-sight will cross different regions. For clarity only one lobe is shown. The line-of-sight of the Earth is indicated by the dashed line. Bottom panel: a viewing angle of 90 and a magnetic inclination of 45 are assumed. Pulse components as a function of pulsar phase. The γ-ray pulses are shown, the leading radio pulse, hard magnetospheric and soft thermal X-ray emission [60].

89 4.2. Pulsar Features >0.1 GeV J Counts Counts Counts Counts >1.0 GeV GeV GeV Pulsar Phase Figure 4.4. Light-curves for PSR J with period P = 316 ms [26].

90 80 Chapter 4. Pulsars: Current Status Figure 4.5. Schematic view of pulsars: Ω identifies the rotation axis, B the magnetic field axis, α is the magnetic inclination angle and ξ is the viewing angle. required. The phase lag of the radio peak should then be of order This is possible in the outer magnetic models. If the phase with respect to the radio peak is 0.6 (see figure 4.8) then none of the outer-magnetosphere models can fit the description. The preferred explanation is then that the pulsar is actually a class I object with an invisible weak P1. To summarize, the phase is well predicted by SG and OG models, however, the shape of the light-curve is less well modeled. This suggests that the models are incomplete. The observations of 16 radio quiet γ-ray pulsars [62] point to the SG and OG models too. The lack of the radio signal can be explained if the γ-ray beam is much wider than the radio beam which does not cross the line of sight of the observer.

91 4.2. Pulsar Features >0.1 GeV J Counts Counts Counts >1.0 GeV GeV GeV Counts Radio Flux (au) Parkes 1.4 GHz Pulsar Phase Figure 4.6. Light-curves for PSR J with period P = 197 ms [26].

92 82 Chapter 4. Pulsars: Current Status 100 >0.1 GeV J Counts Counts 40 >1.0 GeV GeV 40 Counts GeV Counts Radio Flux (au) Parkes 1.4 GHz Pulsar Phase Figure 4.7. Light-curves of PSR J with period P = 88.9 ms [26].

93 4.2. Pulsar Features >0.1 GeV J Counts >1.0 GeV Counts Counts GeV GeV Counts Radio Flux (au) Nancay 1.4 GHz Pulsar Phase Figure 4.8. Light-curves of PSR J with period P = 167 ms[26].

94 84 Chapter 4. Pulsars: Current Status Minimum Emission Height Another clue that the emission takes place at high altitudes is given by the value of the maximum observed energy pulsations, ǫ max 4 GeV, which determines the minimum emission height r. Using a polar cap model, r can be estimated by [63]: r (ǫ max B 12 /1.76GeV ) 2/7 P 1/7 R (4.1) where B 12 = B/10 12 G is the surface polar field strength, P the period and R the neutron star radius. Inserting the PSR J parameters gives a lower limit for r 1.8 R, thus excluding emission very close to the neutron star surface.

95 4.2. Pulsar Features Luminosity By studying the total γ-ray luminosity we get information about the geometry of the emission. The total luminosity is defined as: L tot γ = πf(α, ξ E )Φ obs d 2 (4.2) where Φ obs is the observed phase-averaged flux, d is the distance to the source and f is a correction factor which takes into account the angle α between the magnetic field axis and the rotation axis, and the viewing angle, ξ E, i.e. the angle between observer and the rotation axis. This factor quantifies how much of the emission the observer is actually seeing and is very model dependent. For the polar cap model, where the emission takes place close to the poles within a few stellar radii, the beam of emission is small and consequently f 1. For outer gap models, both OG and SG, where the radiation is thought to arrive from higher altitudes, f 1. Radio and the current gamma data are not enough to completely determine the geometry of the pulsar, but the narrow radio pulse suggests a large value of α. Using the pulse profile atlas of Watters [64] shown in figure 4.9 it is possible to estimate an allowed region for both angles. The atlas shows, depending on the model, which characteristics the pulsars have as a function of viewing and magnetic inclination angle. The polar cap model is excluded, the other two models have a good range of solutions Spectrum The spectral shape and the high energy cut-off energy also depends on the emission model. Assuming that the spectrum has an exponential cut-off power law of the form: dn de = ke Γ e ( E Ec )b (4.3) where Γ is the photon index at low energy, E c is the cutoff energy, k a normalization factor and b is a parameter that quantifies how exponential the spectrum is. For b = 0 equation 4.3 becomes a pure power-law, while super exponential behavior is described by b > 1. An example of the spectrum is shown in figure 4.10, the pulsar is PSR J The fit for the total pulse gives E c = (2.4±0.3) GeV and suggests b = 1. The cut-off energy values for the spectra of P1 and P2 are respectively (1.9±0.3) GeV and (2.8±0.5) GeV. The emission up to 10 GeV and the smooth slope for higher energies is further proof of the outer-magnetic models, though the difference between the two peaks is still not well understood.

96 86 Chapter 4. Pulsars: Current Status Figure 4.9. Atlas of pulse profile properties for polar cap, two pole caustic and outer gap model (different columns). The y-axis is showing the viewing angle, the x-axis the magnetic inclination angle. First row: peak number, the cyan line delimits broad peaks. Second row: separation between 2 main peaks. Third row flux factor f(α, ξ E ) [64].

97 4.3. Polarization Energy Flux (ergs cm2 s1 ) Energy (GeV) Figure Energy spectrum for PSR J , the data have been fitted with a power law with an exponential cutoff: P1 (squares), P2 (diamonds) and total pulse (circles). To avoid confusion P2 data points have been plotted 2.5% higher [65] Millisecond Pulsars Millisecond pulsars (MSPs) are a particular type of pulsars with short spin periods P < 30 ms and very low spin down rate P = dp/dt < They originate from binary systems in which they have been spun-up by the mass accretion from their companion. Thus they can have ages of years whereas normal pulsars have ages of years. MSPs have smaller values of their magnetic fields so that the pair production through interaction with the magnetic field is more difficult, moreover the short period results in larger polar caps. These features allow us to study γ-ray emission at the poles. So far the results of Fermi regarding MSPs show that the predicted number of these objects is in good agreement with outer magnetic models. However the measured Ė is too low to be able to create e+ e pairs. Also here the classical OG and SG are not able to explain completely the emission mechanism. 4.3 Polarization From current observations it is clear that high energy emission takes place at high altitudes, producing wide fan beams. Which of the outer magnetospheric models better describes the emission is still unclear. The light-curves need better statistics, and this will be achieved in the coming years. Information from other energy bands is also required to study the dependency on the energy of the peaks. Radio observations will give information about the magnetic angle and the viewing angle, thus confining the possible scenarios (see figure 4.9). Polarization measurements

98 88 Chapter 4. Pulsars: Current Status will in an independent way provide more information on the underlying mechanism. The polarization patterns differ according to the predicted model, however, the differences are easier to detect than by examination of the light-curves. Figures 4.11 and 4.12 show the radiation characteristic at high energies predicted by the SG and OG model, respectively. The polarization angle shape depends also on the viewing angle and the magnetic inclination. In the optical bands polarization measurements of the Crab pulsar have ruled out the polar cap and outer gap models. The fast swings of the position angle and the minima in the polarization degree predicted by the two pole caustic model are in agreement with the observations made with OPTIMA (Optical Pulsar TIMing Analyzer) [8] (see figure 4.13). In the X/γ-ray band polarization has not yet been exploited as described in chapter 1, but hopefully the new missions will detect the polarization in the high energy band.

99 4.3. Polarization 89 flux a) O d) O g) O S 70.3 P [%] ψ [ ] P [%] ψ [ ] flux P [%] ψ [ ] flux b) O c) O φ e) N N O f) N O φ h) O S O i) O S O S S φ Figure Radiation characteristic patterns predicted by SG model for a pulsar with magnetic inclination α = 60 for 9 different viewing angles. In each frame the top figure shows the light-curve, the second shows the polarization angle and the third shows the polarization degree, all as function of the phase. The corresponding light-curve is overplotted in gray in second and third picture as a reference [66].

100 90 Chapter 4. Pulsars: Current Status flux a) d) g) 70.3 P [%] ψ [ ] P [%] ψ [ ] flux P [%] ψ [ ] flux b) c) φ e) f) φ h) i) φ Figure Radiation characteristic patterns predicted by the OG model with magnetic inclination α = 65 for 9 different viewing angles. In each frame the top figure shows the light-curve, the second shows the polarization angle and the third shows the polarization degree, all as function of the phase. The corresponding lightcurve is overplotted in gray in the second and third panels as reference [66].

101 4.3. Polarization 91 Figure The position angle (top panel) and degree (bottom panel) of optical polarization measured by OPTIMA are shown. The two vertical lines mark the positions of the two peaks. The fast swings corresponding to the peaks are predicted by the two-pole caustic model [8].

102 - 92 Chapter 4. Pulsars: Current Status 4.4 Pulsars in a Broader View Understanding the radiation emission mechanism of pulsars gives us a deeper knowledge about one possible final stage of stars. It also provides the opportunity of studying acceleration of particles at GeV energies, and may also help in understanding other astrophysical problems. For example, recent results from the PAMELA experiment [67] show an unexpected behavior in the cosmic-ray positron fraction N(e + )/[N(e + ) + N(e )]. At high energy it starts to increase instead of decreasing as expected from secondary production models, shown in figure )) )+ φ(e + ) / (φ(e + φ(e Positron fraction 0.02 PAMELA Energy (GeV) Figure PAMELA positron fraction: the points show the experiment results, while the line shows the predicted model. The measured ratio increases at high energies, whereas the model predicts a lower ratio [68]. A simple explanation would be that the positron excess originates from highenergy processes from one or several pulsars. Pulsars indeed have a harder e + e spectrum than that from secondary cosmic-ray origin. Pulsars contribute both with e + and e, but since the number of electrons N(e ) >> N(e + ), the electrons originating from pulsars can be neglected. The contribution of pulsars, either from local pulsars or from the sum of all pulsars distributed in the Milky Way, could dominate the cosmic ray spectrum at higher energies. The e + e pairs created in pulsars can escape the magnetosphere through open field lines or after joining the pulsar wind. In [69] the injection spectrum for the galactic pulsar contribution is approximated by:

103 4.4. Pulsars in a Broader View 93 dn e de e Ṅ 100 (E e /GeV) 1.6 exp( E e /80 GeV)GeV 1 s 1 (4.4) where Ṅ100 is the pulsar birth rate per century and E e is the cutoff energy of the pulsar spectrum. Only pulsars of age 10 5 years may contribute: in younger pulsars charged particles are not free to diffuse in the interstellar medium because they are still confined in the nebula, older pulsars will have diffused over too large a volume. In figure 4.15 the cosmic ray positron fraction produced by the sum of the pulsars in the Milky Way is shown in comparison to the predicted model. Figure 4.16 shows the spectrum of the cosmic ray positrons. PAMELA data are well fitted assuming an injection rate with Ṅ100 = 4. This shows that the injection energy spectrum needs to be tuned better. It is possible also to estimate the effect of single pulsars, for a detailed study see [69] and [70]. PoGOLite may help in determining the emission mechanism. Once the model is known one can restrict the parameter space of the injection spectrum for the galactic pulsars. Figure Positron fraction predicted assuming injection spectrum of equation 4.4 for different pulsar birth rates, the measurement of HEAT (green) and PAMELA (red) are shown. Another explanation of the increase of antimatter ratio at high energy could be the presence of dark matter which would annihilate in the galactic halo producing (e.g) γ-rays, electrons, positrons, protons and antiprotons. The shape of the spectrum can be explained by the presence of dark matter, but standard scenarios (e.g. based in supersymmetric extensions to the Standard Model of particle physics) are not favored due to the normalization of the observed excess, and the lack of an excess for cosmic-ray antiprotons [69].

104 94 Chapter 4. Pulsars: Current Status Figure Spectrum of cosmic ray positron: continuous spectra resulting from the sum of all pulsars throughout the Milky way, dashed line is the prediction of secondary positrons [69]. The injection spectrum of equation 4.4 has been used for different N. 4.5 The Crab Pulsar and Nebula The Crab pulsar is one of the most studied pulsars, being hosted in the Crab Nebula, which is one of the brightest X-ray sources in the northern hemisphere. The Nebula is a remnant of a supernova explosion observed in AD 1054, at a distance of 6.5 kly with coordinates RA 05 h 34 m s and DEC The nebula emits over a wide energy range, from radio to γ-rays. It is widely used for calibration at high energies, since contrary to other wavebands, the X/γ-ray regime does not have calibration stars. The Crab nebula is powered by the Crab pulsar, which accelerates electron-positron pairs to high energies. These particles lose energy while crossing the nebula, which is permeated by a magnetic field, and emit synchrotron radiation. The emitted intensity can be considered constant since the nebula is extended over a diameter of four light years, and the nebula flux should not vary on a timescale shorter than a few years [71]. The emitted synchrotron radiation will be polarized (see chapter 1) and a study of the polarization can give information about the structure of the magnetic field and structure of the nebula. The Crab nebula will be the primary target of the PoGOLite pathfinder. This will allow calibration of the instrument in flight and will prove the principle of polarization detection: the flux of the Nebula will be used to calibrate the flux rate as is customary for X-ray detectors. In order to simulate the different contributions one needs the spectral information of both components, pulsed and unpulsed. Next the spectral properties of the Crab nebula and pulsar are summarized. These will be later used as input for the simulations in chapter 5. The total Crab photon flux can be described by a power law:

105 4.5. The Crab Pulsar and Nebula 95 N = k E p (4.5) where k is the normalization constant with dimension counts/kev/cm 2 /s and p is the photon index. The parameters have been previously measured by different experiments. The results are shown in figure 4.17, and the canonical values in the X-ray regime are the ones measured by Toor and Seward [72], k = 9.7±1.0 and p = 2.10±0.03 in the hard X-ray band. These values will be used also when simulating the total Crab, nebula and pulsar, in chapter 5. Figure Spectral parameters of the Crab for various X-ray missions, the horizontal lines represent the operational energy of the instrument, the energy scale is in kev. Top panel: photon index, where the canonical value is indicated by the black dotted line. Second panel: the normalization factor where the canonical value is indicated by the black dotted line. The bottom panel shows the density column, which is not relevant for the discussions in this chapter [71].

106 96 Chapter 4. Pulsars: Current Status The pulsar spectrum can be described also by a power law. The index for different energy bands as a function of the phase of the pulsar is shown in figure Figure The phase resolved spectral indices measured by BeppoSax in two different energy bands: kev (panel a) and kev (panel b) [73]. The mean value of the photon index is approximately 1.9 in the energy band of kev. There is little information available about the normalization factor of the pulsar spectrum, but the light-curve of the pulsar is well known and has been measured by many experiments. In figure 4.19 the pulse profiles of the Crab measured by IBIS/INTEGRAL [74] in 4 different energy bands (20-40, , , and kev), are shown. The profile can be divided in two regions: on-pulse and off-pulse region. The pulsar is on for phase values and in this interval the pulsar component is summed with the nebula contribution. For phase values between the pulsar is off and only the nebula contributes to the flux. A useful quantity to estimate the contribution of the pulsar is the pulsed fraction defined as: F = F ON F OFF F ON + F OFF (4.6) where F ON is the flux integrated over the bins , and F OFF is the flux integrated over the interval For the energy band of PoGOLite the pulsed fraction is about 0.15 (see figure 4.20).

107 4.5. The Crab Pulsar and Nebula 97 Figure Light-curves of the Crab measured by IBIS/INTEGRAL in the 20-40, , , and kev bands. The off-pulse phase is from (dashed line), the on-pulse phase from (continuous line) and comprises the bridge emission between the peaks [74].

108 98 Chapter 4. Pulsars: Current Status Figure Pulsed fraction of the Crab pulsar/nebula as a function of energy, the solid line shows a linear fit, with 1σ error given by the dashed lines. In the energy range of PoGOLite the pulsed fraction is about 0.15 [74].

109 Chapter 5 Studies of PoGOLite Pathfinder Performance The final goal of the PoGOLite experiment is to extract a polarization signal from astrophysical objects. In order to succeed in this, one needs to know how the polarimeter transforms the source signal into the output signal, the acquisition data. One way could be to study the response of each PDC detector unit and then to convolve them together. Another way, adopted for PoGOLite, is to perform computer simulations using a mass model of the instrument. In this chapter the simulations performed for the PoGOLite pathfinder for observing the total Crab, pulsar and nebula, are described. With these simulations the parameters needed for the polarization measurement are calculated using the final design of the pathfinder instrument [75]. The change of atmospheric depth due to different elevation angles of the sources during flight is taken in consideration. In the last section a polarization analysis method is described. This is applied to measure the polarization of the total Crab (pulsar and nebula) using simulated data. 5.1 Observation simulations with Geant4 The mass model consists of a computerized representation of the detector including both geometric and chemical composition. Different types of particles can be used as input, and their energy, direction of arrival, and polarization angle are specified. If the incoming particles and the detector material are known, the interactions and trajectories of each particle can be traced. The energy deposited in the different parts of the detector can be treated as real data. With this technique it becomes relatively easy to change any part of the detector or to change the properties of the incoming particles. The mass model plays a crucial role at any stage of the mission: during development it allows the design to be studied, observations to be planned and it helps in modeling the systematics. In order to create the mass model, Geant4 [48] is used. Geant4 is a C++ software toolkit developed to simulate 99

110 100 Chapter 5. Studies of PoGOLite Pathfinder Performance the passage of particles through matter. It is based on the Monte Carlo technique; the simulated particle moves in small steps, for which the interaction probabilities are calculated and compared to a random number. If the random number is lower than the calculated probability the particle will interact, otherwise it will move on. Geant4, originally developed at CERN for high energy experiments, is nowadays used in different branches and applications of particle physics, due to the fact that it has the capability of simulating particles from a few hundred ev up to TeV. The user interfaces to the Geant4 framework with a C++ code, in which the geometry and material of the detector, the properties of the incoming particles and the physical processes are set. Depending on which physical processes are involved in the experiment, the corresponding Geant4 modules will be selected Simulation Setup The code used in this work is called polaripogo which was previously developed for simulations of the neutron background [46]. Previously different groups of PoGO- Lite collaboration were using two slightly different versions of the code, which have now been merged into one [75]. In the current version it is also easier to pass input parameters, the different neutron background contributions have been merged into one, and the output format has been cleaned up. Detector In Geant4 the detector is described as volumes of the corresponding geometrical shapes in space. Physical properties are assigned according to the type of material, which is specified by selecting type of atoms and the density or the pressure. The PDCs consist, in the Geant4 model, of only one type of plastic scintillator and BGO. The anti-coincidence shield consists of BGO elements. The polyethylene shield, and the aluminum structure are taken into account (see figure 5.1). The PMTs are only considered at the analysis stage as described in section Particles The particles are fired one by one through the detector, and information about the hits of the particle and any secondary particles produced are saved in the output file. Only photons from the total Crab (pulsar and nebula) and background neutrons are considered. Other types of background, e.g. charged particles and γ-rays, are negligible [46] (see figure 2.19). The photons are generated in the energy range kev from a probability distribution in accordance with their spectrum [71]: F = 9.7 E 2.1 kev 1 cm 2. (5.1) where F is the flux and E is the energy of the photons. The photons are generated on an imaginary disc which has a radius of 63.9 cm, placed at infinity in front of the detector. The disc is bigger than the actual cross section of the detector volume, so that when the detector is tilted, it will be evenly illuminated by the source (see figure 5.2). The polarization angle can be specified as well as the inclination of

111 5.1. Observation simulations with Geant4 101 Figure 5.1. Geant4 PoGOLite pathfinder model: (left) side view of the detector, (right) top view of the detector. The sensitive detector (magenta) is 30 cm wide (side to side), the pressure vessel (blue) has an external radius of 20 cm. The aluminum structure (grey), has a maximum diameter of 73.5 cm. The total length is cm. The polyethylene is inside the aluminum structure. the detector (in practice the position of the source with respect to the detector is specified and the detector is fixed in space). The degree of polarization could be also specified at this stage, but it is less time consuming if it is created later on in the analysis, since any polarization degree is a linear combination of fully polarized and unpolarized radiation (see section 5.4). (a) (b) Figure 5.2. Crab simulations configuration: (a) photons entering straight into the detector, (b) photons entering with an angle of 10 into the detector. The green dots indicate the starting and ending point. Most of the lines end inside the detector, i.e. most of the photons interact in the polarimeter. The lines outside the detector end at infinity. The neutrons are created by protons and alpha particles entering the Earth s

112 102 Chapter 5. Studies of PoGOLite Pathfinder Performance atmosphere. Therefore their energy spectrum depends on the latitude and altitude at which the experiment is flown, and on the solar activity during the flight. The neutron flux has been calculated in [47] for solar minimum and for a magnetic latitude of 42 (typical of Texas). These conditions are an approximation for the flight of PoGOLite, since it will be flown at a lower magnetic latitude and during a higher solar activity. In figure the neutron energy spectra for different altitudes are shown. The spectrum for 5 g/cm 2 is the one that better represents the flight conditions of the PoGOLite pathfinder (see section 5.2.3). The energy spectrum for 5 g/cm 2 can be parametrized by the following equation [35]: f i (E) = A i E ai, (5.2) where f i are the flux values over energy intervals i = 1,2,3,4. A i and a i are constants obtained by fitting the neutron flux spectrum for 5 g/cm 2. The values and the energy intervals are reported in table 5.1. energy A i [kev 1 cm 2 s 1 ] a i 1 kev - 1 MeV MeV - 15 MeV MeV - 70 MeV MeV - 1 GeV Table 5.1. Neutron energy spectrum fitting parameters (see equation 5.2). The direction of the neutrons is randomly taken from the same disc which is used for generating the Crab photons, but in this case the disc is moving on a sphere. The probability of finding the disc on the bottom hemisphere is 80% (see figure 5.4), since the neutrons are created in the underlying atmosphere [76]. The output file describes all events that have generated a hit in the detector either by a photon or a neutron. It contains the type of input particle, and the depositions and locations of the energy. Another file contains the information about position in space of the PDCs, and depends only on the detector s geometry Analysis Steps In what follows the data will be analyzed such that a single final modulation curve is produced. The output file is first digitized, resulting in a file containing the energy deposit for each detector element. Quenching If the incident particle is a hadron, a quenching factor is taken into account, which describes the partial energy loss of the hadrons in form of heat. The light yield of a hadronic interaction will be lower than for a photon with the same energy deposition. The quenching factor depends on the energy deposited and on

113 5.1. Observation simulations with Geant4 103 Figure 5.3. Neutron spectra at various depths from the top of the atmosphere, for a solar minimum and for magnetic latitude of 42 [47]. the particle created in the interaction of the hadron with the nucleus as shown in table 5.2. If the deposition is in the BGO the energy after quenching is multiplied by 0.1, since the BGO is a more efficient absorber [51]. Event selection In the next step, valid events for polarization measurements are selected. An incoming photon generates a valid event if it undergoes Compton scattering in a fast scintillator and if the emitted photon is absorbed in the fast

114 104 Chapter 5. Studies of PoGOLite Pathfinder Performance Figure 5.4. Neutron simulation configuration: the green dots indicates start and ending points of generated neutrons. The trajectories start on a sphere located around the detector. 80% of the neutrons start from the lower hemisphere and end above. Particle/Energy Energy after quenching [MeV] neutrons <1 MeV E E 2 neutrons 1 MeV E photons 0 Table 5.2. Hadron quenching energy, E is the energy of the incoming particle.

115 5.1. Observation simulations with Geant4 105 scintillator of a different PDC. Valid events with total deposited energy between kev are selected. In this range the Crab flux is higher than the background rate (see figure 2.20). The scattering angle of the photon is reconstructed by connecting the center of the two PDCs containing two hits, the Compton scattering site and the photo-absorption site. If the energy of the incoming photon is so large that the photon Compton scatters twice before being photo-absorbed, the scattering site with the lowest energy deposition will be neglected since the deviation from the trajectory will be small. Consequently one can neglect the correction in the azimuth angle. The PMT response is taken into account by assuming an energy resolution of 2 kev [46]. In the final step the energy threshold to select a valid event is introduced. This is 2 kev for plastic scintillator and 30 kev for the BGO crystals of the side and bottom anti-coincidence shield. A higher energy deposit in one of these elements will reject the event [46]. Smearing In the same analysis routine the smearing of the azimuthal angle is performed. Since the polarimeter is pixilated the azimuthal scattering angle has to be smeared. This is needed because all events will be merged to construct one modulation curve. When reconstructing the azimuthal angle of the real data, there is no positional information of where within the scintillator the energy is deposited. With the simulated data this information is available, but the same conditions as with real data are used here. When a photon undergoes Compton scattering in a PDC and is photo-absorbed in a second PDC, there is an uncertainty of where exactly both events take place. This is about ±30 if Compton scattering and photo-absorption are in adjacent PDCs; the hexagonal shape of the PDC allows to have six adjacent PDCs. The uncertainty becomes ±15 when the absorption takes place in the second ring around the Compton scattering center. The reconstructed azimuth angle of different scattering events, registered in one pair of PDCs, will be the same for all these events. The reconstructed azimuth angle is the one obtained by connecting the two centers of the PDCs, even though the events are not centered in the PDCs. Figure 5.5 shows an example of how two events with two different angles are reconstructed as having the same azimuthal scattering angle. In order to take into account this effect, the azimuth angle distribution is smeared out. This is done by choosing randomly the azimuthal scattering angle from a Gaussian distribution. The standard deviation width, σ, is obtained by fitting the distribution of the simulated events in the PDCs with a Gaussian centered around the center-to-center angle. If the hits are not in adjacent PDCs cells, the σ will be smaller. The value of σ has been found to depend on d, the separation between Compton and photo-absorption site, as follows [77]: ( ) 1 σ = d (5.3) d where d is given in units of numbers of PDCs. If the interactions are in adjacent PDCs, d = 1 and σ = 25.4, which is approximately the value one would get by considering a Gaussian distribution with FWHM = 60 (FWHM = 2 2 ln 2σ). The

116 106 Chapter 5. Studies of PoGOLite Pathfinder Performance smearing reorders statistically the scattering angles, and since the final measurement is of the total polarization this is enough to remove the uncertainty on the azimuth angle. The azimuthal scattering distribution, both in the case of smearing and no smearing for a 100% polarized signal with polarization angle 0, are shown in figure 5.6. The distributions have been fitted with a modulation curve (equation 1.18). The fit of the smeared data (green curve in figure 5.6) gives a modulation factor of 0.203±0.007 and an angle of (178.7±1.8). The fit of the unsmeared data (red curve in figure 5.6) gives a modulation factor of 0.503±0.006 and an angle of (135.2±0.3). This shows that if the data are not smeared both the polarization angle and the modulation factor, and consequently the polarization degree, are affected and therefore the smearing needs to be taken into account. The smearing is not applicable for neutron induced events since the neutrons have a shorter mean free path, the result is a modulation with angle 60. If the analysis would be performed on each ring of PDCs separately, then the smearing would not be needed. One would get a modulation curve for each ring of PDCs around the Compton scattering center. Figure 5.5. Azimuth scattering angle reconstruction: example of how two events with two different angles are reconstructed the same angle. In order to take into account this effect the azimuth angle distribution can be smeared out. The use of the smearing allows to reconstruct angles smaller than 60, thus the number of bins when reconstructing the azimuthal distribution can be increased. From here on the number of bins will be set to 40, which is a good compromise between signal to noise and number of bins. The output of the analysis is the azimuthal distribution of the valid events, selected and analyzed as specified above, and fitted with the modulation curve in equation 1.18.

117 5.1. Observation simulations with Geant events/bin modulation with no smearing modulation with smearing azimuth angle Figure 5.6. Comparison between smeared and unsmeared data: the distribution of the smeared data (green histogram) are fitted with the (green) modulation curve. The unsmeared data (red histogram) are fitted with the modulation (red) curve. The fit of the smeared data gives a modulation factor of 0.203±0.007 and angle of (178.7±1.8). The fit of the unsmeared data gives a modulation factor of 0.503±0.006 and angle of (135.2±0.3).

118 108 Chapter 5. Studies of PoGOLite Pathfinder Performance 5.2 Performance Studies Determination of M 100 One parameter that characterizes the instrument is M 100, the modulation factor obtained when the instrument is exposed to a 100% polarized source. This value is also used to calculate the actual polarization degree (see equation 1.18). M 100 can be either measured at test beam experiments, where the polarization of the incoming beam is well known, or through computer simulations. This parameter depends on the energy of the incoming radiation. In what follows M 100 has been estimated through simulations for a source with a flux of 1 Crab, in the reconstructed energy range kev and for an observation time of 6 hours. The incoming beam is 100% polarized and the polarization angle has been changed in steps of 10 from 0 to 170. The azimuthal distribution of the events in the energy range of kev, shown in figure 5.7, is then fitted with the modulation curve described by equation This is repeated for all 18 sets of data, one set for each step in angle. The distribution of the fitted modulation factors is shown in figure 5.8. The error on the individual fits is for all cases. The mean value of the distribution is 0.278±0.005, thus the spread is due only to the error on the fit. The change in polarization angle is used only to check any presence of systematic errors in the simulations, since M 100 does not depend on the angle. The result is shown in figure 5.9. No apparent dependence on the polarization angle is evident. The conclusion therefore is that the detector mass model does not yield any systematic effects concerning the reconstruction of the polarization angle. The azimuthal distribution of the real data will be fitted with the modulation curve, and the estimated modulation factor will be divided by M 100 to get the polarization degree value. The error on this will be dominated by the error on the modulation factor since the error on the polarization degree is given by: σ P = M σm 2 M 100 M 2 + M2 σ2 M 100 M (5.4) This is the error obtained by propagating the errors on M 100 and M. The relative error on the measurement of M will be greater than the one on M 100 since the latter has been measured with higher number of events. It follows that σ P = σm M Minimum detectable polarization (MDP) As already mentioned in chapter 1, an important figure of merit which describes how well a polarimeter can detect polarization at a certain confidence level, usually 99%, is the MDP, defined as (see appendix A for derivation):

119 5.2. Performance Studies 109 events/bin azimuth angle Figure 5.7. Azimuthal distribution of 100% polarized photon beam fitted with a modulation curve described by equation 1.18, used to determine M 100. events/bin 7 Entries 18 Mean RMS M 100 Figure 5.8. Distribution of M 100 created by using 18 values of the fitted modulation factor. Each modulation factor has been fitted from a 6 hour simulation data. The input was 1 Crab source and the radiation was 100% polarized. Each of the 18 sets has a different polarization angle. The angle goes from 0 to 170 in steps of 10.

120 110 Chapter 5. Studies of PoGOLite Pathfinder Performance modulation factor polarization angle [degree] Figure 5.9. Modulation factors used to estimate M 100 versus input polarization angle. No apparent dependency on the polarization angle is reveiled. MDP 99% = 4.29 (RS + R B ) (5.5) M 100 R S T where R S and R B are the source and background rates respectively, T the observation time and M 100 is the modulation factor for a 100% polarized source. The MDP quantifies the minimum level at which the instrument can detect significantly polarization in absence of instrumental systematics. MDP 99% represents the probability of 1% to exceed this value by chance. Inserting the values expected for the 6 hour flight of PoGOLite pathfinder in the reconstructed energy band kev, R S = 2.39 s 1 and R B = 1.44 s 1 (see table 2.2), gives a MDP = (8.5±0.2)%. The detector will be able to detect polarization only above this value with a high confidence level. Having a high value of M 100 results in a lower MDP, but it does not help if the background flux is greater than the source flux. A longer exposure time lowers the MDP as well. The same quantity can be estimated through simulations. In the absence of a polarization signal, the photo-absorption events will be distributed uniformly around the scattering center. Random values between -π to π are taken with equal probabilities to simulate uniform azimuthal scattering distribution. First events are used, the amount of events expected from the total Crab in a 6 hour flight by PoGOLite. Figure 5.10 shows the distribution of the azimuthal angle which is then fitted with the same curve used to find the modulation factor in the real data (see equation 1.18). Even though the data do not contain an input modulation, it is still possible to fit the data with the modulation curve. This gives

121 5.2. Performance Studies 111 rise to a spurious polarization determination. This procedure is repeated times, saving for each run the fitted modulation factor. The distribution of the modulation factors for events is shown in red in figure The area of the modulation factors distribution is summed up to the 99% of the total area. The integral limit is then divided by M 100, which gives the MDP 99%. For events the MDP is 6.7%. This can be compared with the theoretical value derived by using the equation 5.5 with R B = 0. The formula gives a MDP 99% = 6.8±0.1, in agreement with the value obtained through simulations. events/bin azimuth angle Figure Uniform random distribution of events with azimuth angles from -π to π. The data with no input polarization can be fitted with a modulation curve. This gives rise to a spurious polarization determination. If the same procedure is repeated considering also background, 4788 events, the total number of events becomes Before fitting the modulation curve to the data, one has to remove the expected background from each bin. In this case the histograms contains 40 bins, so from each bin 750 events are removed. The data are fitted with the same curve and the procedure is the same as described before (black histogram in figure 5.11), the result is a MDP = 8.6%, which is within the error of the theoretical value. If the background is not removed the same amount of total events give a MDP = 5.4% (green histogram in figure 5.11), which would indicate a better performance of the detector, which is not the case. This shows that it is very important to remove the correct level of background, especially if the polarization degree of the source of interest is low. A wrong estimate of the background could make extracting polarization from the detected signal statistically impossible. If the same procedure is repeated for longer exposures, the azimuth distribution will become flatter and the modulation factors distribution narrower.

122 112 Chapter 5. Studies of PoGOLite Pathfinder Performance counts/bin modulation distribution Crab: MDP = 6.7% modulation distribution total: MDP = 5.4% modulation distribution total - background: MDP = 8.6% modulation Figure Distribution of fitted modulation factors measured on Crab events (red), on total (Crab and background) events (green), and on the background reduced events. All events are taken from random uniform distribution with no input modulation. The MDP has been calculated for different exposure times, taking into account also the background. The results are reported in figure 5.12 and for comparison the theoretical curve (equation 5.5) is plotted in the same figure. Longer observations will allow the measurement of low polarization degree values, but usually with exposure time other systematics appear Effects of Air Attenuation During an observation, targets of interest will move on the sky due to the rotation of the Earth, giving rise to an elevation and azimuth trajectory. The details depend on the location and time of observation. The change in azimuth will be discussed in chapter 6. The change in elevation affects the flux of the source since the elevation angle determines the airmass, i.e. the thickness of the atmospheric layer between detector and source. In figure 5.13 the elevation trajectory for PoGOLite targets observed from Esrange, Sweden (Latitude: , Longitude: ) on August 15 th 2010 are shown. To quantify the amount of atmosphere between the polarimeter and the observation target the airmass, AM is used, which is defined as [78]: AM = 1 sin(θ) (θ ) 1.6 ) (5.6)

123 5.2. Performance Studies MDP [%] 15 expected MDP time [hours] Figure MDP as function of the observation time where the background has not been considered. The points follow the predicted MDP elevation [degree] Crab Cygnus X local time [hours] Figure Elevation angle of two observation targets observed at Esrange (Sweden) on August 15 th 2010.

124 114 Chapter 5. Studies of PoGOLite Pathfinder Performance where θ is the elevation angle in degrees. For θ >0 (θ <0 is not considered since it would mean the source is below the horizon and thus obscured) the second term of the denominator can be neglected and the AM expression becomes: AM = 1 sin(θ) (5.7) When the source is at the zenith, θ = 90, the absorption due to the atmosphere is at its minimum, and the AM = 1. Whereas at the horizon it reaches the maximum, and one has to use the full expression in equation 5.6, which gives AM = In general, one tries to avoid airmass values greater than 2.0, which applies to elevation angles above 30. The atmospheric depth, ρ, is given by: ρ = ρ 0 AM (5.8) where ρ 0 is the residual atmospheric depth and has an approximate value of 5 g/cm 2 at an altitude of 40 km at the latitude of Esrange. The atmospheric depth, X, at an altitude h is given by the integral of the density of the overlying air: X(h) = h ρ(h )dh. (5.9) The density can be inferred from the ideal gas law and the measurement of the temperature and pressure profiles: ρ = pm Mol RT (5.10) where M Mol = g/mol is the molar mass of air and R = J/(K mol) is the universal gas constant. The temperature and pressure have been measured by P - BACE on the MEAP mission during ascent from Esrange in June 2008 [79]. The profiles are shown in figure The atmospheric depth is then used together with the cross-section of air, shown in figure 5.15, to calculate the air attenuation. Depending on the energy of the radiation, the initial flux, F 0, will be attenuated according to the formula: F = F 0 Emax E min e ρσe de (5.11) which is the integrated probability in the energy interval E min to E max. Here σ Emax/min is the respective cross section, whose values are given in the table 5.3. The attenuation of the flux will lower the number of events of the modulation, and thus the reconstruction of the polarization signal will be affected. In order to estimate the magnitude of this effect, a study of the Crab signal has been done, taking into account the air attenuation as a function of elevation angle. Simulations for the Crab are performed for the total observation time of 6 hours from Esrange for August 15 th 2010 (see figure 5.13). The payload will be at float

125 5.2. Performance Studies 115 Figure Pressure (solid line) and temperature (dashed line) profile measured by P-BACE during ascent over Esrange [79]. energy [kev] σ [cm 2 /g] Table 5.3. Mean values of the air interaction cross section for different energy ranges [80].

126 116 Chapter 5. Studies of PoGOLite Pathfinder Performance Figure Air attenuation due to coherent scattering (solid line), as used in the analysis compared to air attenuation with incoherent scattering (dashed line) [80]. altitude approximately 2 hours after launch. Observations are set to start at an elevation angle of 28 and the duration of the observation is divided into 30 minute intervals. During this time each PDC goes through a complete rotation around the axis of the polarimeter. This rotation, as described in chapter 2, allows possible asymmetries of the detector to be studied. During the analysis each set of 30 minute long data is attenuated according to equation 5.11 with the corresponding elevation angle for the source (see figure 5.13). The resulting count rate as a function of the elevation angle is shown in figure The mean value of the count rate in 6 hours is 1.24±0.09 s 1, compared to 2.39 s 1, which is for constant atmospheric depth. The flux spectrum of the Crab, taking into account the varying air attenuation is shown in figure 5.17 (green curve). The corresponding flux spectrum of the Crab for different values of residual atmospheric depth is also shown. For comparison the flux spectrum for constant atmospheric depth (5 g/cm 2 ) (blue curve) is shown. When taking into consideration the variation of elevation angle the flux spectrum is lowered by approximately a factor 2 compared to having constant atmospheric depth. The dominant neutron background to these measurements is discussed in the next section. 5.3 Neutron Background The neutron background is also expected to change with elevation angle since the neutron background is not isotropic. Approximately 80% comes from below, so

127 5.3. Neutron Background rate [s -1 ] elevation [degree] Figure Detected rate of the Crab signal taking into account variation of atmospheric attenuation for a simulated observation. The atmospheric attenuation depends on the elevation angle. when the detector is pointing at low elevation angles more of the sensitive volume of the detector will be exposed to the neutron background. In order to estimate the increase of background level due to the change in elevation angle, neutron background simulations are performed with the same elevation angles used when studying the variation of the Crab signal rate. The neutron rate as a function of elevation angle is shown in figure The neutron rate has been studied for elevation angle between 28 and 50 in steps of few degrees. These are the elevation angles at which the detector will be every 30 min. For completeness the rate has been studied also for higher elevation angles (70, 80, 90 ). The results of the simulations show that the neutron background does not change appreciably with the elevation angle and the mean value of the expected rate is 1.08±0.09 s 1. This is contrary to what was expected. The side anti-coincidence and the polyethylene shield are indeed effective in attenuating the background. The Crab and neutron background flux as a function of energy are shown in figure The neutron flux is comparable to the Crab flux for an atmospheric depth of 5 g/cm 2. Since the background rate is constant with elevation, it can be removed as an offset from the data. Moreover, the fact that the rate is constant with elevation means that the background only needs to be measured a few times during observation. Above 60 kev the rate of the neutron background dominates the one of the Crab, this suggests an energy cut at 60 kev, but the chosen value of the atmospheric is an upper limit. For a lower value, for example 3 g/cm 2, the neutron background remains below the Crab signal.

128 118 Chapter 5. Studies of PoGOLite Pathfinder Performance /kev) 2 flux (c/s/cm Crab with changing AM for 3 g/cm 2 Crab with changing AM for 5 g/cm 2 Crab with changing AM for 7 g/cm 2 Crab with constant AM for 5 g/cm energy (kev) Figure Expected Crab flux spectra between kev for a 6 hour flight. Different values of residual atmospheric depth and variation of elevation have been considered: (magenta) for 3 g/cm 2, (green) for 5 g/cm 2 and (red) for 7 g/cm 2. For comparison also the flux spectrum for 5 g/cm 2 with no variation of elevation is shown (blue).

129 5.3. Neutron Background rate [s -1 ] elevation [degree] Figure Rate of neutron background taking into account atmospheric attenuation: the neutron background does not change appreciably with the elevation angle. The mean value is 1.08±0.09 s 1. /kev) 2 flux (c/s/cm Crab with changing AM for 3 g/cm 2 Crab with changing AM for 5 g/cm 2 neutron for 5 g/cm energy (kev) Figure Expected Crab flux spectrum (magenta) compared with the background flux spectrum (green) between kev for a 6 hour flight taking into account air attenuation which varies with elevation at a residual atmospheric depth of 5 g/cm 2 and 3g/cm 2. The neutron background is comparable to the Crab signal rate for an atmospheric depth of 5 g/cm 2.

130 120 Chapter 5. Studies of PoGOLite Pathfinder Performance As already discussed, the azimuthal angle distribution of the events induced by the neutrons is affected by the geometry of the polarimeter. In order to see if the neutron induced events affect the polarization signal, the azimuthal distribution has to be studied. For this purpose Fourier harmonic decomposition is used. Any continuous signal can be decomposed into a Fourier series, this applies also to a binned distribution if the number of events in each bin is high enough. The azimuthal distribution of the neutron induced events has been fitted with a modulation curve containing the first six harmonics [46]: f(x) = T 0 (1 + M 1 cos((x φ 1 ) + M 2 cos(2(x φ 2 ) + M 3 cos(3(x φ 3 ) + M 4 cos(4(x φ 4 ) + M 5 cos(5(x φ 5 ) + M 6 cos(6(x φ 6 )) (5.12) where T 0 is a normalization constant, M 1...M 6 are amplitudes of each harmonic contribution and φ 1...φ 6 are the harmonic phases. It has been shown that neutron events induce a modulation at the sixth harmonic, but since different harmonics are orthogonal, this will not affect the polarization signal which contributes with the second harmonic [46]. An example of the azimuthal distribution of the neutron events is shown in figure The signal of a 6 hour flight has been fitted with the function given by equation The amplitude of the sixth harmonic is 0.017±0.009 compared to ± for the second harmonic, the one used to determine the polarization degree, and it is clearly seen in figure In order to check how different elevation angles can affect the signal modulation, the different sets of azimuthal distributions for the neutron events are fitted with the function containing six harmonics (equation 5.12). For each set the six fitted amplitudes, M 1...M 6, are plotted in figure There is no evident dependence on the elevation angle, especially regarding M 2, which is the amplitude of the second harmonic and the one used to determine the polarization angle of the source. The mean value of the Crab rate with variable attenuation, and the neutron background rate can be combined to recalculate the MDP and the result is 12.9%. The modulation curve for a 100% polarized Crab source with polarization angle 0, considering background and air attenuation, is shown (black) in figure For comparison also the modulation curve for constant elevation (green), for constant attenuation and background (blue), and variable attenuation with no background (red), are shown in the same figure. The data sets are fitted with modulation curves and the results are reported in table 5.4.

131 5.3. Neutron Background 121 events/bin azimuth angle Figure Example of azimuthal distribution for neutron events. The signal of a 6 hour flight has been fitted with the function given by equation The amplitude of the sixth harmonic is 0.017±0.009 compared to ± of the second harmonic, the one used to determine the polarization degree. 0.2 neutron modulation M 1 M 2 M 3 M 4 M 5 M elevation [degree] Figure Neutron background harmonics: different harmonic amplitudes for different elevation angles are shown, there is no evidence of dependance on elevation angle. In particular M 3, which is the third harmonic and the one used to determine the polarization angle of the source does not change with elevation. The sixth harmonic is more prominent, as expected.

132 122 Chapter 5. Studies of PoGOLite Pathfinder Performance events/bin attenuated Crab Crab Crab + neutron attenuated Crab + neutron azimuth angle Figure Modulation curve for 100% polarized Crab source and background taking into consideration the effects of the change in elevation angle (black). For comparison also the modulation curve for constant elevation (green), for constant attenuation and background (blue), and variable attenuation with no background (red), are shown. Signal Modulation Angle [rad] Crab 0.269± ±0.01 Attenuated Crab 0.298± ±0.01 Crab + neutron 0.188± ±0.01 Attenuated Crab + neutron 0.15± ±0.02 Table 5.4. Modulation factors for the azimuthal distributions shown in figure 5.22.

133 5.4. Outline of a Polarization Analysis Method Outline of a Polarization Analysis Method In view of the upcoming flight of the PoGOLite pathfinder, a data analysis method has been studied, inspired by the polarization analysis used for INTEGRAL/SPI [6]. The method is applied here to study the polarization of the Crab nebula. If the first mission should be long enough to allow for observations of additional sources, this method can be applied to other objects by changing the input spectrum. The proposed analysis consists of comparing the real observations to simulated data. This method has the advantage of taking into consideration the detector response and systematic errors. Otherwise one would have to convolve the response of each detector element, which is not easy in the X-ray regime. The simulated data are created with the Geant4 PoGOLite detector model using the Crab nebula spectrum and a duration ten times longer than the real observation time in order to model the effects of the response function Polarization Matrix To take into account the polarization of the Crab, 19 sets of data are created: 18 sets are 100% polarized beams with different polarization angles (azimuthal angle of the detector), and one set is unpolarized. The angles are chosen in steps of 10 from 0 to 170 ; these cover the whole range of azimuthal angle because Compton scattering is π-symmetric. From these data sets it is possible to create a data set for any polarization degree. Partial polarization is the incoherent sum of an unpolarized and a fully polarized component [81], thus any percentage polarization data P % can be produced by combining 100% polarized data, P 100, with an unpolarized signal, P 0 according to the formula: P % = np (100 n)p (5.13) where n is the percentage of polarization degree. The change in polarization angle is a smoothly varying function, therefore it is possible to interpolate between the simulated files for angle steps smaller than 10. Data for each 1% from (0-100)% polarization degree and for each 1 in the range of are created. The data between are created by interpolating between 170-0, because of the π- symmetry of the Compton scattering. The result is sets of data. For the analysis only valid events (events with two or three hits in the detector) with measured energy between 25 kev and 80 kev are considered. With these events the azimuthal distribution for each combination of polarization degree and angle is created and saved into a matrix. Each element of the matrix will contain an azimuthal distribution for a pair of polarization degree and polarization angle values, i.e. the modulation curve.

134 124 Chapter 5. Studies of PoGOLite Pathfinder Performance χ 2 Matrix The real data will then be compared using a χ 2 -test to all the elements of the matrix, resulting in a χ 2 matrix. The number of bins used for the simulations has to be the same as that used to bin the real data, otherwise the χ 2 -test will not work, as all the bins have to be paired. In this analysis 40 bins have been chosen, a good compromise for signal to noise ratio. The real data will have a lower number of events compared to the simulations, so the simulation mean level is put equal to the mean level of the data. Every element of the matrix is calculated in the following way: χ 2 (α, P) = 40 i=1 (N i obs Ni sim )2 σ i2 sim (5.14) where α and P are the polarization angle and degree, and identify the matrix element. The index i identifies the bin, Nobs i and Ni sim are respectively the observed data and simulated data in the i th bin, and σ i2 sim is the variance of the simulated data. Here it is assumed that the simulated data, since they have a higher statistics, are the fitting model which usually is a continuous function [82]. The variance σsim 2 is defined as: σ 2 sim = σ 2 Poisson + σ 2 model = N sim + N sim k 1 (5.15) The first term, σpoisson 2, takes into account that the distribution is of Poissonian type, whereas the second term, σmodel 2, describes the fact that the model consists of simulated data, k is the ratio between the duration of the simulations and the duration of observations. For infinitely long model simulations, the second term becomes negligible and the variance of the simulated data, the model, will contain only the Poisson contribution. The minimum χ 2 value gives the best fit, which is the minimum of the matrix, and determines the polarization degree and polarization angle Background and Air Attenuation The data comprise the sum of the signal of the Crab nebula and of the neutron background. Moreover the signal of the source of interest will be attenuated depending on the elevation angle. The background has to be removed from the data before calculating the χ 2, or alternatively simulations of the background have to be added to the simulations of the source. The latter method is more robust regarding systematics induced by the background. Either way, the flux of the background has to be measured. Since it has been shown to be constant (see section 5.2.3) it would be enough to measure the flux of the background at the beginning and at the end of the observations, when the Crab has too low an elevation angle to be observed.

135 5.5. Analysis Procedure 125 During the observation of the Crab the background can be monitored by using the information of the pulsed fraction (see 4.5), which at a particular energy is constant and thus any variation of it could be attributed to the background. This requires the air attenuation to be well known and timing performance from the instrument. Alternatively the background could be studied off-source during the observation of the Crab every 30 minutes, the time needed to perform a complete revolution of the polarimeter around its axis. Probably this is the safest method but it lowers the time of observation of the source. In the worst case, if no measurements of the background are available, the total measured data are compared to the simulated data of the source, and the difference is assumed to be background. 5.5 Analysis Procedure The data analysis procedure can be summarized in the following way: For every 30 minutes data window the source and background level is measured. If it is not possible to measure the background, the simulation of the source is subtracted. The difference is assumed to be background. A good estimate of the air attenuation is very important. A data set corresponding to the total background is generated and added to each element of the polarization matrix, resulting in a new matrix, M SB. The real data are compared to each element of the new matrix, M SB. While doing this, the mean value of the simulated data is normalized to the mean value of the real data, since the exposure time is different. The minimum of the χ 2 matrix indicates the best fit. The fitted polarization degree and angle are the indices of the minimum of the matrix M SB. Once the minimum is found, the confidence level curves for 68%, 95% and 99% are created in the following way: χ 2 = χ 2 χ 2 min (5.16) where χ 2 is 2.3, 5.99, 9.21 for 68%, 95% and 99.9% confidence level respectively. The values of χ 2 assume the fitting of two parameters [83]. The polarization analysis method has been applied to a simulated example, in the following sections Case Study The analysis method (method I) has been tested on a simulated observed data set. The input source is the total Crab Nebula spectrum, assuming a polarization degree

136 126 Chapter 5. Studies of PoGOLite Pathfinder Performance P = 46% and polarization angle α = 123, the values measured by INTEGRAL/SPI [6]. The observation time is 6 hours. Four different cases for the observed data are analyzed: only source contribution, source and background, elevation attenuated source, elevation attenuated source and background. With these examples the effects of the different contributions can be investigated. Case I : source only The simulated observed data contain only the total Crab flux with parameters specified above and constant air attenuation with residual atmospheric depth of 5 g/cm 2. The χ 2 -test is performed and the fitted parameters are P = ( )% and α = ( ). The confidence level curves are shown in figure 5.23 and for comparison the actual value is also shown. For this simplest case, the reconstructed parameters are well within 68% confidence level fitted degree/angle actual degree/angle 55 polarization degree (%) % 68% % polarization angle (degrees) Figure Confidence level curves for polarized Crab signal input: P = 46% and α = 123. The reconstructed values are P = (45±3)% and α = ( ). Case II : source and background To the data of the previous example a constant level of background, expected in a 6 hour flight, has been added. First the χ 2 -test has been performed without correcting for the background, the result is shown in figure 5.24 (top panel). The fitted values are P = ( )% and α = ( ). Thus not removing the background lowers the polarization degree but the reconstructed angle is still within the 68% confidence level. If the background is considered the fitted values are P = ( )% and α =(121±2) (see

137 5.5. Analysis Procedure 127 figure 5.24 bottom panel) and are both within 68% confidence level. The background has been considered by removing an offset from the observed data, instead of adding background to the simulations, since in this example the observed data are simulated as well. With a real observation, the best way is to add background to the polarization matrix and then perform the χ 2 -test. This example shows that a wrong estimate of the background level will affect the reconstruction of the polarization degree, whereas the polarization angle is not affected. This is valid if the background rate is constant as predicted by the simulations. Case III: source with attenuation Here only the source is considered and the air attenuation is taken into consideration, which varies during the flight due to the different elevation angles of the source (see section 5.2.3). This will result mainly in a lowering of the count rate. This is taken into account when normalizing the mean value of the simulations to the mean value of the observed data. The reconstructed values are P = (48±5)% and α = ( ) (see figure 5.25). The determination of the polarization angle is affected by the variation of air attenuation. This is probably due to the fact that for this case the azimuthal distribution gets damped out as shown also in the example in figure Case IV: The last example comprises all the different cases: elevation-attenuated source with background. The reconstructed values without removing background are P = ( )% and α = (124±4) (top panel figure 5.26) whereas removing the background gives a better value of the fitted polarization degree, P = %, the polarization angle does not vary significantly, α = ( ). Both parameters are reconstructed within 68% confidence level (see bottom panel 5.26). Different cases have been analyzed to show how the polarization analysis method applies. The method applies well also with the presence of background if it is correctly removed. The air attenuation introduces a big uncertainty on the polarization angle because the scattering angle distribution is damped out. In order to check systematic effects, the examples are analyzed also by fitting the azimuthal distribution with a cosine function Modulation Curve Method For comparison the polarization degree and polarization angle are determined from directly fitting the modulation curve with a cosine function (method II). The azimuthal distribution of the above examples are fitted with the formula in equation The results are shown in figure 5.27 and the fitted parameters are reported in table 5.5. The data containing a neutron contribution have not been background subracted. This is done in figure 5.28, and for comparison the data containing background are shown again.

138 128 Chapter 5. Studies of PoGOLite Pathfinder Performance fitted degree/angle actual degree/angle 40 polarization degree (%) % 68% 95% polarization angle (degrees) fitted degree/angle actual degree/angle polarization degree (%) % 68% % polarization angle (degrees) Figure Confidence level curves for polarized Crab signal and background input: P = 46% and α = 123 and background level for a 6 hour flight. The top panel shows the reconstructed values if the background is not considered: P = ( )% and α = ( ). The bottom panel shows the reconstructed values after the background has been removed: P = ( )% and α = (121±2), and are both within 68% confidence level.

139 5.5. Analysis Procedure fitted degree/angle actual degree/angle polarization degree (%) % 95% 68% polarization angle (degrees) Figure Confidence level curves for polarized Crab signal taking into account air attenuation: P = 46% and α = 123 and air attenuation from (28-46) elevation angles. The reconstructed values are P = (48±5)% and α = ( ). signal modulation angle [ ] Crab 0.124± ±1 attenuated Crab 0.133± ±2 Crab + neutron 0.082± ±2 Crab + neutron (bg subtracted) 0.127± ±2 attenuated Crab + neutron 0.07± ±1 attenuated Crab + neutron (bg subtracted) 0.154± ±1 Table 5.5. Fitted modulation factors for the azimuthal distribution in figures 5.27 and 5.28.

140 130 Chapter 5. Studies of PoGOLite Pathfinder Performance 50 fitted degree/angle actual degree/angle 40 polarization degree (%) % 68% % polarization angle (degree) fitted degree/angle actual degree/angle polarization degree (%) % 95% % polarization angle (degrees) Figure Confidence level curves for polarized Crab signal taking into account air attenuation and background: P = 46% and α = 123, air attenuation from (28-46) elevation angles and background level for a 6 hour flight. The top panel shows the reconstructed values if the background is not considered: P = ( )% and α = (124±4). The bottom panel shows the reconstructed values after the background has been removed: P = ( )% and α = ( ).

141 5.5. Analysis Procedure 131 events/bin Crab Crab + neutron attenuated Crab attenuated Crab + neutron azimuth angle Figure Azimuthal distribution for four different conditions: (blue) Crab, (green) Crab and neutron background, (red) attenuated Crab, (magenta) attenuated Crab and neutrons. To better illustrate how the two methods apply, the fitted modulation factors for the six same cases are plotted as a function of the polarization degree, determined with the χ 2 -test (see figure 5.29). The data can be fitted linearly, the inclination is ±0.0003, which is M 100 /100, the ratio between modulation factor (y-axis) and polarization degree (x-axis). The value of M 100 is in agreement with the value determined in section 5.2, 0.279± The linear dependence suggests that the two methods are equivalent for determining the polarization degree, even though the errors on the polarization degree determined with the χ 2 -test are greater than the errors of the fit. This is due to the fact that when performing the χ 2 -test the error consists of two contributions, σ Poisson and σ model. The two methods are also equivalent when determining the polarization angle (see figure 5.30) although the error bars on the polarization angle determined via the χ 2 -test are larger this is due to the fact that the matrix is not continuous. The variation in air attenuation introduces a big uncertainty both for the polarization degree and the polarization angle. If the analysis is repeated on a new realization of observations (see figure 5.31), the reconstructed value are P = (44 ±5)% and α = (120±3), the values of the first example are P = (48±5)% and α = ( ). The fitted parameter fluctuates appreciably. In order to study if the errors on the polarization parameters are well estimated during the fitting procedure the distribution of the reconstructed values of different runs is studied. The distribution of the reconstructed values of the polarization

142 132 Chapter 5. Studies of PoGOLite Pathfinder Performance events/bin Crab + neutron Crab + neutron (bg subtracted) attenuated Crab + neutron 2000 attenuated Crab + neutron (bg subtracted) azimuth angle Figure Azimuthal distribution for four different conditions for Crab observations: (green dashed) Crab and neutron background, (green) Crab and neutron background with subtraction of background, (magenta dashed) attenuated Crab and neutron background, (magenta) attenuated Crab and neutron background with subtraction of background.

143 5.5. Analysis Procedure modulation factor polarization degree [%] Figure Comparison beween χ 2 -test and cosine fitting for determination of polarization degree: on the x-axis the polarization degree determined with the χ 2 - test procedure, on the y-axis the modulation factors determined with the fitting procedure. The linear dependence suggests that the two methods are equivalent in determining the polarization degree. The inclination is ± , which is M 100 /100, in agreement with the value determined in section 5.2.

144 134 Chapter 5. Studies of PoGOLite Pathfinder Performance pol. angle method II [degree] pol. angle method I [degree] Figure Comparison beween χ 2 -test and cosine fitting for determination of polarization angle: on the x-axis the polarization angle determined with the χ 2 -test procedure is shown, and on the y-axis the polarization angle determined with the fitting procedure is shown. The line indicates the relation one to one, but it is not a fit. The two methods seem to be equivalent even though the errors determined through χ 2 -test are overestimated.

145 5.5. Analysis Procedure fitted degree/angle actual degree/angle polarization degree (%) % 95% 68% polarization angle (degrees) Figure Second example of confidence level curves for polarized Crab signal taking into account air attenuation: P = 46% and α = 123 and air attenuation from (28-46) elevation angles. The reconstructed values are P = (44 ± 5)% and α = (120±3).

146 136 Chapter 5. Studies of PoGOLite Pathfinder Performance angle and degree are shown in figures 5.32 and 5.33, respectively. The mean value of the angle is (122±2), mean value for the modulation factor is 0.132± The errors are of the same order as the ones determined by the fit (see table 5.5). The atmospheric attenuation reduces the flux (see section 5.2.3), which results in larger errors on the fitted polarization parameters. events angle Entries 18 Mean RMS polarization angle [degrees] Figure Distribution of the reconstructed polarization angle for observations with variable attenuation, the mean value is (122±2) Conclusions Polarization performance parameters for PoGOLite have been estimated through simulations. The values are M 100 = 0.279±0.005 and MDP = 8.6%. The effect of change in elevation both on the Crab signal and neutron background has been simulated. The Crab signal is found to be strongly dependent on the elevation, due to a thicker atmospheric layer, whereas the neutron background remains constant, even though different parts of the polarimeter will be exposed to different contributions of background due to the change of elevation. A polarization analysis method, based on a χ 2 -test, has been validated. This method is an alternative with respect to the cosine function fitting method, it is unbiased and includes the detector response. The method has been applied to a case study, including air attenuation and background. The background rate needs to be accurately measured to be able to remove it from the data. A wrong estimate of it will affect the polarization degree, but the polarization angle will be reconstructed

147 5.5. Analysis Procedure 137 events modulation Entries 18 Mean RMS modulation factor Figure Distribution of reconstructed modulation factor for observations with variable attenuation, the mean value is 0.132± within 1σ deviation from the real value. Different ways of measuring the background are suggested. This study has shown that during the first flight, PoGOLite will be able to measure the polarization signal of the Crab nebula. The first flight offers also the possibility to measure the backgound level and make sure that it is as expected. In the first flight the air attenuation needs also to be monitored since what is used in the simulations is just an estimate. A future longer flight would give the possibility to have sufficient number of events, in order to observe the sources of interest only for large elevation angles, and therefore low air-mass. A longer observation would also allow to measure the polarization of the pulsar. The contribution is of about 0.15, thus to get the same MDP one needs to observe at least 10 times longer. The polarization matrix needs to contain information about air attenuation and background. The method becomes less flexible but more robust. So far the mass model consists of the perfect representation of the polarimeter. The χ 2 - test offers the possibility to take into account the polarimeter description. This can be done by testing before flight and during flight with known sources. Any systematics resulting from these studies can be included in the mass model, and consequently a more realistic response of the detector will be taken into account when comparing the observation data with the polarization matrix. Fitting the data with a predetermined function, a cosine function in this case, does not offer the possibility of taking into account the detector response, but will be used in the

148 138 Chapter 5. Studies of PoGOLite Pathfinder Performance first stage of the data analysis to get a first estimate of the polarization parameters.

149 Chapter 6 The Star Tracking System The ACS (Attitude Control System) needs to account for target sources moving on the sky and for gondola movements. The orientation of the gondola is surveyed by attitude sensors: DGPS (Differential Global Positioning System), two star trackers, gyroscopes, accelerometers and magnetometers. Only the DGPS and one of the star trackers give absolute attitude information. The other sensors give relative information and are periodically calibrated against drift by the absolute pointing information of the DGPS and star tracker sensors. The sensor outputs are processed by a dedicated ACS computer and control signals are generated for the elevation and azimuth motors to correct the pointing. In this chapter an overview of the ACS will be given. Particular focus is given on one of the two star trackers, described in more detail in section 6.2. The tests and calibrations performed on the star tracker are described, the results of these set the basis for the matching software. A possible matching software is described in 6.3 section and preliminary tests regarding the extraction of stars from the image are shown in section Attitude Control System Design In order to maximize the flux of X-rays from the sources of interest the polarimeter has to be aligned with the source. The movement of the source is predictable, whereas the random oscillations and vibrations of the gondola are not. The task of the ACS is to point to the targets and to measure constantly the attitude for off-line pointing reconstruction. The accuracy goals of the ACS are dictated by the MDP one is interested to measure. Simulations for the pathfinder [75] show that an alignment within 0.3 is needed to be able to measure a MDP of 10% for a 1 Crab source as shown in figure 6.1. The MDP for a an aligned detector is 8.5%. A detailed study of the variation of rate due to the inclination angle is given in [75]. The orientation of the gondola in space is reconstructed redundantly by different types of sensors: 139

150 140 Chapter 6. The Star Tracking System MDP [%] inclination angle [degrees] Figure 6.1. MDP as function of the inclination angle: on the y-axis the MDP, on the x-axis the inclination angle. The green horizontal line is the lower limit of 10% for the MDP. The line intersects the simulated data at an inclination angle of 0.4. a star tracker with a large FOV ( ) which will operate in tracking mode (STR) a star tracker with a small FOV ( ) which will operate in matching mode (STM). This star tracker is the focus of this chapter. a differential global positioning system (DGPS) two 3-axis gyroscopes/accelerometer/magnetometer packages with different precision The attitude control unit (ACU), built around a real time processor, reads out the sensors and combines their outputs to determine the orientation of the gondola and the pointing of the polarimeter. The required control signals are sent to the polarimeter elevation motor and to the azimuthal flywheel. The sensors are subdivided in slow rate absolute sensors and fast rate relative sensors. The group of the slow rate sensors comprises: the DGPS and the STM. The group of the fast rate sensors consists of the 2 Gyro packages and the STR. A diagram of the ACS is shown in figure 6.2. All the sensors and actuators, except the star trackers are custom manufactured by DST Control [84]. The relationship between the PoGOLite payload and the ACS is shown in figure 6.3.

151 6.1. Attitude Control System Design 141 Figure 6.2. Schematic block diagram of the ACS.

152 Figure 6.3. PoGOLite payload with ACS in parked position: (left) side view, (center) front view, (right) top view. The prolungation of the star trackers and aurora monitor unit identify their FOV. 142 Chapter 6. The Star Tracking System

153 6.2. Star Tracking Matching System (STM) Star Tracking Matching System (STM) The aim of the star tracking system is to provide the ACS with an absolute pointing solution of an accuracy of the order of 0.1. This information is used to calibrate the other sensors. Usually balloon experiments which were flown during both day and night time used a Sun sensor during day and a star tracker during night in order to provide absolute pointing solution. The solution adopted by PoGOLite consists of one star tracking camera equipped with special optics elements to be able to operate also during the day, in this way the same instrument is used during the flight with no need in switching between instrument and algorithm. The task of the star tracker system is the localization of stars and identification of patterns of stars. It acquires pictures of the sky, extracts information about relative positions of the stars and determines the coordinates of the center of the image by comparing the star pattern with a star catalog, e.g. Sky2000 [85]. Since this operation has to be performed both during night and day different obstacles have to be faced. At a typical altitude of 40 km the sunlight is scattered from the residual atmosphere and it scatters off the surface of the balloon. The star tracker design and software has been inspired by star trackers of other experiments: it uses the similar camera and optics ad hoc for the special environment during day light used in HEFT [86] and the software makes uses of some routines developed for the star tracker of BLAST [87] Star Tracker Design The star tracker design has to be optimized to maximize the number of stars available for the star matching. This is not straight-forward for operation during daylight. There are two important considerations. Firstly, the solid angle of each pixel of the image should be small to reduce the sky background. Secondly, the wavelength region that gives a low sky brightness and good star detection efficiency should be chosen. The star tracker, figure 6.4, consists of a Retiga-EXi CCD camera from Qimaging [88] which is read out by a PC104 computer system (MSM800BEV) from Digital-Logic [89]. On the camera is mounted a 200 mm f/2 Nikon Nikkor IF- ED lens. These components are housed in a pressure vessel connected through a fused silica window (not present during the tests described in this thesis) to a baffle system. CCD Camera The digital camera Retiga-EXi from Qimaging [88] is equipped with a Sony ICX285 progressive-scan interline monochrome CCD with an array of µmsquare pixels with a 100% fill factor. The camera has an electronic shutter which can expose from 40 µs to 17.9 minutes in 1 µs increments. The well capacity, i.e. the maximum number of electrons that can be stored by a single pixel before

154 144 Chapter 6. The Star Tracking System Figure 6.4. Star tracker camera assembly. saturation, is e. The 12 bits digital output gives a maximum value of = The CCD is connected through an IEEE 1394 Firewire interface to a PC104 computer system, and the digital output is translated to a 16 bit output in order to store the image on the computer. The conversion does not affect the quality of the image, but has to be taken into account when calculating the noise level. The data are transferred from the CCD to the computer at a speed of 400 Mbps, thus the transfer of a complete picture takes about 1 ms. The quantum efficiency of the CCD (plotted in figure 6.5) is maximal at 600 nm. The IR cut-off filter which is usually supplied with the camera is not used. Optics The CCD camera is equipped with a lens chosen as a compromise between having a large field of view but at the same time having the flux of one star distributed on not more than a few pixels. These are determined by the signal-to-noise ratio, the diffraction limited spot size, the field of view and the use of filters. The requirements are fulfilled by a 100 mm diameter Nikon Nikkor IF-ED lens, which has a focal length of f = 200 mm. The focus ranges from 2.5 m up to infinity, the aperture goes from a maximum of f/2 to a minimum value of f/16. The CCD size and the focal length of the lens determine the FOV through the formula [90]:

155 6.2. Star Tracking Matching System (STM) quantum efficiency (%) λ (nm) Figure 6.5. Quantum efficiency of the CCD versus wavelength. This response does not contain the IR filter that is usually installed on the camera. FOV = 57.3 A focal length. (6.1) The FOV is in one dimension, A is the width of the imaging area, 8.98 mm and 6.71 mm for the whole CCD chip, and 6.45 µm for a single pixel in both directions. Inserting the values the formula gives a FOV of for the entire chip, and a FOV of for a single pixel. The selected FOV assures a high spatial resolution. At the same time one has to make sure that images taken with such a FOV will always contain enough stars to be able to perform the matching. The average number of stars in the FOV increases rapidly with magnitude as shown in figure 6.6. The size of the aperture is chosen to be as large as possible, i.e. f/2, to collect as much light as possible. The aperture choice affects the size of diffraction spot, δ, described by the formula [90]: δ = 2.44λf/# (6.2) where λ is the wavelength, f/# the f-number and 2.44 an integration constant. In the red band λ = 650 nm. The size of the diffraction spot for f/2 (f/2.8) is 3.2 µm (4.4 µm) which is smaller than 1 pixel. So the light of a point source placed at infinity will be concentrated on one, two or four pixels depending on where the photon hits the pixel. Chromatic aberration can also cause broadening [91]. Ideally a star has to cover more than one pixel in order to distinguish from cosmic rays,

156 146 Chapter 6. The Star Tracking System number of stars in CCD FOV 40 red magnitude 35 optical magnitude magnitude Figure 6.6. Magnitude distribution for a field of view similar to the one of the star tracker and averaged on the whole sky. The star database Sky2000 [85] has been used. The dashed histogram shows the number of stars versus the red magnitude value, the continuous histogram is the distribution of stars versus optical magnitude. The number of stars in the red drops faster than the one in the optical because of lack of measurement in this wavelength region. Both are cut at magnitude 9 since it is the magnitude limit of the CCD as described in section

157 6.2. Star Tracking Matching System (STM) 147 but should not cover too many pixels since this will decrease the signal-to-noise ratio. The lens has a Nikon R60 filter which cuts out the light below 600 nm (see figure 6.7). This helps in reducing the sky background, but also rejects some starlight. The properties of the CCD and the lens are summed up in table transmittance (%) λ (nm) Figure 6.7. Transmission curve of the R60 filter, which attenuates out all wavelengths below 650 nm.

158 148 Chapter 6. The Star Tracking System CCD Sensor QImaging EXi Light Sensitive Pixels Exposure Time 40 µs to 17.9 min in 1 µs increments Pixel Size 6.45 µm 6.45 µm Linear Full Well 18000e Read noise 8e Dark Current 0.15e /pixels/s for T = 25 C Digital Output 12-bit Nikon Lens focal length 200 mm lens diameter 100 mm max. aperture f/2 min. aperture f/22 Table 6.1. Summarized properties of QImaging EXi CCD Camera and Nikon Lens. Baffle System Additional background can be caused by reflection of direct sun light entering the camera opening, this can be reduced by the baffle system attached to the front of each camera. The baffle system prevents a source that is placed at an angle greater than 7 from the optical axis from illuminating directly the CCD and eliminates primary reflections from sources placed at an angle greater than 10 from the optical axis [87]. During the flight from Esrange in August 2010 the Sun and the observation targets will be separated by more than 50 (see figure 6.8), thus the baffle system is somewhat over-specified, but will be evaluated for future flights at other times of the year. The baffle design has been taken from BLAST and adapted to PoGOLite. The design is scaled to a shorter length (see figure 6.9). The shield consists of a cm long tube of FR4 (Flame Retardant 4) with diameter 15.6 cm. Inside 10 knifeedged aluminum rings are placed (see figure 6.10). The distance at which they are placed and their radius has been calculated through ray-tracing simulations [92]. The inside of the baffle is coated with Aeroglaze Z306 which is an absorptive polyurethane coating with absorption coefficient close to unity and emissivity 0.89 [93]. This coating prevents internal reflections reaching the CCD chip.

159 6.2. Star Tracking Matching System (STM) azimuth [degree] Crab - Sun Cygnus X-1 - Sun local time [hours] Figure 6.8. Azimuth angle separation between sources of interest and the Sun for a PoGOLite flight on August 15 th from Esrange.

160 Figure 6.9. Drawing of PoGOLite baffle system, the position and the radius of the knife-edged rings are shown, the dimensions are in mm. 150 Chapter 6. The Star Tracking System

161 6.2. Star Tracking Matching System (STM) 151 Figure Picture of the baffle system before the Aeroglaze paint is applied to the collimator rings. Control System During flight the temperature and atmospheric conditions can vary, thus it has to be possible to focus the lens. The aperture will be kept fixed at f/2. The focus ring is driven through gearwheels by a stepper motor from Lin Engineering [94]. The motor is driven by a controlling board EZ Stepper EZ17 from Allmotion [95] which is connected through a serial port to the PC104 computer system. The motor full step is 0.9 which can be subdivided into 8 micro steps. In the next section a study of the focus is presented and the performance of the matching software as a function of the focus setting is studied. Temperature monitoring and heaters will also be part of the control system CCD Calibration The star tracker requires several tests and calibrations before starting to develop the star matching software. This is the primary focus of the remainder of this chapter. Regarding the CCD, the efficiency of each pixel has to be measured, and hot or dead pixels have to be masked away. Regarding the optics, the region of best focus setting has to be set, and a calibration using the measured intensity of known sources is performed. Hot Pixels Every CCD has hot pixels, which are pixels with a higher rate of charge than neighboring elements. The number of hot pixels can increase with temperature and

162 152 Chapter 6. The Star Tracking System exposure time. The final goal of the PoGOLite CCD is to take pictures of stars that on the CCD will have a size comparable to that of a pixel, so it is very important to identify hot pixels which could be misinterpreted as possible point sources. Once identified it is possible to mask them or assign to them the mean value of the surrounding pixels. To map out the hot pixels a sequence of pictures with a closed shutter have been taken. By looking at pixel intensities in the image one can find pixels which have a much higher intensity than the background. The background in this case is due to thermal noise. Different pictures are taken using typical exposure times expected for flight and the hot pixels are identified (see figure 6.11), their coordinates are saved in a file which is used later on during image analysis. The number of hot pixels is 13, which is negligible compared to the total number of pixels, Figure Map of the hot pixels. The graph contains the hot pixel map calculated by taking consecutive pictures. The position of the hot pixels match between exposures. Flat-Field (Pixel Calibration) The flat-field correction reduces artifacts in the CCD image due to variations in the pixel efficiency. The pixel calibration is done by illuminating evenly the CCD with a bright source, which was fulfilled using the bright sky. The exposure time has been set to 0.2 ms in order to guarantee that none of the pixels saturates. The baffle system was used to reduce the scattered light. To build a flat-field from the sky images the value of each pixel was divided by the image mean and a number of such flat-fields were then averaged to reduce the Poisson noise. The resulting flatfield image is shown in figure The pixels in the center are more illuminated

163 6.2. Star Tracking Matching System (STM) 153 than those at the edges. This is due to the fact that the lens and baffle system are optimized for radiation that travels in the center of the field of view. When the flux of stars is sought, the flat-field correction has to be taken into account and the image of interest has to be divided by the flat-field image. When doing these observations the efficiency of the baffle system was also tested. This was done by pointing the camera approximately 80 and 60 from the direction of the Sun (same separation from the Sun during flight) and comparing the mean value of the measured flux when the baffle entrance was shielded and unshielded from the direct sun light. The difference is about 0.5% and 0.7% for the two different angles respectively, which is an order of magnitude less than the Poisson noise. This means that the baffle system operates as expected. Sensitivity To calibrate the CCD response a series of images with stars of known magnitude and color have been taken [1]. The intensity is calculated by integrating the intensity of the pixels in a circle around the pixel of maximum intensity. Since the CCD camera is sensitive to wavelengths greater than 600 nm the measured emission of the stars will be mostly in the red wavelength band. The region of observation is approximately known, and with the help of a star catalogue the exact coordinates have been calculated. The image has been corrected with the flat-field image, and hot pixels have been taken into account. The flux has been calculated with IRAF PSF routine [96]. The red magnitude is taken from a star database, in this case Sky2000 [85]. The efficiency of the CCD is linear in photon flux so one can write: ( ) N m = 2.5 log (6.3) k or equivalently thus N = k m (6.4) k = N m (6.5) where k is a calibration constant, N is the number of counts/sec and m the magnitude of the star, in this case the red magnitude. The measurement gives <k>= For any star with known red magnitude one can predict the counting rate N: N = m. (6.6) One can also compute the value of magnitude to which the counting rate of background corresponds. Taking a typical value, N sky = /s/pixel, for the background at 40 km at wavelength of 650 nm [91] one can calculate the corresponding magnitude:

164 154 Chapter 6. The Star Tracking System Figure Flat-field correction, the gray scale represents the normalized fluctuations around the mean value of 3 flat-field images. The bottom of the image is darker on the bottom because the CCD is read out from the top.