Investigation of the Galactic Magnetic Field with Ultra-High Energy Cosmic Rays
IInvestigation of the Galactic Magnetic Fieldwith Ultra-High Energy Cosmic Rays
Martin Erdmann, Gero M¨uller, Martin Urban
Phys. Institute 3A, RWTH Aachen University, D-52056 Aachen, GermanyE-mail: [email protected]
Abstract:
We present a method to correct for deflections of ultra-high energycosmic rays in the galactic magnetic field. We perform these corrections bysimulating the expected arrival directions of protons using a parameterizationof the field derived from Faraday rotation and synchrotron emission measure-ments. To evaluate the method we introduce a simulated astrophysical scenarioand two observables designed for testing cosmic ray deflections. We show thatprotons can be identified by taking advantage of the galactic magnetic field pat-tern. Consequently, cosmic ray deflection in the galactic field can be verifiedexperimentally. The method also enables searches for directional correlationsof cosmic rays with source candidates. a r X i v : . [ a s t r o - ph . H E ] O c t Introduction
The magnetic field of our galaxy is presumed to cause substantial deflections of ultra-high energy cosmic rays prior to their observation. To understand the deflections,the directional dependence of the field pattern and the directional variations in themagnitude of the field are most relevant.Explicit predictions for deflections depending on the cosmic ray arrival direction,its energy and charge can be obtained through recent parameterizations of the shapeand magnitude of the galactic magnetic field [1, 2, 3, 4, 5]. They are based on 40 , Astrophysical scenario
Here we assume that a subset of active galactic nuclei (AGN) can be considered assources of cosmic rays. As navigators to select these AGN sources experimentallywe use the arrival directions of 24 high energy neutrinos published by the IceCubeCollaboration [8]. These neutrinos have energies above E = 40 TeV, and were notassigned strong evidence for resulting from atmospheric background.For the AGNs we use the VCV catalogue [9] and consider AGNs with distances z < . N = 231ultra-high energy cosmic rays with distributions similar to the one published bythe Pierre Auger Collaboration [11]. For this we combine 10% of an astrophysicalscenario simulated with the CRPropa program [6] with 90% isotropic cosmic raysfollowing the geometrical acceptance of the observatory [12].For the 10% contribution of the astrophysical scenario we generate 10 cosmicrays at each of the 22 selected AGN sources. As the initial composition we use a flatdistribution of nuclei with charges between Z = 1 , ...,
26. Their minimum energiesare E = 50 EeV, and their maximum energies correspond to their rigidities Z × E max with E max = 500 EeV.Upon arrival at a 0 . ,
152 equally sized pixels of approximately 1 deg. The matrices contain theprobability of a cosmic ray entering the galaxy with energy E at direction i to beobserved in direction j . The technical details of the lenses and their production areoutlined in [14]. The lenses used in this contribution have been calculated with theCRPropa program and the JF12 parameterization of the galactic magnetic field [2].We then select cosmic rays according to the geometrical acceptance of the ob-servatory [12], and an energy distribution corresponding to the measured energyspectrum [15]. Of these cosmic rays we randomly select the 10% contribution ofcosmic rays arriving from the AGN sources where we require 70% to be protons.The total sample of the 231 simulated cosmic rays therefore contains 7% protonsignal and 93% background (grey circular symbols in Fig. 1a).2 Analysis method
To investigate the galactic magnetic field using the cosmic ray data set described inthe previous section, we simulate their expected arrival directions assuming that allcosmic rays are protons. We start these proton simulations with the same set of the22 AGNs mentioned above.To take into account effects of extragalactic magnetic fields we apply a Fisherprobability distribution centered at each AGN direction with a concentration pa-rameter κ depending on the AGN distance and the cosmic ray energy. For an AGNat distance D = 10 Mpc and a proton with E = 52 EeV the angular spread amountsto σ = 1 / √ κ = 6 deg.This probability distribution is then projected onto the Earth using the corre-sponding magnetic lens described above. To obtain a single direction for which thearrival probability is greatest, we calculate the radius r containing 50% of thearrival probabilities. We select the pixel with the smallest radius r and use thecenter of this pixel as the expected arrival direction of the proton.The procedure for calculating the expected arrival direction of protons withenergies E = 5 , , ,
50 EeV is visualized exemplarily in Fig. 1b. The star symboldenotes the initial direction outside the galaxy. Note that the direction of the lowestenergy proton also corresponds to the deflection of an ionized Neon nucleus ( Z = 10)with energy E = 50 EeV. This implies that - in directions with a sufficiently strongmagnetic field - protons in the cosmic ray data can be identified to some extent bysmall angular distances to the expected arrival directions. In Fig.2a we visualize two angular distances used in this analysis. The angle α denotes the angular distance between the measured arrival directions of a cosmicray and its nearest AGN. The angle α GMF denotes the angular distance betweenthe measured cosmic ray and the expected arrival direction of a proton with anAGN-coincident direction outside the galaxy.In Fig.2b we show the cumulated number of cosmic rays arriving within a distanceof angle α ◦ to their nearest AGNs. The triangular symbols present the angulardistances between the measured cosmic rays and the expected arrival directionsfor protons including the magnetic field corrections. The histogram denotes theuncorrected angular distances between cosmic rays and AGNs. Below a few degrees,more cosmic rays appear near AGN directions when including the field corrections.These small angular distances are consistent with our simulations of the protons,3hich supports the above-mentioned third assumption of our model that protons inthe cosmic ray sample can be identified to some extent by exploiting the magneticfield deflections.In Fig.2c we present the change in the angular distances α − α GMF without andwith magnetic field corrections. At positive values the cosmic rays come closer tothe expected arrival directions, while at negative values the cosmic rays are nearerto the AGNs without field corrections. In the region with small angles we find morecosmic rays with improved angular distances when applying the field correctionscompared to events for which the uncorrected distance is smaller.We quantify the change in the angular distances by the asymmetry A ≡ N ( α > α GMF ) − N ( α < α GMF ) N ( α > α GMF ) + N ( α < α GMF ) (1)which can take on any value from − α ◦ = 5deg the angular asymmetry in the data is found to be A = 0 .
96. This positive valueis a measure of the overall improvement in the angular distances between cosmicrays and AGNs when applying the field corrections.We also investigate clustering of cosmic rays with AGN directions. In Fig.2d wepresent the frequencies of the cluster sizes m where we count associations of cosmicrays with AGNs within 5 deg angular distance. This yields configurations containingsinglet, doublet, triplet, and sextet clusters ( m = 1 , , , P ( n , ..., n ; N − N hit ) = N ! n ! ...n ! ( N − N hit )! p n ... p n (1 − p iso ) N − N hit (2)The value P describes the expected level of trivial clustering between the N = 231cosmic rays, and the 22 AGNs where the latter are distinguished by identifiers.AGN i has an average hit probability of p i , and was correlated with n i cosmicrays. The total number of cosmic rays associated with one of the AGNs is N hit = (cid:80) i n i . The remaining N − N hit cosmic rays without AGN correlations had a no-hitprobability of (1 − p iso ). Summing the hit probabilities for the AGNs at their nominalarrival directions for angular distances below 5 deg gives p iso = 5 . p iso = 5 . ( P GMF ) = − .
3. Without the fieldcorrections the level of clustering is smaller and results in log ( P ) = − .
5. Thechange in the clustering strength thus amounts to log ( P GMF ) − log ( P ) = − . In the previous section we performed the analysis on the simulated data set using thecorrect magnetic field and the correct set of AGN sources. With 7% signal protons inthe data and 93% background contributions, the two observables indicated overallimprovements in terms of the angular asymmetry A = 0 .
96, and the clusteringstrength log ( P GMF ) − log ( P ) = − .
8. The results are visualized in Fig.3a,c,d bythe red cross.Below we investigate whether the same improvements can be obtained by chance.In a first test we apply typical values for the expected deflections in the magneticfield; however, we assume neither that the cosmic rays and AGNs are truly corre-lated, nor that the above pattern of the magnetic field is correct.We use a simulation of 10 ,
000 event samples with the AGN directions, isotropiccosmic ray arrival directions, and random patterns for the galactic magnetic fieldcorrections. The geometrical acceptance of the Pierre Auger Observatory is includedas presented in [12]. The distribution of the change in the clustering strength versusthe angular asymmetry obtained from these simulations is shown in Fig. 3a by thebox symbols, and appears to be centered at zero with a slight anti-correlation in thetwo observables. In 0 .
05% of the events we find equal values or improvements in thetwo observables with respect to the values obtained in the data analysis.In a further test we use lenses produced for correcting deflections of antiprotonsin the galactic magnetic field. These lenses reverse the galactic magnetic field forprotons. Applying the reversed field in our data analysis instead of the correct fieldorientation, the angular asymmetry and the change in the clustering strength bothdisappear (red cross in Fig. 3b; the box symbols refer again to a simulation withrandom field directions, isotropic cosmic rays, and nominal AGN directions). Thus,the above-mentioned second assumption on the validity of the field parameteriza-tions can be evaluated in comparison with analyses using random directions andfield reversal.We also investigated the above-mentioned first assumption on angular corre-lations between AGNs and cosmic rays. For this test we took the nominal fieldparameterization and the nominal cosmic ray arrival directions, but 22 chance di-rections instead of the AGNs (box symbols in Fig. 3c, compared to the cosmic ray5ata analysis denoted by the red cross). Also here the chance distribution is cen-tered at zero, and is disjunct from the values obtained with the data. A similardistribution is obtained when using isotropic cosmic rays, while keeping the nominalfield parameterization (JF12) and the nominal AGN directions (not shown here).Thus, finding improvements at the level of our data analysis with arbitrary direc-tions is unlikely, implying that angular correlations of cosmic rays and sources canbe evaluated.We also studied the influence of a potentially limited knowledge about the sourcedirections. In this test we first performed the analysis using the correct magneticfield and the nominal cosmic ray data set (red cross in Fig. 3d). We then variedthe AGN positions within an angular uncertainty of 15 deg. Such variations couldappear, e.g., when studying direct correlations of cosmic rays and cosmic neutrinos.The box symbols show the results of the 10 ,
000 variations. Even if the sourcedirections are not perfectly known, an improvement in the two observables owing todeflections in the galactic magnetic field can be observed.In applications of our method to measured cosmic rays data we therefore expectstriking effects if the galactic magnetic field parameterization and the directions ofthe sources are correct.
In this contribution we presented a method for evaluating deflections of cosmic raysin the galactic magnetic field. By making use of a field parameterization derivedfrom Faraday rotation and synchrotron emission measurements we calculate theexpected arrival directions of protons and use this for further analysis.To explore this method we introduced two observables designed for investigatingcosmic ray deflections, namely an angular asymmetry and a measure of clusteringstrength. Applying the analysis to a simulated astrophysical scenario we demon-strated that the magnetic field corrections improve directional relations of cosmicrays and their sources if the correct field and source directions are used in the anal-ysis. This even works if the source directions are known with limited precision.If incorrect assumptions on the field or an arbitrary set of sources are used, theimprovements in the observables remain marginal. In view of the galactic mag-netic field parameterizations based on measurements we thus expect that cosmicray deflections in the galactic field can be verified experimentally.In general, and independently of the AGN application, our method of magneticfield corrections enables studies of directional correlations between cosmic rays andmessenger particles suitable to indicate directions of cosmic ray sources.6 cknowledgments
We are grateful for financial support to the Ministerium f¨ur Innovation, Wissenschaftund Forschung des Landes Nordrhein-Westfalen and to the Bundesministerium f¨urBildung und Forschung (BMBF).
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B685 (2010)239 8) b)Figure 1: a) Simulated astrophysical scenario. The star symbols denote AGNswith the color corresponding to their distance. The circular symbols represent thecosmic rays (7% proton signal, 93% background contributions). b) Simulations ofthe expected arrival direction of protons after traversing the galactic magnetic field.The star symbol denotes the initial direction outside the galaxy, the cross symbolsshow the expected arrival directions of protons with different energies, and the colorcode gives relative probability distributions.9) b) α < α [°]10 P N correcteduncorrected c) –15 –10 –5 0 5 10 15 α – α GMF [°]051015 m i n ( α , α G M F ) [ ° ] d) N Figure 2: a) Angular distances of a cosmic ray to the nearest AGN direction andto the expected arrival direction assuming protons. b) Cumulated number of cosmicrays associated with AGN arrival directions with (symbols) and without magneticfield corrections (histogram) as a function of the maximum angular distance α ◦ . c)Change in the angular distance before and after applying the magnetic field cor-rections. The vertical line separates reduced ( >
0) and enlarged ( <