On Anisotropy of Ultra-High Energy Cosmic-Rays

0.26 MB·English

by  Tamar Kashti

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0 On Anisotropy of Ultra-High Energy Cosmic-Rays
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n Tamar Kashti
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J Weizmann Institute of Science, Israel

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] Abstract
E
H We briefly summarize our study on anisotropy of Ultra-High Energy Cosmic-Rays (UHECRs),
. inwhichwedefineastatistics thatmeasuresthecorrelation between UHECRsandLargeScale
h
Structure (LSS). We also comment here on recently published paper by Koers and Tinyakov
p
that compared our statistics to improved KS statistics.
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o
r
t
s Key words: ultrahighenergycosmicrays,cosmicrays,largescalestructure
a PACS: 95.85.Ry,98.65.-r
[

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v The origin of cosmic rays of energies > 1019 eV is a puzzle [1,2,3]. The arrival di-
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rection of UHECRs show no correlation with the galactic disk, which point towards
5 extra-galactic origan. A suppression of the spectrum at ∼ 5×1019 eV is expected due
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2 to the GZK suppression [4,5]. The suppression was observed by HIRES [6] and the new
. AugerObservatory[7],seefig.1(a).Thus,cosmic-rayswithenergiesabove∼5×1019 eV
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can reach us only from sources with distance below ∼ 100 Mpc. In these distances, the
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9 Universe is not isotropic, implying that correlationwith LSS can give us information on
0 the origin of UHECRs.
: There arefew leading candidates asthe sourcesofUHECRs. Assuming thatUHECRs
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i are protons, the large magnetic fields needed for acceleration requires source luminosity
X of L & 1012L Γ2/β for protons with 1020 eV, where L is the Sun luminosity and Γ
⊙ ⊙
r is Lorentz factor of the magnetized plasma [3]. Therefore, the only known astrophysical
a
sources that reaches these energies are Active Galactic Nuclei (AGNs) and sources of
Gamma-ray bursts. The anisotropyof UHECRs from these sources should be correlated
withLSS.AnotherpossiblesourceofUHECRsisthedecayofnewheavyparticlescoming
from top-down models [1], which predict isotropic signal.
In [8], we derive the expected all sky angular distribution of the UHECR intensity,
and defined a statistics X that measures the correlationbetween the predicted and
C,UB
observedUHECRarrivaldirectiondistribution.Following[9],weconsideramodelwhere
the UHECR flux is produced by cosmological sources of protons tracing the large scale
PreprintsubmittedtoElsevier 29January2009
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m
1/
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1.
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e
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10 1
1 Xgal. model
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6 Auger
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E HiRes
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10 100
E [EeV]
Fig.1. (a)The spectrum ofHIRESand Auger afterashiftof ∆E/E=+23% inthe calibrationofthe
absolute energy scaleof theAuger experiment. Thesolidlineisthe spectrum that wouldbegenerated
by a cosmological distribution of sources of protons, with intrinsic spectrum dlogn/dlogE = −2. (b)
Thepositionsofthe27Augereventswithenergyexceeding5.7×1019 eV,overlaidontheintensitymap
obtainedinthebiasedmodel,ingalacticcoordinates.
galaxy distribution. We assume that the sources are intrinsically identical and that the
numberdensity ofsourcesisdrawnfromaPoissondistributionwith anaveragegivenby
b[δ]s¯(z), where s¯(z) is the averagecomoving number density of sources at redshift z and
b is some bias functional of the local fractional galaxy over density, δ ≡ δρ/ρ¯. The LSS
galaxy density field is derived from the PSCz catalogue [10]. For the bias functional we
consider three models: an isotropic (I) model, b[δ] = 1; an unbiased (UB) model where
the source distribution traces the galaxydistribution with b[δ]=1+δ; anda biased (B)
model, b[δ]=1+δ for δ >0 and b[δ]=0 otherwise.
The statistics we defined in [8], whichmeasuresthe correlationbetweenpredictedand
observed UHECR arrival direction distributions, is:
(N −N )(N −N )
i i,iso i,M i,iso
XC,M =X .
N
i,iso
{i}
Here{i}isasetofangularbins,N isthenumberofeventsdetectedinbini,andN is
i i,M
the averagenumberofevents expectedto be detectedinthe M (e.g.isotropic,unbiased,
biased)model.InordertoavoidsensitivitytothepossibledistortionoftheUHECRinten-
sitymapbymagneticfields,weused6◦×6◦ angularbinsandexcludedtheGalacticplane
region,|b|<12◦. The value of X can be straightforwardly calculated using the nu-
C,UB
mericalrepresentationsoftheUHECRmapsathttp://www.weizmann.ac.il/∼waxman/criso.
The X statistics is more sensitive to expected anisotropy signature than the com-
C
monly used power spectrum, C = 1 m=ℓ a2 (e.g. [11]), and the two-point corre-
ℓ 2ℓ+1Pm=−ℓ ℓm
lation function, W(D) = N Θ(D−D ) (e.g. [12]). This can be seen from table
Pi Pj<i ij
1(a). The anisotropy signal is stronger at lower energy: Although the contrast of the
fluctuations inthe UHECR intensityis higherathighenergy,the signalbecomes weaker
at higher energies since the number of observed UHECR drops rapidly with energy, see
table 1(b). In [8] we also show that a few fold increase of the Auger exposure is likely
to increase the significance to > 99% CL, but not to > 99.9% CL (unless the UHECR
source density is comparable or larger than that of galaxies).
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XC,UB P(I/UB)P(I/B)P(UB/B)
E>40EeV,100events P(I/UB)P(I/B)P(UB/B)
E>20EeV (1205events) 45% 94% 45%
XC,UB 23% 79% 42%
E>40EeV 300events 39% 94% 52%
XW({D=10,20,30,40}) 7% 12% 10%
E>60EeV(94events) 31% 87% 42%
XC({ℓ=2}) 6% 8% 7%
E>80EeV(31events) 22% 63% 24%
Table1
Probabilities P(M1|M2) to rule out model M1 at a certain confidence level (CL), assuming that the
UHECRsourcedistributionfollowsmodelM2.Calculatedfrom10000MonteCarlorealizationsforAuger
exposure. (a) Comparing different statistics, XC,UB, XC(ℓ) = Pℓ(Cℓ−Ciso,ℓ)2/σℓ2, where σℓ2 is the
variance, and XW (defined similarly for the two-point correlation function). (b) Comparing different
energythresholdswithXC,UB statistics.
Auger reported in [13] a correlation between the arrival direction distribution of 27
UHECRs of > 5.7×1019 eV and between the angular distribution of low-luminosity
AGNsincludedintheV-CAGNcatalog[14].However,theV-CAGNcatalogismerelya
compilation of AGN data available in the literature, and is therefore incomplete both in
itsskycoverageandinitsluminositycoverage,hencetheresultsof[13]areunclear.Using
the X statistics, we analyzed [13] data, see fig. 1(b). According to our analysis, the
C,UB
dataisinconsistentwithisotropyat∼98%CL,andconsistentwithasourcedistribution
that traces galaxy density. Note, however,that the optimization of the energy threshold
made in [13] raises the concern that the significance with which isotropy is ruled out
maybe overestimated.
Recently, [15] compared the X statistics to an improved KS statistics. They
C,UB
showed that for most energy thresholds the X statistics have higher probability
C,UB
to rule out isotropy (see their table I). However,they get probabilities that are different
then ours for X . This is probably due to the fact that they use a different galaxy
C,UB
redshift catalog, the catalog of Kalashev et al. [16], deduced from 2MASS XSC [17]. We
believethatthiscatalogisnotsuitablefortheanalysisofCRanisotropy,sinceitincludes
mainlyphotometricredshifts,whichhavesystematicuncertaintyof30%thatdependson
the luminosity, thus distorting the density field. Note that the future “2MASS Redshift
Survey” [17] will improve PSCz, by measuring redshifts of 100,000 galaxies till 85 Mpc.
References
[1] P.Bhattacharjee andG.Sigl,Phys.Rept.327,109(2000).
[2] M.NaganoandA.A.Watson, Rev.Mod.Phys.72,689(2000).
[3] E.Waxman,Pramana62,483(2004), andhistalkintheseproceedings.
[4] K.Greisen,Phys.Rev.Lett. 16,748(1966).
[5] G.T.ZatsepinandV.A.Kuzmin,JETPLett.4,78(1966).
[6] R.Abbasiet al.[HiResCollaboration],Phys.Rev.Lett. 100,101101(2008).
[7] J.Abrahamet al.[PierreAugerCollaboration],Phys.Rev.Lett. 101,061101(2008).
[8] T.KashtiandE.Waxman,JCAP0805,006(2008).
[9] E.Waxman,K.B.FisherandT.Piran,Astrophys.J.483,1(1997).
[10] W.Saunders et al.,Mon.Not.Roy.Astron.Soc.317,55(2000).
[11] G.Sigl,F.MiniatiandT.A.Ensslin,Phys.Rev.D70,043007(2004).
[12] D.DeMarco,P.Blasi,A.V.Olinto,JCAP01,002(2006).
[13] AugerCollaboration,Science, 318(5852), 938;J.Abrahamet al.,Astropart.Phys.29,188(2008).
[14] M.-P.V´eron-Cetty&P.V´eron,A&A455,773(2006).
[15] H.B.J.KoersandP.Tinyakov,arXiv:0812.0860[astro-ph].
[16] O.E.Kalashev,B.A.Khrenov,P.Klimov,S.SharakinandS.V.Troitsky,JCAP0803,003(2008).
[17] Jarrett,T.H.2004,PASA,21,396,http://www.cfa.harvard.edu/∼huchra/2mass/
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