FERMI GBM detections of four AXPs at soft gamma-rays

Transcription

1 FERMI GBM detections of four AXPs at soft gamma-rays Felix ter Beek Thesis for the degree Master of Science in Astronomy & Astrophysics University of Amsterdam November 2012 Supervisor: Prof. dr. W. Hermsen Daily supervisor: Dr. L. Kuiper

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3 Abstract Anomalous X-ray Pulsars (AXPs) are believed to be magnetars, i.e. neutron stars powered by the decay of extremely strong magnetic fields ( Gauss), as they show outbursts and persistent emission with luminosities exceeding the rotational energy loss. Distinct spectral features of their persistent emission are: a (mostly thermal) component at soft X-rays that can be described by the magnetar model, and a non-thermal component peaking at soft gamma-rays. There is no consensus on the underlying emission process of this second component. More observations at hard X-rays and soft gammarays are required to constrain the models aiming to describe this non-thermal emission. The Fermi Gamma-ray Burst Monitor (GBM) is the most suitable instrument for detecting the pulsed emission of AXPs above 100 kev. We analyzed the CTIME data from the GBM NaI detectors (8 kev - 2 MeV) to measure the pulsed emission of four AXPs ; 4U , 1RXS J , 1E and 1E The flux values derived from these observations are consistent with published INTEGRAL ISGRI ( kev) and RXTE PCA/HEXTE ( kev) measurements in the overlapping energy range and are further constraining the spectral shape. We found evidence for a spectral break below 300 kev for 4U , 1E and 1E The new spectral findings are shortly discussed in the framework of the magnetar model. 3

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5 TABLE OF CONTENTS Table of Contents 1 Introduction The pulsar class Rotation powered pulsars Accretion powered pulsars Magnetars Basic pulsar parameters Magnetic field strength at the surface Characteristic age The [P, P]-diagram Magnetar spectral energy distribution RXSJ E U E Candidate models and emission processes Synchrotron radiation Thermal bremsstrahlung Inverse Compton scattering Instrumentation and Event Selection The FERMI mission FERMI GBM Event selection Flux determination Data reduction and results Timing Analysis RXSJ E U E Spectral analysis RXSJ E U E Summary and Conclusions 49 References 51 5

6 LIST OF TABLES List of Figures 1 The (P,dP/dT)-diagram The soft X-ray spectrum of 1RXSJ The X-ray spectrum of 1RXSJ The X-ray spectrum of 1E The X-ray spectrum of 4U The X-ray spectrum of 1E Sketch drawing of a twisted magnetic loop Simulated inverse Compton spectrum Simulated magnetar spectra The response function (cm 2 ) of the GBM detectors The orientation of the GBM detectors Energy dependence of the GBM NaI effective area (cm 2 ) per channel Angular dependence of the GBM NaI effective area (cm 2 ) in ch Angular dependence of the GBM NaI effective area (cm 2 ) in ch Observed light curve (120 phase bins) of 1RXS J Pulse profile of 1RXS J summed over channels Pulse profiles of 1RXSJ in channels Pulse profile of 1E summed over channels Pulse profiles of 1E in channels Pulse profile of 4U summed over channels Pulse profiles of 4U in channels Pulse profile of 1E summed over channels Pulse profiles of 1E in channels Updated high-energy spectrum of 1RXSJ Updated high-energy spectrum of 1E Updated high-energy spectrum of 4U Updated high-energy spectrum of 1E List of Tables 1 Pointing angles of GBM detectors in spacecraft coordinates List of FERMI GBM observations used in this work Phase-coherent timing models Pulsed count rates of 1RXS J in channels Pulsed count rates of 1E in channels Pulsed count rates of 4U in channels Pulsed count rates of 1E in channels Best-fit parameters for fitting spectral models The observed pulsed flux of 1RXSJ The observed pulsed flux of 1E The observed pulsed flux of 4U The observed pulsed flux of 1E

7 LIST OF TABLES List of Acronyms AXP Anomalous X-ray Pulsar SGR Soft Gamma Repeater GRB gamma-ray burst SAA South Atlantic Anomaly FERMI FERMI Gamma-Ray Space Telescope GLAST Gamma-ray Large Area Space Telescope LAT Large Area Telescope GBM Gamma-ray Burst Monitor CGRO Compton Gamma-Ray Observatory COMPTEL COMPton TELescope INTEGRAL INTErnational Gamma-Ray Astrophysics Laboratory IBIS Imager on Board INTEGRAL Satellite ISGRI INTEGRAL Soft Gamma-Ray Imager SPI SPectrometer on INTEGRAL RXTE Rossi X-Ray Timing Explorer PCA Proportional Counter Array HEXTE High Energy X-ray Timing Experiment Suzaku Suzaku XIS X-ray Imaging Spectrometer XMM-Newton X-ray Multi-mirror Mission - Newton EPIC European Photon Imaging Camera Chandra Chandra X-ray Observatory ACIS Advanced Ccd Imaging Spectrometer SWIFT SWIFT gamma-ray burst mission XRT X-Ray Telescope 7

8 LIST OF TABLES 8

9 1.1 The pulsar class 1 Introduction Pulsars are a class of astronomical objects from which pulsed emission is observed. The pulsar class can be divided in three main subclasses, based on the energy source and emission mechanism of the pulsar Rotation powered pulsars The first pulsar detection took place in 1967 with the Mullard Radio Astronomy Observatory (Hewish et al. 1968), and was soon followed by detections of other pulsars at different locations (Pilkington et al. 1968). These pulsars where suggested to be rotating magnetized neutron stars by Pacini (1968), Gold (1968), but this theory was met with skepticism from other scientists who believed the pulsars to be white dwarfs instead. However, the discovery of the Crab pulsar with a pulse period of 33 ms disproved the white dwarf interpretation, and after Richards & Comella (1969) observed the spin-down rate of the Crab pulsar to be as predicted by Pacini (1968) the skepticism against the neutron star interpretation faded. Historically, all known radio pulsars were consistent with being rotation powered. Thesepulsarsarerotatingmagnetized(B Gauss)neutronstarswithmagnetic dipole emission. As the emission is powered by the loss of rotational energy, the total luminosity is constrained by the spin-down luminosity, which can be derived from the period and period derivative. Ė = d dt ( ) IΩ 2 2 = 4π 2 I P P = P P 3 [erg s 1 ] (1) where Ė is the spin-down luminosity, I = 1045 g cm 2 is the moment of inertia for a typical neutron star, Ω = 2π/P is the angular velocity and P is the rotation period of the pulsar in s Accretion powered pulsars Accretion powered pulsars are accreting neutron stars, producing pulsed emission because of their orbital motion in a binary system. The energy source of this class of objects is the gravitational potential energy of the accreted matter. Ė = GMṁ R = ṁ [erg s 1 ] (2) where Ė is the accretion luminosity, M = g and R = 10 6 cm are the mass and radius of a typical neutron star and ṁ is the rate of mass accretion in g s 1. The accretion luminosity of these objects is limited by the Eddington luminosity, the luminosity at which the radiation pressure is equal to the gravitational pressure. L Edd = 4πcGm p σ T M = [erg s 1 ] (3) where L Edd is the Eddington luminosity and M = g is the mass of a typical neutron star Magnetars Magnetars are neutron stars that are formed in such conditions that efficient helical dynamo action takes place during the first seconds after gravitational collapse 9

10 1 INTRODUCTION of a star (Duncan & Thompson 1992, Thompson et al. 2002), and therefore have very high magnetic field strength (B > Gauss). Because of their high magnetic field strength, magnetars quickly lose most of their rotational energy to magnetic dipole braking. Internal magnetic stresses cause the stellar crust of the magnetar to undergo sudden adjustments, also called starquakes, inducing twists to the magnetic dipole field. These starquakes can be observed as outbursts and timing glitches. The untwisting of the strong magnetic field leads to a current of charged particles along the magnetic field lines which heats the stellar surface. Historically there are two types of magnetar candidates, Soft Gamma Repeaters (SGRs) and Anomalous X-ray Pulsars (AXPs). SGRs The first observed Soft Gamma Repeater (SGR) burst originated from SGR and was detected on 7 January, 1979 by one of the KONUS experiments (Mazets & Golenetskii 1981, Laros et al. 1986). Soon after that an extraordinary bright burst was observed on 5 March, 1979 (Mazets et al. 1979). The burst had a very bright (L erg s 1 ) spike, followed by a 3-minute decay, during which 8-second pulsations were visible. One day later, on 6 March, 1979 Mazets et al. (1979) observed another, much weaker, burst from the same source. After these first observations several other sources with repeated bursts in the X- and γ-rays were detected. Several years later, in 1994, SGRs were discovered to show persistent X-ray emission by Vasisht et al. (1994), Rothschild et al. (1994), Murakami et al. (1994). A breakthrough in SGR and magnetar physics was reached when Kouveliotou et al. (1998) measured the period and period derivative of SGR From these measurements, they found that the observed persistent X-ray flux of this SGR is two orders of magnitude higher than what can be explained from rotational energy loss, indicating that SGR is not rotation-powered. Moreover, they derived a magnetic field strength of Gauss by assuming that the rotational energy loss is due to magnetic dipole braking (to be discussed in section 1.2.1). From these observations, Kouveliotou et al. (1998) argue that SGRs are powered by the decay of their huge magnetic fields, as described in the magnetar model (Duncan & Thompson 1992). As the already developed magnetar model could give an explanation for the observed glitches, bursts, and X-ray luminosity, the magnetar interpretation of SGRs was quickly accepted. It is noteworthy that SGRs have both active and dormant periods. During an active period an SGR can show several hundreds of bursts in a week, while during a dormant period it can occur that no bursts are detected for several years. AXPs The first Anomalous X-ray Pulsar (AXP) to be discovered was 1E (Fahlman & Gregory 1981), a bright X-ray pulsar with a 7-second period and erg s 1 luminosity in the 2-4 kev band. The period derivative was derived to be s s 1 (Koyama et al. 1987), indicating a spin-down luminosity of erg s 1, much lower than the observed X-ray luminosity. A few more sources with similar characteristics were found, and were eventually categorized as AXPs because of their high X-ray luminosities. AXPs cannot be powered by rotation because their observed luminosities are several orders of magnitude larger than the derived rotational energy loss, but it is also unlikely that they are powered by accretion because of the lack of observed bright optical counterparts or 10

11 1.2 Basic pulsar parameters orbital modulation. Their luminosities, inferred magnetic field strengths, rotational periods and period derivatives (all similar to values observed for SGRs) made AXPs magnetar candidates, but the magnetar interpretation was not readily accepted because of the lack of observed glitches and bursts from these sources. Only after AXPs were observed to show glitches (Kaspi et al. 2000, Kaspi & Gavriil 2003, Dall Osso et al. 2003) and SGR-like bursts (Kaspi et al. 2003, Gavriil et al. 2004) the magnetar interpretation of AXPs became widely accepted. 1.2 Basic pulsar parameters By measuring the period P and period derivative P of a pulsar it is possible to give an estimate of the age and magnetic field strength at the surface if we assume that the pulsar does not accrete mass and that the rotational energy loss is due to magnetic dipole breaking Magnetic field strength at the surface In general a non-accreting pulsar will gradually lose kinetic energy due to magnetic dipole braking, slowing down the rotation of the neutron star. Ė = d dt ( ) IΩ 2 2 = 4π 2 I P P 3 (4) where Ė is the rate of energy loss, I is the moment of inertia, Ω is the angular velocity and P is the rotation period. An estimate for the rate of energy loss follows from the magnetic dipole model (Pacini 1967; 1968, Ostriker & Gunn 1969). Ė = 2 m 2 Ω 4 sin 2 α 3c 3 (5) whereė istherateofenergyemissionthroughmagneticbraking, m isthemagnetic dipole moment, Ω = 2π/P is the angular velocity and α is the angle between the rotation axis and the dipole axis. Sinceαisusuallyanunknownparameteritiscommonpracticetoset2 m sinα = BR 3, where B is the magnetic field strength on the surface at the equator and R is the radius of the neutron star. Ė = 8π4 B 2 R 6 3c 3 P 4 (6) 3c3 P B = 8π 4 R Ė = 3c3 I 6 2π 2 R 6P P (7) By filling in typical values for I (10 45 g cm 2 ) and R (10 6 cm) we obtain an expression for the magnetic field strength of a pulsar at the equator, assuming that the emission process for the bulk of the emission is dipole radiation. B = P P [Gauss] (8) where P is the period of the pulsar in s and P is the period derivative in s s 1. Noteworthy is that for some pulsars the magnetic field strength at the surface surpasses the critical magnetic field strength B QED = Gauss, above which quantum electrodynamic physics start playing a significant role. 11

12 1 INTRODUCTION Characteristic age By assuming a spin-down formula for dipole emission ν ν 3 and solving for τ = t t 0 one finds an expression for the age of a pulsar. [ τ = ν ( ) ] [ 2 ν 1 = P ( ) ] 2 P0 2 ν ν 0 2P 1 (9) P If one assumes the rotation period at birth of the neutron star (P 0 ) to be much smaller than the current rotation period one can derive the commonly used expression for the characteristic age of a pulsar. τ = P 2P (10) It should be noted that the characteristic age is only a first order estimate of the true age of a pulsar, and that deviations from this estimate due to temporal variations can be significant. Figure 1: The [P, P]-diagram. Displayed in this diagram are all known pulsars with measured [P, P] in black dots, lines of equal characteristic age τ in dark blue and lines of equal magnetic field strength B in dark red. The critical magnetic field strength for electrons B QED = Gauss is shown as a bright red line. AXPs and AXP candidates are marked with boxes, SGRs and SGR candidates are marked with triangles. Data from pulsar/magnetar/main.html and were used for making this diagram The [P, P]-diagram The [P, P]-diagram is a valuable tool in displaying the basic characteristics of the pulsar population. Figure 1 displays all known pulsars with measured [P, P]. In this figure three main groups can be identified: The largest group has B Gauss, and the majority of the pulsars in this group are radio pulsars, powered by the loss of rotational energy. The next group has P < s s 1 and P < 50 ms, and includes millisecond pulsars and other recycled pulsars. 12

13 1.3 Magnetar spectral energy distribution The group of most interest for this work is the group with P > 1.0 s and B > B QED, where B QED = Gauss is the critical magnetic field strength for electrons. This group includes all currently known AXPs and SGRs plus AXP and SGR candidates, with the possible exception of SGR (Rea et al. 2010). Note that all pulsars in this group are young pulsars, with τ 10 4 year. Figure 2: The phase-averaged soft X-ray spectrum of 1RXS J as measured with XMM-Newton EPIC-PN (Rea et al. 2005). The black line shows an empirical fit with an absorbed black body plus power law. 1.3 Magnetar spectral energy distribution In this work we aim to increase the knowledge on the spectral energy distribution of the persistent magnetar emission. We will first present a short overview of the observations before this work in this section and of the possible emission processes for these observed spectra in section 1.4 before discussing our own observations. A typical soft X-ray ( kev) spectrum of an AXP (Fig. 2) can be fit empirically with a black body (kt 3-4 kev) plus soft power-law (Γ 4-3, defined as F E Γ ), or with a double black body model (Rea et al. 2005). The magnetar model (Thompson et al. 2002) explains the observed soft X-ray spectra as thermal X-ray spectra from the stellar surface with non-thermal tails due to resonant cyclotron scattering against charged particles in the twisted magnetosphere. The non-thermal spectral tail is harder for more strongly twisted magnetospheres because the current through the magnetosphere increases with the magnetic twist, leading to a higher density of charged particles and thus a higher optical dept to resonant cyclotron scattering. As the magnetar model could give an explanation for the observed luminosities, spectra below 10 kev, glitches and outbursts of AXPs and SGRs, it was thought for a short while that the observable characteristics of AXPs were fully understood. But in 2004 a new spectral component was discovered when persistent hard X-ray (> 10 kev) emission was observed from 1E (Molkov et al. 2004, Kuiper et al. 2004), 1RXS J (Revnivtsev et al. 2004) and 4U

14 1 INTRODUCTION (den Hartog et al. 2004). It is not unlikely that other AXPs and SGRs have similar hard X-ray emission, at a luminosity lower than detection limits of currently available instruments. For this work we studied four AXPs: 1RXS J , 1E , 1E and 1E In the following subsections the X-ray characteristics of these AXPs will be shortly presented. Figure 3: X-ray spectraof 1RXSJ (den Hartog et al. 2008b). Inthis figureare displayed: pulsed flux measurements by XMM-Newton EPIC-PN in black, RXTE PCA in blue, RXTE HEXTE in aqua and INTEGRAL IBIS-ISGRI in red with triangle markers; total flux measurements by XMM-Newton EPIC-PN (< 12 kev) in black, INTEGRAL IBIS-ISGRI in black with triangle markers, INTEGRAL SPI in grey with triangle markers and CGRO COMPTEL (> 1000 kev) in black; and empirical fits to the total spectra with a power law in grey and with a logparabola (logf = alog 2 E +bloge +c) in blue RXS J RXS J was discovered during the ROSAT all sky survey (Voges et al. 1999), and was measured to have a period and period derivative of P = 11 s and P = s s 1 (Kaspi et al. 1999, Gavriil & Kaspi 2002). 1RXSJ was the first AXP that was observed to glitch (Kaspi et al. 2000, Kaspi & Gavriil 2003, Dall Osso et al. 2003). The X-ray pulse profile of this AXP has been observed to change significantly with energy above E = 4 kev (Sugizaki et al. 1997, Israel et al. 2001, Gavriil & Kaspi 2002). Subsequent phase-resolved spectral analysis confirmed this observation (Israel et al. 2001, Rea et al. 2003; 2005). Moreover, the soft X-ray ( kev) spectrum of 1RXSJ has been observed to be time variable (Rea et al. 2005), with an increased flux and a harder spectral tail near the glitch epochs. The recent soft X-ray observations with XMM-Newton EPIC-PN can be fit empirically with a black body with temperature kt 0.46 kev plus a power law with index Γ 2.8 (Rea et al. 2005). During an INTEGRAL hard X-ray survey, Revnivtsev et al. (2004) discovered a point source with emission in the kev energy band at the position of 1RXS J In more recent publications by den Hartog et al. (2008b) (Fig. 3) using data from INTEGRAL IBIS-ISGRI, RXTE PCA/HEXTE and XMM-Newton EPIC-PN, the hard X-ray emission (> 10 kev) is found to be stable within instrumental uncertainties over almost a decade of observations. den Hartog et al. (2008b) observes 14

15 1.3 Magnetar spectral energy distribution Figure 4: X-ray spectra of 1E (Kuiper et al. 2008). In this figure are displayed: pulsed flux measurements by RXTE PCA, RXTE HEXTE and INTEGRAL IBIS-ISGRI; total flux measurements by XMM-Newton EPIC-PN (AXP plus supernova remnant), Chandra ACIS (only AXP) model fit, INTEGRAL IBIS-ISGRI and CGRO COMPTEL; and an empirical fit to the pulsed spectra at E > 15 kev with a power law. Note that the observed pulsed spectrum is harder than the observed total spectrum. The measurements are consistent with 100% pulsed emission at E > 100 kev. that the pulse profile changes significantly with energy at 2-10 kev, and then remains stable up to 300 kev. The spectral index of the hard X-ray emission is determined to be Γ 1.1. Indication for a spectral break of the hard X-ray emission, other than constraining upper limits set by non-simultaneous (April 1991 to May 2000) observations with CGRO COMPTEL in the MeV band (Kuiper et al. 2006), was not found E E was discovered as an 11.8 s X-ray pulsar by Vasisht & Gotthelf (1997) with ASCA, and was later observed to have a period derivative of P = s s 1 (Gotthelf et al. 2002). The soft X-ray spectrum as observed with Chandra ACIS can be described as a black body with temperature kt 0.44 kev plus a power law with index Γ 2.0 (Morii et al. 2003). Hard X-ray (> 10 kev) emission from 1E was first detected during an INTEGRAL hard X-ray survey (Molkov et al. 2004), and was later confirmed to be originating from the AXP 1E through detection of pulsed hard X-ray emission with observations by RXTE PCA/HEXTE (Kuiper et al. 2004). Kuiper et al. (2004)observes thatthe shapeofthepulse profilechanges significantly at 2-10keV, and then remains stable within observational uncertainties up to 100 kev. The pulsed hard X-ray emission (Fig. 4) is observed to have a spectral index of 0.94±0.16 up to 150 kev. Moreover, the observations are consistent with a pulsed fraction of 100% at 100 kev. Emission in the MeV band was not found with non-simultaneous (April 1991 to May 2000) observations with CGRO COMPTEL (Kuiper et al. 2006). 15

16 1 INTRODUCTION Figure 5: X-ray spectra of 4U (den Hartog et al. 2008a). In this figure are displayed: total flux measurements by XMM-Newton EPIC-PN (< 11.5 kev) in black, INTEGRAL IBIS-ISGRI ( kev in black with square markers, INTEGRAL SPI ( kev in red and CGRO COMPTEL (> 750 kev) in black; and empirical fits to the total spectra with a power law in grey and with the sum of three logparabola (logf = alog 2 E +bloge +c) in blue U U was discovered by the Uhuru X-ray observatory in the seventies (Forman et al. 1978). The period and period derivative of the AXP have been measured at P = 8.7 s and P = s s 1, respectively (Gavriil & Kaspi 2002). Subsequent soft X-ray (< 10 kev) observations with ASCA (White et al. 1996), Chandra (Patel et al. 2003) and XMM-Newton (Göhler et al. 2005) indicate that the spectrum of 4U can be described as a black body with temperature kt 0.4 kev plus a power law with index Γ 3.5. Hard X-ray (> 10 kev) emission from 4U was first detected by den Hartog et al. (2004) using INTEGRAL observations. After the first discovery of non-thermal hard X-ray emission from 4U a more detailed spectral analysis was done with combined multi-year observations with INTEGRAL, RXTE, XMM-Newton, ASCA and CGRO COMPTELl (den Hartog et al. 2008a) (Fig. 5). In this analysis, it is found that the pulse profile of 4U changes significantly with energy at kev, and then remains stable within observational uncertainties for higher energies. The observed hard X-ray spectrum has a spectral index Γ = 0.93±0.06 up to 200 kev, and is expected to show a spectral break in the range kev, imposed by upper limits from INTEGRAL SPI and nonsimultaneous (April 1991 to May 2000) CGRO COMPTELL (Kuiper et al. 2006) observations E E was first discovered as an X-ray source by Lamb & Markert (1981) with the Einstein observatory. Based on X-ray observations with XMM-Newton and Chandra Gelfand & Gaensler (2007) proposed 1E to be a magnetar, though no X-ray pulsations were detected. Soon thereafter, Camilo et al. (2007) confirmed 1E to be a pulsar through radio observations. The pulsar was measured to have period P = s and period derivative P = (2.318 ± 0.005) s s 1. From these numbers a 16

17 1.3 Magnetar spectral energy distribution Figure 6: Spectral evolution of 1E (Kuiper et al. 2012) from October 2008 to December The figure displays pulsed flux measurements by RXTE PCA (filled circle markers) and RXTE HEXTE (filled square markers), divided in several time segments. surface magnetic field strength (Eq. 8) of B Gauss can be derived. Halpern et al. (2008) first detected X-ray pulsations from 1E in 2007 in a period of increased activity, and concluded that the AXP was recovering from an outburst that would have taken place in Strong SGR-like bursting activity was detected from 1E on 3 October 2008(Krimm et al.2008,israel et al.2010,kaneko et al.2010)and22january2009 (Gronwall et al. 2009). Based on a 100 ks follow-up observation with INTEGRAL 2 days after the 22 January outburst, Baldovin et al. (2009) reported a detection in the hard X-rays with a spectral index Γ = 1.8 ± 0.2. After a consecutive 300 ks observation (Kuiper et al. 2009, den Hartog et al. 2009), the spectral index was measured at Γ 1.5. The initial discovery of transient hard X-ray emission was followed by observations with Suzaku (Enoto et al. 2010), Chandra (Ng et al. 2011, Bernardini et al. 2011), XMM-Newton(Bernardini et al. 2011), INTEGRAL(Bernardini et al. 2011), RXTE (Ng et al. 2011) and SWIFT (Bernardini et al. 2011, Scholz & Kaspi 2011) over a timespan of 1.5 years following the outburst of 22 January Making use of the large amount of 1E observations with SWIFT, RXTE and INTEGRAL, Kuiper et al. (2012) studied the spectral and temporal evolution of the AXP during the recovery from the outburst in January They find that the pulsed hard X-ray (> 10 kev) emission is highly variable in time, reaching a maximum 70±30 days after the outburst, followed by a gradual decay. The observed pulsed spectra are displayed in Figure 6. As 1E is very noisy in the period following the January 2009 outburst there are constraints in the availability of phase-coherent timing solutions which we need for our further analysis. As a result, we only analysed 1E at MJD , a timespan overlapping with segment 3 and segment 4 in Figure 6. During this timespan, the pulsed hard X-ray (> 10 kev) emission is near its maximum. 17

18 1 INTRODUCTION 1.4 Candidate models and emission processes The magnetar model (Thompson et al. 2002), where AXPs and SGRs are modelled as highly magnetized (B > Gauss) neutron stars with twisted magnetic fields, offers a viable explanation for the observed soft X-ray (< 10 kev) spectra, bursts and glitching behaviour, but no consensus has yet been reached on an emission process for the observed hard X-ray (> 10 kev) emission. The proposed emission processes include fast-mode breakdown magnetohydrodynamic waves (Heyl & Hernquist. 2005a;b), synchrotron radiation at 100 km above the stellar surface (Thompson & Beloborodov 2005), thermal bremsstrahlung near the stellar surface (Thompson & Beloborodov 2005, Beloborodov & Thompson 2007), inverse Compton scattering in a twisted magnetosphere (Baring & Harding 2007, Beloborodov 2011; 2012), resonant cyclotron scattering in a twisted multipole magnetosphere (Pavan et al. 2009) and comptonization in a fallback accretion disk (Trümper et al. 2010). We will focus on the work of Thompson and Beloborodov, who have been modelling emission processes for hard X-ray (> 10 kev) emission within the magnetar framework and have been continually updating their modelling in response to observational results. Thompson & Beloborodov(2005), Beloborodov & Thompson(2007), Beloborodov (2011; 2012) theorized that particles are injected in a magnetic loop from the stellar surface (where B > Gauss) and are accelerated to relativistic speeds. Due to the high magnetic field strength (B > Gauss) in the inner part of the loop, these relativistic particles cause cascades of electron-positron pair production, forming a corona of e ± plasma. The e ± density in the corona is self-regulated because the plasma shields the electric field, acting as a bottleneck to e ± pair creation. As electrical currents flow through the corona, the magnetic field gradually untwists. Magnetic field lines with small radii untwist on a shorter time scale than those with larger radii (Beloborodov 2011), leading to a shrinking j-bundle of electric currents concentrated near the magnetic axis. Under certain circumstances it is possible to reach a quasi-stable configuration of the j-bundle, self-regulated near a threshold of MHD instability. Using this scenario as a basis, there are several possible emission processes. The following sections will introduce synchrotron radiation, thermal bremsstrahlung and inverse Compton scattering as possible emission processes for high energy (E > 15 kev) emission of magnetars Synchrotron radiation Thompson & Beloborodov (2005) theorized that cyclotron resonant scattering causes a strong radiative drag on charged particles, causing a strong electric field at a height of 100 km above the stellar surface, where the electron cyclotron energy is in the kev range. As a result, electrons and positrons injected in this region undergo runaway acceleration caused by the radiative drag force and up-scatter photons above the threshold for e ± pair creation. The e ± pairs emit synchrotron radiation with a spectral peak at 1 MeV and a spectral index dependent on the strength of the magnetic twist Thermal bremsstrahlung Thompson & Beloborodov (2005), Beloborodov & Thompson (2007) theorized that the persistent hard X-ray emission is produced in a thin transition layer between the relatively cool stellar surface and the hot magnetar corona. The layer is heated 18

19 1.4 Candidate models and emission processes to kt 100 kev by incoming charged particles which are accelerated in the corona, and emits thermal bremsstrahlung. The resulting emission has a spectral index Γ 1 with a spectral break at 100 kev. the pulsed fraction through this emission process can be very high (up to 100%) if the magnetosphere is only locally twisted Inverse Compton scattering Beloborodov (2011; 2012) theorized that the soft X-ray (E < 15 kev) emission is up-scattered against the highly relativistic e ± plasma in the j-bundle. In the inner part of the j-bundle, where B > Gauss, all energy is processed through e ± pair creation and no radiation can escape. In the outer part of the j-bundle, where B < Gauss, the bulk of the energy is radiated away. As inverse Compton scattering in general is strongly beamed along the flow direction of the particles, the resulting X-ray emission is expected to be anisotropic. In the outermost part of the twisted magnetosphere, on the equatorial plane with respect to the magnetic dipole axis, the electrons and positrons collide and annihilate, causing an emission line at E = 511 kev with luminosity equal to 10% of the total luminosity. See Figure 7 for a sketch of a magnetic loop. γ >>10 e + hν sc kev kev γ 1 γ >>10 e + hν sc Figure 7: Sketch of a twisted magnetic loop. The inner zone (where B > Gauss) is shaded in blueand the annihilation zone is shaded in pink. The figureis from Beloborodov (2012). Detailed radiative transfer calculations (Beloborodov 2012) indicate that the emission is indeed highly anisotropic (Fig. 8), and that the pulsed fraction and the shape of the pulse profile can be highly variable with photon energy (Fig. 9). Because of the high anisotropy with respect to the magnetic dipole axis, the modelled spectra for the total and the pulsed emission are highly dependent on the orientation of the rotationaxis and the magnetic dipole axis with respect to the line of sight and on the azimuthal extension (i.e. axisymmetric or confined to a certain azimuthal range) of the j-bundle with respect to the magnetic dipole axis. 19

20 1 INTRODUCTION Figure 8: Simulated magnetar spectra in the hard X-rays for four different angles between the line of sight and the magnetic dipole axis. The figure is from Beloborodov (2012). Figure 9: Simulated magnetar spectra for an orthogonal rotator, i.e. a magnetar with angle α = 90 between the rotation axis and the magnetic dipole axis, with an axisymmetric j-bundle. The left figure displays spectra for an angle β = 20 between the rotation axis and the line of sight, the right figure displays spectra for β = 90. The solid lines indicate the total simulated spectra, while the dashed lines display the difference between the maximum and the minimum emission of the pulsed signal. Many different configurations of the rotation axis and the magnetic dipole axis are possible. The figures are from Beloborodov (2012). 20

21 2 Instrumentation and Event Selection 2.1 The FERMI mission The FERMI Gamma-Ray Space Telescope (FERMI), formerly known as Gammaray Large Area Space Telescope (GLAST), was launched in June 2008, and has since then been orbiting the Earth in a low orbit of 550 km above the Earth surface. The mission is aimed toward bringing γ-ray astronomy to a new level by detecting and observing γ-rays from a wide range of point sources and phenomena. During the first 11 months after launch, FERMI detected 1451 sources in the 100 MeV GeV range with a > 4σ significance (Abdo et al. 2010). The primary instrument on board of the FERMI spacecraft is the Large Area Telescope (LAT), a pair conversion telescope sensitive over an energy range of 20 MeV to > 300 GeV. The secondary instrument is the Gamma-ray Burst Monitor (GBM), consisting of scintillation detectors, with an energy range of 8 kev to 40 MeV. The FERMI spacecraft orbits the Earth once every 95 minutes. While in scanning mode, the satellite tilts 35 north and south on alternating orbits. As the instruments on board FERMI have very wide field of view ( 2.4 sr for the LAT), the whole sky is covered at least once every two orbits (Atwood et al. 2009). The role of the GBM is to extend the energy range of the LAT to the hard X-ray band, and to detect gamma-ray bursts (GRBs). When a GRB is detected, the burst mode is triggered. During this mode the time resolution is increased and the LAT is pointed in the direction of the GRB. For this work we only used observation data from the GBM as the energy range of this instrument is most suited for observing hard X-ray ( kev) emission. 2.2 FERMI GBM The FERMI GBM (Meegan et al. 2009) consists of 12 NaI detectors (8 kev to 2 MeV) and two BGO detectors (200 kev to 40 MeV). The instrument provides three main data products: CTIME, CSPEC and TTE. CTIME provides the counts accumulated every 0.256s (0.064s in burst mode) in 8 energy channels for each detector. CSPEC provides the counts accumulated every 4.096s (1.024s in burst mode) in 128 energy channels. TTE (Time Tagged Events) provides event data with a time resolution of 2µs in 128 energy channels during bursts only. The FERMI GBM is designed to detect only thegeneral direction of all incoming bursts and to measure X-ray spectra of these bursts. Therefore the detectors have very wide angular response functions (Fig. 10) and are pointed in different directions (Fig. 11, Table 1). These characteristics make this instrument unsuitable for fine imaging or pointed observations. These same characteristics, however, make the FERMI GBM a suitable instrument for detecting persistent pulsed emission with period P > 0.512s. For our work we used the CTIME data product because the time resolution of the CSPEC data product is too low for a timing analysis on AXPs and the TTE data product is only provided during burst mode. Although at first sight the energy range of the BGO detectors appears interesting for our work, we chose to only use observations by the NaI detectors because the angular response function (Fig. 10) of the NaI detectors offers the possibility for a much better background suppression through event selection than what would be possible for the BGO detectors. 21

22 2 INSTRUMENTATION AND EVENT SELECTION ) 2 Photopeak Effective Area (cm kev simulated measured 279 kev simulated measured 662 kev simulated measured ) 2 Photopeak Effective Area (cm kev simulated measured 898 kev simulated measured 1836 kev simulated measured Source Position (degrees) Source Position (degrees) Figure 10: The effective area (cm 2 ) of the GBM NaI (left) and BGO (right) detectors as a function of the angle between the detector pointing vector and the source direction. The figures are from Meegan et al. (2009). Table 1: Measured (Meegan et al. 2009) orientation of GBM NaI detectors in spacecraft coordinates. Detector Azimuth Zenith ID [ ] [ ] NaI NaI NaI NaI NaI NaI NaI NaI NaI NaI NaI NaI Figure 11: The orientation of the GBM detectors. Note that in this drawing the LAT is located below the GBM, therefore none of the detectors are pointed in that direction. The image is from Meegan et al. (2009). 22

23 2.3 Event selection 2.3 Event selection After it s launch, FERMI has been collecting and archiving observation data since August For our timing analysis, we used the archive data from August 2008 until December 2010 for 1RXS J , 1E and 1E , and we used archive data from 24 Januari 2009 until 28 Februari 2009 for 1E Due to the wide angular response functions (Fig. 10) the GBM is expected to observe X-rays from the whole sky simultaneously. As a result, AXP pulsations should be present in our full data set, but the background radiation is very high. We applied a number of selection criteria to our data set in order to maximize the signal-to-noise ratio. Widening the OFF-period during the passage over the South Atlantic Anomaly (SAA). Once every orbit, FERMI passes through the SAA, an area where the Van Allen radiation belt of the Earth dips down to an altitude of km. The instruments on board of FERMI are deactivated during the SAA passage (the OFF-period) to protect them from cosmic particles. We found that the background level of the GBM is significantly increased just before and just after the SAA passage, and thus we widened the OFF-period with 300 s before and after. Screen the data for bursts and flares. The scientific goal of the GBM is to monitor bursts and flares, but for our data analysis these phenomena are considered as background radiation. For this reason we discarded those parts of our data set where bursts and flares are visible. Compute the angle α between the Earth zenith and the source direction, and discard events for which α > 110. Since the Earth is opaque to X-ray radiation, we need to ensure that the source we want to observe is not blocked from view by the Earth. With a radius of 6370 km and an atmosphere height of 100 km the Earth is observed to have a radius 70 from FERMI. Compute the angle β between the Earth zenith and the detector pointing, and discard events for which β > 128. The Earth atmosphere is a significant X-ray source, therefore we discard events collected during time periods for which the Earth enters significantly in the field of view. By testing our selection procedure on Hercules X-1, an X-ray binary with strong pulsed emission with a period of 1.24 s in the X-ray band, we found that using a selection criterion of β < 128 leads to the best signal-to-noise ratio. Compute the angle γ between the detector pointing and the source direction, and select γ < 58 for channel 2 and lower, or γ < 84 for channel 3 and higher. At high source angle γ the detector effective area for radiation from the source direction decreases significantly (Fig. 10), therefore events recorded at high source angle γ are more likely to originate from background radiation than events recorded at low source angle γ. We suppress the background radiation by discarding events for which the source angle γ exceeds a certain threshold value. By testing our selection procedure on Hercules X-1 we found that using a threshold value of 84 for channel 3 and higher (> kev) and 58 for channel 2 and lower (< kev) leads to the best signal-to-noise ratio. 23

24 2 INSTRUMENTATION AND EVENT SELECTION We applied these selection criteria to all events in our data set. Table 2 lists the time window and the total screened exposure, summed over all NaI detectors for each of the four AXPs that are analyzed for this work. Table 2: List of FERMI GBM observations used in this work. The screened exposure is summed over all NaI detectors. Source Start End Screened exposure Screened exposure [MJD] [MJD] (Ms) (Ms) ch.0,1,2 ch.3,4,5,6,7 4U RXS J E E

25 2.4 Flux determination 2.4 Flux determination Themeasuredcountrate cn t ofadetectorinchannelnwithenergyinterval[e m,e + m] can be used to compute the flux F n in that channel if the effective area Ǎn for that channel is known. F n = c n t Ǎ n E m (11) In the case of the FERMI GBM, the effective area A i (E γ,θ,φ) of detector i is a function of the direction of incoming photons (θ,φ) and of the photon energy E γ. We also need to take into account the redistribution matrix R i (E γ.e m,θ,φ), which gives the chance that a photon of energy E γ is detected with energy E m. The first step is to average (A i (E γ,θ,φ) R i (E γ.e m,θ,φ)) over all detectors i and photon directions (θ,φ), using the observed exposure per detector per direction T i (θ,φ) as a weight. A(E γ ) R(E γ,e m ) = Ti (θ,φ) (A i (E γ,θ,φ) R i (E γ.e m,θ,φ)) Ti (θ,φ) (12) Then we integrate A(E γ ) R(E γ,e m ) over E m to obtain the effective area per channel Ǎ n (E γ ) (Fig. 12). Ǎ n (E γ ) = E + m E m A(E γ ) R(E γ,e m ) de m (13) And finally we compute the weighted average of Ǎn(E γ ) over E γ by assuming a spectral shape f(e γ ) for the source. Ǎ n = 0 f(e γ ) Ǎn(E γ ) de γ E + m E m f(e γ) de γ (14) Figure 12: The energy dependence of the effective area (cm 2 ) of the GBM NaI detectors per energy channel, averaged over different detectors and source positions using the recorded exposure as weight. For this figure the recorded exposure of 1RXS J was used. 25

26 2 INSTRUMENTATION AND EVENT SELECTION We based our flux reconstruction of FERMI GBM observations on data from instrument response simulations(kippen et al. 2007, Bissaldi et al. 2009), consisting ofasetofresponsematricesr(e γ,e m ); oneforeachof272differentsourcepositions, for each of 12 NaI detectors. See Figure 13, 14 for the angular dependence of the detector effective area. For our estimate of the spectral shape f(e γ ) in Equation 14 we initially assumed f(e γ ) = Eγ 1, andthentookaniterativeapproachbyusing theresult ofanempirical spectral fit for the spectral shape f(e γ ) in the next iteration of flux reconstruction. Figure 13: The angular dependence of the effective area (cm 2 ) of the NaI detectors in kev, assuming a F E 1 spectrum. The cross indicates the detector pointing, andthedashedlinemarkstheboundarywherethesourceangleγ equals58. The [φ, θ] coordinates are in FERMI spacecraft coordinates. The above figures were obtained by integrating response matrices from(kippen et al. 2007, Bissaldi et al. 2009) over measured energy and photon energy (using f(e γ ) = Eγ 1 as weight) and interpolating at 2 2 intervals. 26

27 2.4 Flux determination Figure 14: The angular dependence of the effective area (cm 2 ) of the NaI detectors in kev, assuming a F E 1 spectrum. The cross indicates the detector pointing, andthedashedlinemarkstheboundarywherethesourceangleγ equals84. The [φ, θ] coordinates are in FERMI spacecraft coordinates. The above figures were obtained by integrating response matrices from(kippen et al. 2007, Bissaldi et al. 2009) over measured energy and photon energy (using f(e γ ) = Eγ 1 as weight) and interpolating at 2 2 intervals. 27

28 2 INSTRUMENTATION AND EVENT SELECTION 28

29 3.1 Timing Analysis 3 Data reduction and results The GBM is a non-imaging instrument with a very wide field of view. The instrument is not designed to accurately locate individual events from a point source. We can, however, use the GBM to measure the pulsed flux component of our target AXPs by applying a timing analysis. We chose to use a method of timing analysis known as epoch folding. After barycentering all events (i.e. convert for each event the arrival time at the FERMI spacecraft to the arrival time at the center of mass of the solar system) we used a set of phase-coherent timing models (Table 3, derived from RXTE PCA monitoring data) to compute the phase for each event. The epoch-folded events are then binned into a fixed number of phase bins, and are divided by the exposure per phase bin to obtain the phase-folded light curve. For our analysis we used a number of n bins = 120 phase bins for intermediate results. Sampling effects For a pulsar period of P 10 s each of the phase bins in the intermediate results hasawidth of t 0.08s(120phase bins), much smaller thanthe0.256s(scanning mode) time resolution of the GBM CTIME data. As the intermediate results are clearly oversampled, we expected these light curves to be dominated by noise. Figure 15: (Left) Observed light curve (120 phase bins) of 1RXSJ using FERMI GBM CTIME data. The oscillation in the data is of a much higher frequency than the pulse frequency of 1RXSJ (Right) Fourier strength S n, defined as S 2 n = (A n / A n ) 2 + (B n / B n ) 2 where A n and B n are the best fit values for fitting a Fourier series A n cos(2nπφ) + B n sin(2nπφ) to the observed light curve. The strong oscillations at n = 43 and n = 34 are due to the s binning period of the CTIME data. The light curve of 1RXS J (Fig. 15), however, displays an unexpected strong oscillation. The time scale of the oscillation is much shorter than the expected pulse period (P s) of 1RXSJ and the amplitude is much larger than the Poisson error bars (χ 2 = for 119 degrees of freedom). To better understand the cause of this artifact, we fit the observed light curve with a discrete Fourier series A n cos(2nπφ) + B n sin(2nπφ), and define S n as 29

30 3 DATA REDUCTION AND RESULTS Table 3: Phase-coherent timing models as derived from RXTE PCA monitoring data. Φ = ν (t t 0 )+ 1 2 ν (t t 0) ν (t t 0) 3 Φ 0 Source Start End t 0,Epoch ν ν ν Φ 0 [MJD] [MJD] [MJD,TDB] [Hz] [Hz/s] [Hz/s 2 ] 4U U RXSJ RXSJ RXSJ E E E

31 3.1 Timing Analysis follows: S n = ( An A n ) 2 + ( Bn B n ) 2 (15) A Under the null hypothesis we expect n A n and Bn B n to be normally distributed with zero mean and unit variance for all n, so that the resulting Sn 2 is expected to follow the chi-square distribution with 2 degrees of freedom (Abramowitz & Stegun 1972). In the case of a pulsar observation we expect Sn 2 to deviate from the χ 2 2 distribution for low n. The S n diagram of 1RXSJ (Fig. 15) displays distinct peaks at n = 43 (P s) and n = 34 (P s). The explanation for these strong Fourier modes is that they originate from the s sampling of the CTIME data, and that these sampling effects survived through our timing analysis because the period of 1RXS J is a near-integer multiple of the sampling period of the GBM CTIME data. In this interpretation the second harmonic (P = s) of the GBM CTIME sampling effect is reflected against the Nyquist frequency of the binning used for our timing analysis, and is observed as an oscillation with period P s. We checked this hypothesis by repeating the epoch folding analysis using a number of n bins = 100 phase bins, in which case we found strong Fourier components at n = 43 and at n = 14. After closer inspection, we found similar - but much weaker - artifacts in the observed light curves of 1E and 4U We could not detect similar features for 1E , possibly due to the worse signal-to-noise ratio for observations on 1E when compared to the other observations. Considering that the cause of the sampling effects are well understood and are limited to specific Fourier modes we correct for the sampling effects by fitting these specific Fourier modes and subtracting them from the observed light curves. All light curves of 4U , 1RXS J and 1E shown hereafter are corrected for these sampling effects. Significance test A frequently used test to estimate the significance of a pulse detection is the Zn 2 test. Through analysis of a limited number of Fourier modes a statistical variable, Zn, 2 is obtained which is distributed according to the χ 2 2n distribution under the null hypothesis. For our work, however, the Zn 2 test as described by Buccheri et al. (1983) is unsuitable because it assumes an equal exposure per phase bin. For this reason we will use an alternative for the Zn 2 for significance testing. First we perform a least Chi Square fit on the observed light curve with a limited number of Fourier components f = n i=1 A icos(2iπφ)+b i sin(2iπφ), and then we define a statistic T 2 n. T 2 n = n i=1 ( Ai A i ) 2 + ( Bi B i ) 2 (16) A Under the null hypothesis i A i and B i B i are all normally distributed with zero meanandunitvariance, sothattn 2 followsaχ2 2n distribution(abramowitz & Stegun 1972). This property allows us to use the Tn 2 statistic to estimate the significance of a pulse detection in a way very similar to how the Zn 2 statistic is used in other works. 31