Cosmic Rays, their Energy Spectrum and Origin

Transcription

1 Chapter 1 Cosmic Rays, their Energy Spectrum and Origin 1 The Problem of Cosmic Rays Most cosmic rays are not, as the name would suggest, a type of electromagnetic radiation, but are nucleonic particles that travel through the universe with velocities that approach the speed of light. These particles have always formed a controversial topic for the physicists that studied them. The focus of cosmic ray studies in this thesis is concerned with the most energetic of these particles, with energies exceeding ev. Of particular interest is their origin and the ability of astrophysical objects to accelerate particles to these great energies. To thoroughly investigate their origin we must first determine any anisotropy or clustering of cosmic ray arrival directions in our sky, measure the basic composition or mass of the cosmic rays and resolve the energy spectrum at these energies. The Pierre Auger detector has been built with the expectation that it will fully resolve these three aspects of cosmic ray research. The detector combines two of the techniques used to measure cosmic rays at these energies. Both of these techniques measure the properties of the cascade of particles created by a cosmic ray when it collides with the atmosphere, termed an Extensive Air Shower (EAS). The surface detector technique measures properties of the air shower particles as they hit the ground. The complementary fluorescence technique measures the fluorescence light the air shower produces as it traverses the atmosphere. This thesis will examine in detail two large sources 1

2 2 CHAPTER 1. COSMIC RAYS of error present in the fluorescence technique; the Cherenkov contamination of the fluorescence light and the amount of atmospheric scattering suffered by these two types of light. The extra information provided by the stereo imaging of an event should produce a reduction in these sources of error in the shower analysis procedures for the measurement of the primary particle energies and the estimation of their composition. 2 The Energy Spectrum of Cosmic Rays Our current understanding of the problem of cosmic rays can be best understood by reviewing the features of their energy spectrum, shown in Figure 1.1. This energy spectrum has been constructed from data collected by cosmic ray observatories operating over the past century. A primary goal of all cosmic ray observatories is to further resolve the energy spectrum as this will enable a more complete understanding of the origin and propagation of cosmic rays throughout the universe. The energy spectrum can be described by a relatively featureless power law with only two observable changes in spectral slope which have been named the knee and the ankle. We can break the spectrum up into three sections based on these two features, both of which seem to indicate a change in the origin or composition of cosmic rays at crucial energies. 2.1 Below the Knee The region below the knee of the energy spectrum of cosmic rays is the most clearly understood. The flux of cosmic rays up to an energy of about ev [2], which is just below the knee, is large enough for them to be directly detected from high flying balloon and satellite experiments. In these experiments the primary cosmic ray is directly intercepted and measured. Thus, measuring the composition of these cosmic rays is straight-forward and has been found to consist mostly of Hydrogen and Helium nuclei. The beam also consists of Lithium, Beryllium and Boron, with heavier nuclei present in smaller concentrations. The knee has been observed to occur at an energy of about ev [3]. Below this energy the spectrum follows the simple power law relationship, dn de E γ (1.1)

3 2. THE ENERGY SPECTRUM OF COSMIC RAYS 3 Figure 1.1: The energy spectrum of cosmic rays, showing the only two clearly observable features, the knee and the ankle, in an otherwise featureless power law spectrum. [1]

4 4 CHAPTER 1. COSMIC RAYS with a slope (γ) 2.7 as found, for example, by Aglietta et. al. (2000) [4]. The mathematical theory of shock acceleration within a supernovae produces a predicted spectral slope of γ = 2 [5]. When we account for the effect galactic fields and particles will have on the propagation of cosmic rays we arrive at a spectral slope very close to what has been measured. So it is generally accepted that the dominant sources of cosmic rays for this region of the spectrum are galactic supernovae. 2.2 The Knee of the Cosmic Ray Energy Spectrum The knee of the cosmic ray energy spectrum was first measured by Kulikov and Khristiansen in 1958 [3]. It is a feature of the spectrum that is still not completely understood. Astrophysicists believe that it is accompanied by a change in the proportion of light hydrogen nuclei to heavy iron nuclei, a change in the chemical composition, but this has not been conclusively proved. Above ev cosmic ray particles can no longer be observed directly in balloon experiments as the particle flux at Earth has dropped too low. However, at these energies the cosmic rays begin another process in the atmosphere that allows us to measure them on the ground. This process, called an extensive air shower, was first recognised by Pierre Auger (1939) [6]. It occurs when the primary cosmic ray collides with an atmospheric nucleus, which creates an ongoing cascade of secondary particles in the atmosphere. The particles resulting from these collisions can be measured by an array of detectors spread across an area of the Earth. Some such detectors are: EAS Top [4], Kascade [7] and MSU [8]. Various models describing the structure of the knee have been put forward including, but not limited to, diffusion models, compact source models and inefficient acceleration mechanisms. Descriptions of how these models generate the knee have been discussed in Horandel (2002) [9] and Candia et al. (2000) [10]. 2.3 The Ankle of the Cosmic Ray Energy Spectrum The only other clearly observable feature on the energy spectrum of cosmic rays is the ankle, a flattening of the spectrum which occurs at about ev [11]. This region of the spectrum is more vigorously debated than the knee

5 3. PROPAGATION 5 as fewer events have been recorded above this energy. A number of major detectors which operated in this region of the spectrum are, Fly s Eye [12], HiRes [13], AGASA [14], Pierre Auger [15], Yakutsk [16], SUGAR [17] and Haverah Park [18]. The basic detection technique for cosmic rays above the ankle remains the same as for energies above the knee. However, above this energy fluorescence light is generated by the passage of the charged air shower particles through the atmospheric nitrogen, which can be measured by distant light detectors. This method pioneered by Bunner and Greisen (1967) [19] has been used by the Fly s Eye, HiRes and Pierre Auger detectors. The ankle is believed to be generated as another, extragalactic, source of protons begins to dominate the spectrum. However, the experiments working in this energy range are currently unable to get consistent results on the anisotropy, composition or structure of the energy spectrum above ev, which suggests that more data are needed to be able to accurately define the origin of the most energetic cosmic rays. 3 Propagation As cosmic rays travel through the galaxy they interact with galactic particles and fields. For cosmic rays with energies much less than ev the movement of the particle within the galactic magnetic field is contained by the galaxy. These particles will not travel in straight lines from their origin to the Earth, so the only property that can be directly measured from them is their energy density. To determine the source of cosmic rays with energies below ev we compare the measured energy density with the energy density predicted by a proposed origin of cosmic rays. For ultra high energy cosmic rays (UHECR), with energies that exceed ev, the galactic magnetic field has a very small effect on the particle s direction and so it may be possible to directly measure the vectorial direction of their origin. However at this energy the photons of the microwave background radiation begin to have a relative energy that matches that needed for photo-

6 6 CHAPTER 1. COSMIC RAYS pion production to occur through, p + γ 2.7K n + π + p + π p + e + + e (1.2) The theory related to this process, entitled the GZK cutoff, was first put forward by Greisen (1966) [20] and by Zatsepin and Kuz min (1966) [21] and it concludes that above ev cosmic rays will strongly interact with the cosmic microwave background radiation and will not be able to travel further than approximately 200 Mpc. Since this is small in cosmological terms, if cosmic rays have an origin that is exclusively extra-galactic, a suppression in the energy spectrum should be observed. The GZK cutoff has not been either conclusively proved or discredited. Conflicting information exists in regard to the flux of cosmic rays that are present at these energies. A study performed by Baltrusitis et al. (1985) [22] with the Fly s Eye detector showed that the flux of cosmic rays above this energy was less than was expected, seeming to confirm the presence of the GZK cutoff. Later studies performed with the HiRes detector [23] [24] confirmed this result, but the observations made with the AGASA detector have reported seeing no sign of the GZK cutoff [25]. In these studies the number of UHECRs used was small and may not have been an accurate representation of the flux of cosmic rays at these energies. Also, the error on the calculation of the cosmic ray energy was very large, 30%, above ev and it has not been determined if these results actually agree with each other within their error margin [26]. Clearly the number of events measured within this energy range is limited and the problem should be solved after further significant observations have been made. In addition, a few very high energy events have been observed which shows that there may be a local source of UHECR, and may indicate that the GZK suppression will be found to be very much reduced in effect. One of these events was observed by Fly s Eye in 1992 with an energy of ev [27] and the AGASA array in 1994 observed another event with an energy of ev [28].

7 4. ANISOTROPY 7 4 Anisotropy Below ev the arrival directions of cosmic rays are close to isotropic. At these energies the arrival directions of cosmic rays are scrambled by galactic magnetic fields. Above this energy the arrival directions of cosmic rays begin to show structure and the map of the sky as seen by cosmic ray detectors for UHECR (> ev) is expected to be anisotropic. On the large scale this structure may show a clustering of cosmic ray arrival directions that coincides with the galactic or the super galactic planes. Anisotropy associated with either of these planes will prove that cosmic rays originate from either within the Milky Way, or travel here from a close-by galaxy. Coincidences in the arrival directions of cosmic rays associated with smaller scale structures such as M87 or the whole nearby Virgo cluster of galaxies are also possible. The detectors that operate above ev have reported differing results due to the small number of events that have been measured. Of particular interest is the anisotropy reported by the AGASA detector, which had the largest body of high energy events recorded before the Pierre Auger Observatory was built. The AGASA detector has studied two energy regions, that between ev, and all the events above ev. For the lower energy region, ev, AGASA reported an anisotropy in the direction of the galactic center [30]. Above ev Takeda et al. (1999) [29] reported no significant large-scale anisotropy in the arrival directions of cosmic rays with either the galactic or super galactic plane. An event excess that lay close to the super galactic plane at ev was not significant enough for anisotropy along the super galactic plane to be observed, but had a chance probability of occurring of less than 1%, this finding is shown in Figure 1.2 (ii). The number of events used in this analysis was 40 and the observed excess involved a cluster of three events. The fluorescence detector HiRes that operates in the same energy region as AGASA has reported seeing no anisotropy in the arrival directions of cosmic rays around the energy ev. The study involved 271 events with energies above ev [31]. The strongest clustering observed was consistent with an expected isotropic arrival direction map and, hence, no significant anisotropy in the arrival directions of cosmic rays was found. A study performed by Letessier-Selvon et al. (2005) [32] with the data collected from the Pierre Auger detector was performed in the direction of the galactic center at an energy of about ev. No significant clustering above the statistical fluctuations

8 8 CHAPTER 1. COSMIC RAYS Figure 1.2: The anisotropy map generated by data from AGASA. The dots, empty circles and empty squares represent events with energies, ev, ev and > ev, respectively. The dashed lines represent the galactic and super galactic planes and GC is the galactic center. Plot (i) is in the reference plane of the sky, plot (ii) is in the reference frame of the Milky Way. The gray areas on the map represent areas of the sky AGASA could not properly observe as the detector is situated in the northern hemisphere [29].

9 5. COMPOSITION 9 associated with an isotropic sky were observed, which is not consistent with the results recorded by the AGASA detector. 5 Composition The current level of knowledge of the composition of cosmic rays is constrained by the different detection techniques used at the different energies of the spectrum. Below the knee, cosmic rays are measured in balloon experiments and the mass of the cosmic ray particle can be directly measured. Cosmic rays of these energies consist mostly of protons, but heavier nuclei are present in smaller proportions. Above ev, however, the composition of the initial cosmic ray must be inferred from the properties of the air shower cascade it has started in the atmosphere. At this energy it is no longer possible to talk about an individual cosmic ray mass, but rather the general mass trend of the majority of the cosmic rays measured for an energy range. We now speak of the composition as being heavy, composed mostly of iron nuclei, or of being light, composed mostly of protons. A heavier nucleus has a shorter interaction length than a single proton because we can assume that the interaction probability of a nucleus can be composed of the sum of the interaction probabilities of each individual nucleon [34]. In general, a heavier nucleus will create a shower with a shallower depth of maximum and a higher muon content at ground level. The many experiments operating in the energy range around the knee, ev, measure the muon content of the air showers they detect as a compositional indicator, but cannot agree on whether the composition is heavier or lighter. It has been proposed [35] that this disagreement can be explained by the different nuclear models used to describe the collision of the cosmic ray with an atmospheric nucleus, but more information about nuclear interactions at these energies is necessary to finally resolve this question. Above the ankle, the fluorescence technique allows us to measure the composition of cosmic rays through the elongation rate, the slope of a plot of the depth at which the maximum number of charged particles occurs in an air shower against the logarithm of the energy of the cosmic ray. The expected depth of maximum, X max is simulated for many events, when it is assumed that cosmic rays are either, always protons or always iron nuclei. Comparing

10 10 CHAPTER 1. COSMIC RAYS Figure 1.3: The energy dependence of the mean depth of air shower maximum for cosmic rays measured by the HiRes detector, or the elongation rate. The cross-hatched area represents the error associated with the data. There is a definite trend from a heavy to a light composition when either the QGSJet or SIBYLL models of nuclear interactions are used [33].

11 6. POSSIBLE SOURCES OF ORIGIN 11 this simulated data to the measured data will show the general trend in the mass composition of cosmic rays. Abu-Zayyad et al. (2001) [33] performed this kind of elongation rate analysis on the data generated by the HiRes detector, the results of which can be seen in Figure 1.3. This figure shows that the average mass of cosmic rays decreases with energy for cosmic rays with energies greater than ev because the trend of the data moves towards agreement with the always proton cosmic ray composition line. This agrees with the theory that at about ev a proton-strong extra-galactic source of cosmic rays begins to dominate the spectrum. However, the AGASA detector, that operates with a surface technique at the same energies as HiRes, has not observed any change in the composition of cosmic rays at the highest energies [36] [37]. It may be that it is the detection techniques that are causing the discrepancy between the experimental results [34]. The Pierre Auger project, with its larger collection area and ability to cross correlate the fluorescence and surface detector techniques is expected to resolve the composition of cosmic rays at the highest energies. 6 Possible Sources of Origin The biggest unanswered question in the field of ultra high energy astrophysics is where do cosmic rays come from?. The best way to explore the possible acceleration sites of cosmic rays is to review a Hillas diagram as shown in Figure 1.4. This diagram explores the size of astrophysical objects with respect to the strength of their magnetic field and so the ability of such objects to accelerate and contain UHECR s, in this case with an energy of ev. The first thing we notice about this plot is there are very few astronomical objects which are potentially able to accelerate particles to ev. There are only three types of objects that can accelerate protons to this energy, neutron stars, active galactic nuclei (AGN) and radio galaxy lobes. The galactic halo can accelerate iron nuclei to this energy, but the galaxy itself, supernovae and sunspots are unable to accelerate particles to ev. These objects are divided by the acceleration mechanism they employ to generate UHECRs. Neutron stars, active galactic nuclei and sunspots produce UHECRs through the direct acceleration of a particle in a magnetic field. The rest of the objects accelerate particles through shock acceleration, described by first order Fermi principles.

12 12 CHAPTER 1. COSMIC RAYS Figure 1.4: The diagonal lines represent the relative size the magnetic field of an object needs to be to contain cosmic rays that are protons (the solid line), and iron nuclei (the dashed line). Any object that projects above the diagonal lines can potentially accelerate particles up to ev [38].

13 6. POSSIBLE SOURCES OF ORIGIN Fermi Acceleration Models The first theory of stochastic particle acceleration proposed by Fermi involves the interaction of a charged particle with vast magnetised clouds. The particle is scattered by the clouds with a series of glancing collisions. In these collisions the velocities of the particle and the cloud will either be in the same direction, or opposite as shown in Figure 1.5. The particle will gain energy from collisions where the velocities are in the opposite directions and will lose energy when the velocities are in the same direction. Since the collisions where the velocities of the particle and the cloud are opposite to each other are the most likely, on average the particle will gain energy with a relative energy gain E E proportional to the square of the velocity of the cloud, E E ( vcloud ) 2 (1.3) c For this second order acceleration process, v cloud c and so the time this process takes to accelerate a particle to relativistic energies can be larger than the age of the universe. In response to this the theory has been reworked to include the effect of a shock wave passing through the cloud, as occurs in the magnetised cloud surrounding a supernovae. In this case the shock front must be passing through the interstellar medium with a velocity higher than the speed of sound. The particle is contained by the magnetic field of the supernovae shell, but can pass through the shock and remain contained. If the particle passes through the shock then it will receive a relative energy gain of, E E v cloud c (1.4) In this case of first order acceleration, the time taken for the particle to achieve relativistic speeds is well within the age of the universe. This form of acceleration process naturally derives a power law spectrum that fits the spectrum of cosmic rays observed on Earth. Thus it is considered very likely that this is the acceleration mechanism for most cosmic rays. Supernovae Supernovae fulfill the requirements imposed by first order Fermi shock acceleration. The shock wave of the exploding star travels faster than the speed of

14 14 CHAPTER 1. COSMIC RAYS Figure 1.5: The two types of collision that can happen between a magnetised cloud and a charged particle, (i) velocities of the cloud and particle are in opposite directions, (ii) velocities of the cloud and particle are in the same direction. Note that there may be any angle between the velocity of the cloud and the particle up to 90, the velocities have been drawn parallel for simplicity.

15 6. POSSIBLE SOURCES OF ORIGIN 15 sound and the magnetic fields are of the correct strength. Fransson and Bjornsson (1998) [39] examined the radio spectrum from the supernova SN1993J in the M81 galaxy. They observed the synchrotron-emitting hot spots of the supernova and were able to determine the injected electron spectrum to be dn/de E 2.1, and that strong particle acceleration was occurring in the shocks of the supernova shell. The particle production spectrum from a supernova that is accelerating particles due to first order Fermi acceleration principles can be calculated from the observed cosmic ray particle density at a specific energy range. Hillas (2005) [40] found that this spectrum was dn/de E 2.04, which is very close to that measured in SN1993J. Radio Galaxy Lobes A galaxy that produces radio lobes has a super-massive black hole at its center that produces enormous jets of particles which radiate in the radio part of the electromagnetic spectrum. It had long been known that the electromagnetic spectrum emitted by the hot spots in the lobes of radio galaxies could be explained as the synchrotron radiation coming from charged particles accelerating by 1st order Fermi acceleration principles. Biermann and Rachen (1993) [41] showed that the observed spectrum of cosmic rays above ev will fit the acceleration of protons in the hot spots of the lobes of Fanaroff-Riley Class II radio galaxies by first order Fermi principles if the injection spectra is E 2. Other types of galaxies that have associated radio lobes, like BL-Lac objects and AGN may also be the origin of cosmic rays, see reference [38] for a more complete discussion of the acceleration properties of these objects. 6.2 Point Source Models The point source model of cosmic ray acceleration is the most direct method of particle energy gain. In this case a rotating magnetic neutron star or a rotating accretion disk generates an electric field that accelerates the particle. However the amount of acceleration provided by any one object is highly dependent on the individual properties of that object and so these sources cannot generate the power law spectrum observed on Earth in a natural way [38].

16 16 CHAPTER 1. COSMIC RAYS 6.3 Topological Defects The basic idea of a topological defect is that particles of type X that are embedded in Space-Time have been left over from the Big Bang. These particles have a mass m X > ev. The particles were prevented from decaying immediately after the Big Bang and decay with some random time frame comparable to the current age of the universe. The X particles decay into a more traditional form of matter, which have an energy that can be in excess of ev quite easily [34]. The theory is attractive because it does not rely on the acceleration ability of astrophysical objects. If this is the acceleration mechanism for the highest energy cosmic rays then the GZK cutoff will be very much reduced in effect as the particles may have excessive energies ( ev) quite easily and so be able to survive many interactions with the CMBR. The anisotropy of this acceleration method would be non-existent or may indicate an empty region of the sky. 7 Chapter Summary The acceleration source of UHECR is one of the most interesting questions in high energy astrophysics today. There are three theories that describe how a particle may be accelerated up to ev, the stochastic particle acceleration method, the direct compact source method and the top down theory. If particles are accelerated through the Fermi acceleration technique then a broad anisotropy in the direction of the super galactic plane is expected and the GZK cutoff should be clearly seen. For the direct method of acceleration the particles should point towards known compact source objects. If the origin of cosmic rays is something more exotic, like the top-down model, then no anisotropy should be observed and the GZK cutoff will not be clearly present.

17 Chapter 2 Extensive Air Showers 1 Components of an EAS The collision of a cosmic ray particle with an atmospheric nucleus begins a cascade process in the atmosphere, called an extensive air shower. The cosmic ray will probably be hadronic and the collision will break the target, atmospheric nucleus into its constituent nucleons. The enormous momentum of the cosmic ray will cause these particles to travel in the same basic direction. The energy of the cosmic ray becomes split up among the nuclear fragments, which then go on to interact with other atmospheric nuclei, creating a chain of events that will propagate down through the atmosphere. In addition to the resulting nuclei, much of the energy of the initial cosmic ray is transmuted to create pions, both neutral and charged. The neutral pions will decay into two gamma rays before they can interact with other atmospheric nuclei. The longer lived charged pions may decay or may interact with atmospheric nuclei. They decay into muons and neutrinos, but this decay is less probable with pions of higher kinetic energy. These interactions are documented in Figure Hadronic The depth of the first collision of the cosmic ray in the atmosphere is random, but on average is 70 g/cm 2 for a proton and 25 g/cm 2 for an α particle [42] at an energy of ev. During the collision the target nucleus will break up into nucleons as will the cosmic ray itself if it is a nucleus. The collision thus 17

18 18 CHAPTER 2. EXTENSIVE AIR SHOWERS Figure 2.1: Schematic diagram of a hadronic air shower showing the products of each interaction and decay [42].

19 1. COMPONENTS OF AN EAS 19 creates neutrons (n), protons (p), anti-protons ( p), anti-neutrons ( n), heavy mesons (K) and hyperons(y) as well as any fragmented nuclei that may survive the collision. These nuclear and heavy particles will collide with more atmospheric nuclei until their energy has dropped below the threshold energy of the reaction. The interaction of an air shower hadron with an atmospheric nucleus creates a number of secondary particles including pions, neutrinos or electrons. The charged pions have a half-life that is comparable to their probable time of nuclear interaction with an atmospheric nucleus, especially when they are traveling below relativistic velocities, and this interaction will create more pions, both charged and neutral. The number of nuclear interactions that occur in an air shower, drops off rapidly with increasing atmospheric depth due to the large amount of energy that goes into each interaction. Eventually the nuclear particles have all been reduced to an energy below that needed for a nuclear interaction to occur and so are no longer created within the cascade. 1.2 Muonic The decay of a charged pion creates a charged muon and a neutrino. The muons do not interact with the atmospheric nuclei and lose energy slowly through ionisation. At the level of energy of an air shower they have a long half life compared to the dilated time they spend traversing the atmosphere and many will continue beyond the level of the Earth s surface. The muons are used to detect primary cosmic rays with the surface technique and with detectors placed beneath the surface of the Earth. There is a chance that a muon will decay within the atmosphere where it will create an electron or positron and two neutrinos. The weakly interacting neutrinos created in these processes continue on through the Earth and are not used in the air shower detection process. 1.3 Electromagnetic If the initial cosmic ray is not a hadronic particle, but a gamma ray, the resulting air shower will consist almost entirely of gamma rays, electrons and positrons, ie. it will be completely electromagnetic. If we study how this simpler cascade will propagate through the atmosphere we can understand proton induced air showers because the dominant part of an air shower is

20 20 CHAPTER 2. EXTENSIVE AIR SHOWERS the electromagnetic component. Now, as the initial gamma ray passes close to a nucleus, it will undergo pair production and create an electron-positron pair. The positron and the electron will interact with nearby nuclei and create gamma rays due to the Bremsstrahlung radiative process. Some of the positrons will annihilate with atmospheric electrons to create more gamma rays. These cascade electrons and positrons cause Cherenkov radiation to be emitted and they also excite nearby molecules causing them to fluoresce. Both processes are discussed later in this chapter. So, the number of electromagnetic particles present in the cascade will grow exponentially until the energy losses dominate. The number of charged particles in an air shower drops off after this point as the electrons are attenuated by the atmosphere and are no longer considered part of the cascade process. For a hadron-induced air shower the short-lived neutral pions created by the hadrons are very unlikely to interact with atmospheric nuclei and will decay into two gamma rays traveling in the same direction as the initial π. Those gamma rays initiate the electromagnetic part of the air shower by pair production. For each neutral pion created by the hadronic section of the air shower, two gamma ray induced air showers can be said to emanate, so a proton induced air shower is like a superposition of many gamma ray induced cascades. 2 Longitudinal Profile of an EAS The growth and decline of the number of charged particles present in an EAS can be defined using various mathematical models. These models all relate the number of charged particles present within an air shower as a function of shower growth. One such model, the Gaisser Hillas profile is the only development profile considered in this thesis. 2.1 Gaisser Hillas Profile The Gaisser Hillas profile was first defined by Gaisser and Hillas in 1977 [43]. This profile uses the atmospheric slant depth to define the position or the current stage of an air shower s growth. The slant depth, X slant, is the atmospheric depth, X, corrected for the geometrical effect of an air shower axis not

21 2. LONGITUDINAL PROFILE OF AN EAS 21 Figure 2.2: The atmospheric depth, X, is the mass of a column of air with a unit cross sectional area above height h. The slant depth X Slant is the atmospheric depth corrected for the angle, α which the air shower makes with the Earth s surface.

22 22 CHAPTER 2. EXTENSIVE AIR SHOWERS Figure 2.3: A plot of a Gaisser Hillas function, N max and X max are clearly visible as particles and 750 g/cm 2, respectively. being perpendicular to the surface of the Earth. X slant = X sin α (2.1) Here the angle α is the angle the shower axis makes with the Earth s surface as in Figure 2.2. Atmospheric depth is generally used to describe the radiation absorption capability of the atmosphere. For a uniform absorber, only the thickness of the absorber needs to be considered. However the atmosphere is composed of several types of gases and particles with a density profile that decreases exponentially with increasing height, hence the density of the air needs to be included when considering its absorbence. This is done by considering the mass of a vertical column of air with a unit cross-sectional area, generally measured in grams per square centimeter (g/cm 2 ). Then the mass per unit area of the atmosphere above a certain height is defined as being the atmospheric depth. The Gaisser Hillas function relates the slant depth to the number of parti-

23 3. FLUORESCENCE LIGHT 23 cles present in the shower through, ( X X0 N(X) = N max X max X 0 ) Xmax X 0 λ [ ] Xmax X exp λ (2.2) λ and X 0 are essentially free parameters, with typical values around, λ = 70g/cm 2 and X 0 = 0g/cm 2. It follows that there will be some depth, X max, where a maximum number of charged particles, N max, will exist as in Figure 2.3. The parameter X max is used in the elongation plots described in Chapter 1 Section 5 and may be used to infer the mass composition of the primary cosmic ray. 3 Fluorescence Light Fluorescence radiation is produced when an external source of radiation causes the atoms or molecules of a medium to become excited. This external radiation can be in the form of electromagnetic radiation or charged particles. an air shower, the external radiation consists mainly of electrons created by the cascade process, and the fluorescent medium is nitrogen. The fluorescent atmospheric nitrogen spectrum calculated by Bunner 1967 [19] is shown in Figure 2.4 where the distinct lines of emission between 300 nm and 400nm can be seen. The emission peaks in Figure 2.4 are due to the transition in N 2 and N 2 + from a higher molecular energy state to a lower one. The main emission peaks are at 315 nm, 337 nm and 358 nm and are due to N 2, the remaining peak at 391 nm is due to N + 2. The emission peaks are of course due to the transition between molecular energy states, the full discussion of which is beyond this thesis, but can be found in [19]. The photon yield, ɛ, per electron given by Nagano 2004 [44] was found from nitrogen gas that had been excited by electrons, and is written as a function of pressure p at a constant temperature T in Kelvin: ɛ = p RT (hν) ( ) ( ) de Φ dx 1 + p p For (2.3) where R is the specific gas constant (N 2 : m 2 s 2 K 1 and Air : m 2 s 2 K 1 ), de dx is the energy loss in ev kg 1 m 2, hν is the photon energy (ev) and p is the reference pressure. The typical value of ɛ for a wavelength range

24 24 CHAPTER 2. EXTENSIVE AIR SHOWERS Figure 2.4: The atmospheric fluorescence spectrum due to nitrogen. [19]

25 4. CHERENKOV LIGHT 25 between 300 and 400 nm is 3.8 photons/m [44] when in air. The variable Φ corresponds to the fluorescence efficiency in the absence of collisional quenching and for the ith emission band is given by, 1 Φ i (p) = 1 Φ i ( 1 + p ) p i (2.4) 4 Cherenkov Light The phenomenon of Cherenkov light can be observed when charged particles traverse a medium faster than the phase velocity of light in that medium. It is very much like the shock wave that occurs when a jet plane breaks the sound barrier in the atmosphere. Whenever a charged particle moves through a medium it distorts the atoms it passes creating an electric polarisation field, but as seen in Figure 2.5 (i) the field is symmetrical around the electron and will cancel itself out, so no radiation may be observed. When the particle is moving very fast the polarisation field generated by the moving particle is no longer symmetrical and the electric field will generate a brief pulse of electromagnetic radiation. Generally the pulsed wavelets will interfere destructively and will cancel each other out, but if the particle is moving faster than the speed of light in the medium, the wavelets will add constructively and may be observed by a distant observer. It is easy to prove from geometry such as in Figure 2.6 that the angle, θ, at which the wavelets are coherent is inversely proportional to the relative velocity of the particle, β = v, and the refractive index, n, of the medium, c cos θ = 1 βn (2.5) The Cherenkov light is emitted in a cone centered around the trajectory of the particle, with an opening angle of θ as seen in Figure 2.6. The existence of this opening angle implies that there exists some threshold velocity of the charged particle, below which Cherenkov light will not be emitted. This is obvious from the definition of Cherenkov light and means there will be some limiting value of energy, E thres, the charged particle must possess to emit Cherenkov radiation, given by,

26 26 CHAPTER 2. EXTENSIVE AIR SHOWERS Figure 2.5: When a charged particle moves through a medium, it distorts the atoms it passes. (i) at low velocity the electric field is symmetrical. (ii) at high velocity a pulse of radiation is emitted as the particle traverses the medium, if the particle is traveling above the phase velocity of the medium the radiation will be coherent [45].

27 4. CHERENKOV LIGHT 27 Figure 2.6: Huygens principle shows that Cherenkov light is coherent within the angle θ. Cherenkov light is emitted in a cone centered around the trajectory of the charged particle [45].

28 28 CHAPTER 2. EXTENSIVE AIR SHOWERS [ ] 1 E thres = m 0 c 2 2n 1 2 (2.6) m 0 is rest mass of the charged particle. The derivation of the yield of Cherenkov radiation in a medium may be found in Jelley 1958 [45]. The yield of the number of photons emitted by a charged particle within a spectral range of λ 1 λ 2 per unit path length is, dn dl α is the fine structure constant ( 1 = 2πα 1 ) ( 1 1 ) λ 2 λ 1 β 2 n 2 (2.7) Cherenkov Light Produced by an Air Shower The Cherenkov light created by an EAS is produced in a very strong froward pointing cone, experimentally found to have an angular spread to 20. This spread is created by the distribution of the angular direction of electrons within an air shower. The strength of the Cherenkov beam and its angular distribution is thus based on the energy and angular distribution of the electrons in the shower and this relationship has been explored by a number of physicists [46] [47] [48]. Since the Cherenkov light produced by an air shower is very bright an Auger detector may see direct Cherenkov light if it views the shower head-on within 20, but it always sees some Cherenkov light that has been scattered out of the beam. The Rayleigh scattered Cherenkov light normally dominates, but Mie scattered Cherenkov light will dominate if there are many aerosols present in the atmosphere. This scattered Cherenkov light is considered to be noise in the calculation of the amount of fluorescence light produced by an air shower and must be removed from the calculations. The only observational difference between fluorescence and Cherenkov light which the fluorescence detectors of the Pierre Auger Observatory can detect is the directional nature of Cherenkov light. At large angles to the beam, which are usually observed by the Pierre Auger fluorescence detectors, Cherenkov light will normally be measured in much smaller quantities compared to the amount of fluorescence light measured. So, the Cherenkov light produced by an air shower can be iteratively removed from most events.

29 5. ATMOSPHERIC SCATTERING AND ATTENUATION 29 5 Atmospheric Scattering and Attenuation The process of scattering occurs when a wave passes through a medium that can be considered to be filled with point discontinuities, such as haze particles suspended in the air, or the atmospheric molecules themselves, where each molecule is separated by a region of empty space. The electric field of the incident wave will cause the suspended particles to vibrate at the same frequency as the incident wave. The vibrating particles will then radiate a secondary electromagnetic wave in phase with and of the same wavelength as the incident wave. Based on the size of the particle with respect to the wavelength of the incident light, the angular pattern of the intensity of the scattered light can be described by either Rayleigh or Mie principles [49]. The wavelength of fluorescence and Cherenkov radiation that is emitted by an air shower falls between 300 to 400 nm, which means that scattering off of air molecules may be described by Rayleigh principles, but scattering off of haze aerosols must be described by Mie principles. For both types of scattering we can simplify our equations by assuming that the light scattered by each particle escapes the path of the light beam and is not re-scattered. This is called single scattering and this assumption holds true to a first approximation. The effect of multiple scattering is being considered by the project, see Roberts (2004) [51] for a discussion of how it can be applied to the data. Now, for a homogeneous medium of constant density, the amount of radiance remaining in a beam of light with an original radiance of E 0 at position x along the beam that is undergoing a scattering process is given by, ( ) x E x = E 0 exp C(λ) (2.8) Here, C(λ) is a constant that describes the basic scattering properties of a medium for a particular wavelength of light and must be experimentally determined. It can be understood by relating it to the concept of visual range, which is described in McCartney 1976 [49] as the distance under daylight conditions, at which the apparent contrast between a specified type of target and its background (horizontal sky) becomes just equal to the threshold of the observer.... From this we can infer that the constant C(λ) is the distance a beam of light must travel before being attenuated to the fraction e 1 of its original strength.

30 30 CHAPTER 2. EXTENSIVE AIR SHOWERS Figure 2.7: The angular patterns of scattered intensity for a fixed wavelength with different particle sizes. (i) Small particle compared to the wavelength, Rayleigh scattering. (ii) Particle size comparable to the wavelength, Mie scattering. (iii) Large particle size compared to the wavelength, Mie scattering. [49]

31 5. ATMOSPHERIC SCATTERING AND ATTENUATION 31 Figure 2.8: The Longtin model of the Mie phase function due to scattering off atmospheric aerosols [50].

32 32 CHAPTER 2. EXTENSIVE AIR SHOWERS Now the quantity transmittance, T, is generally used to describe the attenuation strength of a medium. The transmittance is defined as the ratio between the beam radiance at position, x, to the beam radiance at the inception of the beam, T = E ( ) x x = exp E 0 C(λ) (2.9) It must be noted that Equation 2.9 holds for both the Rayleigh and Mie scattering principles and that the total transmittance, T tot, of the atmosphere is the product of the transmittance of the molecules, T m, with the transmittance of the aerosols, T a, T tot = T m T a (2.10) 5.1 Rayleigh Scattering The atmosphere is a medium that is not of constant density and so we must transform our definition of the transmittance into a quantity that removes the vertical density profile of the atmosphere. The quantity used for this is the vertical atmospheric depth described in Section 2.1. The atmospheric depth, X, is the integral of the density of the atmosphere, ρ(h), as a function of height, h, X = h ρ(h )dh (2.11) When we use a single layer model of the atmosphere where the temperature profile of the atmosphere is assumed to be constant, then Equation 2.11 reduces to ( ) h X = X 0 exp h m (2.12) Here X 0 is the vertical atmospheric depth at some reference height h=0, h is the height above that level and h m is described as the scale height of the atmosphere and can be found from, h m = kt mg (2.13) k is Boltzmann s constant, T is the constant atmospheric temperature, m is the average mass of an atmospheric molecule and g is the acceleration due to gravity. In this case the constant C(λ) is defined as the molecular mass attenuation length X m (λ), and for a wavelength of 355 nm, X m (λ) = 1885g/cm 2.

33 5. ATMOSPHERIC SCATTERING AND ATTENUATION 33 Then the transmittance of a straight light path taken through the atmosphere from height, h, into space will be given by, T m = X X m (λ) sin α (2.14) Here α is the elevation angle the light path may have to the ground. When a non-constant temperature model of the atmosphere is used Equation 2.12 becomes more complicated, but the transmittance is still given by Equation Rayleigh Phase Function To determine the amount of light scattered in any one direction due to a particle we must define the Rayleigh angular phase function. The derivation of this function is beyond the scope of this thesis but may be found in McCartney 1976 [49]. The function has the shape seen schematically in Figure 2.7 (i). It describes the fraction of incident light that will be scattered in the direction θ per unit solid angle, dω, and is given by, dp dω = 3 ( 1 + cos 2 θ ) (2.15) 16π 5.2 Mie Scattering As with the description of the distribution of the molecules within the atmosphere, aerosols do not have a constant density. We assume that the density distribution of aerosols, ρ a (h), falls off exponentially with height, through, ρ a (h) = ρ 0a exp h h a (2.16) Here h a is the scale height of aerosols and ρ 0a is the density of aerosols at a reference height, h = 0, and is assumed to be constant everywhere at this height. We can then describe a similar term to the molecular vertical atmospheric

34 34 CHAPTER 2. EXTENSIVE AIR SHOWERS depth, the particulate vertical atmospheric depth (X a ), by, X a = h1 h 2 ρ 0a exp h h a dh = ρ 0a h a [ exp h 1 h a exp h 2 h a ] (2.17) Now we define a quantity that is equivalent to the mass attenuation length used in the Rayleigh model by integrating over a horizontal path of length Λ a (λ) at the reference height, where this path length is called the aerosol attenuation length and must be measured for the atmosphere at specified wavelengths. It is the horizontal distance the light beam must traverse before being attenuated to a fraction of e 1 of its original strength. So, X a (λ) = but at the reference height, ρ a (0) = ρ 0a Λa(λ) 0 ρ a (0)dx (2.18) X a (λ) = ρ 0a Λ a (λ) (2.19) Now the actual density of aerosols at sea level ρ 0a cannot be measured without prior knowledge of the scattering properties of the aerosol particles, which is what we are trying to find. So we describe the transmission factor within any slice of the atmosphere that lies between the heights h 1 and h 2 as, [ T a = exp h a Λ a (λ) sin α ( exp h 1 exp h )] 2 h a h a (2.20) And we find that the aerosol density factor has disappeared. This definition of the transmission factor is independent of the density profile of aerosols in the atmosphere. So the correction for the extra amount of light lost by a light track that is at an angle α to the ground, is simply given by 1/ sin α. Mie Phase Function The phase function for Mie scattering is much more complicated than that for Rayleigh scattering and cannot be easily described mathematically. The Pierre Auger project uses the Longtin phase function [50] seen in Figure 2.8 which describes a forward pointing lobe seen in Figure 2.7 (ii).

35 6. CHAPTER SUMMARY 35 6 Chapter Summary The extensive air showers that are created by UHECR s are complicated structures that span the energy range from atomic molecular excitation to nuclear collisions at extremely high energies. Air showers enable the measurement of cosmic rays above ev, where the flux of cosmic rays has dropped below a level where it is practical to directly measure cosmic rays with balloon or satellite detectors. The detection of UHECR relies on our knowledge of all the molecular interactions that can occur in the atmosphere.

36 36 CHAPTER 2. EXTENSIVE AIR SHOWERS

37 Chapter 3 The Pierre Auger Detector The Pierre Auger Project in Argentina has been built to study ultra high energy cosmic rays (UHECR). The Pierre Auger project employs both the fluorescence and surface detector techniques to measure cosmic rays. The detector, shown in Figure 3.1, will consist of four fluorescence detectors overlooking an array of 1600 surface detectors. The array will cover an area of 3000 km 2 and will be the largest cosmic ray detector ever built. It is expected that the large number of UHECR observed by the Pierre Auger detector will finally resolve the form of the energy spectrum of cosmic rays above ev. The surface detector technique can be run continuously, but cannot measure the energy of a cosmic ray in a model independent way. The fluorescence technique, first proposed by Bunner and Greisen [19], involves measuring the track of fluorescence light created by the movement of the charged particles in an EAS through the atmosphere. This technique is a direct way to measure the energy deposited by an UHECR in the atmosphere but, unlike the surface detector technique, it cannot be run during the day or on moonlit nights. The Pierre Auger Project will make use of the continuous operation of the surface detector technique plus the high precision of the fluorescence technique to measure cosmic rays. 1 Air Fluorescence Detectors Fluorescence detectors measure the scintillation radiation produced by the motion of charged air shower particles through atmospheric nitrogen. There are only three fluorescence detectors that have been built in the world, Fly s Eye, 37

38 38 CHAPTER 3. THE PIERRE AUGER DETECTOR Figure 3.1: A geographical surface image of the Pierre Auger Detector in the province of Mendoza in Argentina. The positions of the four fluorescence detectors as they overlook the array of 1600 surface detectors are shown.

39 1. AIR FLUORESCENCE DETECTORS 39 HiRes and Pierre Auger. Of these the Fly s Eye detector is no longer operational and the Pierre Auger Observatory is still under construction. Compared to other techniques the fluorescence technique produces a model independent measurement of the energy and axis geometry of an extensive air shower. 1.1 Fly s Eye The Fly s Eye detector was the first successful project to use the fluorescence technique to measure UHECR s. The detector was stationed at the Dugway Proving Ground in Western Utah, and was operational from 1981 to 1992 [52]. The detector was upgraded to a two station detector in 1986 to consist of Fly s Eye I and Fly s Eye II which were separated by 3.3km. Fly s Eye I consisted of 67, 62-inch spherical mirrors that were arrayed around the site. Associated with each mirror were photomultiplier tubes (PMTs) that collected the light focused by each mirror. Each mirror and PMT unit observed a designated angular region of the sky so that the total array observed the entire night sky [12]. Fly s Eye II consisted of 36 spherical mirrors, with 15 PMTs located at the focal plane of each mirror. Fly s Eye II observed one half of the night sky, in the direction of Fly s Eye I [11]. The Fly s Eye detector observed the highest energy cosmic ray every detected [27] and proved that cosmic rays could be successfully recorded using the fluorescence method of detection. 1.2 HiRes In 1993 a single-site prototype High Resolution Fly s Eye detector (HiRes) was built on the site of Fly s Eye I. The prototype HiRes overlooked the Chicago Air Shower Array (CASA) and the Michigan Muon Array (MIA). This arrangement allowed for a collaboration to exist between the three projects to study correlations between the different UHECR measurement techniques. The prototype was operational for two years before being succeeded by the completed detector. The completed HiRes detector consisted of two fluorescence detectors spaced 12.6 km apart. The HiRes I site was completed in 1998 and the HiRes II site in HiRes I consists of 22 spherical mirrors 2 m in diameter. The 256 PMTs are positioned at the focal plane of each mirror, behind a nm UV bandpass filter. The detector views the full azimuthal range of 360 and an elevation of 2 to 17 above the horizon. HiRes II consists of

40 40 CHAPTER 3. THE PIERRE AUGER DETECTOR 43, 2 m diameter spherical mirrors with 256 PMTs situated at each mirrors focal plane, behind a UV band-pass filter of the same wavelength range used in HiRes I. The detector views the full azimuthal range of 360 with an elevation range of 3 to 30 above the horizon. The HiRes detector continues the studies begun with the Fly s Eye detector and first demonstrated the strength of being able to detect an EAS using both the fluorescence technique and an array of surface detectors [13]. 1.3 Pierre Auger The Pierre Auger detector is the first fully integrated hybrid detector to employ two of the techniques used to observe UHECR. Two sites will be built, the southern site which is under construction in the province of Mendoza in Argentina and a proposed northern site, to be constructed in southeast Colorado, USA [53]. The southern site consists of two types of detectors. The completed areas of the detector are currently recording events with both fluorescence and surface detectors. The surface array will consist of 1600 surface Cherenkov detectors that are based on the detectors used by the Havarah Park array. The four fluorescence detectors that will overlook the array are based on the detectors pioneered by the Fly s Eye detector in Utah. The two techniques can only be run together about 10% of the time due to the constraint of running the fluorescence detectors on clear moonless nights. 2 The Pierre Auger Fluorescence Detectors The fluorescence detectors of the Pierre Auger Project are designed to enable scientists to observe the growth of an air shower as it develops throughout the atmosphere. Three of the four fluorescence detectors are operational at the site in Argentina. These are Los Leones, completed in 2003, Coihueco, completed in 2004, and Los Morados completed in Since fluorescence light is produced in proportion to the energy the initial cosmic ray deposits in the atmosphere, these detectors can accurately determine the initial energy of a cosmic ray in a model independent way. The fluorescence technique can record the actual depth at which the air shower maximum occurs and is able to extrapolate the likely mass of the cosmic ray particle from that depth.

41 2. THE PIERRE AUGER FLUORESCENCE DETECTORS 41 Each detector is composed of 6 spherical mirrors, 3.4 m in diameter accompanied by 440 PMTs positioned in the focal plane of a mirror. The six mirrors of each site combine to view an azimuthal angle of 180 and an elevation angle range of 2 to 30 above the horizon. The detectors are placed on the edges of the array of surface detectors as in Figure 3.1 as this configuration provides the maximum possible detection area with four fluorescence detectors. 2.1 Physical Layout The fluorescence detectors are each composed of four separate parts as in Figure 3.2, the UV filter, the corrector ring, the spherical mirror and the camera [54]. A UV band pass filter, fitted to the aperture of the detector, reduces the effect of noise signals resulting from the night sky background. This filter is fitted behind an external shutter which, when closed, provides a light-tight environment that stops photons flooding the camera when it is not in operation. The UV filter is composed of 3.25 mm thick glass and acts like a window to prevent dust from entering the enclosure the mirrors are housed in. The filter has a transmission curve that peaks at 85% at 350 nm and drops to almost 20% at 300 and 400 nm and is thus matched to the spectrum of nitrogen fluorescence shown in Figure 2.4. A corrector ring is attached to the diaphragm of the detector to enhance the light collecting area of the mirrors [55]. The ring is circular with an external radius of 1.10 m and an internal radius of 0.85 m. It is divided into 24 segments. Each segment is made of UV transmitting glass and is machined into an asymmetrical profile that will account for the spherical aberration of the mirror. The ring ensures that the angular size of a light spot is no greater than 0.5, or one third of a camera pixel, anywhere on the focal plane. The mirrors used for each detector are segmented into 6 x 6 square elements, each element 60 cm by 60 cm in size, creating a total area of m 2. The radius of curvature for each mirror is 3.4 m. Two techniques were used to manufacture the mirrors, the first used aluminised high quality glass mirrors and the second used a special aluminum alloy that was then covered in a

42 42 CHAPTER 3. THE PIERRE AUGER DETECTOR Figure 3.2: The layout of one of the six mirror bays associated with each detector. The photons from the EAS pass through the shutter to be filtered by the UV filter. The corrector ring at the diaphragm reduces the effect of mirror coma aberrations. The camera consists of 440 PMTs which collect the photons and are connected to data acquisition electronics.

43 2. THE PIERRE AUGER FLUORESCENCE DETECTORS 43 Figure 3.3: A diagram of six Mercedes Stars positioned around a pixel. The units are based on simple Winston cones and will collect most of the light that does not fall directly on a pixel. layer of Al 2 O 3. Both types of mirror are used as the performance of each type exceeded the initial specifications placed on the mirror. The mirror elements were mounted on a rigid support structure that allows each part to be aligned independently. The camera mounted in front of every mirror consists of (440) hexagonal PMTs arrayed in 20 columns and 22 rows as shown in Figure 3.4. Every pixel views an angular size of 1.5 by 1.5 on the sky. Each PMT is mounted in a hole drilled in an aluminum block and the PMTs are placed in a hexagonal pattern to provide the maximum coverage of the image plane. Between each of the pixels is a space caused by the mounting technique as the holes drilled in the aluminum block cannot be spaced too close together without compromising the integrity of the mount. To maximise the light collection capabilities of the camera, optical reflecting surfaces based on Winston Cones are placed in between the pixels. These surfaces shown in Figure 3.3 are referred to as Mercedes Stars in relation to the shape of each unit. Each star is placed at the vertex of three camera pixels to form a reflecting surface with a hexagonal shape that surrounds every PMT. These surfaces increase the light collection capabilities of a camera at the border of each PMT, from an efficiency of 50% to 90%.

44 44 CHAPTER 3. THE PIERRE AUGER DETECTOR Figure 3.4: The patterns of allowable pixel patterns that the second level trigger associates with an event. Rotation and mirror reflections of each pattern are accounted for, as are patterns where one inside pixel is missing. 2.2 Electronics Behind the recording of an activated PMT are electronics that process the time and orientation of any signal with respect to the camera and decide if the flash was generated by a real cosmic ray [15]. Each PMT is connected to a series of electronic circuits that process the signal before transferring it to a buffer where digital filters determine its resemblance to an event. The electronics are composed of the initial, signal receiving analogue electronics and the trigger processing digital electronics. The analogue aspect consists of the head electronics and the front-end boards. The head electronics are the first processing step performed on any signal seen by a PMT. They provide high voltage biasing, signal driving, and a test pulse. The signal from a head electronics unit is received by one of twenty front-end boards attached to each camera. Every front-end board digitizes the signals from 22 pixels [56] with a digitization sampling period of 100 ns. Each digital signal is processed in the digital part of the front-end board where the first level trigger is implemented.

45 2. THE PIERRE AUGER FLUORESCENCE DETECTORS 45 The First Level Trigger examines the ADC values of each pixel as they are processed. When the running sum of ten previous samples in the camera exceeds an adjustable threshold value, the pixel is marked as having a signal. After this running sum has dropped below the threshold value, the time of the signal is extended by 20 µs, to give each pixel a common overlap time for event coincidence [15]. The signal is then passed to a buffer where a possible coincidence between pixels can be checked by the second level trigger. The Second Level Trigger (SLT) recognises the pattern the triggered pixels make on the camera within a 1-32 µs time constraint. Figure 3.4 shows the five patterns of pixel correlation recognised by the trigger that will ensure the pixels have formed a straight track. The trigger accepts patterns that are rotated or mirror imaged to those in Figure 3.4 and allows that one pixel in the middle of the pattern may be missing [56]. The SLT can read across the face of the camera in 1 µs, searching each column for recognised patterns of triggered pixels. When a coincidence between pixels is observed, the signals are passed to computers associated with each mirror (Mirror PC s) and are digitally stored before the third level of trigger is applied to the data. The Third Level Trigger uses the time structure of each event to ensure the pulse has run across the pattern in a continuous way. It requires that two second level triggers have been recorded within a predetermined time frame and that the combined track length is at least six pixels long. EAS track times are generally between 400 ns and 10 µs and this test on the timing of coincident pixels will reject fast Cherenkov flashes, nearby muons and any direct hits on a PMT. Slower moving noise events are also rejected, such as satellites, aircraft, planets and stars. 2.3 Reconstruction After the events have passed the triggering requirements of the electronics they are stored in the central computing facility at Malargüe [57]. These data will then be processed by the reconstruction software written specifically for the Pierre Auger Project. The calculation of the initial energy of a cosmic ray and the determination of its spatial geometry are the properties of the cosmic ray that are sought by the project. The Offline software is written in C ++ to

46 46 CHAPTER 3. THE PIERRE AUGER DETECTOR ensure portability and possesses a modular nature to allow members of the project to implement their own changes and improvements. The software can be roughly divided into three sections, the input and manipulation of the raw data, the application of physical models and the output of the final analysis of the properties of the cosmic ray. The initial task of the reconstruction software is to determine the amplitude of the signal across the camera with respect to a measured background signal, and to perform a final check on the event to remove any noise events that may have passed the three levels of trigger. The physical models that define the response of a detector are used to transform the data to a profile of the real photons that passed the diaphragm as a function of time. The timing and orientation of the triggered pixels describes the spatial geometry of the event and, when the atmospheric effects are accounted for, the number of fluorescence photons produced by an EAS can be derived. This number is in direct proportion to the amount of energy the initial cosmic ray has deposited in the atmosphere and hence the initial energy of the particle. See Chapter 4 for a more in-depth review of the reconstruction software used by the project. 2.4 Atmospheric monitoring, the Laser system An estimate of the attenuation suffered by fluorescence light between an air shower and a detector is vital to the calculation of the amount of energy deposited in the atmosphere by a cosmic ray. This requires an accurate knowledge of the scattering effects of atmospheric molecules and aerosols, described by Rayleigh and Mie principles, respectively. The Rayleigh phase function (see Chapter 2) is well known and follows the mathematic formula given by Equation 2.15, while the attenuation coefficients are dependent on the atmospheric density and temperature. These factors are measured for the Auger project through the use of radio sondes in weather balloons as were launched by Keilhauer et al. [2003] [58] from Los Leones, Coihueco and the town of Malargue. Monitoring the variable aerosol attenuation effect is more difficult. The main monitoring system is based on that proposed by Roberts [2001] [59] and consists of a laser positioned at the center of the array, which fires vertical laser beams into the atmosphere at specific intervals. The laser is a BigSky 355 nm 5mJ frequency tripled yag laser mounted in a temperature stabilising rack.

47 3. THE PIERRE AUGER SURFACE DETECTORS 47 The laser is connected to a GPS module that fires the laser after a specific number of nanoseconds past a GPS second. The power of each laser shot is transmitted to a recording station by a radio or cell phone modem and the whole array is powered by solar panels. These laser shots are identified from real events by the GPS nanosecond they occur at. Since the initial intensity of the laser and its orientation in space are known, it is simply a matter of accounting for the Rayleigh attenuation suffered by the laser beam and then reconstructing the aerosol scattering properties. An additional atmospheric monitoring system was proposed by Cester et al [2001] [60] and consists of four steerable LIDAR telescopes positioned at each fluorescence detector site. Each LIDAR telescope contains a pulsed laser beam and a receiver telescope. The pulsed laser beam is capable of shooting a 5 ns pulse of UV light (at 355 nm) into the atmosphere. The receiver telescope consists of up to four 0.5 m 2 parabolic mirrors each with an associated PMT. This unit points in the same direction as the laser and measures the returning scatter of the laser pulse as a function of time. The determination of the backscatter and aerosol attenuation coefficients is completed through the use of inversions as proposed by Klett and Fernald [61, 62, 63]. The problem with these techniques is their inability to solve for both the backscatter and attenuation coefficients simultaneously. Hence the LIDAR system is complemented by CIMEL Sun photometers which measure the intensity of well known stars to determine the atmospheric aerosol optical depth independently [64]. The backscatter coefficients can also be determined by measuring the Raman light backscattered from atmospheric nitrogen, but this light is very faint and hard to measure accurately. Since there is so much ambiguity present in the determination of the aerosol attenuation coefficients using the LIDAR system, it is yet not relied on as the main atmospheric monitoring system. 3 The Pierre Auger Surface Detectors The surface detectors of the Pierre Auger Project are based on those developed for the Havarah Park array. Essentially the detectors are tanks of water that act as Cherenkov radiators, with PMTs situated to detect the flash of light produced by the high energy particles of an air shower as they move through the tank. The number of tanks deployed as of the 3rd of March 2006 is 1124

48 48 CHAPTER 3. THE PIERRE AUGER DETECTOR Figure 3.5: A diagram of a surface detector showing the positions of the PMTs, the solar panel and the antenna each detector uses to communicate with the central facility. and the number operational is 928. The surface detectors are able to run continuously as they are not subject to the light produced by either the Sun or the Moon. However, the tank array can only measure the two dimensional front of the air shower as it hits the ground and so is limited in its ability to accurately reconstruct the initial properties of a cosmic ray. The surface detectors rely on the current level of understanding of particle interactions at and beyond current accelerator energies. The Large Hadronic Collider is expected to be able to create collisions with lab frame energies of ev [65] which is still three orders of magnitude below the most energetic cosmic ray detected by the Fly s Eye detector in Hence for any cosmic ray that is detected with an energy above that probed in particle accelerators, the calculation of the initial properties of the cosmic ray relies on our ability to accurately extrapolate the interaction properties of highly energetic particles. 3.1 Physical layout The tanks are placed at regular positions on a triangular grid spaced at 1.5 km intervals. They are constructed from molded polyethylene and are 3.6 m

49 3. THE PIERRE AUGER SURFACE DETECTORS 49 in diameter and 1.55 m high. They are filled with 12 kl of high purity water. Three PMTs of diameter 20 cm are placed at the top of each tank, looking down into the water. Each tank is powered by two solar panels attached to the top of the tank, and the tanks keep in contact with the central facility by means of a specifically designed radio system as can be seen in Figure 3.5. Each tank is an autonomous unit, recording signals from EAS and relaying recorded signals through the communications antenna positioned on top of every tank [15]. 3.2 Reconstruction The first step in the reconstruction of an air shower from the data collected by the surface detectors, is to fit a plane front to the timing information of the triggered surface detectors. This plane defines the zenith and azimuth angles of the air shower to an accuracy within two degrees [15]. The location of the core position of the air shower is determined through an interpolation of the shower signal in the triggered detectors. A lateral distribution function (LDF) can then be fit to describe the expected shower particle density at ground level for any distance from the core. The Pierre Auger Project has access to a variety of LDF s to describe the properties of an air shower. The energy of the initial cosmic ray is related to the normalisation of the LDF which we approximate to enable us to determine the signal, S(1000), that would be recorded in a tank 1000 m from the core. The arrival angle of the air shower needs to be accounted for to improve the use of S(1000) in determining the primary particle energy. Shower slant angles are accounted for using constant intensity curves to determine how S(1000) depends on the slant angle (θ) for fixed energies. This constant intensity curve, CIC(θ), is used to find S(1000) at the median Auger zenith angle of 38. It defines the parameter S 38, the signal in the detector 1000 m from the core when the shower has an angle of 38 to the vertical. S 38 is related to S(1000) by, S 38 = S(1000) CIC(θ) (3.1) Typical curves for CIC(θ) can be found in Sommers (2005) [66]. The energy reconstruction of the surface detectors has been calibrated using the fluorescence detectors, where the energy of an air shower calculated by the fluores-

50 50 CHAPTER 3. THE PIERRE AUGER DETECTOR cence detectors is plotted against the S 38 parameter [66] which has produced a model independent determination of the energy of an air shower through, E = 0.16 S = 0.16 [ ] 1.06 S(1000) (3.2) CIC(θ) 4 The Stereo Viewing of Air Showers The Pierre Auger Detector measures cosmic rays using both a surface and a fluorescence detector technique, allowing for better reconstruction of the properties of a cosmic ray than could be found by either technique alone. In addition to this, the higher energy events, above ev may be collected in stereo by two or more fluorescence detectors. This stereo viewing of an event enables extra reconstruction techniques to be applied to the data as detailed in the following sections. 4.1 Geometry The precision of the reconstruction of the spatial geometry of an air shower can be improved when it is calculated from the data collected by two fluorescence detectors. To calculate the geometry of an air shower, a plane is fitted to the arc created by the projection of the triggered pixels on the hemisphere of the sky for each detector (see Chapter 4 Section 1.2). This shower-detector plane (SDP) contains the axis of the air shower and a point representing the detector. In monocular reconstruction, the timing of the camera pixels as they are triggered is the only resource that can be used to find the geometry of the shower axis within the SDP. In stereo, the intersection of the two SDP planes found from the data collected by each detector defines the shower axis as in Figure 3.6. The arrival time of the light produced by the air shower is used to increase the accuracy of the reconstruction for an event recorded in stereo. A χ 2 minimisation is performed on the timing information from each detector and the geometry of the shower axis to determine a more precise result. This additional reconstruction step is especially useful when the opening angle between two detector SDPs is very small. In this case the vector cross product of the two SDPs cannot be relied on to produce an accurate result. Hence, for small angles of intersection the accuracy of the stereo geometrical reconstruction is low without the additional information provided by the triggering time

51 4. THE STEREO VIEWING OF AIR SHOWERS 51 Figure 3.6: The intersection of two SDPs defines the shower axis when an event has been recorded in stereo.