PROCEEDINGS OF THE 31st ICRC, ŁODZ 2009 1

A study of the Correlation of Arrival Directions of UHECRs withthe Large Scale Structure of the Universe

Dongsu Ryu∗, Hyesung Kang†, and Santabrata Das‡

∗Department of Astronomy & Space Science, Chungnam National University, Daejeon 305-764, Korea†Department of Earth Sciences, Pusan National University, Pusan 609-735, Korea

‡Korea Astronomy and Space Science Institute 61-1, Hwaam Dong, Yuseong-Gu,Daejeon 305 348, Korea

Abstract. Ultrahigh energy cosmic rays (UHECRs)are believed to originate from astrophysical sources,which should trace the large scale structure (LSS) ofthe universe. On the other hand, the magnetic fieldin the intergalactic space (IGMF), which also tracesthe LSS of the universe, deflects the trajectoriesof the charged UHECRs and spoils the positionalcorrelation of the observed UHECR events with theirtrue sources. To explore this problem, we studieda simulation of the propagation of UHE protonsthrough the magnetized LSS of the universe, reportedearlier in Das et al. (2008), in which the IGMFwas estimated based on a turbulence dynamo model(Ryu et al. 2008). Hypothetical sources were placedinside clusters and groups of galaxies in the simulateduniverse, while observers were located inside groupsof galaxies that have similar properties as the LocalGroup. We calculated the statistics of the angulardistance between the arrival directions of simulatedUHE proton events and the positions of candidatesources in our simulation. We compared the statisticsfrom our simulation with those calculated with theAuger data. We discussed the implication of ourworks on the nature of the sources of UHECRs.

Keywords: ultrahigh energy cosmic rays, large-scale structure of universe, intergalactic magneticfields.

I. INTRODUCTION

Recently the Pierre Auger Collaboration reported asignificant anisotropy in the arrival directions of ul-trahigh energy cosmic rays (UHECRs) [1]. In theirstudy, the nearest neighbor of a given UHECR event isidentified among the active galactic nuclei (AGNs) listedin the 12th edition of Veron-Cetty (VC) catalog [2]. Themaximum correlation was observed for 20 events outof total 27 events with energy above 57 EeV, when theclosest AGN is searched within the angular separationof 3.2◦ among 442 AGNs with redshift z ≤ 0.018(corresponding to the distance D ≤ 75 Mpc for h−1 =0.7). Their study demonstrated a potential association ofUHECR events with the sky position of nearby AGNs.However, the statistical significance of this correlationanalysis may not yet be robust, since the number ofdetected events at extremely high energy is still rathersmall. But at least it implies that the sources of UHECRs

might be correlated with the matter distribution in thelocal universe.

In the correlation analysis, a priori knowledge ofthe intergalactic magnetic field (IGMF) is essential asit guides the propagation of UHECRs through the in-tergalactic space. Even with considerable observationalefforts, the nature of the IGMF is still poorly known,especially in the low-density regions like filaments,sheets and voids, where activities are relatively weak.In Ryu et al. (2008) [3], we suggested that a part of thegravitational energy is transferred to the magnetic fieldenergy as a result of the turbulent dynamo amplificationof weak seed fields in the large scale structure (LSS)of the universe. This model predicts that ∼ 1 % of theintergalactic space is magnetized with the field strengthB > 10 nG, and that the IGMF follows largely thematter distribution in the cosmic web.

Adopting this IGMF model, we estimated that only∼ 35 % of UHE protons above 60 EeV may arrivewithin 5◦ of their sources located inside the GZK spherewith radius of 100 Mpc [4]. Considering that the meandeflection angle of super-GZK protons caused by theIGMF in our model is ∼ 15◦ [4], it is natural to expectthat, in the correlation study of the Auger UHECRevents, a significant fraction of the identified sourcecandidates within 3.2◦ may not be the true sources ofthe UHECRs. In order to explore how the distributionof source candidates and the IGMF in the local universeinfluence the correlation analysis of UHECRs, we usedthe simulation results reported earlier in Das et al (2008)[4].

II. SIMULATION SETUP

Following [1], we set the maximum limit of thesource-to-observer distance as 75 Mpc. Inside the sim-ulation volume of radius 75 Mpc, ∼ 500 source can-didates (comparable to the number of AGNs from VCcatalog) were placed in the highest temperature regionsof the cosmic web. Observers were placed in the regionscorresponding to groups of galaxies with the halo tem-perature similar to that of our Local Group. For eachUHE proton event above 60 EeV, we computed twoangular distances: separation angle and deflection angle.The separation angle, S, is the angular distance betweenthe arrival direction of a given event and the positionof the nearest AGN among 500 source candidates. The

2 RYU et al. CORRELATION STUDY OF UHECR ARRIVAL DIRECTIONS

Fig. 1: Distribution of separation angle (S) as functionsof distance (DS) of the nearest AGNs in the sky insidea sphere of radius 75 Mpc. Black dots are for the eventsrecorded in our simulation. White circles connected withsolid line represent the mean values, 〈S〉, in the distancebin of [DS , DS + dDS ].

deflection angle, θ, is the angular distance between thearrival direction of a given event and its true sourceposition. Note that the nearest AGN may be not thetrue source of that event, and S would be on averagesmaller than θ. Here, we denote DS as the distance tothe nearest AGN with the separation angle S, and Dθ asthe distance to the true source with the deflection angleθ.

In our simulated universe, the intergalactic spacewas magnetized by turbulent plasma motions generatedduring the structure formation [3]. For simplicity, theinjection proton spectrum at source locations was char-acterized by a power low in the energy range above6 × 1019 eV with the exponent of γ = 2.7.

III. RESULTS

A. Separation Angle and Deflection AngleIn Figure 1, we show the distribution of separation

angle (S) versus the distance of the nearest source(DS). Each dot denotes a recorded event obtained fromsimulation. The white circles connected with solid linerepresent the mean values of S for the events fromAGNs with the distance bin of [DS , DS + dDS ]. Wenote that the mean separation angle 〈S〉 shows a U-shape distribution (see the discussion below). Overall〈S〉 is smaller than ∼ 4◦ for all DS , and does not changesensitively with DS . The mean separation angle over allthe simulated events is 〈S〉sim = 3.6◦.

In Figure 2, we compare the results of our simulationwith the Auger data [5]. Asterisks denote the highest

Fig. 2: Mean (dotted line) and median (solid line) valuesof separation angle, S, as functions of DS for therecoded events in our simulation. The solid vertical lineswith marks connect the first and third quartiles in thegiven DS bin. Asterisks denote the highest energy Augerevents that are correlated with the sky position of nearbyAGNs [5].

energy 27 Auger events that are correlated with theposition of nearby AGNs listed in VC catalog. Themean separation angles for the 20 events that gives themaximum correlation, for the 26 events that excludesthe event with S > 27◦ and for all the 27 events are〈S〉Auger = 1.91◦, 3.23◦ and 4.13◦, respectively. Thefilled circles connected with dotted line represent themean values of S (same as those in Figure 1), whilethe filled circles connected with solid line refer to themedian values of S for the simulated events. For agiven distance bin, [DS , DS + dDS ], the solid verticallines with marks on the both sides of the median values(the first and third quartiles) provide the measure ofdispersion on S. Note that 15 out of 27 Auger events liewithin the quartile marks obtained from our simulationdata.

Figure 3 shows the distribution of the deflection angle(θ) of UHE proton events with truce sources at distanceDθ. Again each dot represents a simulated event. Thewhite circles connected with dotted and solid lines arefor the mean and the median values of θ, and the solidvertical lines with marks denote the spread of θ inthe distance bin [Dθ, Dθ + dDθ]. The distribution of θ

shows a bi-modal pattern divided around an intermediatedistance at Dθ ∼ 20 Mpc [4]. The events with small Dθ

are likely to be the cases in which both the source andobserver belong to the same filament. These particlesare more likely to travel through strongly magnetizedfilaments rather than void regions, resulting in large

PROCEEDINGS OF THE 31st ICRC, ŁODZ 2009 3

Fig. 3: Distribution of deflection angle (θ) as functionsof distance (Dθ) of true sources. The mean (solid line)and median (dotted line) values of (θ) among the eventsfrom source with the distance bin of [Dθ, Dθ +dDθ] areshown. The solid vertical lines with marks connect thefirst and third quartiles in the given Dθ bin.

deflection angles. On the other hands, for the eventswith large Dθ, the particles come from distant sourcesassociated with different filaments. Some of UHECRsmay fly through voids and arrive with small Dθ, whilemost are deflected significantly by the IGMF. The U-shape distribution of 〈θ〉 with minimum at Dθ ∼ 20Mpc, as well as the U-shape distribution of 〈S〉 in Figure1, are the consequence of the bi-modal pattern, and aclear signature of the magnetized LSS of the universe.

The mean deflection angle of all the simulated eventsis 〈θ〉sim = 14◦, which is ∼ 3 times larger than 〈S〉sim.One might wonder if deflection angles of this magnitudecould erase the anisotropy in the arrival directions ofUHECRs, which is observed in the Auger data. However,the large deflection angle does not necessarily leadto the general isotropy of UHECR arrival directions,since the IGMF distribution is also correlated withthe LSS. Suppose UHECRs are ejected from sourcesinside the Local Supercluster. Some of them will flyalong the Supergalactic plane and arrive at Earth withrelatively small θ. Some of them may be deflected intovoid regions, but they may not get reflected back tothe direction toward us due to lack of the turbulentIGMF there. In this scenario, the irregularities in theIGMF serve as the ‘scatters’ of UHECRs. So we willobserve fewer UHECRs from void regions where bothsources and scatters are underpopulated. Consequently,the anisotropic behavior in arrival directions could bemaintained even for the large values of 〈θ〉, substantiallylarger than that of 〈S〉, if both source locations and the

Fig. 4: Cumulative fraction of events with separationangle smaller than S. Open circles denote the resultfor the 27 Auger events [5]. Solid curve is from oursimulation. The K-S test implies the two distributionsare consistent with each other.

IGMF distribution are anisotropic in the local universe.In order to test the validity of our models for the

distributions of the IGMF and nearby AGNs, we com-pare the distribution of S obtained from our simulationwith that of the Auger data. In Figure, 4 we showthe cumulative fraction of events, F (≤ log S), for theAuger data (open circles) and the simulation data (solidline). The Kolmogorov-Smirnov (K-S) test yields themaximum difference of D = 0.17 between the twodistributions, so the significance level of P ∼ 0.37. Itmeans that we cannot reject the null hypothesis that thetwo distributions are statistically identical.

B. Probability of Finding UHE Proton SourcesSince the deflection angle caused by the IGMF is

larger than the mean angular separation, that is, 〈θ〉 >

〈S〉, there is a good chance that for a given UHECRevent, the closest source in the sky may not be itstrue source. To explore the implication, we calculatethe fraction of true identification, f , as the ratio of thenumber of events for which nearest objects are in facttrue sources to the total number of simulated events.This is a measure of the probability to find the truesources of UHE protons in our model, when the nearestcandidates are chosen blindly (which is the best we cando with observed data). In Figure 5, we show the fractionas function of separation angle, S. For S ∼ 2◦, thefraction is ∼ 50 %. As separation angle increases, thefraction decreases gradually to ∼ 10 %, indicating lowerprobability to find the true sources at larger separationangles. On average, in only 1 out of ∼ 3 cases, the true

4 RYU et al. CORRELATION STUDY OF UHECR ARRIVAL DIRECTIONS

Fig. 5: Fraction (f ) of recorded UHE proton events forwhich their true sources are identified as the closestAGNs in the sky, as a function of separation angle (S).

sources of UHE protons can be identified, if we assumethat our model for the IGMF is valid.

IV. SUMMARY

In the search for the sources of UHECRs, understand-ing the propagation of charged particles through themagnetized LSS of the universe is important, if UHECRsoriginate from extragalactic sources. At present, thedetails of the IGMF is still uncertain, mainly due tothe limited available information from observation. Inthis contribution, we adopted a realistic model universethat was described by a cosmological structure forma-tion simulation [3]. Our simulated universe represents acharacteristic volume of the cosmic web, in which thedistribution of the IGMF was calculated by a physicalmodel based on turbulent dynamo. Hypothetical sourcesof UHE protons were placed at the deepest gravitationalpotential wells along the LSS, and observers were placedat groups of galaxies like our Local Group.

We then followed the propagation of UHE protonsabove 60 EeV ejected from the hypothetical sourceswithin a sphere of radius 75 Mpc with observers atthe center, in the simulated model universe [4]. Wecalculated two angular distances for a given UHE protonevent: the separation angle S from its nearest sourcecandidate and the deflection angle θ from it true source.The distribution of S depends on the relative skydistributions of UHECR events and source candidates.We find the mean value of S for simulated events is〈S〉sim ≈ 3.6◦, while 〈S〉Auger ≈ 4.13◦ for the 27 Augerevents (〈S〉Auger ≈ 3.2◦, if the event with S > 27◦ isexcluded). On the other hand, the distribution of θ isgreatly affected by the IGMF in the LSS. The mean

value is 〈θ〉sim ≈ 3〈S〉sim ≈ 14◦ for the simulatedevents. (For the 27 Auger events, of course, there is noway to estimate the true deflection angles.)

We tested whether the distributions of separation an-gle, S, for simulated events and the 27 Auger events areidentical. The significance level that the two distributionsare drawn from the identical population is P ∼ 0.37,according the Kolmogorov-Smirnov test. Thus, we arguethat our simulation results are in a fair agreement withthe Auger data.

We point that, although the mean deflection angle〈θ〉sim is large, the arrival directions of UHECRs wouldstill carry the anisotropy signature of our local universe,since the IGMF is also correlated with the matter distri-bution in the LSS.

The fact that 〈θ〉sim > 〈S〉sim implies that some ofthe identified source candidates may not be the truesources, if we assume that our model of the IGMF iscorrect. We estimate the probability of true identificationas the ratio of the number of true source identificationto the total number of simulated events. This probabilityis ∼ 50 % at S ∼ 2◦, but only 20 − 30 % forS = 3◦−4◦ and decreases to ∼ 10 % at larger separationangle. This suggests that identifying the sources ofUHECRs from positional correlation analysis may notbe straightforward.

Finally, we note that 〈S〉 and 〈θ〉 show U-shape distri-butions, resulting from the bimodal pattern in which θ ison average larger for either nearby sources (Dθ < ∼ 10Mpc) or distant sources (Dθ > ∼ 30 Mpc) with itsminimum at the intermediate distance, Dθ ∼ 20 Mpc.This is a characteristic imprint of the structured IGMFto the deflection angle distribution. We suggest that theimprint can be tested with the distribution of S, whenenough observed UHECR events are accumulated.

The work of DR and HK was supported by theKorea Research Foundation Grant funded by the KoreanGovernment (MOEHRD) (KRF-2007-341-C00020).

REFERENCES

[1] Pierre Auger Collaboration, 2007, Science, 318, 939[2] Veron-Cetty, M. P. & Veron, P. 2006, A&A, 455, 773[3] Ryu, D., Kang, H., Cho, J., & Das, S. 2008, Science, 320, 909[4] Das, S., Kang, H., Ryu, D. & Cho, J. 2008, ApJ, 682, 29[5] Pierre Auger Collaboration, 2008, Astroparticle Physics, 29, 188