Advanced Algorithms for
Ultra-High-Energy Cosmic Ray Detection with the
EUSO-TA Experiment
Fredrik Viberg
Space Engineering, masters level
2016
Luleå University of Technology
Advanced algorithms for Ultra-High-Energy Cosmic ray
detection with the EUSO-TA experiment
Abstract
Cosmic rays at energies 1018 eV and above are known as Ultra High Energy Cosmic Rays
(UHECR). UHECR are charged particles that are accelerated by the biggest accelerators in our universe. Candidate accelerators generating these UHECR are super novas, black holes and neutron stars. But where and what these intergalactic accelerators is at large still unknown.
One of the experiments in the forefront of research in this field is JEM-EUSO, a planed space based telescope for detecting UHECR particles as they enter Earth’s atmosphere. Made possible by the advances in photon detectors and light weighted Fresnel lenses. A ground based pathfinder experiment was carried out in 2015 called EUSO-TA to test the optics and photomultiplier tech-nologies.
When the UHECR enters the atmosphere it collides with the atoms generating a number of secondary particles which in turn interacts with other atoms in the atmosphere generating a cascade of secondary particles. These trails are known as Extensive Air Showers (EAS). Mostly electrons are generated and in turn they excites the nitrogen atoms in the atmosphere which generate a isotropic characteristic fluorescence light. The JEM-EUSO telescope is designed to detect and measure the photon flux. From the photon flux it will be able to estimate the energy of the initial UHECR. JEM-EUSO will cover the largest area of EAS search and increase statistics of UHECR data.
This thesis describes the method and development of algorithms made for EAS analysis and detection based on EUSO-TA data. A simulation of EUSO-TA focal surface was developed, simu-lating background, stars and EAS.
The algorithms developed involves a background subtracting filter, line detection using Hough transform and a neural network for decision making. The Hough transform is used in computer vision and is a method used to detect lines in the pictures. It successfully identified both simulated and captured UHECR incoming direction with small errors.
Sammanfattning
Kosmisk str˚alning med energi p˚a 1018 eV ¨ar k¨anda p˚a engelska som Ultra High Energy Cosmic
Rays (UHECR). UHECR ¨ar laddade partiklar som ¨ar accelererade av de st¨orsta acceleratorerna i v˚art universum. Men vad och vart dessa intergalaktiska acceleratorer ¨ar n˚agonstans ¨ar fortfarande ok¨ant.
Ett experiment i framkanten av denna forskning ¨ar JEM-EUSO, ett planerat rymd baserat teleskop som ska leta efter UHECR n¨ar det g˚ar in i Jordens atmosf¨ar. Detta ¨ar m¨ojligt gjort genom framstegen inom foton detektorer och l¨att viktiga Fresnel linser. Ett mark baserat f¨orberedande experiment var genomf¨ort 2015 kallat EUSO-TA, f¨or att testa optiken och foton detektions teknolo-gin.
N¨ar en UHECR n˚ar atmosf¨aren kolliderar den med atomer vilket genererar flera sekund¨ara partiklar vilket i sin tur interagerar med andra atomer i atmosf¨aren vilket orsakar en kaskad av sekund¨ara partiklar. Dessa kedje event kallas f¨or Extensive Air Showers (EAS). Mest elektroner genereras vilket i sin tur exciterar kv¨ave atomer i atmosf¨aren vilket genererar ett isotropiskt karak-teristiskt fuorescence ljus. JEM-EUSO teleskopet ¨ar designat att detekterat och m¨ata foton fl¨odet fr˚an EAS. Utifr˚an foton fl¨odet s˚a kan man uppskatta energin av den inkommande UHECR. JEM-EUSO kommer att t¨acka den st¨orsta arean som letar efter EAS och p˚a s˚a s¨att kunna ta fram v¨ardefull information om UHECR.
Denna examens uppsats beskriver metoden och tillv¨agag˚angss¨attet f¨or algoritmer skapta f¨or EAS analys och detektion baserat p˚a EUSO-TA data. Simulation av EUSO-TA fokal yta var utvecklad att simulerar bakgrund, stj¨arnor och EAS. De algoritmer som utvecklas omfattar ett bakgrund subtraktions filter, linje identifiering med Hough transformation och ett neuralt n¨atverk f¨or EAS detektion. Hough transformation ¨ar anv¨ant inom dator syn och ¨ar en metod anv¨and f¨or att identifiera linjer i en bild. Den lyckas identifiera b˚ade simulerad och f˚angad UHECRs inkommande riktning med sm˚a fel.
Neurala n¨atverk anv¨ands inom maskin inl¨arning f¨or klassificering och regressions problem. Med anv¨andning av exempel data fr˚an simulationer eller verkliga event n¨atverket automatiskt ¨
Acknowledgments
List of Figures
1 The flux of cosmic ray particles (multiplied by E3) as a function of their energy.
The flux for the lowest energies (1010eV or below) are mainly attributed to solar cosmic rays, intermediate energies 1010 to 1015eV are galactic cosmic rays, and highest energies 1015eV and above to extragalactic cosmic rays. In the figure are features such as the knee and ankle pointed out. How much the flux corresponds to in area are written to give a feel for how drastic the the cosmic ray with high
energies reduces. Ref. [25] . . . 3
2 A plot of the cosmic ray spectrum above 1012 eV taken from Ref. [26]. All particle cosmic ray flux multiplied by E2observed by ATIC, Proton, RUNJOB, Tibet AS-γ, KASCADE, KASCADE-Grande, HiRes-I, HiRes-II and Auger. LHC energy reach of p − p collisions (in the frame of a proton) is indicated for comparison. . . 4
3 Showing Heitler models of electromagnetic cascades (a) and the hadronic extension (b), taken from Ref. [33]. In (a), after each radiation length λr in the medium every particle in the shower is assumed to split into two new particles, with each electron emitting a photon through Bremsstrahlung radiation, and each photon producing a e−e+pair. Fig. (b) shows a similar model of the hardronic shower. At each interaction length λI a number Nch a number of charged pions and number of 12Nch neutral pions are created. π0 are assumed to decay to γγ pairs, creating electromagnetic showers. Both showers are assumed to split in their manner of fashion until the individual particles reaches a critical value. Where the energy is to low to continue the process, at which point all π± decay to muons. . . 4
4 Show how a the different types showers makes up the EAS and their individual spread. At each step, roughly 1/3 of the energy is transferred from the hadronic cascade to the electromagnetic shower. Figure taken from Ref. [11] . . . 7
5 The relative velocitis seen at the diffrent reference frames. . . 9
6 Particle with m mass with relativistic speed between two approaching walls. Gains kinetic energy by inelastic collisions on the walls. . . 10
7 Hillas digram showing the possible classes of astrophysical objects versus their size and magnetic field strength taken from Ref. [26] . . . 11
8 Take from Ref. [30]. Correlation of the arrival directions of UHECR with AGN from the VCV catalog. Shaded/Colored part of the sky is not visible by Auger. The gray squares are AGN within z less then 0.018. The Auger data is shown as circles and the 21 are half filled. The 13 black dots are form HiRes events. The thin lines show the six regions of the sky to which Auger has equal exposure. The thick pink line is the super-galactic plane. . . 12
9 Cosmic ray composition abundance as a function of nuclear charge and the abun-dance of particals in the Solar system (out side the heliosphere), for E < 1014, take from Ref. [28]. . . 13
10 The shower maximum in the atmosphere hXmaxi and RM S(Xmax) as function of the cosmic ray primary energy. Measured by Pierre Auger Ref. [35]. Monte Carlo simulations from different hadronic interaction models are displayed for primary protons (blue) and primary iron nuclei (red). . . 14
11 Illustration taken from. Ref. [44] and depicts the isotropic light emission (solid circles), Cherenkov beam along the shower axis (dashed arcs) and the direct (dashed lines) and the scattered (dotted lines) Cherenkov light contributions. Where the fist figure to the right shows the direct fluorescence light and direct Cherenkov light hit the detector and the right one shows the how the direct fluorescence light and scattered Cherenkov reach the detector. . . 16
12 Surface arrays and telescope of Telescope Array. . . 16
13 Schematic figures of over the Pierre Auger observatory and its detectors. . . 18
14 Illustrating the observation technique used observing EAS from space. . . 20
17 The top one is a traditional lens while the bottom one is a Fresnel lens. se how the
lens has been cut ut in section but kept it continuity. . . 22
18 Shows focal surface and how it is built up. . . 22
19 Showing the EUSO-ballons structure, the gondol and launch. . . 24
20 Top Left: The focal surface of the EUSO-TA each destingushible cube is a MAPMT with 64 channels.Top Right. A CAD image showing the structure of the EUSO-TA telescope where there are two franel lenses and the PDM at the back.Bottom Left: the relization of the EUSO-TA telescope.Bottom Right: The EUSO-TA is placed infront of the Telescope Array UHECR observatory in Utah. . . 24
21 The Mini-EUSO conseptual design. Two Fresnel lenses, one PDM, one infra-red camera and another for photography in the visible spectrum. . . 25
22 Left: Shows the data captured by the focal surface, the white areas to the bottom right in the figure are non operational MAPMT. Right: Shows histogram over the photon counts in the right image upper half. From the fit the mean µ can be found. 27 23 Plots of the mean (µ) pixel count captured on the focal surface against time, together with error bars which is the standard deviation. Right:The mean over 128 GTU is a short time period which explains why the mean i constant. Left:Each point is the average of 3200 mean values to cover a longer time period, here a gradual increase over time most likely to some light source coming in view like the moon. This cover the 19 min of captured data. The average value of the mean here are 2.8 ± 1.7. . . 27
26 Histogram of Persei(Algol) and the fit of Eq. 20 result of the fit can be seen in Tab. 1. Right: One second of data when this was captured corresponded to 128 GTUs. The Gaussian distribution makes a good fit to the shape. Left: One min of data corresponds to 7680 GTUs. But here one can see that the star has moved a little bit which makes the fit a bit distorted. . . 28
24 Star Algol apprenses on one frame. . . 28
25 Integrating 128 frames. . . 28
27 Fit on a less bright star marked with the star nr. 13879 in Fig.24 and 25 . . . 29
28 Captured data from a laser with 85 mJ power placed 100 km away from the detector. Right: One GTU of the captured laser as it travels upwards through the sky. Left: Seven frames of the laser as it ravels upwards through the sky. In addition the avrage photon count has been subtracted to make the laser clearer. This resemble much of how the UHECR appears on the focal surface. . . 29
29 Gaussian fits performed on the test laser. Right: Shows the Gaussian fit of single laser captured in Fig. 28a. Left: Shows the summed and averaged of Fig. 28b along the y-axis and a Gaussian fit performed on it. Fit values is shown in table 2 . . . 30
30 Shows the histogram and profile of fitted Gaussian parameters of 160 integrated laser pulses. Top Left: Histogram of the 160 laser pulses GTUs integrated and averaged. Top Right: Profile of the fitted height value of one dimensional Gaussian parameter. This corresponds to the highest number of photon collected on each row. Bottom Left: Profile of the Gaussian standard deviation of the laser. It corresponds to scattering of the laser light in the atmosphere. Bottom Right: Profile showing the number of photons reaching the detector calculated according to Eq. 21. . . 31
31 Confirmed UHECR events from EUSO-TA data. Top Figures: Shows a captured UHECR in two frames. It travels slanted down wards and a bit hard to se in the second pictured but are in the bottom left corner. Bottom Left: Shows a UHECR traveling straight down wards. Bottom Right: Shows a slant UHECR traveling down wards. . . 32
32 The UHECR event in Fig. 31c showed here is summed and averaged over the y-axis. Then it is fitted to the Gaussian distribution. A averaged histogram of the UHECR event fit performed height=5.2 ± 1.2, mean= 1.3 ± 1.3, std =4.3 ± 2.3 . . . 33
34 Output of simulated focal surfaces. Left: Shows one GTU containing the UHECR where it is several magnitudes stronger then the background. Stars are not visible since in one frame they are comparable to the background. Right: Shows 128 GTUs integrated Here the stars are visible. . . 35 35 Simulated focal surface. Left: One frame with a weaker cosmic ray event, stars still
not visible. Right: 128 GTUs integrated now instead the background has drowned the UHECR event. Stars visible. . . 35 36 Comparison between one frame after filter and 128 integrated filtered frames. . . . 36 37 The filtering process on a GTU with a UHECR event on it. . . 37 38 Figures taken from Ref. [45]. Illustrates in Fig. (a) shows how three dots (equivalent
to pixels on the focal surface) gets transformed to the Hough space in Fig. (c). Notice how the line which passes through all of the points, has the same values in r and θ in Hough space. This will be the intersection points of the sinusoidal in Hough space. 38 39 Result of developed Hough transform. The red line in (a) shows the line that
is transformed. The black thin line is the identification of the line made by the implemented Hough transformed, ideas why the black line is not a perfect match is discussed later in the section. Fig (b) shows the Hough space of the red line. The highest point in the histogram is the r and θ are the parameters of the line. . . 39 40 The Hough transform the error here is 0.5◦. . . 39 41 The angle error at different angles with use of the fit to find the line parameters.
With a mean error = 0.53◦ . . . 40 42 Hough transform on simulated UHECR and stars. Notice that stars have little to
no effect in how the intersection of the sinusoidal intersection on the Hough space. 40 43 Hough transform result of figure 36a. The error in the found angle is 0.5◦ . . . 41 44 Image right shows the Hough transform of the image to the left. Gaussian fit is
used around the highest point on the Hough transform to find a better angle. The Hough space has been zoomed on the fit to review how well the fit is. The error in the found angle is 0.88◦ . . . 41 45 Hough transform on background. Seen in Hough space there is no clear intersection.
The line drawn is still based on the highest point in the Hough transform but there might be several points of equal height. . . 42 46 The Hough transform on real cosmic ray event. The line found by the method of
using the highest points, has the parameter θ = −1.5◦, r = 13.5 and is super imposed on the UHECR. . . 42 47 Hough transform on real cosmic ray data. The line found by Gaussian fit around the
highest point in the Hough space, parameters found are θ = −1.6◦, r = 12.1. The Hough line is marked on the UHECR for comparison. The Hough space is zoomed in on the fit to review it. The center is not on the maximum point but is trying to fit the Gaussian distribution. . . 43 48 Hough transform on the EAS seen in fig 31d θ=145.6 r=-6.8 . . . 43 49 This EAS is captured on two separate frames. On (a) there is a clear track present
while on (b) it is hard to distinguish a where it is. (c) is the integration of (a) and (b). It should represent the best line description of the two events are from the same EAS . . . 44 50 An illustration of a Perceptrons can take several arguments and give one output. . 46 51 . . . 47 52 Shows the schematic idea over the gradient decent. The figure depicts a how iteration
54 Shows the result of the training the neural network for a classification problem. The NN learns to classify the points with very low error just after a hundred iterations with a 250 data points for training and testing. Top Left: Shows the weights impact of each variable on the network. Top Right: The structure of the neural network. Bottom Left: Shows the resulting output of the test set. Background here would be zero and signal would be one. Bottom Right: Shows a surf plot of the resulting neural network, it looks much like a step function. . . 51 55 After training in 25000 epoch, figures are the same as in figure 54. Top Left: Shows
the impact of the variable on the network during the learning period. Top Right: The structure of the neural network. Bottom Left: Shows a histogram of the resulting output of the test set. Bottom Right: Shows a surf plot of the resulting neural network, it looks much like a smiley. . . 52 56 The typical simulated EAS in the training of the first neural network. A clear
distingt line. . . 53 57 Traning and testing on simulation data. . . 54 58 The typical simulation image with lower SNR. Here the signal is much harder to
distingish. . . 54 59 Network results after 100 epcohs training with 10 000 training data. The network
was able to classify 98.11% correctly. . . 55 60 18 real events capured by EUSO-TA 3 are the EAS captured air shower and 15
background frames. . . 56 61 Output of 3000 background GTUs. Where most of it is classified as signal. Note
that no signal events where classified here. . . 56 62 Results from training network using real background data together with simulated
Contents
1 Introduction 1
2 Cosmic Rays 2
2.1 Extensive Air Showers . . . 2
2.2 Propagation . . . 6
2.2.1 Greisen-Zatsepin-Kuz’min limit . . . 6
2.2.2 Magnetic field effects . . . 6
2.3 Accelerators . . . 8
2.3.1 Fermi accelerations . . . 8
2.3.2 Unipolar inductor . . . 10
2.3.3 Potential acceleration sources . . . 11
2.4 Composition . . . 12 3 Observation of UHECR 14 3.1 Surface Arrays . . . 14 3.2 Air Fluorescence . . . 14 3.3 Detection sites . . . 15 3.3.1 Telescope array . . . 15
3.3.2 Pierre Auger Observatory . . . 16
4 JEM-EUSO Experiment 19 4.1 Brief history . . . 19
4.2 Observation from space . . . 19
4.3 Sience Objectives . . . 23
4.4 Pathfinders . . . 23
4.4.1 EUSO-Balloon . . . 23
4.4.2 EUSO-TA . . . 23
4.4.3 Mini-EUSO . . . 25
5 EUSO-TA data analysis 26 5.1 Instrument description . . . 26 5.2 Background . . . 26 5.3 Stars . . . 28 5.4 Laser . . . 29 5.5 Cosmic rays . . . 31 5.6 Simulation . . . 33 6 Algorithms 36 6.1 Filter . . . 36 6.2 Hough Transform . . . 37 6.2.1 Simulation . . . 40 6.2.2 EUSO-TA data . . . 42
6.2.3 Concluding remarks: Hough transform . . . 43
6.3 Neural network . . . 46
6.3.1 Sigmoid neurons and Cost function . . . 46
6.3.2 Gradient decent and backward propagation . . . 47
6.3.3 Network Architecture . . . 49
6.3.4 Initial examples . . . 50
6.3.5 Input parameters for UHECR detection . . . 52
6.3.6 Training and Testing on simulated data . . . 53
6.3.7 Test on EUSO-TA data . . . 55
6.3.8 Concluding Remarks: Neural Network . . . 58
1
Introduction
Cosmic rays are defined as a charged nuclei or photons that originate from space. The energy of incoming cosmic rays ranges over several order of magnitude from 106eV to above 1020eV. Cosmic rays with energies of 1018 eV or above are named Ultra High Energy Cosmic Rays (UHECR) and will be the focus in this thesis. The first reports of their existence where made in the 1960s when the measurements of a cosmic rays with energy above 1018eV Ref. [32] and 1020eV Ref. [31] made by John Linsley at the Volcano Ranch air shower array in New Mexico.
These UHECR are believed to have intergalactic origin and are accelerated by the largest ac-celerators in the universe. These intergalactic accelerators accelerate particles to much larger energies then the LHCs proton-proton head on collision (which is approx. 1017 eV). What exactly
2
Cosmic Rays
Ionized particles coming form outer space have been given the common name of Cosmic rays. The search for cosmic rays started with an experiment done 1912 by Victor Hess measuring atmospheric ionization from balloons using an type of electrometer. It was a surprise to everybody back then when the result was that the ionization increased higher in the atmosphere. It was only known at the time that ionization caused by natural radioactive material and was though to decrease with altitude Ref. [30]. By proving the opposite Hess drew the conclusion that the particles responsible for the ionization at high altitudes had their origin from outer space. The name “Cosmic Ray”was given to these particles due to their presumed origin in the cosmos.
These Cosmic ray bombards the Earth atmosphere every day affecting it in different ways. Theo-ries such as induced ionization in the atmosphere which disintegrate N2and O2molecules changing
the chemistry in the atmosphere. Ozone with free oxygen and nitrogen can bond together in the upper atmosphere, depleting the ozone layer and forming nitrates Ref. [42]. The nitrates formed can find their way to the Earth’s surface though rain and act as a fertilizer for plant life. In the same way cosmic ray continuously produce various unstable isotopes in the Earth’s atmosphere, such as carbon-14. The cosmic ray flux has kept the level of carbon-14 in the atmosphere roughly constant for the last 100.000 years, which makes it possible to use radiocarbon dating Ref. [17]. Measuring the energy and plotting it against the average flux, Fig. 1. Which is based on a collection of 30 years experiment data. It shows that the flux follows a overall decreasing power law function. Some features are marked in the figure called knee and ankle which are points of interests. These features are where the flux deviates from the over all trend of the power function and the cause of this are some interesting physical phenomena still not fully understood.
The flux decreases with increasing energy, by about a factor of 500 per decade in energy. This results in the flux going from more than 1000 particles per second and m2 at GeV energies to
about one particle per m2 per year at a 1015eV , and further, to less than one particle per km2
per century at 1020eV . As the flux decreases so does our ability to detect them. Making energies
at 1014 to be detected by covering a large area with detectors. Where the largest span an area of
several thousand per km2 for detection of the highest energies. These sites use indirect methods
to detect a UHECR event to increase the likelihood of observing one. These indirect methods involves the detection of Extensive Air Showers (EAS) which will be explored in the next section. Fig.2 shows the lower end of this spectrum from cosmic ray observations. Here the features are depicted better. A bump at 1015.5 eV representing the knee and the ankle at around 1018eV. Followed by steep cut at around 1020 eV which are the highest measured UHECR ever detected.
2.1
Extensive Air Showers
When a UHECR enters the atmosphere the cosmic ray particle interacts with the nucleus in the atmosphere. This will produces a large number secondary particles, the secondary particles will in turn create more secondary particles in a cascading effect. The number of secondary particles is directly related to the energy of the incoming cosmic ray.
The most dominant of the secondary particles is the electron. They will particularly cause nitrogen particles to excite to a unstable state and when returning to ground state it will emit characteristic fluorescence light in the ultraviolet (UV) band with wavelengths between 300 and 420 nm. The light is isotropically distributed, intensity of this light is proportional to the energy released in the atmosphere, Ref. [30].
Going in on more details on how the energy is estimated from the EAS. A simple model describing this process and how to related the energy of the initial UHECR is the Heitler model Ref. [33]. This model is broken up in two kind of showers as seen in Fig. 3.
• Electromagnetic showers: This involves electrons (e−), positrons (e+) and photons (γ)
undergoing repeated splittings. Either by photon bremsstrahlung production from a elec-tron, positron or e−e+ pair production, Fig. 3a). Bremsstrahlung photon production is
Figure 1: The flux of cosmic ray particles (multiplied by E3) as a function of their energy. The
flux for the lowest energies (1010eV or below) are mainly attributed to solar cosmic rays,
interme-diate energies 1010 to 1015eV are galactic cosmic rays, and highest energies 1015eV and above to
Figure 2: A plot of the cosmic ray spectrum above 1012 eV taken from Ref. [26]. All particle
cosmic ray flux multiplied by E2 observed by ATIC, Proton, RUNJOB, Tibet AS-γ, KASCADE,
KASCADE-Grande, HiRes-I, HiRes-II and Auger. LHC energy reach of p − p collisions (in the frame of a proton) is indicated for comparison.
Figure 3: Showing Heitler models of electromagnetic cascades (a) and the hadronic extension (b), taken from Ref. [33]. In (a), after each radiation length λr in the medium every particle in the
shower is assumed to split into two new particles, with each electron emitting a photon through Bremsstrahlung radiation, and each photon producing a e−e+pair. Fig. (b) shows a similar model
of the hardronic shower. At each interaction length λI a number Nch a number of charged pions
and number of 12Nch neutral pions are created. π0 are assumed to decay to γγ pairs, creating
Every particle undergoes a splitting after it travels a fixed distance d which is related to the radiation length in that medium λr as d = λrln(2). After n steps the particle number
is Nn = 2n and their individual energy is E0/Nn. This development continues until the
individual energy for the particles is too low for pair production or bremsstrahlung. Heitler model takes this energy to be the critical energy. This energy threshold is about Eγ
c = 80M eV
in Air.
Consider the shower initiated by a single photon or electron with energy E0. The cascade
reaches maximum size N = Nmaxwhen all particles have energy Ecγ, so that:
E0= EcγNmax (1)
The electromagnetic shower reaches it penetration depth Xmax when the shower reaches it
maximum size. This is obtained by determining the number of splitting nc for the energy
per particle to be reduced to Eγ
c. Since Nmax = 2nc we can obtain from Eq. 1 that nc =
ln[E0/Ecγ]/ln(2), giving:
Xmaxγ = ncλrln(2) = λrln[E0/Ece] (2)
Another parameter that is being presented is the elongation rate (Λ) it is the rate of increase of Xmax with E0 defined as:
Λ ≡ dXmax dlog10E0
= 2.3λr (3)
This elongation rate is about 85 g/cm2 in air.
Extensive simulations of electromagnetic cascades confirm these properties although the par-ticle number at maximum is overestimated ny a factor 2 to 3. The overestimation for several reasons, mainly that multiple photons are often radiated during bremsstrahlung which will leave the electron with less energy to continue the cascade. Moreover many e± range out in the air.
Simulation that accounted for those effects shows that the number of photon greatly out-number the out-number of electrons and positrons by a factor of six. The maximum electron size is much less then predicted in Heitler’s models. To extract the number of electrons Nefrom
Heitler’s overall size N , one can adopt a correlation factor Ne= N/g where g = 10. This is
a order of magnitude estimation.
Despite its limitation the Heitler model reproduces two basic features of EM shower devel-opment which are confirmed by simulations and by experiments:
– The maximum size of the shower is proportional E0.
– The depth of maximum increases logarithmically with energy, at rate of 85 g cm−2 per
decade of primary energy.
• Hadronic Showers: Hadronic air shower Fig. 3b) model is similar to the electromagnetic showers. The atmosphere is presumed to be in layer of fixed thickness λIln(2), where λI is
now the iteration length of strongly interacting particles. For pions in air, λI ≈ 120gcm−2
Ref. [20]. When the hardrons interacts when traversing one layer it produces Nch charged
pions (π±) and 12Nch neutral pions (π±), the multiplicity Nch of charged particles produced
in hadronic interactions is a slowly increasing function in the laboratory frame and grows as E1/5 in proton-proton interactions. The neutral pions immediately decay to photons, initiating electromagnetic showers. The charged pions continue until the π± fall below the critical energy Eπ0 where they then are assumed to decay, yielding muons.
Consider a single cosmic ray proton entering the atmosphere with energy E0. After traversing
n atmospheric layers there are Nπ = (Nch)n total charged pions. Assuming equal division
of energy during particle production, these pions carry a total energy of (2/3)nE 0. The
remainder of the primary energy E0 has gone into electromagnetic showers from π0 decays.
The energy per charged pion in the atmospheric layer n is therefore. Eπ=
E0
(32Nch)
To calculate the energy of the initial cosmic ray both electromagnetic showers and hadroinic showers has to be considered. Fig. 4 shows a schematic view of how the both processes makes up the EAS. The primary energy is calculated using both the total number of pions Nπ and electromagnetic
particles Nmax in the sub-showers. Similar to Eq. 1, the total energy in this case is:
E0= EγcNmax+ EcπNπ= gEcγ(Ne+
Ecπ gEcγ
Nπ) ≈ 0.85GeV (Ne+ 24Nπ) (5)
The participial use of Eq. 5 requires adjustment to account for experimental details. One such detail could be that the measurement of particles are done after the shower maximum. Another is that the relative sensitivity of an experiment to photons and electrons effect the interpretation of measured value of Ne.
Another effect of the EAS are the Cherenkov light. Caused by that several of these secondary particles will have velocity of greater then the speed of light in that medium, this will cause an effect called the Cherenkov light and much like how a sonic boom from a super sonic aircraft traveling faster than the speed of sound in that medium. Similar effects with light occurs when a charge participial travels through a dielectricum faster than the speed of light in that medium. This generates photons in a cone like shaped formation of photons traveling in the same direction as the charged particle generating the photons. This light can in turn be scattered by molecules and aerosol in the atmosphere. Part of the Cherenkov light will be diffused isotropically diffused and reflected when reaching land, sea or clouds.
2.2
Propagation
UHECR travel a long way to reach Earth. Understanding the propagation through interstellar space becomes ever so important in the question of searching after the source of the UHECR. Two effects are the most prominent when considering interstellar travel for UHECR which will be presented in this section.
2.2.1 Greisen-Zatsepin-Kuz’min limit
This effect was calculated by Kenneth Greisen Ref. [21], Vadim Kuzmin, and Georgiy Zatsepin, Ref. [47] hence the name, as a consequence of the cosmic background radiation (CBR) interaction with UHECR. This effect limits the cosmic ray kinetic energies for energies approaching 1020eV .
There is two interactions that can happen.
p + γ → π + n (6)
p + γ → p + e++ e− (7) Fig. 2 is a shows the high energy end of the spectrum. Here cosmic ray spectrum are made with observational data, which shows indications of this theoretical limit at the very end of the cosmic ray spectrum. By showing a beginning of a much steeper decline in flux. Cosmic ray protons has in this part of the spectrum 1019− 1020 eV enough energy to interact and scatter with the cosmic
back ground photons. This will make the particle energies end up with considerably less then the initially had about ≈ 22 % less Ref. [21]. This will make UHECR from sources grater than about 50 Mpc practically impossible to reach us without scattering on the CBR.
Measurements have been recorded to pass this limit of 1020 eV, but there are several possible
reasons why this could have happened. One is that there is a measurement errors or that the UHECR source could be within the GZK limit (50 Mpc), though it is currently known where and what those sources could be.
2.2.2 Magnetic field effects
• Galactic magnetic fields: In other words magnetic field that are inside our galaxy. The galactic magnetic has a large scale structure, this means that cosmic rays coming from the same direction will be scatter in a similar way and the scattering will shift the arrival direction away form the true source. Study in this area such as (Han et al., 2006) Ref. [22] shows in principle the magnetic field strength is proportional to the matter density in the galaxy and is decreasing with distance from the center. The field decrease in the galactic plane is best described with an exponential function eRGC8.5 where RGC is in kpc. This expression is valid of RGC bigger then 3 kpc. The field inside this circle is difficult to study and is not well
known. The deflection of charged particles of charge Z and energy E should not exceed 10◦Z(40EeV /E).
• Extragalactic magnetic field: Much less is know about this subject. Studies done by (Kronberg, 1994) Ref. [27] shows that magnetic fields of galaxy clusters has been observed to have µGauss magnetic fields (Gauss is another unit of measuring magnetic flux density 1 Gauss= 10−4 Tesla) and a upper limit of 10−9Gauss = 1nGass if the correlation length of the field Lc is 1 Mpc, the average distance between galaxies. Even such small fields can
affect the propagation of UHECR.
Angular deflection due to random walk θ would then be θ = 2.5◦E20−1B−9d100L
1 2
C (8)
where E20 is the energy in units of 1020eV , B−9 of the magnetic field strength in nGauss,
d100 is the source distance in units of 100 Mpc and Lc is the correlation lenghth in Mpc.
The random walk causes a propagation path length ∆d that is larger than the distance to the source and causes increased energy loss. That parameters depend on the square of the parameters above.
∆d = 0.047E20−2B−92 d2100LCM pc (9)
These parameters can change drastically if the UHECR encounters an extended region with organized magnetic field. In principle this should be a rare occasion expect close to a powerful astrophysical system where such fields have been observed. Depending on the field strength, its direction toward us, and structure of the field, the angular deflection could be much larger.
2.3
Accelerators
Anything with a inductive electric field can get charge particle to accelerate. Question is what are acceleration process that can get charge particles up to and beyond 1018 eV. The most
com-mon explanation is the Diffusive Shock acceleration (Fermi first order acceleration) and unipolar induction which will be discussed here. Followed by some suggestions of where they could come from.
2.3.1 Fermi accelerations
There are two types of Fermi acceleration, first and second order. The second one was elaborated by Fermi himself in 1949 Ref. [18] and involved charged particles gaining energy by magnetic mirroring when colliding with interstellar clouds. These interstellar clouds would have different relative velocities within the cloud and make so that the charge particle gains energy with head on collisions. This second order Fermi acceleration have some problems of being highly unlikely to gain significant energy since the random velocities of interstellar clouds are relatively small.
This led to the first order Fermi acceleration Ref. [6] which is also known as Diffusive Shock acceleration. Where a shock wave comes form a solar flares or super nova remains accelerate plasma to a higher velocity then the surrounding plasmas. In the between the shocked plasma wave and unshocked plasma is the shock barrier.
Taken that the shock travels at the speed of vu. In the frame of the shock it sees the cold gas
approaching at speed vuand the hot gas behind it streaming away at vd=14vu. Next consider the
at vuand the shocked gas behind it at 34vu. As the charge particle cross the shock it is accelerated
up to the mean speed of 34vu, as viewed from the frame of the unshocked gas. See Fig. 5.
Figure 5: The relative velocitis seen at the diffrent reference frames.
In order for this charged particle to gain more energy it has to cross the shock again, this can happen by thermal motion or tangled magnetic field. That takes the charge particle over the shock to the unshocked gas. With the respect of the frame it just where at it is once again accelerated by 34vu. This happens multiple times.
In order to review whats going on with the increase of energies on thees elastic collisions lets consider this similar example. Lets say an particle with mass m is traveling at a mildly relativistic speed v between two scattering surfaces with a distance L from each other. The scattering surfaces are approaching each other with the speed V << c where c is the speed of light, see Fig. 6.
If the particle collides alternately head-on with each scatter it will gain energy at a rate: dE
dt = rate of collisions × Energy change per collision (10) Using the fact that the particle is relativistic to our advantage the momentum increase at each collision is γmV so we can calculate the energy increases via E = pc.
dE dt ≈ v L∗ γmV c ≈ γmc2V L ≈ EV L = E τ (11)
Where τ is the time between particle scatters on the walls. The particles energy will increase exponentially as the distance L gets shorter.
Going back to the participle accelerated by shock wave. The energy after n number of cross-ings will be E = E0∗ βn where E0is the initial energy and β is fractional change in kinetic energy
for each crossing. The particle wont cross the chock wave indefinitely. The net momentum flux of the shocked gas downstream will carry the charge particle away in due time.
Calculating the number of particles remaining in the shocked region after each crossing n can be calculated as N = N0Pn where N0is the initial nr of parcels and P is the chance to remain in
each crossing. It can then be shown that the number of particles relates to the energy according to a power law:
Figure 6: Particle with m mass with relativistic speed between two approaching walls. Gains kinetic energy by inelastic collisions on the walls.
This is interesting since the cosmic ray spectrum Fig. 1 also follows a power law function which speaks in favor of this model. Summarizing the Diffusive Shock acceleration:
• Provides an efficient method for accelerating particles in supernova remains shock waves. • Requires prior injection of superthermal speed particles.
• Energy losses are ignored
• This model neglects detailed physics of the magnetic field .
For the intrigued reader is refereed to Longair book in Astrophysics Ref. [36]. 2.3.2 Unipolar inductor
An additional source for the UHECR has been theorized to be the Unipolar inductors. A unipolar inductor is a metal disc rotating in a magnetic field which generates a electric current. This is also know as disk dynamo or Faraday disk.
Here it is a unipolar inductor in a astrophysical sense which can be created with a celestial body that has a magnetic field and surrounding high conductive plasma. Celestial bodies which are consider to be able to accelerate the charged particles to the ultra high energy regime are neturon stars or black holes.
Rapidly rotating neurons stars generally create relativistic outflows (“winds ”), where the com-bination of the rotational energy and the strong magnetic field induces am electric field E = v ×Bc. Where B are the magnetic field and v velocity of the outflowing plasma. This creates a large voltage drop, which can accelerate particles to high energy.
The basic ability to accelerate particles to a given energy by the Unipolar inductor is limited by ability of the accelerating object to contain the particles inside the acceleration region. This is given by The Lamor radius for the charged particle. Hillas 1984 Ref. [23] summerized the conditions on potential acceleration sources using the relation between the maximum energy of the particle of charge Ze and the zise and strength of the magnetic field of the site:
Emax= βZe(
B 1µ)(
R
Figure 7: Hillas digram showing the possible classes of astrophysical objects versus their size and magnetic field strength taken from Ref. [26]
Where β represents the velocity of the accelerating shock wave or the efficiency of the accelerator. Fig. 7 show the what is known as a Hillas diagram. Marked in the diagram one sees the necessary conditions in terms of magnetic field and size of the astrophysical objects to be able to generate corresponding max energy by unipolar induction. This shows a few possible sources that is able to reach these extreme energies.
2.3.3 Potential acceleration sources
The first study to correlate arrival direction with potential accelerator source was by (Stanev et al, 1995) Ref. [39]. Here they used 143 events with energy more then 2∗1019detected by Haverah Park array, Vulcano Ranch and preliminary data from AGASA (Akeno Giant Air Shower Array). The work concludes that the UHECR has non-uniform arrival direction and that the arrival directions shows some correlation with the Super Galactic Plane (SGP) which is the plane of weight of almost all extragalactic objects within redshifts below 0.04 Ref. [16]. Where redshift is caused by the Doppler effect and indicating how fast objects moves away from the observer. Red shift is calculate in none relativistic terms by z ≈vc.
When more data from AGASA begin to dominate the 1990s the correlation with the SGP started to decrease. Claims where made of a large scale isotropy and small scale anisotropy. The anisotropy where defined by the fact that three pairs and a triple of events coming within 2.5◦ of each other were found Ref. [40]. Where 47 of the events had energy over 4 ∗ 1019 eV. The
probability for this to happen in a isotropic distribution is less then 1 %.
In 2007 the collaboration working with the Pierre Auger telescope (see section 3.3.2). Published a study Ref. [12] using the data Auger telescope had collected over 3.7 years and energies above 6 ∗ 1019eV. The data collected showed a significant correlation with the 12th edition of the V´ eron-Cetty and V´eron (VCV) catalog of a nearby Active Galaxy Nuclei (AGN) lying with in 75 M pc. Same analysis was done in 2008 Ref. [13] with 27 high energy events. Twenty of these events were within 3.1◦ angular distance of the AGN form the VCV catalog only 7.4 was expected for a
Figure 8: Take from Ref. [30]. Correlation of the arrival directions of UHECR with AGN from the VCV catalog. Shaded/Colored part of the sky is not visible by Auger. The gray squares are AGN within z less then 0.018. The Auger data is shown as circles and the 21 are half filled. The 13 black dots are form HiRes events. The thin lines show the six regions of the sky to which Auger has equal exposure. The thick pink line is the super-galactic plane.
This strong correlation was surprising because of several reasons. First of all the VCV optical catalog includes many low power objects that are not likely to accelerate particles to such high energies. Secondly, the 0.018 redshift does not correspond to the GZK horizon for energies of 57 ∗ 1018eV .
Analysis was repeated with HiRes experiment in 2008 Ref. [1] as close to the Auger as possible. Only two of 13 events with similar energy correlated with the same AGNs so the conclusion was the opposite. HiRes and Auger has not the exact same coverage of the sky. This result is still controversial since HiRes sees one half of the Auger field of view.
Auger collaboration also published in 2010 Ref. [15] an update to the experiment in 2007. Compared to 27 events back then they now had 69 events above 55 ∗ 1018eV . The 69 events
published are seen in Fig. 8 together with HiRes 13 events of the area. With analysis done on the 69 events lowered the correlation to 42%, compared to 72% previously in 2007. The event reconstructing is constantly improving so changes may occur the number of events that are above or below 55 ∗ 1018.
While no source can be identified yet or if the UHECR are isotropically distributed or not, and where new conclusions can be drawn from each new analysis done with a bigger sets of events. It is clear that a increase in statistics is necessary to better answer the question of where these UHECR comes from.
2.4
Composition
The composition of cosmic rays can be measured directly for energies up to ≈ 1014eV by space
based experiments and is shown in Fig. 9. There is a overabundance of the cosmic rays by several orders of magnitude of secondary elements such as lithium, beryllium and boron relative to the general abundance in solar system. This can be explained by the phenomena of “primary” versus “secondary” cosmic rays. Primary cosmic rays are those particles which are accelerated by some astrophysical source, whereas secondary cosmic rays are created by the spallation of primary cosmic rays. Spallation is the emission of a small number of nucleons as the result of a heavier nucleus being hit by a high-energy particle. This process is a natural result of both low energy interactions with the Galactic medium, and GZK-type energy loss mechanisms like photo-disintegration of nuclei. The same effects of overabundance occurs for the secondary nuclei just before iron. Ref. [8].
For higher energies then 1014 eV, composition is best derived from the development of EAS initiated when the primary cosmic ray interacts with the atmosphere. The currently best indication of the composition of the primary particle at energies above ≈ 1014 eV is to study the how far the
depth in the atmosphere of the shower maximum, Xmax, given in g/cm2. On average the shower
Figure 9: Cosmic ray composition abundance as a function of nuclear charge and the abundance of particals in the Solar system (out side the heliosphere), for E < 1014, take from Ref. [28].
mass of the primary cosmic ray which generated the shower, Ref. [30]. So on average protons travels deeper in the atmosphere then a iron nucleus with the same energy E, hXp
maxi > hXmaxF e i. Another
useful measure of composition is the particle content of the shower such as the number of muons: proton shower have fewer muons than showers caused by heavier nuclei with the same energy. In practice, observed shower maximum and particle numbers are compared with Monte Carlo air showers simulation which involve an extrapolation to higher energies of hadronic interaction known at energies of laboratory accelerators (¡ TeV).
Observation of shower properties in cosmic ray with energies from the knee to just below the ankle in the cosmic ray spectrum, Fig. 1. Indicates a general trend from light primaries dominating at the knee to heavier primaries dominating up to ≈ 1017, Ref. [9]. Just before the ankle, the trend
seems to reverse back toward a lighter composition, being consistent with light primaries at 1018eV
as shown in Fig. 10. Where Fig. 10 shows Pierre Auger data on hXmaxi and RM S(Xmax) for 3754
events at energies 1018 together with a range covered by simulations for protons and iron nuclie
Figure 10: The shower maximum in the atmosphere hXmaxi and RM S(Xmax) as function of the
cosmic ray primary energy. Measured by Pierre Auger Ref. [35]. Monte Carlo simulations from different hadronic interaction models are displayed for primary protons (blue) and primary iron nuclei (red).
3
Observation of UHECR
The flux of cosmic rays above energies 1015eV is so low that observing it directly becomes
unfeasi-ble. This resorts to methods of observing the events indirectly, like observations of the EAS. In this chapter a overview of the different detection methods followed by sites that uses these detection method in search of UHECR.
3.1
Surface Arrays
Scintillation arrays detectors is an classical way of detecting EAS. It is made of scintillates which is a material that emits photons when energy is deposited in it when hit by high energy photons. These photons leads to a photon multiplier which generates a electron cascade that is measured by the anode. The number of photons created in the scintillation yield and the energy deposited and in turn the pulse height measured by the anode is proportional to the number of photons generated by the scintillation.
It is also possible to measure the Cherenkov light generated by the UHECR. The detector used for this is similar to that of the scintillation detectors and are called just Cherenkov detectors. These are made up of a volume of water which is viewed by one or more photon multipliers tubes. Particles with high enough energies emit Cherenkov photons as they pass the water. These photons are reflected by the walls of the water tank and is detected by one or more photon multiplier.
3.2
Air Fluorescence
This method of determining the energy of the UHECR involves measuring the flux of photons created by excited nitrogen molecules in the atmosphere. The photon flux is measured in the UV range of 300 nm to 430 nm. This method of measuring the the photon flux energy allows for detection of EAS with energies higher than u 1017 eV by so called the air fluorescence method.
the other method since it is the detection method the JEM-EUSO experiment uses.
The number of emitted fluorescence photons is proportional to the energy deposited in the at-mosphere. They are proportional to each other according to a parameter known as the fluorescence yield which in turn depends on the pressure, temperature and composition of the atmosphere.
Fig. 11 shows the schematics of a EAS observation using air fluorescence detection method. The directly observed fluorescence light (e.i none scattered) emitted at a certain slant depth Xi
is measured by the detector at time ti. Given the fluorescence yield Y f
i at this point of the
atmosphere, the number of photons produced can be calculated according too: Nγf(Xi) = Y
f
i wi∆Xi (14)
Where ∆Xi is the slant depth interval and widenotes the energy deposited per unit depth and is
defined as: wi= 1 ∆Xi Z 2π 0 dϕ Z ∞ 0 rdr Z ∆zi dzdEdep dV (15)
Where the dEdep
dV is the energy deposit per unit volume (ϕ, R, z) are the cylindrical coordinates.
The distance interval ∆zi along the shower axis is given by the slant depth interval ∆Xi. The
fluorescence yield Yif is the number of photons expected per unit deposited energy for the atmo-spheric pressure and temperature at slant depth Xi. Since the fluorescence photons in Eq. 14 is
distributed over the area of a sphere 4πr2
i, where riis the distance to the detector. Only a fraction
Ti of these photons reach the detector due to atmospheric attenuation. If the fluorescence detector
has some area A and efficiency the measured photon flux at the detector (from the fluorescence) will be: yif = Yifwi∆Xi TiA 4πr2 i (16) The direct and scatter Cherenkov contribution to the photon flux can be determined in the same way and the total photon flux that reaches the detector is:
yi= yif+ y Cd i + y
Cs
i (17)
With photon flux at the detector profile reconstruction can be done to estimate the energy deposit wi. Once the energy profile has been determined it can be integrated for the total energy
deposited in the atmosphere.
Knowledge of the complete energy profile is required for the calculation of the initial particle energy. Often only parts of the EAS can be captured due to limited field of view and in turn only parts of the energy profile is measured. In order to estimate the energy one has to resort to an appropriate function for the extrapolation to unobserved parts is needed. A possible choice is then the Gaisser-Hillas function, which will not be further explored here. More information about Gaisser-Hillas and details of the calculation for estimation wi can be read in M. Unger et. al.
Ref. [44].
3.3
Detection sites
Here two of the biggest sites for UHECR will be presented. Each of them covering different part of the hemisphere and both contribute to a great extent in the search of UHECR.
3.3.1 Telescope array
Figure 11: Illustration taken from. Ref. [44] and depicts the isotropic light emission (solid circles), Cherenkov beam along the shower axis (dashed arcs) and the direct (dashed lines) and the scattered (dotted lines) Cherenkov light contributions. Where the fist figure to the right shows the direct fluorescence light and direct Cherenkov light hit the detector and the right one shows the how the direct fluorescence light and scattered Cherenkov reach the detector.
The telescope array hybrid detection was fully operational in March 2008 and have since then collected data for identifying potential sources in the north hemisphere for UHECR, contributed to the cosmic ray spectrum and identified mass composition of the initiate UHECR Ref. [19].
Plans have been made to expand the area to approximately 3000 km2 with surface detectors
with 2.08-km apart and two additional telescope batteries. This is about increasing the area by four and the project is called is called TA x4. Reason for this expansion is to increase accuracy for the direction of incoming particles and better determination of mass composition.
(a) Image showing the surface detector, Ref. [41].(b) Black Rock Mesa telescope with doors open. Ref. [46]
Figure 12: Surface arrays and telescope of Telescope Array.
3.3.2 Pierre Auger Observatory
The Pierre Auger Observatory is the world largest cosmic ray observatory, located in in western Mendoza Province, Argentina and can be observes the south hemisphere, in contrast to Telescope Array. It started collecting data 2004.
three photomultiplier tubes are installed symmetrically at a distance of 1.2 m from the center of the tank lid.
(a) Shows the gemoentry of the area. Ref. [2]
(b) Image showing the schematic the Cherenkov surface
detec-tor. Ref. [2] (c) A schematic view of the fluorescence
detector in Ref. [14].
4
JEM-EUSO Experiment
JEM-EUSO (Japanese Experiment Module - Extreme Universe Space Observatory) is an collabo-ration project for the research of Ultra high energy cosmic rays. The goal is to build a in orbit, wide field view, near-UV capturing telescope at orbit altitude at 400 km. The instrument will face Earth and capturing the fluorescence light produced by extensive air showers (EAS) events during night. Reason for a in orbit based instrument is to increase the observational area and in turn increase the statistical data.
4.1
Brief history
The idea of space-based observations of UHECR was first proposed by John Linsley in the early 1980s to NASA Ref. [7]. The Satellite Observatory of Cosmic Ray Showers, SOCRAS. The idea was not considered feasible with the imaging and space technology of the 80s. The idea was later taken up by Yoshiyuki Takahashi, who developed the concept of MASS, the Maximum-energy Ayger (Air)- Shower Satelite. The breakthrough in imaging technology was the use of lightweight unphased segmented double Fresnel lens optics. Which decreased the size of the telescope. The MASS change name to Airwatch and was later evolved in Europe into EUSO. ESA selected the mission and made changes to have the telescope attached to the Columbus module on the ISS (international space station) and a studie of feasibility of EUSO started in 2001 and was success-fully compleated in 2004. EUSO was technology wise ready to be procedure, but ESA did not continue the program manly because of financial constrains in ESA and Europe, and because the programmatic uncertainties of the ISS related to the Columbia accident.
In 2006 the Japanese and US teams, under leadership of Yoshiyuki Takahashi, redefined the mission as an observatory attached to KIBO the Japanese Experiment module (JEM) of the ISS. They renamed the mission JEM-EUSO and started a new feasibility study and was targeting launch in 2013. In 2010 the EUSO mission was also included in a ESA program. The feasibility study of JEM-EUSO mission profile, led by JAXA made significant improvement to the JEM-EUSO mission profile, targeting eventually a launch in 2016. From those study came the Atmospheric Monitoring system consisting of a LIDAR and a Infrared Camera. More details about the history and JEM-EUSO can be found in the introduction paper Ref. [4].
4.2
Observation from space
Figure 14: Illustrating the observation technique used observing EAS from space.
The observed area is 2 ∗ 105km2in nadir mode and can reach 7 ∗ 105km2when the telescope is
tilted, Fig. 16. Which would make this one order of magnitude larger then the Pierre Auger Obser-vatory and a leap in annual exposure, Fig. 15. Another advantage of the space based telescope is a uniform full sky exposure in contrast with its ground counter parts which observe either north or south hemisphere. This is an important aspect to minimize systematics in the statistical analysis studies of arrival directions Ref. [43]. In addition observing from space brings the possibility to observe in cloudy conditions since, in most cases, the shower occurs above the could top. Ref. [3] The expected annual exposure of JEM-EUSO in the nadir mode around 1020 eV is equivalent to
Figure 15: Shows the expected anual exposure for JEM-EUSO compared to other instruments.
Figure 16: A footprint of the observational area from nadir is the blue area and white and orange is when the telescope is tilted 20 and 30 degrees, respectively Ref. [4].
The optics consist of three Fresnel lenses with diameters of 2.65 m. The combination of these three lenses gives a full angle FoV of 60◦ and a angular resolution of 0.07◦. This resolution corresponds to 550 m on the ground at an altitude of 400 km and facing Nadir.
Figure 17: The top one is a traditional lens while the bottom one is a Fresnel lens. se how the lens has been cut ut in section but kept it continuity.
The focal surface (FS) is the surface that captures the photons. The focal surface is built up from 64 Multi-anode Photomultiplier Tubes (MAPMTs). Four of the MAPMTs are grouped together to form a Elementary Cell (EC). Where in turn the EC are grouped together three by three to form one Photon Detection Module(PDM). Then 137 of these PDM makes up the focal surface of JEM-EUSO, see Fig. 18. This surface has diameter of 2.3 m and has 0.3 Mpixels.
Figure 18: Shows focal surface and how it is built up.
range. The rate of photons from an EAS on the focal surface is extremely low and so the most beneficial read-out strategy is to use photon counting. This means counting the individual anode pulses coming from the collection and multiplication of single photoelectrons.
4.3
Sience Objectives
JEM-EUSO hopes to initiate new astronomy in the Extreme Energy Cosmic Ray (EECR) field. The missions main objectives can be summeized:
• Possibly identify the particles and accelerating sources using the arrival direction, and study acceleration mechanisms with the observed events.
• Clarify the trans-GZK intensity profile of distant sources and make a systematic survey of nearby sources.
• Separate gamma rays and neutrinos form nucleons and nuclei which allows testing of the super-heavy particals (SHP) models that assume long-lived particles produced on the early era of the universe.
While the first objective is pretty clear, if one knows the arrival direction of the UHECR and one can trace back the particles to its origin direction in space, while taken in account the cosmic magnetic fields.
4.4
Pathfinders
In the development of the JEM-EUSO a series of ”pathfinders” (which are experiments to test the observational technique and to validate the specific technologies). Include in these pathfinder experiment are the EUSO-Balloon, developed by French laboratory involved with the JEM-EUSO and lead by balloon division of CNES, French Space Angency. EUSO-TA a ground based telescope, data from EUSO-TA experiment is used in this thesis to explore the capabilities for analysing and triggering options. EUSO-mini which also is a pathfinder experiment set to test the technology in in-sute from the ISS.
4.4.1 EUSO-Balloon
Was the first pathfinder to be realized and launched in August 2014 in a collaboration with the French Space Agency CNES. It was a balloon-borne experiment carrying a telescope which is in principle the same through out all pathfinder experiments. The telescope is carrying two Fresnel lenses 1 x 1 meter a photon detection module with 2304 pixels which is very much the same as in EUSO-TA in the next section.
The balloon made a 5 hours flight before descending back to the ground Since it is still very unlikely that a an actual EAS for a experiment with 5 hours flight time. The solution was a laser to simulate the florescence that was set on a helicopter accompanying the balloon through out the flight. The experiment was considered nominal and was the first to use the principle observation method of looking after EAS from the edge of space Ref. [37].
4.4.2 EUSO-TA
Figure 19: Showing the EUSO-ballons structure, the gondol and launch.
the observatory. Captured UHECR by EUSO-TA can not on the ground calculate the energy of the UHECR due to it is designe for space and has a time resolution made for it. Telescope Array gives the energies of the incoming events.
Figure 20: Top Left: The focal surface of the EUSO-TA each destingushible cube is a MAPMT with 64 channels.Top Right. A CAD image showing the structure of the EUSO-TA telescope where there are two franel lenses and the PDM at the back.Bottom Left: the relization of the EUSO-TA telescope.Bottom Right: The EUSO-TA is placed infront of the Telescope Array UHECR observatory in Utah.
4.4.3 Mini-EUSO
The Mini-EUSO is similar to EUSO-TA in many aspects and is under development. It is to be the first test of space observed EAS. It is to be installed in the international space station. Differences in design from EUSO-TA is the smaller and circular Fresnel lenses and the addition of two cameras placed at the rim of the EUSO-TA, se Fig. 21. The two additional cameras, one being sensitive to the infra-red spectrum and the other in the visible spectrum. Data from the cameras will help in the measurements of the emission of the Earth and the study of transient phenomena.
5
EUSO-TA data analysis
This section will explore the data captured by the EUSO-TA testing campaign in 2015. Much of the analysis was done using ROOT Ref. [24] software. ROOT is developed by CERN for analyses with big data sets. Since ROOT data files are optimized for taking small memory space and easy to open and read capability. It also has a extensive library of functions for plotting, viewing, fitting, regression and more. For these reasons it was chosen to be used when making analysis. ROOT is programed and initially only used in C++, later the developer made Python usable as well which is the programing language used in this master thesis. Python was chosen because of its high level language which makes it easier to write and read code.
Parameters taken forth in the following sections from the EUSO-TA data is going to be used as to build a simulation of the night sky seen by the focal surface.
5.1
Instrument description
Quick summery of the EUSO-TA instrument. See fig20 • 36 Multi Anode Photon Multiplier Tubes (MAPMT)
• Each MAPMT has 64 channels making a total of 2304 pixels/channels on the focal surface. • FOV 11◦x 11◦
• GTU 2.5 µs
5.2
Background
The background of EUSO-TA Fig. 22a is a combination of the thermal noise and the constant weak luminosity of the night sky. The noise is fitted to a Poisson distribution Eq. 19 to get the mean(µ). The Poisson distribution is the limit of the Binomial distribution:
P (x) = N ! x!(N − x)!p
x(1 − P )N −x (18)
Which is used in independent trials of a process in which the outcome of a single trials is binary, for example coin flips. Where N is the number of trials and p is probability for the event. If the number of trials (N ) goes to infinity and the probability(p) of the event approaches zero, in such a way that the mean µ = N p remains finite. Which is essentially describes the process for which the single trial probability of success is very small but in which the number of trials is so large that there is nevertheless a reasonable rate of events. Example of such process are radio active decay.
An important feature of the Poisson distribution is that in only depends on the variable µ. It can be shown that the variance equals the mean (σ2= µ). The standard deviation is then σ =√µ Ref. [29].
P (x) = µ
xe−µ
x! (19)
(a) The Focal surface of EUSO-TA captured data of a clear sky.
(b) A histogram filled with the pixels from the up-per half of the FS shown in (a), fitted with Poisson distribution.
Figure 22: Left: Shows the data captured by the focal surface, the white areas to the bottom right in the figure are non operational MAPMT. Right: Shows histogram over the photon counts in the right image upper half. From the fit the mean µ can be found.
Creating a histogram with pixel value for each pixel in the upper half of the focal surface and fit that to a Poisson distribution, Fig. 22b. This can be done for each captured frame in succession to check the mean (µ) variation with time.
The pixel values are filled and fitted in histogram to get the µ in Poisson distribution for each GTU, 128 frames/GTU in succession are fitted in this fashion to generate Fig. 22b which show the mean over 128 GTUs. Fig.22b shows a constant mean of the background over 128 GTU.
To see if it was any overall change over time the entire file is read Fig. 23b, but here each point is the average of 3200 frames. Also Fig. 23b reveals a growing trend of light over all in the night sky, that could be explained by the light sources effecting the whole sky like the sun or moon.
(a) Mean of 128 GTUs (b) Mean of 19 minutes with captured data.
(a) One second of integrated GTUs. (b) One min of integrated GTUs.
Figure 26: Histogram of Persei(Algol) and the fit of Eq. 20 result of the fit can be seen in Tab. 1. Right: One second of data when this was captured corresponded to 128 GTUs. The Gaussian distribution makes a good fit to the shape. Left: One min of data corresponds to 7680 GTUs. But here one can see that the star has moved a little bit which makes the fit a bit distorted.
5.3
Stars
Fig.24 shows the data capture during passing of an stars. The strongest one is Persei (Algol) which is bright star in the Perseus constellation Ref. [38]. To make some of the weaker star more apparent one can integrate over several frames to make stars more apparent as shown in Fig. 25, where 128 GTU are integrated. Since the statistical background will fluctuate while the stars light just add linearly, which result in an higher signal to noise ratio.
Figure 24: Star Algol apprenses on one frame. Figure 25: Integrating 128 frames.
The stars are fitted to the two dimensional normal distribution.
f (x, y) = 1 2πσXσY exp(−1 2[ (x − µX)2 σ2 X +(y − µY) 2 σ2 Y ]) (20)
Fig.26a shows a fit of the Algol star integrated one second which is 128 GTU in this case. These fits standard deviation values are equal to the point spread of EUSO-TA. In in Fig. 26b the same star is fitted during one minute of added frames which seams a bit to long since the star have moved a bit which puts a error in the fit. Table 1 shows the parameters from the fit.
(a) One second of integrated GTUs. (b) One minute of integrated GTUs.
Figure 27: Fit on a less bright star marked with the star nr. 13879 in Fig.24 and 25
height Standard deviation x Standard deviation y Algol one sec 2039.3 ± 38.4 0.93 ± 0.0016 0.97 ± 0.0168 Algol one min 118 942 ± 285.7 0.92 ± 0.002 0.97 ± 0.002 Small star one sec 483.1 ± 21.5 0.96 ± 0.07 1.5 ± 0.1 Small star one min 27 527 ± 154.1 0.86 ± 0.009 1.5 ± 0.01
Table 1: The fitted Gaussian parameters from the stars. Not shown are the mean of x and y since it is arbitrary where the stars appear.
5.4
Laser
Test with laser was also performed. The potable laser output energy was 85 mJ and placed 100 km from the detector. The laser fired pulses that travels upwards on the focal surface see fig 28a. It takes 7 GTU for the laser to travel across the focal surface and integrating over that time one can capture the whole laser, Fig.28b. The laser test shows similarity to how the EAS event will be appear seen from space. The scattering of the laser as it travels through the atmosphere appears similar to that of fluorescent light from UHECR.
(a) Single GTU laser test. (b) Seven GTU integrated laser events.
Figure 28: Captured data from a laser with 85 mJ power placed 100 km away from the detector. Right: One GTU of the captured laser as it travels upwards through the sky. Left: Seven frames of the laser as it ravels upwards through the sky. In addition the avrage photon count has been subtracted to make the laser clearer. This resemble much of how the UHECR appears on the focal surface.
In Fig. 29b the histogram seen in Fig. 28b has been summed along the y-axis and averaged. A one-dimensional Gaussian fit performed on the summed laser in Fig. 29b.
(a) Laser test captured single GTU (b) Seven laser GTUs summed.
Figure 29: Gaussian fits performed on the test laser. Right: Shows the Gaussian fit of single laser captured in Fig. 28a. Left: Shows the summed and averaged of Fig. 28b along the y-axis and a Gaussian fit performed on it. Fit values is shown in table 2
height Standard diveation x Standard diveation y Single frame fig(29a) 10.4 ± 2.0 1.1 ± 0.5 1.7 ± 0.6.2 Integrated frame 19.7 ± 1.9 4.5 ± 4.2 NA
Table 2: The Gaussian fit on the laser result.
The laser pulses was fired repeatedly in succession. An analysis the average features of 160 laser pulses Fig. (30a). A one dimensional Gaussian fit was performed to every y-row in the histogram. From the fitted parameter a profile of the height-, standard divination (in x)- and photon count was performed as in Fig.30. In Fig. 30b there one can se how less photon reach the detector since more atmosphere gets between the laser and the detector. This is also appearer in the Fig. 30c where the standard divination grows higher up in the atmosphere which is also due to the atmospheric scattering caused by traveling through more atmosphere to reach the detector.
(a) Integrated 160 laser pulses.
(b) Profile of the lasers top photon count.
(c) Profile of the standard deviation (d) Profile of the total number of photons
Figure 30: Shows the histogram and profile of fitted Gaussian parameters of 160 integrated laser pulses. Top Left: Histogram of the 160 laser pulses GTUs integrated and averaged. Top Right: Profile of the fitted height value of one dimensional Gaussian parameter. This corresponds to the highest number of photon collected on each row. Bottom Left: Profile of the Gaussian standard deviation of the laser. It corresponds to scattering of the laser light in the atmosphere. Bottom Right: Profile showing the number of photons reaching the detector calculated according to Eq. 21.
