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A feasibility study for finding Cosmic-Ray Anisotropy with
the Antares Detector
Eline Wieldraaijer
July 19, 2012
Abstract
An analysis method for making a skymap of cosmic rays with the Antares detector ispresented. The method is used on all 12-line data which is of sufficient quality.
The final analysis is based on 1.280·107 events and variations at the 1% are found. Thiseffect is larger than the cosmic ray anisotropy found by earlier experiments. And thereforeit is most likely that this experiment has not yet reached the required level of accuracy.Suggestions for modification of the method in order to improve the accuracy are given.
1
Populaire Samenvatting
Op grond van een aantal theoretische argumenten kan worden verwacht dat op aarde uit allerichtingen evenveel kosmische straling komt. Uit verschillende experimenten is gebleken dat ditniet het geval is, twee recente voorbeelden hiervan zijn de experimenten gedaan met de IceCubedetector en de Milagro detector. Beide detectoren hebben kaarten van de hemel gemaakt en uithun analyses blijkt een onregelmatigheid van ongeveer 0.1%. Een sluitende theoretische verklaringhiervoor is er niet. Dit project is erop gericht dit effect te vinden met de ANTARES detector.
De ANTARES detector is een zogenaamde water cherkenov detector in de Middellandse zee.Wanneer geladen deeltjes zich door water bewegen met een snelheid die sneller is dan de lokalesnelheid van het licht in water remt het deeltje af, hier komt blauw licht bij vrij. ANTARESbestaat uit 12 lijnen met aan iedere lijn 60 modules die in staat zijn dit licht te detecteren. Uithet signaal van deze modules worden sporen van deeltjes gereconstrueerd.
De analyse bestaat uit het kijken naar de richting van de sporen in de detector, maar hieropmoeten een aantal correcties en selecties worden uitgevoerd. Alleen data van voldoende kwaliteitdie in een kegel van 30 van boven maar niet recht van boven komt wordt gebruikt. Door de bouwvan de detector is de detector zelf niet in alle richtingen even gevoelig, hiervoor moet wordengecorrigeerd. De skymap wordt gemaakt in het equatoriale coordinatensysteem, dit systeem zitvast aan de sterrenhemel en niet aan de aarde. Niet ieder gedeelte in dit systeem is even vaakzichtbaar geweest voor de detector, hiervoor wordt ook een correctie uitgevoerd.
Het resultaat van de analyse is een effect in de orde van 1%, dit is veel groter dan het effectwaar naar gezocht is, er is dus een probleem met de analyse, de oorzaak hiervan is niet duidelijk.Het kan komen doordat de correcties voor de twee bovengenoemde effecten niet nauwkeurig genoegzijn of het effect niet goed genoeg begrepen is. Om dit op te lossen is er een betere analyse nodig,die in meer detail naar de correctieeffecten en de selectie van de data kijkt. Ook meer data omstrenger te kunnen selecteren zou kunnen helpen.
2
Contents
1 Introduction 4
2 Cosmic-Ray Anisotropy 42.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Compton-Getting effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.3 Recent Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 Antares 53.1 Cherkenov light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4 Method 74.1 Data selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4.1.1 Run selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.1.2 Event selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4.2 Azimuth correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84.3 Time normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104.4 Bin size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104.5 Final steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
5 Results 115.1 Azimuth histogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115.2 Time histogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115.3 Plotted events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115.4 Final results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135.5 Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
6 Discussion 15
7 Conclusion 16
List of Figures
1 The skymap made by IceCube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 The Milagro declination bands presented in such a way that it resembles a skymap 63 The layout of the finished 12 line Antares Detector, the distances between the lines
are about 70 meter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 The azimuth-zenith system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 The normalization histogram for the local system in the B, b coordinate system . . 126 The time histogram for all runs, note that the bin content has not physical meaning,
only the proportions do . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 The histogram with raw normalized events . . . . . . . . . . . . . . . . . . . . . . . 138 The finals results for the original . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 The final results for the 90 · 180 rebin . . . . . . . . . . . . . . . . . . . . . . . . . 1410 The final results for the 45 · 90 rebin . . . . . . . . . . . . . . . . . . . . . . . . . . 1411 The final results for the 45 · 45 rebin . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3
1 Introduction
Due to the magnetic field of the galaxy one would expect that the direction of cosmic rays israndomized so their arrival directions are isotropic. Around 1970 it was observed [5] that thereis a small derivation from this isotropy for which there is currently no good explanation. In thelast few years detectors like IceCube [2] and Milagro [4] have observed this and analyzed it morequantitatively.
The purpose of this experiment is to determine if it is possible to observe this effect withthe Antares Detector. In this report I will first talk about the theory of this effect, and give adescription of the Antares detector. Then I will describe in detail my analysis method, and presentthe results. In the end I will discus the implications and draw a conclusion.
2 Cosmic-Ray Anisotropy
2.1 History
An early first conclusive measurement of cosmic-ray anisotropy was published in 1975. Gombosiet all [5] observed an anisotropy in the sidereal frame of showers produced by cosmic-ray primarieswith an energy of about 6 · 1013 eV. Their experiment consisted of four sets of Geiger Mullercounters on the corners of a grid of 8x8 meters located on a mountain in Bulgaria. The Geiger-Muller counters were operated in coincidence mode, so an event was only recorded if all detectorsdetected it. The number of events was analyzed in 3 hour bins in sidereal time by fitting it to afunction containing linear parameters and multiple Fourier series. An anisotropy in the siderealframe of 10−3 [5] was observed.
2.2 Compton-Getting effect
There is not a generally accepted theoretical explanation for this effect, in 1935 Compton andGetting published a paper [3] in witch they explain something that is now known as the Compton-Getting effect. This is sort a of doppler effect for cosmic rays, when the earth moves througha background of cosmic rays in a certain direction, then more cosmic rays can be seen in thatdirection. They predict a sinusoidal variation during the sidereal day with a period of exactly oneday and present data that shows this variation. The Gombosi result however does not agree withthis data.
2.3 Recent Results
Modern detectors like IceCube and Milagro have made skymaps.IceCube is a detector on the south pole, at the time of the experiment it consisted of 22 strings
with 60 optical sensors each. Their analysis is based on 3.8·109 events. It is done by plotting theevents in a skymap, because the detector is at the south pole no corrections for the rotation ofthe earth have to be made, the same part of the sky is always visible then they fitted a first andsecond order harmonic function to the one dimensional projection of the skymap. An anisotropyof (6.4± 0.2) · 10−4. [2] was found. The skymap can be seen in Figure 1.
Milagro is a detector based on man made tanks rather than natural bodies of water or ice.They have done a more complex analysis with a method they call forward-backward asymmetry.They defined a function which expresses the difference between two bins that are opposite to eachother. This method should be more sensitive than just plotting events because it eliminates factorsthat are dependent on the circumstances at that particular moment. Then harmonic fits on thisfunction are done for different declinations. They do not claim to make a skymap, but when theresults of the different declination bands are plotted in the correct order something that looks likea skymap is produced, which can be seen in Figure 2. Because of the difference in the methodand presenting the result the milagro anisotropy can not be easily compared to other experiments,the maximum amplitude of the fit of one of the declination bands is 3 · 10−3, their analysis is
4
Figure 1: The skymap made by IceCube
based on 7 years of data with a total of 9.59 · 1010 events. In this paper the compatibility withthe Compton-getting effect is also discussed. Based on these results it is not possible to rule outthe effect entirely but it is certain that it is not the only effect present. Another interesting noteis that the effect has been getting stronger at the end of the 7 year period, a possibility is that ithas something to do with the solar cycle. [4]
3 Antares
Antares is a water Cherenkov detector in the Mediterranean sea located at a depth of about 2400meters and about 40 km south of Toulon. It consists of 12 strings which have 25 storeys 14.5 apartwith 3 optical modules each. The lines are arranged in the pattern that can be seen in Figure 3,they are between 60 m and 70 m apart. The modules point downward by 45 to be more sensitivefor events coming from below.
The main use of the detector is to observe (muon)neutrinos’s from cosmic origin trough theEarth, as the earth will stop muons from other sources, there is a very small possibility that thesereact with matter in the earth to form muons, the Cherkenkov light these muons produce can thenbe observed by the photomultiplier tubes in the optical modules.
An optical module consists of a glass sphere with a diameter of 43 cm, with a photomultipliertube with a diameter of 25 cm and circuit board to provide power and amplify and digitalize theinput inside, it also contains a blue led for testing purposes. The photomultiplier tube is shieldedfrom the earths magnetic field by a shield made of mu-metal, a nickel-iron alloy with very highmagnetic permeability [1].
The signal coming from the optical modules is then transported to a Local Control module, thatcontains all the electronics to control the power, and to perform data acquisition and triggering.Every story contains one. The data from the lines is then though cables that run over the seabedtransported to the Junction Box, from there a long cable transports the data to the shore whereit is stored for reconstruction and analysis.
3.1 Cherkenov light
When a charged particle enters a dielectric medium at a speed faster than the speed of light inthe dielectric medium there is an effect called Cherenkov radiation.
The charged particle polarizes the atoms of the medium it travels trough, when the particlehas passed the displaced atoms fall back to there original state emitting light. At normal speedsthis light is comes from all directions and interferes destructively.
5
Figure 2: The Milagro declination bands presented in such a way that it resembles a skymap
Figure 3: The layout of the finished 12 line Antares Detector, the distances between the lines arebetween 60 and 70 meter
6
When the particle moves faster than the speed of the light in the medium the photons emittedfrom the disturbance can not reach each other to interfere. A wave front that can be comparedto a sonic boom ocures. This is called Cherenkov radiation, cherkenkov detectors work by usingthis as the signal.
4 Method
To find an anisotropy the origin of the tracks is plotted in the equatorial coordinate system, to dothis in a proper way a few things need to be taken in to account.
• Not all the reconstructed data coming from the detector are muons originating from a cosmic-ray induced airshower. To minimize the number of fake events the data needs to meet certainquality criteria. This is done at two levels, first the runs that are suitable are selected andthen the events within those runs that meet the selection criteria are selected.
• Because angular acceptance of the detector is not flat, a normalization in the local systemis needed, this is done using data.
• Only a part of equatorial system is visible, and not all parts have been observed the sameamount of time. A correction for this effect is needed.
4.1 Data selection
4.1.1 Run selection
Because Antares was built up in phases and has had some cable problems in the past not all runsuses all 12 lines, for this analysis only data with 12 lines is used. The reconstructed runs have aproperty called QualityBasic that can be 0 to 4, this analysis only uses runs with quality basic 3and 4, this means that the run meats the following criteria.
• effective duration Teff > 1000 s
• no double frames
• no synchronization problems
• reasonable muon rate: 0.01 Hz ≤ muon rate ≤ 100 Hz
• apparent duration ≈ effective duration: 0 ≤ Tapp − Teff ≤ 450 s
• at least 80% of the optical modules expected to be working at the time of the run are working
• baseline < 120 kHz
• burst fraction < 0.4
Tapp is defined as the difference between the start time and the end time, Teff is the real timethat has been used to take data, i.e. the time between the beginning of the first event and theend of the last event. The baseline is the continuous average count rate and the burst fractionindicates how much time is spent above baseline rate plus 20%. It parameterizes how many sortbursts of light are registered in the detector.
All the runs that will be used are put in a list, this list it is split up in a 20% and a 80% part.The 20% part is used to test the analysis and make adjustments if needed, after this is done theanalysis is applied to all data. Because the runs are in chronological order this is done by puttingone in five in order in the 20% list, not the first 20%, so both the 20% and the 80% list containruns from the entire period.
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4.1.2 Event selection
Within the runs are events, which contain reconstructed tracks, only the muon with the highestenergy in every event is used.
Some cuts are applied on the properties of those tracks. λ is a parameter that describes howwell the track been reconstructed, the higher this λ is the more likely it is that the particle is asingle muon, for this analysis λ > −6 is required, which is a track of good quality, but allows forthe track also to be a very close set of tracks.
When only 1 line is used in the reconstruction the azimuth is effectively random, because thedetector does not know where it came from. To prevent these events polluting the data it isrequired that at least 3 lines are used in the reconstruction.
Because the acceptance of the detector for cosmic events gets lower closer to the horizon due tothe amount of water overburden, which causes an effective lager energy cuts on the cosmic events,only events that have Z < 22.5 are used, where Z is the zenith angle. Initially this was set atat 30 but for reasons explained later it has been reduced to 22.5. Events coming from directlyabove are also excluded for reasons explained later, this is done by requiring Z > 2.5 · 10−3 whereZ is in radians.
In summary the cuts on the reconstructed tracks are:
• Number of used lines ≥ 3
• λ > −6
• Z < 22.5
• Z > 2.5 · 10−3
4.2 Azimuth correction
The acceptance of the detector varies with zenith angle and azimuth due to geometrical effectsoriginating from the design of the detector. When an event is more horizontal it is less likely thatthe detector will detect it. This is because it has fewer hits om the track so reconstruction is lessefficient. In the azimuthal direction the detector is not symmetric because of the configuration ofthe lines, which can be seen in Figure 3, when the horizontal component of a particle goes betweenthe lines the probability of detection is lower than when it gets crosses them in a more randomway. Because this effect is not easy to calculate the data is used to correct for it. This does notbias the data because the correction is done in the local coordinates. These coordinates spreadover the full right ascension an declination due to the rotation of the earth.
This effect is accounted for by normalization, a histogram with all the selected events in thelocal system is made and this histogram is later in the process used to weight each individualevent. Because the number of events gets lower closer to the horizon, events close to the horizonwould get a very high weight, because there are few of these events they would induce a largeamount of noise. To prevent this a cut is made on the zenith angle. To determine to which anglethe acceptance is still good enough a simplified theoretical model is used.
The distance l from the surface of the water to the sea floor is.
l =d
cos θ
where d is the depth d and an angle to the normal of the sea floor θ, which is equal to the zenithangle.
The energy spectrum of the muons is approximately given by [6]:
dNµ
dEµ≈ 0.14 C E−2.7µ
1
cm2 s GeVdΩ
where C is some factor we assume is constant. When muons enter the water they lose energy, it isassumed that they stop when their energy is zero, it is also assumed that the detector is responsive
8
to muon’s of all energies, which is not the case. The number of muon’s left per solid angle whenall the muons with energy smaller than Estop are stopped by the water is equal to:
Nrm = 0.14 C dΩ
∞∫Estop
E−2.7µ dEµ ≈ 0.082 C dΩ E−1.7stop
in units of cm−2 s−1, the number and dΩ can be absorbed into C, together with the conversionform cm to m. So
Nrm = C2 E−1.7stop
A muon loses approximately 2.5 MeV/cm (250 MeV/m) when it travels trough water [7], so:
Estop = 0.25 l =0.25 d
cos θ
which means that:
Nrm = C3
(cos θ
d
)1.7
because the value of C2 is unknown and only Nrm(θ) with respect to Nrm(0) is needed theconstant is divided out:
Nrel =Nrm(θ)
Nrm(0)= (cos θ)1.7
when Nrel is required to be at least 0.8, θ ≈ 29. Initially the cut on the zenith angle was set to30, but this model does not fit the data because the number of events declines faster. Later 22.5turned out to be a better choice.
When making the normalization histogram all the bins need to have the same size, otherwisethey are not suitable to use as a weight. In a spherical coordinate system this can be done bytaking the cosine of one of the angles. In the zenith (Z) azimuth (A) system d cosZ dA has thesame size in the whole system. The problem of this system is that the bins near the pole (at Z =0) are triangular and very long, this is because cosZ = 1 at the pole the derivative is very smallso when Z changes cosZ does not change very much. Bins like this are not suitable to make anormalization histogram because at the pole the most of the events happen, if they are all put inone bin normalization near the pole would be impossible. This is solved by doing a coordinatetransformation to a system where the pole of the azimuth-zenith system has has a cosine of 0. Inthat system all the bins have a nearly equal shape at the pole.
In Figure 4 a picture of the zenith-azimuth system can be seen. This system is rotated 90degrees clockwise around the y-axis, and then expressed in a new set of coordinates called b andB, b takes the place of Z and B takes the place of A. In the zenith-azimuth system a vector isdescribed in the following way:
~v = l(sin z cosAx+ sin z sinAy + cos zz)
in the rotated system this becomes
~v = l(cos zx+ sin z sinAy − sin z cosAz)
but in the b, B system this is equal to
~v = l(sin b cosBx+ sin b sinBy + cos bz)
this gives three equations,
sin b cosB = cos z
sin b sinB = sin z sinA
cos b = − sin z cosA
9
Figure 4: The azimuth-zenith system
the last one can be used directly, the first two can be combined to
B = cos−1(
cos z
sin cos−1(− sin z cosA)
)If A > π B is replaced by -B, this prevents that two points get mapped to the same place due tothe limited range of inverse trigonometric functions.
In the B, cos b system all events are plotted with a resolution of half a degree for B and 1/360for cos b.
4.3 Time normalization
To correct for the time effect a histogram is made with the relative amount of time that eachpart of the sky in equatorial coordinates has been observed. This is done in discrete steps of1.44 · 10−3 Julian days. This value is chosen because the earth rotates 360 degrees in in a day,so one degree takes 1/360 days(≈ 2.78 · 10−3 days), with a resolution of one degree in both rightascension (α) and declination (δ), and limited computing time in mind this time resolution is thebest compromise.
The histogram is made as follows: the first time of the first event in the run is determined, thenfor every time step all bins in the histogram that are visible at that time are raised by one. Thenthe time is raised by one step and the same is done for the new time. This stops if the differencebetween the time of the simulation and the time of the last event is smaller than 0.72 · 10−3, halfa time step. This process is repeated for every run and the visibility is plotted in the the samehistogram.
4.4 Bin size
When the equatorial coordinate system is binned in both angles instead of in the cosine of δ, thebin size varies with δ. The area of a bin is given by.
A = r
δmax∫δmin
αmax∫αmin
sin δ dα dδ = r∆α(cos δmax − cos δmin)
where ∆α is the difference between αmin and αmax, r is the radius.Because of the geographical location of Antares the pole of this system is never visible with
the selected cut on A, this means that the shape of the bins is not a problem in this case.
10
4.5 Final steps
When all of the above is executed the direction of the muon with the highest energy is plotted inthe equatorial coordinate system for all events, with on both axis a binning of one degree. Theazimuth-zenith histogram in the cos b, B system is used as a weight for each event. For every eventthe A and Z are converted to cos b and B and the weight is looked up in the pre-made histogram,the event is then plotted in an histogram with α on the x-axis and δ on the y-axis. This histogramis then divided by the time histogram and the bin size histogram. From this histogram three newre-binned histograms are made:
• 360x180 (original)
• 180x90
• 90x45
• 45x45
For all four of these histograms the last and the first filled bins on the δ-axis are thrown away,because they are partially filled as a result of the rebinning. The average of the remaining filledbins is calculated and the factional difference from the mean , given by:
v =n− aa
is plotted. Where v is the final value of the bin, n content of the bin in the histogram from theprevious step and a is the average content of the filled bins in the histogram. The result of thisoperation is the final skymap.
5 Results
The steps that are described in the previous section are first applied to 20% of the selected runs,except for the azimuth routine, because this does only look at the position of the events in thelocal system. After it is applied to 20% of the data the result is looked over for mistakes. If thereare none the other 80% is added.
5.1 Azimuth histogram
The azimuth normalization histogram for all runs can be seen in Figure 5, this histogram wasmade using the original cut of 30 on z. In center 4 bins an excess of events can be observed,the cause of this unknown. It has been brought down dramatically by excluding events with verysmall values of z.
5.2 Time histogram
The time histogram for all runs can be seen in Figure 6. The number of events in the bins is not ofany physical value, it tells how may times the simulation has calculated the bin has been visible.It is strongly dependent on the properties and the resolution of the simulation.
5.3 Plotted events
The uncorrected histogram of the plotted events of all runs without the with system normalizationcan be seen in Figure 7. This plot shows the weighted number of events in each bin, it should benoted that the different size of the bins and the time effect can be seen in this plot.
11
B (radians)-0.6 -0.4 -0.2 0 0.2 0.4 0.6
cos
b
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0
500
1000
1500
2000
2500
3000
3500
4000
B, b
Figure 5: The normalization histogram for the local system in the B, b coordinate system
Right Ascension (degrees)0 50 100 150 200 250 300 350
Dec
linat
ion
(d
egre
es)
0
10
20
30
40
50
60
70
80
90
0
5000
10000
15000
20000
25000
30000
35000
40000
Observed
Figure 6: The time histogram for all runs, note that the bin content has not physical meaning,only the proportions do
12
Right Ascension (degrees)0 50 100 150 200 250 300 350
Dec
linat
ion
(d
egre
es)
0
10
20
30
40
50
60
70
80
90
0
500
1000
1500
2000
2500
Direction
Figure 7: The histogram with raw normalized events
Right Ascension (degrees)0 50 100 150 200 250 300 350
Dec
linat
ion
(d
egre
es)
0
10
20
30
40
50
60
70
80
90
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Event
Figure 8: The finals results for the original
5.4 Final results
The result of the final analysis for the 4 binnings can be seen in Figure 8, 9, 10 and 11. In thehistograms with the larger bins there is clearly an excess of events at δ of about 200, and thereare less events below 200. This excess has a magnitude of about a percent.
5.5 Statistics
The final analysis is based on 1.280·107 events. In the histogram with the most bins these eventsare in 46 · 360 = 16560 bins, this makes an average of 1.280 · 107/16560 ≈ 773 events per bin. Inthe 45 · 45 histogram are only 10 δ bins. This means that 6 · 360 = 2160 original bins did not endup in this histogram due to the filled neighbor condition, this number is negligible, and for theother rebinned histograms it is less. The 45 · 45 histogram has an average of 773 · 4 · 8 ≈ 2.4 · 104
events. Using the fact that this is a counted number this means that σ =√
2.4 · 104 ≈ 155. Usingthe formula for the fractional difference:
v(σ) =2.4 · 104 − (2.4 · 104 ± 155)
2.4 · 104=∓155
2.4 · 104≈ ∓6.4 · 10−3.
13
Right Ascension (degrees)0 50 100 150 200 250 300 350
Dec
linat
ion
(d
egre
es)
0
10
20
30
40
50
60
70
80
90
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Event
Figure 9: The final results for the 90 · 180 rebin
Right Ascension (degrees)0 50 100 150 200 250 300 350
Dec
linat
ion
(d
egre
es)
0
10
20
30
40
50
60
70
80
90
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
Event
Figure 10: The final results for the 45 · 90 rebin
14
Right Ascension (degrees)0 50 100 150 200 250 300 350
Dec
linat
ion
(d
egre
es)
0
10
20
30
40
50
60
70
80
90
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
Event
Figure 11: The final results for the 45 · 45 rebin
The same calculation has been done for all the re-binned histograms at different values of σ andcan be seen in Table 1
binning average σ v(σ) v(2σ) v(3σ) v(4σ) v(5σ) v(6σ)180 · 360 773 27.8 0.036 0.072 0.11 0.14 0.18 0.2290 · 180 3092 56.6 0.018 0.036 0.054 0.072 0.090 0.1045 · 90 12368 111 0.0090 0.018 0.027 0.036 0.045 0.05445 · 45 24736 457 0.0064 0.013 0.019 0.052 0.032 0.038
Table 1: The significance of the numbers for the different histograms
Table 1 takes only the statistical error of the number of events into account. There are alsoerrors arising form the time and local system normalization. The error from the time histogramis assumed to be neglectable because the time histogram is made by a precise simulation. Thebin size is a degree and the time steps assure that the last bin is visible in at least two loops,it is possible that a small systematic error can occur because of the stop an start times of thesimulation.
The local system normalization however suffers from the same statistical errors as the plottedevents. A bin at 22.5 has a minimum of about 900 events, this gives a σ of 30, which meansthat the error which arises from the edge of the normalization histogram is not negligible, butshould be smaller than the statistical error in the not rebinned histogram. The statistics of thenormalization histogram also improves closer to the center because there are more events in thecenter, this means that better statistics are used for normalization of most events.
Both of these errors occur in another coordinate system and are therefore randomized, thismeans that there effect should not be systematic
6 Discussion
The effect visible in Figure 11 is of the order of a percent, this is a lot bigger than expected. Ifonly the statistical error in the number of events is taken in to account the effect is significant.This means that the precision of the analysis method is not yet sufficient to be sensitive to the
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effect. To identify what is causing this, further analysis is needed. The effect could have severalsources.
The error in the normalization in the local system is at the the moment not understood verywell. Further analysis of this error is needed to exclude that the effect is not caused by badstatistics, and make a more informed decision on the binning of this histogram. Another ideais to gain more theoretical understanding of the geometrical effects in the detector, and maybesimulate the effect instead of using real data. This could take away the statistical error but wouldintroduce a systematical error coming from the simulation.
The time histogram in another potential source of this effect. Because the simulation workswith defined time steps and checks bins always in the same order there is a small excess at theleft of the visibility of each run. This effect should be randomized because the difference in thetime each part of the sky has been watched in the δ is of the order of 10%. It is unlikely that thishas caused the effect. To be sure a new time-simulation could be made which reverses the orderof the checked bins, if the effect then appears on the other site of the skymap the effect is causedby the time simulation.
A point that is not taken in to account during the data selection is the triggering of the detector,different triggers have different purposes and all these triggers are reconstructed and used withoutdiscrimination in this analysis. It is unknown if this can cause the effect but it is something thatneeds to be looked at.
Another point is the trade-off between data quality and statistics, although this can not directlyexplain the effect seen here. The cut on λ > −6 is not motivated well, if it is too strict a lot ofgood events could be thrown away. If it is not strict enough badly reconstructed tracks will endup in the data. Further investigation is needed to determine the optimal selection here. Looseningthe QualityBasic cut by defining criteria more suited to this analysis could also increase statistics.
7 Conclusion
The effect that was looked for has not been found. The time coverage over the declination an theright ascension is not at all uniform but varies by about 10%, and the acceptance corrections arealso large. This means that the method needs to be more stringently an systematically checked.Some effects that need to be checked have been indicated, but in general more statistics (whichwill allow for more strict cuts to be made) will be first necessary. The results presented here arebased on 1.280·107 events. When only is looked at the statistics of the number of events per binthe results for the rebinned histogram seem to be significant.
References
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[3] Arthur H. Compton and Ivan A. Getting. An apparent effect of galactic rotation on theitensitiy of cosmic rays. Phys. Rev. Lett., June 1935.
[4] A.A. Abdo et al. The large scale cosmic-ray anisotropy as observed with milagro. Astrophys.J.,2008.
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