The influence of the observatory latitude on the study of ultra high energy cosmic rays
Rita C. dos Anjos, Vitor de Souza, Rogerio M. de Almeida, Edivaldo M. Santos
PPrepared for submission to JCAP
The influence of the observatorylatitude on the study of ultra highenergy cosmic rays
Rita C. dos Anjos, a,b, Vitor de Souza b Rogerio M. de Almeida c Edivaldo M. Santos d a Departamento de Engenharias e Exatas, Universidade Federal do Paraná (UFPR),Pioneiro, 2153, 85950-000 Palotina, PR, Brazil. b Instituto de Física de São Carlos, Universidade de São Paulo, CP 369, 13560-970, SãoCarlos, SP, Brasil. c EEIMVR, Universidade Federal Fluminense, Volta Redonda, RJ, Brazil. d Instituto de Física, Universidade de São Paulo, Rua do Matão trav. R 187, 05508-090, SãoPaulo, Brazil.E-mail: [email protected], [email protected], [email protected]ff.br, [email protected]
Abstract.
Recent precision measurements of the Ultra High Energy Cosmic Rays (UHECR)arrival directions, spectrum and parameters related to the mass of the primary particle havebeen done by the HiRes, Pierre Auger and Telescope Array (TA) Observatories. In thispaper, distributions of arrival directions of events in the nearby Universe are assumed tocorrelate with sources in the 2MASS Redshift Survey (2MRS), IRAS 1.2 Jy Survey, PalermoSwift-BAT and Swift-BAT catalogs, and the effect of the latitude of the observatory onthe measurement of the energy spectrum and on the capability of measuring anisotropy isstudied. The differences between given latitudes on the northern and southern hemispheresare quantified. It is shown that the latitude of the observatory: a) has an influence on thetotal flux measured and b) imposes an important limitation on the capability of measuringan anisotropic sky. Corresponding author. a r X i v : . [ a s t r o - ph . H E ] M a r ontents The international community studying UHECR has recently done a big effort in the directionof a common interpretation of the data measured by several observatories [1, 2]. However,bringing together measurements performed by different experiments is not an easy task. Inthe past, the discrepancies between the measurements from several observatories have beenascribed to experimental particularities and analysis procedures. Detector uncertainties andbiases, different analysis assumptions, lack of events or discrepant interpretations based ondifferent extrapolations of the hadronic interactions properties have been enough to explainall the differences among the measurements. Presently, the improvement of our understandingabout the detection techniques, the multiplication of significant parameters extracted from theair shower, the construction of large and stable observatories and the extension of acceleratordata to even higher energies have minimized the unknown contributions to the differencesbetween the most important quantities measured by several observatories.In this new era, precision measurements of the UHECR energy spectrum, arrival di-rections and parameters related to the mass of the primary particle have been done by theHiRes [3], the Pierre Auger and TA Observatories [4, 5]. The Pierre Auger Observatory hasmeasured a correlation of events with energy above 57 EeV with AGNs closer than 75 Mpc [6].In the following years, the strength of the correlation has decreased with the accumulationof larger statistics and the most updated results are compatible with isotropy of events withenergy above 53 EeV [7] at the 2 σ level. On the other hand, the HiRes Collaboration haspublished a similar study with less statistics in which no correlation with AGNs is seen [8]and recently the TA Collaboration also reported no statistically significant correlation withAGNs [9]. Despite the lack of correlation with AGNs, TA has recently reported indicationsof anisotropy centered at R.A. = 146 ◦
7, decl. = 43 ◦ ◦ scale [10].The energy spectrum measured by the HiRes [3], the Pierre Auger [4] and TA [5] Ob-servatories agree remarkably well in the shape up to . eV, but show an offset in thetotal measured absolute flux. It has been shown that the differences in the total measuredflux can be explained by energy shifts within the estimated systematic uncertainty in thereconstructed energy of each experiment [11].The most reliable technique used by these observatories to determine the UHECR com-position is the measurement of the atmospheric depth at which the shower reaches its max-imum ( X max ), as determined by telescopes that detect the fluorescence light emitted by airmolecules. The comparison of the data measured by the experiments is not straightforwarddue to different analyses used by each group [12]. The Pierre Auger Observatory measureda significant change in the trend of (cid:104) X max (cid:105) with energy at . eV [13, 14], which can be– 1 –nterpreted as an increase of the abundance of heavier elements in the measured data [15].The X max data measured by the HiRes and TA Observatories are statistically compatiblewith constant abundance, but also with a changing composition (as suggested by Auger) inthe energy range from eV to eV [12, 16, 17].The comparison of the main measurements made by the three observatories shows dis-crepancies that could go beyond the detection particularities and differences in the analyses.If the extragalactic magnetic field is not extreme and the UHECR particles are not all heavy,the deviation of the highest energy particles ( E > . eV) is not expected to be large [18].Under these assumptions, it is expected that the measurement depends on the location of theobservatory on Earth. It has been already shown that the normalization of the flux measuredby each experiment might depend on the latitude of the Observatory [19].The calculation presented in this paper quantifies the differences in flux at a few latitudeson Earth for E > . eV. The effect of the latitude on the capability of an observatoryto determine an anisotropy signal is also investigated. The catalogs 2MASS Redshift Survey(2MRS) [20], IRAS 1.2 Jy Survey [21], Palermo Swift-BAT [22] and Swift-BAT [23] havebeen used as templates for the UHECR sources distribution. Calculations were done withthe incomplete catalogs, as they are published, but we have also completed the originalcatalogs with sources isotropically distributed in the sky and whose distances are such thatthe number of sources in small bins of redshift scales as ∝ z . The incompleteness of thecatalogs is discussed along the paper when necessary. Throughout the paper sources havebeen considered to have equal UHECR luminosity. The contribution of each source to theflux measured by each observatory is calculated taking into account its exposure function.The organization of the paper is as follows. In Section 2, the influence of the latitude ofthe experiment on the energy spectrum measurement is evaluated. In Section 3, the influenceof the latitude on the capability of measuring an anisotropy signal is shown. In Section 4, theconclusions are presented. The contribution of a point source to the total flux measured on Earth can be written as: J sCR ( E ) = W s πD s (1 + z ) Φ ( E ) , (2.1)where Φ o ( E ) is the energy spectrum at the source, D s is the comoving distance of the sourcefrom Earth, z the redshift of the source and W s is the exposure. For a full detection efficiency,the exposure can be calculated analytically [24]. In order to taking into account the deflectionsdue to magnetic fields along the particle propagation, we have performed a Gaussian smearingwith 30 degrees of resolution on the resulting coverage map using the Coverage and AnisotropyToolkit [25] developed by members of the Pierre Auger Collaboration as a tool to consider thedeflections due to extragalactic magnetic field in the construction of sky maps. We choose alarge angle of 30 degrees to show that the difference in the measured energy spectrum betweenhemispheres is significant even for large values of the smearing angle.In order to study the effect of the latitude on the measured energy spectrum, the relativecontribution of the sources in the nearby Universe ( z < . ) in the 2MASS Redshift Survey(2MRS), IRAS 1.2 Jy Survey, Palermo Swift-BAT and Swift-BAT catalogs was calculated.The contribution of each source received a weight ( P s ) given by P s = W s πD s (1 + z ) . (2.2)– 2 –he weight was calculated for observatories placed at four latitudes in each of the northernand southern hemispheres ( ±
35 and ±
55 degrees). Sources have been divided in shells of10 Mpc distance from Earth.Figures 1 and 2 show the relative contribution of each distance bin to the total fluxmeasured on Earth at latitudes ±
55 degree. Figure 1 was calculated with the sources ineach catalog as published. In Figure 2, we have completed the original catalog with sourcesisotropically distributed in the sky, so that the number of sources scales as ∝ z in bins ofredshift. The dependence on the latitude is clear in both figures: I) the northern hemisphere isexposed to a larger flux than the southern hemisphere and II) the relative contribution of eachshell in distance is different for each latitude. If we consider the catalogs completed, the effectis pronounced only up to 70 Mpc. This in turn could imply a difference in the compositiondetermined by each observatory since the abundance is affected by the propagation of theparticles in the intergalactic medium.Figures 1 and 2 also show that the differences between the Northern and Southern skiesare dominated by local sources ( D s < Mpc). The further the source, less it contributesto the total measured flux and more isotropic the sky is. The ratio between Northern andSouthern hemiphere of the integral of the quantity (Number of sources × P s ) shown in 2 isbasically one for distance larger than 100 Mpc. The incompletness of the the catalogs regard-ing the obscurance due to the galactic plane is also neglegible for the studies presented inthis paper. The solid angle covered by the galactic plane for observers in the Northern andSouthern hemispheres are identical and correspods to 8.6% of each coverage. The conclusionbelow are based on differences of fluxes measured by observatories in Northern and Southernhemispheres. Therefore the results presentd here are valid under the assumption that the ob-scured sky seen by a Northern and Southern observatory have the same isotropic distributionof sources.The difference between the energy spectrum measured by northern and southern obser-vatories for energies above . eV was studied in detail including the propagation of theparticles in the intergalactic medium. We pursue the analysis of the specific astrophysicalscenario with sources in the nearby Universe, since the fraction of surviving hadrons with E > . eV is relevant up to z ∼ . [26]. For each source in the catalogs with z < . ,50,000 events have been generated and propagated through the intergalactic medium to Earth.The 1D propagation was done using the CRPropa (v. 2.0) program [27]. CRPropa is a publicsoftware to simulate the propagation of nuclei in the intergalactic medium, taking into ac-count the most important interactions and radiation backgrounds. The propagation includesthe energy losses for protons and nuclei due to interactions with the cosmic microwave back-ground (CMB) and the extragalactic background light (EBL) [28]. Two cases were considered:pure proton and pure iron nuclei emission. The calculations assume an emission power lawspectrum dN/dE ∝ E − β , with β = 2 . , E min = 10 . eV and E max = Z × eV, where Z is the charge of the cosmic rays.Particles arriving at Earth from each source were weighted by the corresponding expo-sure (equation 2.2), taking also into account the deflections due to magnetic fields duringthe particle propagation. Figure 3 shows as an example the resulting energy spectra for lat-itudes ± ◦ for pure iron nuclei emitted for sources distributed according to the incomplete(Figure 3a) and completed (Figure 3b) Swift-BAT catalog. The effect of the latitude on theenergy spectrum is small but clear.Figures 4 and 5 show the percent difference of the flux measured in each hemisphere asa function of energy for latitude ±
55 degrees for proton and iron leaving the sources. The– 3 –MASS Redshift Survey (2MRS), IRAS 1.2 Jy Survey, Palermo Swift-BAT and Swift-BATincomplete (Figures 4) and completed (Figure 5) catalogs are shown. For energies above . eV, the number of simulated events arriving on Earth is very small and therefore theresults are less statistically significant. Anisotropy of UHECR arrival directions is usually quantified by comparison between thearrival directions of these particles with a template of sources detected in other wavelengthsand by independent techniques. Since the exposure of the sources in the catalog is a functionof the Observatory latitude, the capability of the method in detecting an anisotropy signal isalso a function of latitude.The standard 2pt method [29, 30] was used to quantify the detection power or detectionefficiency of an observatory at a given latitude. In this method, any departure from isotropyis measured through a pseudo-log-likelihood function σ P = (cid:80) i ln P i ( n obs | n exp ) in which P i isthe Poisson distribution: if k = n obs , then P i ( n obs | n exp ) = n kexp exp ( − n exp ) /k ! , n obs is thenumber of counts observed and n exp is the expected number of counts from isotropic samples.The 99% C.L. significance level for rejecting isotropy was chosen as a reference. The isotropyexpectation at 99% C.L. significance level ( σ P ) was calculated using events.Mock skies were generated following the source distribution given by all the catalogslisted above. Each mock sky was constructed with a limited number (varying from 10 to 90in steps of 10) of events allowing us to study the dependence of the detection power on thenumber of events measured by the experiments. The direction of the events were randomlydrawn from the direction of the sources in the catalog listed above. Therefore each mock skyrepresents a possible realization of a limited number of events coming from a given distributionof sources. The events were weighted according to Equation 2.2, with exposure map W s andsmeared by a 2D Gaussian 4 degrees wide (standard deviation) to take into account thepossible deflections of the particles, due to the random component of the magnetic field.The total number of mock skies generated was with the same number of events, foreach mock sky the probability of departure from isotropy was calculated ( σ P ). The probabilityof measuring anisotropy, given an anisotropic sky ( β ), is given by the ratio of mock skies with σ P < σ P . The detection power of the observatory ( − β ) is defined as the effectiveness ofdetecting the signal hypothesis. Figures 6 and 7 show the detection power of observatorieslocated at ±
35 degrees as a function of the number of events. The plot on the left of Figure 8shows that the observatories in the north have a larger power to detect anisotropy if ananisotropic sky is given. The detection power as a function of the number of events from thecatalog Swift-BAT (incomplete and complete) with observatories at latitudes ±
35 degreesis shown for sources closer (red) and farther (blue) than 50 Mpc. It is clear that the majorcontribution to the difference between north and south observatories is due to the nearbysources.We have done the calculations for latitude ± ± ±
45 and ±
55 degrees. Theeffect of the latitude on the power to detect anisotropy using the 2-pt method is importantonly for latitudes larger than ±
35 degrees.We have simulated sources up to 300 Mpc. The contribution of sources beyond thisdistance is ∼
10% of the total flux. The inclusion of extra isotropic sources beyond this distancewould result in a decrease of the detection power calculated in this section for observer inboth hemispheres. However if for
D >
Mpc the sources are isotropic for the North and– 4 –outh hemisphere, the conclusions would remain the same. Figures 6 and 7 shows differencesfrom North and South hemispheres therefore they would only be affected if sources beyond300 Mpc were anisotropic in the North and South skies.
In the present paper, the influence of the latitude of the Observatory on the measured flux andcapability to measure anisotropy of UHECR was studied. Particles are propagated to Earthfrom sources distributed according to the 2MASS Redshift Survey (2MRS), IRAS 1.2 Jy Sur-vey, Palermo Swift-BAT and Swift-BAT catalogs and the particles were propagated to Earth.The catalogs were completed with sources isotropically distributed in the sky and whose dis-tances are such that the catalog becomes complete above 100 Mpc. The incompleteness of thecatalogs are not important for the calculations because they would affect equaly observers inboth hemispheres. This study considers that sources have the same UHECR intrinsic lumi-nosity. The exposures of observatories at different latitudes were taken into account in orderto build the energy spectrum and assess their capability to detect anisotropies.The influence of the latitude on the flux was quantified as a function of energy (seeFigures 4 and 5). The differences between the flux measured by north and south observatoriesat ±
55 degrees for energies above . eV can be as large as 20% for incomplete catalogs and5% for completed catalogs. The influence of the latitude on the power to detect anisotropy,by comparing mock skies generated according to the sources distribution from the catalogs,was also calculated. Observatories in the northern hemisphere with latitude larger than 35degrees have a greater capability to determine an anisotropic sky than the southern ones forthe catalogs used here as anisotropy templates for anisotropy.The calculations done here show that an anisotropy of the sources of UHECR breaksthe symmetry between northern and southern observatories and introduces a dependenceof the total measured flux for latitudes larger than ±
45 degrees and of the capability todetermine anisotropic skies on the latitude of the observatory for latitudes larger than ± Acknowledgments
This work is funded by FAPESP (2010/07359-6,2014/19946-4), CAPES and CNPq.
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A three-point cosmic ray anisotropy method , J.Phys.G , , 115203 (2009). Distance [Mpc]0 50 100 150 200 250 300 s P · N u m b e r o f s ou r ces -6 -5 -4 -3 -2 -1 = 55 z < 0.072 l Distance [Mpc]0 50 100 150 200 250 300 s P · N u m b e r o f s ou r ces -6 -5 -4 -3 -2 -1 = -55 z < 0.072 l Figure 1 : Histograms of number of sources multiplied by the exposure versus distance fromEarth. The exposure has been calculated for observatories located at ±
55 degrees of latitude.The left figure shows the northern locations and the right figure shows the southern locations.The relative contribution to the flux from each bin in distance considered is shown. It is alsopossible to note differences between southern and northern latitudes.– 7 – istance [Mpc]0 50 100 150 200 250 300 s P · N u m b e r o f s ou r ces -6 -5 -4 -3 -2 -1 = 55 z < 0.072 complete l Distance [Mpc]0 50 100 150 200 250 300 s P · N u m b e r o f s ou r ces -6 -5 -4 -3 -2 -1 = -55 z < 0.072 complete l Figure 2 : Histograms of number of sources to completed catalogs multiplied by the exposureversus distance from Earth. The exposure has been calculated for observatories located at ±
55 degrees of latitude. The left figure shows the northern locations and the right figureshows the southern locations. The relative contribution to the flux from each bin in distanceconsidered is shown. It is also possible to note differences between southern and northernlatitudes. log(E/eV) d N / d E ( a r b i t r a r y un i t s ) E Swift BAT 70 - Iron = -55 l = 55 l (a) Swift BAT-70 log(E/eV) d N / d E ( a r b i t r a r y un i t s ) E Swift BAT 70 - Iron - Complete = -55 l = 55 l (b) Swift BAT-70 complete Figure 3 : Energy spectrum measured at Earth as a function of energy. Sources from theSwift-BAT catalog (a) and completed Swift-BAT (b) with equal UHECR luminosity and z < . were considered. Particles were propagated from source to Earth using the CRPropaprogram. The contribution of each source was weighted by its exposure as calculated forobservatories at ± degrees of latitude. Blue line dashed correspond to +55 degrees and redline correspond to − degrees locations. The simulated spectrum at the source were powerlaw with index β = 2 . , E min = 10 . eV and E max = Z × eV.– 8 – og(E/GeV)19.6 19.7 19.8 19.9 20 20.1 20.2 20.3 · N o r t h N o r t h - S ou t h -20020406080100 0.072 £ = 55 z l Proton 2MRSIRAS 1.2JyPALERMO Swift BATSwift BAT 70 log(E/GeV)19.6 19.7 19.8 19.9 20 20.1 20.2 20.3 · N o r t h N o r t h - S ou t h -20020406080100 0.072 £ = 55 z l Iron 2MRSIRAS 1.2JyPALERMO Swift BATSwift BAT 70
Figure 4 : Relative difference of the flux measured by observatories located in the northernand southern hemispheres at equal latitudes. Sources from the catalogs with equal UHECRluminosity and z < . were considered. Particles were propagated from source to Earthusing the CRPropa program. The contribution of each source was weighted by its exposure.In the left panel is shown the case in which only proton have been emitted by the sources. Inthe right panel is shown the case in which only iron nuclei have been emitted by the sources.The simulated spectra at the source were power laws with index β = 2 . , E min = 10 . eVand E max = Z × eV. log(E/GeV)19.6 19.7 19.8 19.9 20 20.1 20.2 20.3 · N o r t h N o r t h - S ou t h -20020406080100 0.072 Complete £ = 55 z l Proton 2MRSIRAS 1.2JyPALERMO Swift BATSwift BAT 70 log(E/GeV)19.6 19.7 19.8 19.9 20 20.1 20.2 20.3 · N o r t h N o r t h - S ou t h -20020406080100 0.072 Complete £ = 55 z l Iron 2MRSIRAS 1.2JyPALERMO Swift BATSwift BAT 70
Figure 5 : Relative difference of the flux measured by observatories located in the northernand southern hemispheres at equal latitudes. Sources from the completed catalogs with equalUHECR luminosity and z < . were considered. Particles were propagated from sourceto Earth using the CRPropa program. The contribution of each source was weighted by itsexposure. In the left panel is shown the case in which only proton have been emitted by thesources. In the right panel is shown the case in which only iron nuclei have been emittedby the sources. The simulated spectra at the source were power laws with index β = 2 . , E min = 10 . eV and E max = Z × eV. – 9 – umber of events ) b P o w er ( - -4 -3 -2 -1 Latitudes North 352MRS (2MASS)Swift BAT 70PALERMOIRAS 1.2Jy Number of events ) b P o w er ( - -4 -3 -2 -1 Latitudes South 352MRS (2MASS)Swift BAT 70PALERMOIRAS 1.2Jy
Figure 6 : Comparison between the values of power (1 − β ) according to the number of eventsfor the catalogs 2MASS Redshift Survey (2MRS), IRAS 1.2 Jy Survey, Palermo Swift-BATand Swift-BAT to the latitudes ±
35 and z < . to the Southern and Northern latitudes.The power of the observatory ( − β ) is defined as the effectiveness of detecting the signalhypothesis. See text for details. Number of events ) b P o w er ( - -4 -3 -2 -1 Latitudes North 35 - Complete2MRS (2MASS)Swift BAT 70PALERMOIRAS 1.2Jy Number of events ) b P o w er ( - -4 -3 -2 -1 Latitudes South 35 - Complete2MRS (2MASS)Swift BAT 70PALERMOIRAS 1.2Jy
Figure 7 : Comparison between the values of power (1 − β ) according to the number of eventsfor the catalogs 2MASS Redshift Survey (2MRS), IRAS 1.2 Jy Survey, Palermo Swift-BATand Swift-BAT complete to the latitudes ±
35 and z < . to the Southern and Northernlatitudes. The power of the observatory ( − β ) is defined as the effectiveness of detecting thesignal hypothesis. See text for details. – 10 – umber of events ) b P o w er ( - -4 -3 -2 -1 Latitudes - Swift BAT 70 50 Mpc £ d 200 Mpc £
50 Mpc < d
35 South35 North
Number of events ) b P o w er ( - -4 -3 -2 -1 Latitudes - Swift BAT 70 Complete 50 Mpc £ d 200 Mpc £
50 Mpc < d
35 South35 North
Figure 8 : Comparison between the values of power (1 − β ) according to the number of eventsfor the catalog Swift BAT 70 for observatories at latitudes ±
35 degrees. Red representssources closer than 50 Mpc and blue represents sources distant 50 to 200 Mpc from Earth.The power of the Observatory ( − ββ