Angular correlation of cosmic neutrinos with ultrahigh-energy cosmic rays and implications for their sources
PPrepared for submission to JCAP
Angular correlation of cosmicneutrinos with ultrahigh-energycosmic rays and implications fortheir sources
Reetanjali Moharana and Soebur Razzaque
Department of Physics, University of Johannesburg,P. O. Box 524, Auckland Park 2006, South AfricaE-mail: [email protected], [email protected]
Abstract.
Cosmic neutrino events detected by the IceCube Neutrino Observatory with energy (cid:38) TeV have poor angular resolutions to reveal their origin. Ultrahigh-energy cosmic rays(UHECRs), with better angular resolutions at > EeV energies, can be used to check if thesame astrophysical sources are responsible for producing both neutrinos and UHECRs. Wetest this hypothesis, with statistical methods which emphasize invariant quantities, by usingdata from the Pierre Auger Observatory, Telescope Array and past cosmic-ray experiments.We find that the arrival directions of the cosmic neutrinos are correlated with ≥ EeVUHECR arrival directions at confidence level ≈ . The strength of the correlation decreaseswith decreasing UHECR energy and no correlation exists at energy ∼ EeV. A search inastrophysical databases within ◦ of the arrival directions of UHECRs with energy ≥ EeV,that are correlated with the IceCube cosmic neutrinos, resulted in 18 sources from the
Swift -BAT X-ray catalog with redshift z ≤ . . We also found 3 objects in the Kühr catalog of radiosources using the same criteria. The sources are dominantly Seyfert galaxies with Cygnus Abeing the most prominent member. We calculate the required neutrino and UHECR fluxes toproduce the observed correlated events, and estimate the corresponding neutrino luminosity(25 TeV–2.2 PeV) and cosmic-ray luminosity (500 TeV–180 EeV), assuming the sources arethe ones we found in the Swift -BAT and Kühr catalogs. We compare these luminosities withthe X-ray luminosity of the corresponding sources and discuss possibilities of acceleratingprotons to (cid:38)
EeV and produce neutrinos in these sources. a r X i v : . [ a s t r o - ph . H E ] J u l ontents The IceCube Neutrino Observatory, the world’s largest neutrino detector, has recently pub-lished neutrino events collected over 3-year period with energy in the ∼ TeV– PeV range[1]. Shower events, most likely due to ν e or ν τ charge current νN interactions, dominate theevent list (28 including 3 events with 1–2 PeV energy) while track events, most likely dueto ν µ charge current νN interactions, constitute the rest. Among a total of 37 events about15 could be due to atmospheric neutrino ( . +5 . − . ) and muon ( . ± . ) backgrounds. Abackground-only origin of all 37 events has been rejected at 5.7- σ level [1]. Therefore a cos-mic origin of a number of neutrino events is robust. The track events have on average ∼ ◦ angular resolution, but the dominant, shower events have much poorer angular resolution, ∼ ◦ on average [1], thus making them unsuitable for astronomy.Meanwhile the Pierre Auger Observatory (PAO) [2] and the Telescope Array (TA) [3],two of the world’s largest operating cosmic-ray detectors, have recently released UHECRdata collected over more than 10-year and 5-year periods, respectively. Together they havedetected 16 events (6 by PAO [2] and 10 by TA [3]) with energies (cid:38) EeV. The totalpublicly available (cid:38)
EeV events including past experiments is 33. While lower-energycosmic ray arrival directions are scrambled by the Galactic and intergalactic magnetic fields,at (cid:38) EeV energies the arrival directions of UHECRs tend to be much better correlatedwith their source directions and astronomy with charged particles could be realized [4]. Fewdegree angular resolution can be achieved at these energies, which is much better than theIceCube neutrino shower events and is comparable to the neutrino track events.The astrophysical sources of UHECRs with energy (cid:38) EeV need to be located withinthe so-called GZK volume [5, 6] in order to avoid serious attenuation of flux from them due tointeractions of UHECRs with photons from cosmic microwave background (CMB) and extra-galactic background light (EBL). The astrophysical sources of neutrinos, on the other hand,can be located at large distances and still be detected provided their luminosity is sufficientlyhigh. However, because of weakly interacting nature of neutrinos and limiting luminosity ofastrophysical sources, only nearby neutrino sources can be identified, thus making neutrinoastronomy possible. – 1 –e explore here a possibility that both UHECRs and IceCube cosmic neutrino events areproduced by the same astrophysical sources within the GZK volume. Since widely acceptedFermi acceleration mechanism of cosmic rays at the sources take place over a large energyrange, it is natural that the same sources produce (cid:38) PeV cosmic rays, required to producecosmic neutrinos observed with energies down to ∼ TeV, and UHECRs with energy ≥ EeV. We employ invariant statistical method [7, 8], independent of coordinate systems, inorder to study angular correlation between cosmic neutrinos and UHECRs. As far we know,this is the first attempt to quantify such a correlation between the IceCube neutrino andUHECR data sets. Existence of such a correlation can provide clues to the origin of bothcosmic neutrinos and UHECRs. We search for astrophysical sources within the angular errorsof UHECRs which are correlated with the neutrino events in order to shed lights on theirplausible, common origins. Finally we calculate required neutrino and cosmic-ray luminositiesfor the sources to produce observed events, and compare these luminosities with their observedX-ray and radio luminosities to check if they are viable sources of both UHECRs and cosmicneutrinos.The organization of this paper is the following. We describe neutrino and UHECR datathat we use in section 2 and our statistical method in section 3. The results of our correlationstudy and source search along the directions of the correlated events are given in section 4.Section 4 also includes calculation of neutrino and cosmic-ray luminosities of the correlatedsources from respective fluxes derived using data. We discuss our results and implications ofour findings in section 5.
We consider 35 IceCube neutrino events, collected over 988 days in the ∼ TeV–2 PeV range,from ref. [1] to study angular correlation with UHECRs. Two track events (event numbers28 and 32) are coincident hits in the IceTop surface array and are almost certainly a pairof atmospheric muon background events [1]. Therefore we excluded them from our analysis.Figure 1 shows sky maps of 35 events in equatorial coordinates with reported angular errors.The majority (26) of the events have arrival directions in the southern sky. Among the 9northern hemisphere events, only 1 is at a declination
Dec > ◦ which happens to be ashower event [1]. The angular resolutions of the track events are (cid:46) . ◦ and those of theshower events vary between . ◦ and . ◦ . Figure 2 shows sky maps in Galactic coordinates.Figures 1 and 2 also show sky maps of available UHECR data with energies ≥ EeV(top panel) and ≥ EeV (bottom panel). The PAO and TA collaborations have publisheddata with energies above 52 EeV (231 events) [2] and 57 EeV (72 events) [3], respectively.Note that the PAO and TA are located in the southern and northern hemisphere, respectively,covering a declination range of − ◦ ≤ Dec ≤ ◦ [2] and − ◦ ≤ Dec ≤ ◦ [3]. The angularresolutions for the PAO events with energy > EeV is < . ◦ [9] while for the TA eventswith energy > EeV it is between . ◦ and . ◦ [3]. Note that the ≥ EeV data sampleis incomplete. Only the AGASA experiment has published data above 40 EeV (40 events)covering a declination range − ◦ ≤ Dec ≤ ◦ and with angular resolution < ◦ [12]. Only ≥ EeV data are available from the other past experiments: Haverah Park [10, 11], Yakutsk[10], Volcano Ranch [10] and Fly’s eye [10]. Note that these were all northern hemisphereexperiments. We could not include 13 events with energy > EeV from the HiRes experimentas the energies of the individual events are not available [13].– 2 – igure 1 . Sky maps of the IceCube > TeV cosmic neutrino events with error circles and UHECRdata in equatorial coordinates. The top panel shows UHECRs with energy ≥ EeV and the bottompanel shows all available data with energy ≥ EeV. The black dotted line is the Galactic plane.
We list in Table 1 all available UHECR data with energy ≥ EeV. This includes6 events from Haverah Park, 1 event from Yakutsk, 8 events from AGASA, 1 event fromVolcano Ranch, the highest-energy (320 EeV) event from Fly’s eye, 6 events from PAO and10 events from TA. We use this list and sublists with PAO and TA data separately to study– 3 – igure 2 . The same as Figure 1 but in Galactic coordinates. correlation with cosmic neutrino events. In addition to ≥ EeV data, we also exploreenergy-dependence of correlation by choosing different energy cuts, ≥ EeV and ≥ EeV,in UHECR data from the PAO, TA and AGASA . Above 80 EeV (60 EeV) there are 22 (136)UHECR events from PAO, 20 (60) from TA and 11 (22) from AGASA. We note that energycalibration across the experiments can vary by as much as ∼ (see, e.g., ref. [14]). We– 4 –xperiment Reference Energy (EeV) RA ( ◦ ) Dec ( ◦ )Haverah Park [10] 101 201 71Haverah Park [10] 116 353 19Haverah Park [10] 126 179 27Haverah Park [10] 159 199 44Haverah Park [11] 123 318.3 3.0Haverah Park [11] 115 86.7 31.7Yakutsk [10] 110 75.2 45.5AGASA [12] 101 124.25 16.8AGASA [12] 213 18.75 21.1AGASA [12] 106 281.25 48.3AGASA [12] 144 241.5 23.0AGASA [12] 105 298.5 18.7AGASA [12] 150 294.5 − . AGASA [12] 120 349.0 12.3AGASA [12] 104 345.75 33.9Volcano Ranch [10] 135 306.7 46.8Fly’s eye [10] 320 . ± . . +5 . − . Pierre Auger [2] 108.2 45.6 − . Pierre Auger [2] 127.1 192.8 − . Pierre Auger [2] 111.8 352.6 − . Pierre Auger [2] 118.3 287.7 . Pierre Auger [2] 100.1 150.1 − . Pierre Auger [2] 118.3 340.6 . Telescope Array [3] 101.4 285.74 − . Telescope Array [3] 120.3 285.46 33.62Telescope Array [3] 139.0 152.27 11.10Telescope Array [3] 122.2 347.73 39.46Telescope Array [3] 154.3 239.85 − . Telescope Array [3] 162.2 205.08 20.05Telescope Array [3] 124.8 295.61 43.53Telescope Array [3] 135.5 288.30 0.34Telescope Array [3] 101.0 219.66 38.46Telescope Array [3] 106.8 37.59 13.89
Table 1 . Available UHECR data with energy (cid:38)
EeV from various experiments. discuss this issue in Sec. 4.2.
To study correlation between cosmic neutrinos and UHECRs, we map the Right Ascensionand Declination ( RA, Dec ) of the event directions into unit vectors on a sphere as ˆ x = (sin θ cos φ, sin θ sin φ, cos θ ) T , where φ = RA and θ = π/ − Dec . Scalar product of the neutrino and UHECR vectors (ˆ x neutrino · ˆ x UHECR ) therefore is independent of the coordinate system. The angle between the– 5 –wo vectors γ = cos − (ˆ x neutrino · ˆ x UHECR ) , (3.1)is an invariant measure of the angular correlation between the neutrino and UHECR arrivaldirections [7, 8]. Following ref. [7] we use a statistic made from invariant γ for each neutrinodirection ˆ x i and UHECR direction ˆ x j pair as δχ i = min j ( γ ij /δγ i ) , (3.2)which is minimized for all j . Here δγ i is the 1- σ angular resolution of the neutrino events.We use the exact resolutions reported by the IceCube collaboration for each event [1].A value δχ i ≤ is considered a “good match” between the i -th neutrino and an UHECRarrival directions. We exploit distributions of all δχ i statistic to study angular correlationbetween IceCube neutrino events and UHECR data. The distribution with observed datagiving a number of “hits” or N hits with δχ ≤ therefore forms a basis to claim correlation.Note that in case more than one UHECR directions are within the error circle of a neutrinoevent, the δχ value for UHECR closest to the neutrino direction is chosen in this method.We estimate the significance of any correlation in data by comparing N hits with corre-sponding number from null distributions. We construct two null distributions, in one casewe randomize only the RA of UHECRs, keeping their Dec the same as in data; and in thesecond case we also randomize
Dec according to the zenith-angle depended sky exposure ofthe UHECR experiments [36], affecting the declination distributions of UHECR data. We callthese two null distributions as the semi-isotropic null and exposure-corrected null , respectively.The semi-isotropic null is a quick-way to check significance while the exposure-corrected null isaccurate when information on particular experiments are available. In both cases we perform100,000 realizations of drawing random numbers to assign new RA and Dec values for eachevent to construct δχ distributions in the same way as done with real data. We find thatthe two null distributions are in good agreement with each other in most cases.We calculate statistical significance of correlation in real data or p -value (chance proba-bility) using frequentists’ approach. We count the number of times we get a random data setthat gives equal or more hits than the N hits in real data within δχ ≤ bin. Dividing thisnumber with the total number of random data sets generated (100,000) gives us the p -value.We cross-check this p -value by calculating the Poisson probability of obtaining N hits within δχ ≤ bin given the corresponding average hits expected from the null distribution. Thesetwo chance probabilities are in good agreement. We apply our statistical method separately to the PAO and TA data, to a combination ofthe both and to all available UHECR data above 100 EeV from all experiments (see Table1). The results are shown in the histograms of Figure 3. The counts in the ≤ δχ ≤ binsfor the blue, filled histograms correspond to the number of correlated neutrino events withUHECRs. Counts in other bins are due to distant pairs of the neutrino events and UHECRsand are uninteresting for us. The counts for the red (green), open histogram in the samebins correspond to the expected number of correlated neutrino events from the semi-isotropicnull ( exposure-corrected null ), after averaging over 100,000 simulated data sets with randomUHECR positions. Both null distributions give similar results.– 6 – C o un t s δχ TA+PAO > 100 EeV
P-value=0.11P-value=0.23 C o un t s δχ PAO > 100 EeV
P-value= 0.0756P-value=0.101 C o un t s δχ All > 100 EeV
P-value=0.073P-value=0.099 C o un t s δχ TA > 100 EeV
P-value=0.086P-value=0.106
Figure 3 . Distributions of δχ found in observed data (blue, filled histograms) and in simulated datacorresponding to the semi-isotropic null (red, open histograms) and the exposure-corrected null (green,open histograms). The histograms have been truncated at δχ = 10 for better display. Significances( p -values) have been calculated for the ≤ δχ ≤ bins. Figure 3 also shows p -values or the probability of finding the correlated events ( ≤ δχ ≤ ) in observed data as a fluctuation of the randomly distributed UHECRs in the sky.The probability − p ≈ is the confidence level (CL) that the IceCube neutrino eventsand all available UHECR data with energy ≥ EeV are correlated. A correlation withsimilar CL exists between the neutrino and PAO-only data sets and between the neutrinoand TA-only data sets. The Poisson probability of obtaining N hits = 7 in PAO data when4 are expected from the semi-isotropic null distribution and N hits = 6 in TA data with 3.8expected from the same null distribution are ≈ . , in very good agreement with our p -values.Similarly, for the combined data set of all UHECRs > EeV, N hits = 12 when expectedvalue is 8.8 corresponds to a Poisson probability of ≈ . , again in very good agreement with– 7 – C o un t s / , N hits TA+PAO > 100EeV C o un t s / , N hits PAO > 100EeV C o un t s / , N hits All > 100EeV C o un t s / , N hits TA > 100EeV
Figure 4 . Comparisons between the N hits distributions in the δχ ≤ bins of Fig. 3 obtainedfrom the semi-isotropic (red solid lines) and exposure-corrected (green solid lines) null distributions.Also plotted are the Poisson distributions (dotted lines) for the average values of the respective nulldistributions in the δχ ≤ bins of Fig. 3. The vertical lines are the observed N hits values in data. our p -value.We remind the readers that the counts in the δχ distributions with TA+PAO data isnot the algebraic sum of the counts in the distributions with TA and PAO data separately.This is because our δχ statistic choose the nearest UHECR data point even if more than oneare present within the error circle of a neutrino event. The same is true for distribution withall UHECRs. We list the correlated events in Table 2 against the neutrino event numbers inref. [1]. Note that we list all UHECRs giving δχ ≤ in the table. There are 7 UHECRswhich are correlated with 2 or more neutrino events. None of the correlated neutrinos arePeV neutrino events.Figure 4 shows a comparison between the two null distributions for UHECRs with– 8 – event no. [1] δχ Energy (EeV) RA ( ◦ ) Dec ( ◦ ) Experiment1 0.41 108.2 45.6 − . PAO0.95 106.8 37.59 13.9 TA2 0.97 150 294.5 − . AGASA11 0.10 100.1 150.1 − . PAO16 0.006 127.1 192.8 − . PAO17 0.77 144 241.5 23.0 AGASA21 0.55 111.8 352.6 − . PAO24 0.78 101.4 285.74 − . TA0.97 150 294.5 − . AGASA25 0.06 150 294.5 − . AGASA0.07 101.4 285.74 − . TA0.10 135.5 288.3 0.34 TA0.12 118.3 287.7 1.5 PAO0.58 105 298.5 18.7 AGASA0.62 123 318.3 3 Haverah Park29 0.18 124.8 295.6 43.52 TA31 0.35 101 201 71 Haverah Park33 0.34 118.3 287.7 1.5 PAO0.40 135.5 288.3 0.34 TA0.74 101.4 285.74 − . TA0.84 105 298.5 18.7 AGASA34 0.20 104 345.75 34 AGASA0.22 135 306.7 46.8 Volcano Ranch0.25 122.2 347.7 39.46 TA0.34 118 340.6 12 PAO0.34 124.8 295.61 43.53 TA0.36 105 298.5 18.7 AGASA0.45 123 318.3 3 Haverah Park0.47 116 353 19 Haverah Park0.50 120 349 12.3 AGASA0.55 120.3 285.5 33.62 TA0.71 134 281.25 48.3 AGASA
Table 2 . IceCube cosmic neutrino events correlated with UHECRs above 100 EeV. energy ≥ EeV in Fig. 3 by using the N hits within the δχ ≤ bin from simulations forboth the null distributions. The two null distributions agree well in all cases except for thecombined analysis of the TA and PAO data. A comparison with Poisson distribution withfrequency for the corresponding cases are also shown. For PAO UHECRs >100 EeV the twonull distributions follow the respective Poisson distributions but not for the other cases. Theblack vertical line represents the observed N hits .We do the same statistical analysis with UHECRs above 80 EeV. The results are shownin Figure 5. There are 6 new correlations in the PAO-only data. Only 10 is expected fromour null distributions as compared to 13 total in data. This reduces correlation between theIceCube and PAO data to ≈ − CL. A list of UHECRs from the PAO correlated withthe neutrino events is given in Table 3. Note that the 2 PeV neutrino event (event number– 9 – C o un t s δχ TA+PAO > 80 EeV
P-value=0.13P-value=0.197 C o un t s δχ PAO > 80 EeV
P-value= 0.127P-value=0.159 C o un t s δχ TA+PAO+AGASA > 80 EeV
P-value=0.267P-value=0.32 C o un t s δχ TA > 80 EeV
P-value=0.064P-value=0.095
Figure 5 . The same as in Figure 3 but for UHECRs with energy ≥ EeV. ≈ PeV each still remain uncorrelated with UHECRswith energy ≥ EeV. There are 6 UHECRs in Table 3 which are correlated with more thanone neutrino events. In particular an 82 EeV PAO event is correlated with 4 neutrino events.Lowering the UHECR energy lower limit to 80 EeV adds 2 new correlated events inthe case of TA-only data with a total of 8 as compared to ≈ . expected from both the nulldistributions, giving a CL of ≈ . Combining the PAO and TA data results in similarsignificance as obtained from individual data sets. Combining the PAO, TA and AGASAdata reduces the significance of correlation.Further lowering the UHECR energy lower limit to 60 EeV gives no significant correlationbetween the IceCube cosmic neutrino data and UHECR data. Figure 6 shows that the numberof correlated events in data is very similar to those expected from the null distributions in allcases. Such a loss of significance is expected when there is no real correlation between the– 10 – event no. [1] δχ Energy (EeV) RA ( ◦ ) Dec ( ◦ )1 0.41 108.2 45.6 − . − . − .
11 0.10 100.1 150.1 − .
15 0.6 82.3 287.7 − .
16 0.006 127.1 192.8 − . − .
21 0.55 111.8 352.6 − .
21 0.6 83.8 26.8 − .
22 0.85 80.9 283.7 − .
24 0.77 80.9 283.7 − .
25 0.095 80.2 283.7 − . . . − . Table 3 . IceCube cosmic neutrino events correlated with UHECRs detected by PAO above 80 EeV. data sets.
As we noted earlier, energy calibration among different UHECR experiments is a widely-debated issue. If UHECR flux is uniform over the whole sky and each experiment measuresthe same primary particles’ energy then the number of UHECR events should be proportionalto the exposures of the experiments. Therefore it is difficult, in particular, to reconcile the10 TA events at > EeV compared to the 6 from PAO, which has 20 times more exposurethan TA. There are many energy rescaling procedure suggested among experiments (see,e.g., refs. [15–17]) to bring their respective measured fluxes close to each other, mostly atthe “ankle” regime. Even these procedures cannot reconcile number of events, after exposurecorrections, above 100 EeV among different experiments. It is plausible that the energyrescaling factors themselves are energy dependent, differing from the ankle regime to theGZK regime. Reconstructing such energy-dependent rescaling factors is beyond the scope ofthis paper. We hope the experimental collaborations will provide such factors in future.To illustrate the energy rescaling effect on our correlation study, we adopt a recentprocedure in ref. [15] which is based on a joint PAO and TA analysis of UHECRs from anoverlapping region in the sky. We decrease the energies of the TA events by 25 % but keepthe energies of the PAO events unchanged [15]. So the number of UHECRs events above100 EeV from TA is now 4, out of which only 2 correlates with the neutrino events in the– 11 – C o un t s δχ TA+PAO > 60 EeV
P-value=0.74P-value=0.80 C o un t s δχ PAO > 60 EeV
P-value= 0.5P-value=0.6 C o un t s δχ TA+PAO+AGASA > 60 EeV
P-value=0.8P-value=0.86 C o un t s δχ TA > 60 EeV
P-value=0.36P-value=0.59
Figure 6 . The same as in Figure 3 but for UHECRs with energy ≥ EeV. δχ ≤ bin (see Fig. 7). Interestingly, however, there are now 6 counts in the ≤ δχ ≤ bin which corresponds to a Poisson probability of 0.0108 according to the semi-isotropic null .A combined analysis of the TA and PAO data considering the above energy rescaling, givesno significant correlation with neutrino data. We search for astrophysical source candidates for UHECRs which are correlated with IceCubecosmic neutrino events, assuming both are produced by the same sources. We use data fromTables 2 and 3 for this purpose. The experimental angular resolution of the UHECRs is of theorder of ◦ . However, Galactic and intergalactic magnetic field can deflect them by more thana few degrees from their source directions. The deflection angle in the intergalactic random– 12 – P-value=0.71P-value=0.634 C o un t s δχ TA > 100 EeV
P-value=0.235P-value=0.327 C o un t s δχ TA+PAO > 100 EeV
Figure 7 . The same as in Figure 3 upper-right and bottom-left panels but the energies for the TAevents have been reduced by compared to the PAO events. magnetic field [18] with strength B rdm and coherence length λ coh is δθ IG ≈ . ◦ Z (cid:18) E cr
100 EeV (cid:19) − (cid:18) B rdm (cid:19) (cid:18) D
200 Mpc (cid:19) / (cid:18) λ coh
100 kpc (cid:19) / (4.1)where Z and E cr are the charge and energy of the UHECR and D is the distance to thesource. The deflection angle in a small-scale Galactic random magnetic field, using Eq. (4.1)with B rdm = 1 µ G, λ coh = 100 pc is much smaller, δθ G ≈ . ◦ Z , for E cr = 100 EeV and D = 10 kpc. However, the deflection angle in the large-scale regular component of theGalactic magnetic field in the disk and in the halo can be larger, ∼ ◦ – ◦ [19, 20]. Hereafterwe assume that UHECRs with energy ≥ EeV are dominantly protons . We also chose aconservative source search region of ◦ around the directions of UHECRs which are correlatedwith cosmic neutrino events.We also limit our source search within a comoving volume with its radius set by the GZKeffect of p UHECR + γ CMB interactions and corresponding energy losses by UHECR protons[5, 6]. A crude estimate of the mean-free-path for this interaction can be obtained from thenumber density of CMB photons with . K temperature in the local universe, which is (cid:15)n ( (cid:15) ) = 1 . × ( (cid:15)/ meV) exp [4 . (cid:15)/ meV)] − − . (4.2)Thus the number density is 244 cm − at the peak photon energy (cid:15) = 2 . k B (2 .
73 K) =0 . meV, where k B = 8 . × − eV K − is the Boltzmann constant. A parametrizationof the UHECR proton’s mean-free-path, using delta function approximation of the pγ crosssection, is given by λ p ≈ . (cid:18) E p
100 EeV (cid:19) − exp (cid:20) . (cid:18) E p
100 EeV (cid:19) − (cid:21) Mpc , (4.3) Note that the mass composition measurement by the PAO collaboration by using shower maxima, whichfavors heavy nuclei as primaries, is done up to an energy ∼ EeV only [22]. – 13 –hich reproduces results from numerical calculations with accurate treatment [21] within ∼ in the ∼ –200 EeV range. For reference, λ p = 539 , 247, 138 and 26 Mpc at E p = 60 , 80, 100 and 200 EeV, respectively. We search for astrophysical sources withinredshift z = 0 . , which corresponds to a luminosity distance d L = 270 . Mpc in Λ CDMcosmology with H = 69 . km s − Mpc − , Ω M = 0 . and Ω Λ = 0 . [23]. The properdistance, d p = d L / (1 + z ) = 241 Mpc, is similar to λ p at 80 EeV.We have used the Swift -BAT 70 month X-ray source catalog [24] to search for astrophys-ical sources which are correlated with UHECR and cosmic neutrino events. In 70 monthsof observations, the catalog includes 1210 objects of which 503 objects are within redshift ≤ . . Out of these 503 X-ray selected objects at least 18 are simultaneously correlated withthe neutrino events and UHECRs above 100 EeV, see Table 4. The correlated X-ray sourcesare all Seyfert (Sy) galaxies except ABELL 2319 which is a galaxy cluster (GC). The X-rayluminosity of these sources vary between L X ≈ – erg s − , with Cygnus A the mostluminous of all. Note that the PAO collaboration has also found an anisotropy at ∼ . CLin UHECRs with energy ≥ EeV and within ∼ ◦ circles around the AGNs in Swift -BATcatalog [24] at distance ≤ Mpc and X-ray luminosity L X (cid:38) erg s − [2]. Our list inTable 4 includes NGC 1142 which is also one of the five sources that dominantly contributeto the anisotropy found in the PAO data [2].In another correlated source search we have used bright extragalactic radio sources withflux density ≥ Jy at 5 MHz from the Kühr catalog [25]. It has 61 sources within knownredshift ≤ . . Only 3 sources from this catalog are correlated simultaneously with IceCubeneutrinos and UHECRs above 100 EeV, see Table 4. Two of these sources are Seyfert galaxiesand the third one is a galaxy cluster. There are two common sources, that are correlated withboth neutrinos and UHECRs, between the Swift -BAT and Kühr catalogs. These are NGC1068 and PKS 2331-240. Both of them are Seyfert galaxies.We have also searched the first AGN catalog (1LAC) published by the
Fermi -LAT col-laboration [26] for possible correlations with neutrino and UHECR arrival directions but didnot find any.It is interesting note that the cosmic neutrino events (nos. 2, 12, 14, 15 and 36) whichare strongly correlated with the Fermi Bubbles [27, 28], except for event no. 2, do not appearin Table 4. This could be a hint to possible extragalactic [29] and Galactic [30] componentsin the neutrino event data. After searching for astrophysical sources correlated with both IceCube cosmic neutrino eventsand UHECRs, we calculate their corresponding fluxes required to produce observed events.First, we describe our point-source neutrino flux calculation method. We assume a power-lawflux of the following form J ν α ( E ν ) = A ν α (cid:18) E ν
100 TeV (cid:19) − κ , (4.4)which is the same for all 3 flavors: α = e, µ, τ . We estimate the normalization factor fromthe number of neutrinos events N ν of any flavor as A ν α = 13 N ν T (cid:80) α (cid:82) E ν E ν dE ν A eff ,α ( E ν ) (cid:0) E ν
100 TeV (cid:1) − κ , (4.5) The centers of the error circles within the Fermi bubbles’ contours Here we tacitly assume that flavor identification is not efficient. – 14 – eutrinoEvent
UHECR
Swift
X-ray Source Catalog [24]RA Dec Experiment Name z Type1 45.6 − . PAO NGC 1142 0.0289 Sy2NGC 1194 0.0136 Sy1MCG +00-09-042 0.0238 Sy2NGC 1068 0.0038 Sy211 150.1 − . PAO 2MASX J10084862-0954510 0.0573 Sy1.817 241.5 23 AGASA 2MASX J16311554+2352577 0.0590 Sy229, 34 295.6 43.52 TA 2MASX J19471938+4449425 0.0539 Sy2ABELL 2319 0.0557 GCCygnus A 0.0561 Sy221 352.6 − . PAO PKS 2331-240 0.0477 Sy22, 24, 25 294.5 − . AGASA 2MASX J19373299-0613046 0.0103 Sy1.534 340.6 12 PAO MCG +01-57-016 0.0250 Sy1.8MCG +02-57-002 0.0290 Sy1.5UGC 12237 0.0283 Sy2349.0 12.3 AGASA NGC 7479 0.0079 Sy2/Liner2MASX J23272195+1524375 0.0457 Sy1NGC 7469 0.0163 Sy1.2352.6 − . Haverah Park NGC 7679 0.0171 Sy2NeutrinoEvent
UHECR Kühr Radio Source Catalog [25]RA Dec Experiment Name z Type1 45.6 − . PAO NGC 1068 0.0038 Sy221 352.6 − . PAO PKS 2331-240 0.0477 Sy234 340.6 12 PAO NGC 7385 0.0255 GC
Table 4 . Sources correlated with UHECRs and neutrino events simultaneously. where T is IceCube lifetime and A eff ,α is effective area for different flavors. We use T = 988 days for IceCube 3-year data release [1] as in our correlation analysis and the followingparametrization, correct within ∼ uncertainty, of the effective areas [31] A eff ,e = (cid:40)(cid:2) . × − ( E ν / TeV) . − . (cid:3) m , TeV < E ν < TeV (cid:2) .
459 ( E ν / TeV) . − . (cid:3) m , E ν > TeV (4.6) A eff ,µ = (cid:40)(cid:2) . × − ( E ν / TeV) . − . (cid:3) m , TeV < E ν < TeV (cid:2) .
389 ( E ν / TeV) . − . (cid:3) m , E ν > TeV A eff ,τ = (cid:40)(cid:2) . × − ( E ν / TeV) . − . (cid:3) m , TeV < E ν < TeV (cid:2) . E ν / TeV) . − . (cid:3) m , E ν > TeV . – 15 –or the limits of the integral in Eq. (4.5) we set E ν = 25 TeV and E ν = 2 . PeV,reflecting uncertainty in energy estimate reported by the IceCube collaboration [1].We use neutrino flux to calculate neutrino luminosity of the corresponding source as L ν = 4 πd L (cid:88) α (cid:90) E ν (1+ z ) E ν (1+ z ) dE ν E ν J ν,α ( E ν ) . (4.7)These luminosities are listed in Table 5. We use two values of κ , the choice κ = 2 . is motivatedby fit to IceCube data assuming an isotropic distribution of events [1, 32] and the choice κ =2 . is motivated by the cosmic-ray spectrum expected from Fermi acceleration mechanisms.Note that N ν = 3 for 2MASX J19373299-0613046, N ν = 2 for 2MASX J19471938+4449425and N ν = 1 for all other sources. Neutrino luminosities listed in Table 5 are within a factor5 of the corresponding X-ray luminosities of the sources. For the radio sources, neutrinoluminosity far exceeds the corresponding radio luminosity.We also calculate UHECR flux from the observed events by using exposure for therespective experiments. We use a power-law form for the observed UHECR flux above 28.8EeV break energy as [33] J uhecr ( E cr ) = A uhecr (cid:18) E cr EeV (cid:19) − . ; E cr ≥ . , (4.8)and derive the normalization factor as A uhecr = N uhecrΞ ω ( δ )Ω (cid:82) E cr2 E cr1 dE cr (cid:0) E cr EeV (cid:1) − . . (4.9)Here Ξ is the total integrated exposure, as mentioned in ref. [34], Ω is the solid angle of the de-tector and ω ( δ ) is the relative exposure for particular declination angle δ . For reference, we usefor PAO, Ξ PAO = 66 , km yr sr and Ω PAO = 1 . π sr [2]; for TA, Ξ TA = 3 , km yr srand Ω TA = 0 . π sr [3]; for AGASA, Ξ AGASA = 1 , km yr sr and Ω AGASA = 0 . π sr[35]. We do not use the Haverah Park event that is correlated with a neutrino event. Wecalculate ω ( δ ) from ref. [36] but adapt it for different experiments by using their respectivegeographical locations and zenith angle ranges. For the lower and upper limits of integrationin Eq. (4.9), we use E cr1 = 80 EeV and E cr2 = 180 EeV, allowing a uncertainty for the100 EeV threshold energy used to search correlation and 150 EeV maximum energy found fora UHECR correlated with a neutrino event and a source (see Table 2).In order to calculate cosmic-ray luminosity of the sources, first we note that if cosmicneutrinos detected by IceCube are coming from the same source that are correlated withUHECRs, then the cosmic-ray flux in Eq. (4.8) needs to be extrapolated down to ∼ TeVwhich is required to produce ∼ TeV neutrinos. Second, the flux in Eq. (4.8) needs to becorrected for GZK suppression above ∼ EeV. Given a cosmic-ray proton luminosity L cr between the generation energies E (cid:48) cr1 = 500 TeV and E (cid:48) cr2 = 180 EeV with ∝ E (cid:48)− κ cr spectrumin a source at redshift z , the cosmic-ray flux on the Earth is [37, 38] J cr ( E cr ) = L cr (1 + z )4 πd L ( κ − E (cid:48) cr1 E (cid:48) cr2 ) κ − E (cid:48) κ − − E (cid:48) κ − E (cid:48)− κ cr (cid:18) dE (cid:48) cr dE cr (cid:19) . (4.10)The cosmic-ray energy at the source and on the Earth are related through various energylosses [37]. Following ref. [38] we have plotted cosmic-ray flux in Fig. 8 using Eq. (4.10) for We assume they are dominantly protons. – 16 –ource name L X (cid:0) erg/s (cid:1) L ν (cid:0) erg/s (cid:1) L cr (cid:0) erg/s (cid:1) /L R (cid:0) erg/s (cid:1) κ = 2 . . κ = 2 . . NGC 1142 . /0.012(74 GHz) 0.95 1.0 0.7 5.4NGC 1194 . / . (1.4 GHz) 0.2 0.2 0.04 0.2MCG +00-09-042 . / . (1.4 GHz) 0.64 0.71 0.3 2.1NGC 1068 . /0.0034(31.4 GHz) 0.016 0.017 0.001 0.0072MASX J10084862-0954510 . / . (1.4 GHz) 3.9 4.32 44 5782MASX J16311554+2352577 . / . (1.4 GHz) 4.1 4.6 1600 220002MASX J19471938+4449425 . / . (1.4 GHz) 6.8 7.6 211 26000ABELL 2319 . / . (1.4 GHz) 3.7 4.1 270 3500Cygnus A . / (14.7 GHz) 3.7 4.1 290 3700PKS 2331-240 . / . (31.4 GHz) 2.6 2.9 9.5 1022MASX J19373299-0613046 . / . (1.4 GHz) 0.24 0.26 1.3 7.3MCG +01-57-016 . / . (1.4 GHz) 0.71 0.78 0.5 3.6MCG +02-57-002 . / . (1.4 GHz) 0.95 1.1 1.0 7.5UGC 12237 . / . (1.4 GHz) 0.91 1. 0.9 6.6NGC 7479 . / . (22 GHz) 0.07 0.08 0.3 1.42MASX J23272195+1524375 . / . (1.4 GHz) 2.4 2.7 280 2900NGC 7469 . / . (365 MHz) 0.3 0.3 2.2 14NGC 7679 . / . (1.4 GHz) - - - -NGC 1068 . /0.0034(31.4 GHz) 0.016 0.017 0.001 0.007PKS 2331-240 . / . (31.4 GHz) 2.6 2.9 9.5 102NGC 7385 - / . (31.4 GHz) 0.7 0.8 0.5 4.0 Table 5 . Neutrino (25 TeV–2.2 PeV) and cosmic-ray (500 TeV–180 EeV) luminosities required for thecorrelated sources in Table 4 to produce observed data. Also listed are
Swift -BAT X-ray luminosity[24] radio luminosity for these sources, with corresponding radio frequencies in parentheses. L cr = 10 erg s − and for various redshift in the range . ≤ z ≤ . . We have also usedtwo different values for κ as we did for neutrino flux calculation.Figure 8 provides a map to estimate cosmic-ray luminosity of the sources listed in Table4 which are correlated with UHECR and neutrino events. The UHECR flux in Eq. (4.8),calculated from data, corresponds to a point in Fig. 8 at E cr ≈ EeV. We estimate thesource luminosity L cr by equating this flux to the expected flux in Eq. (4.10) at 80 EeV forthe redshift of a given source. These luminosities are listed in Table 5. Note that except forNGC 1068 ( z = 0 . ), NGC 1194 ( z = 0 . ) and MCG +00-09-042 ( z = 0 . ) thecosmic-ray luminosity with κ = 2 . is comparable or higher than the neutrino luminosity for– 17 – × × × × - - - - - - - [ L c r / e r g s - ] E c r J c r ( e r g c m - s - ) × × × × - - - - - - - E cr ( eV ) [ L c r / e r g s - ] E c r J c r ( e r g c m - s - ) z 0.01 0.02 0.03 0.04 0.05 0.06 κ = κ = Figure 8 . Expected UHECR flux on the Earth from sources at different redshift . ≤ z ≤ . but with fixed luminosity L p = 10 erg s − in the TeV to 200 EeV range. all sources. The cosmic-ray luminosity exceeds the X-ray or radio luminosities for all sourcesexcept for NGC 1142 and NGC 1194, in case κ = 2 . . We have investigated whether the arrival directions of cosmic neutrinos, detected by IceCube[1], with energy ∼ TeV–2 PeV are correlated with the arrival directions of UHECRs withenergy (cid:38)
EeV. In order to test correlation we have used an invariant statistic, called theminimum δχ [7], which is constructed from the angle between two unit vectors correspondingto the directions of the neutrino events and UHECRs, and weighted by the angular resolutionsof the neutrino events. We have evaluated the significance of any correlation by using MonteCarlo simulations of randomly generated UHECR directions and comparing with data. Wefound that IceCube cosmic neutrinos are correlated with UHECRs with energy ≥ EeVwith significance at
CL. The significance, however, decreases with decreasing energy ofUHECRs, leaving no correlation at an energy threshold of EeV. To take into accounttrial factor, since we searched for correlation with N trial = 3 UHECR energy thresholds, wecalculate post-trial p -value as p post − trial = 1 − (1 − p signal ) /N trial = 0 . , with p signal = 0 . that we found in data.We have searched for astrophysical sources in the Swift -BAT X-ray catalog [24], theKühr radio source catalog [25] and
Fermi -LAT 1LAC AGN catalog [26] within ◦ error circles– 18 –f the ≥ EeV UHECRs which are correlated with cosmic neutrino events, assuming theUHECRs are protons. We made a cut in redshift, z ≤ . , while searching for sources in thecatalogs. This corresponds to a proper distance of 241 Mpc, similar to the mean-free-pathof an 80 EeV proton in the CMB. The choice of ◦ error circle is motivated by deflection ofUHECR protons in the intergalactic and Galactic magnetic fields. We found that 18 sourcesfrom the Swift -BAT X-ray catalog and 3 sources from the Kühr radio source catalog arewithin ◦ error circles of the UHECRs that are correlated with cosmic neutrinos. Except forABELL 2319 and NGC 7385 which are galaxy clusters, the rest of the sources are Seyfertgalaxies with Cygnus A being the most well known. Our finding is consistent with that ofthe PAO collaboration who found significant correlation between UHECR arrival directionsand Seyfert galaxies in the Swift -BAT X-ray catalog [2]. We did not find any source from the
Fermi -LAT 1LAC AGN catalog fitting our search criteria.Estimates of the neutrino and UHECR fluxes for the correlated events were used tocalculate corresponding 25 TeV–2.2 PeV neutrino luminosity and 500 TeV–180 EeV cosmic-ray luminosity under the hypothesis that both originated from the sources we found in the
Swift -BAT and Kühr catalogs. The neutrino luminosities are of the same order as the X-rayluminosities of the sources. The cosmic-ray luminosities, depending on the source spectrum,are comparable or higher than both the neutrino and X-ray luminosities. Comparison betweenthe nonthermal X-ray luminosity with the cosmic-ray or neutrino luminosity gives a possibilitythat the energy in X-ray producing electrons can be compared to that of cosmic-ray protons,both accelerated at the sources.Acceleration of UHECRs near the central black holes of AGNs was proposed over 20 yearsago [39, 40]. Interactions of these UHECRs with UV and X-ray photons could produce high-energy neutrinos [39, 41]. Seyfert galaxies are radio-quite AGNs and do not have strong jets,although parsec scale jets in them have been observed in the last decade [42–44]. Collisionsbetween blobs in this jet and formation of shocks may lead to acceleration of protons toan energy at least up to eV, with subsequent photomeson interactions producing high-energy neutrinos [45]. Acceleration of heavy nuclei and subsequent gamma-ray and neutrinoproduction in radio-quite AGNs have also been discussed [46]. Predictions have also beenmade for GeV–TeV gamma-ray emission from UHECR interactions in Cygnus A [47], whichis also a powerful radio galaxy (3C 405).If a fraction η X of the X-ray luminosity, L X = 10 L erg s − , of the Seyfert galaxies isnonthermal then one can estimate the energy density in magnetic field in the X-ray emittingregion as B / π = η X L X / πR c . Using R ≈ R cm, 3 times the Schwarzschild radiusof a black hole of mass M bh = 10 M (cid:12) , the magnetic field is B = 10 ( η X L ) / R − G. As-suming protons are accelerated in the same region, their maximum energy can be E max = eBR = 2 . × ( η X L ) / eV. This is problematic for the X-ray luminosities of Seyfertgalaxies in Table 5, which are correlated with ≥ EeV cosmic rays, and the magneticenergy density must exceed the nonthermal X-ray energy density by a factor (cid:38) for pro-ton acceleration to ∼ eV. This additional energy could be accommodated if a sizablefraction of the Eddington luminosity, L Edd = 1 . × ( M bh / M (cid:12) ) erg s − , could beconverted to magnetic energy. The required cosmic-ray luminosities ( κ = 2 . ) in Table 5 forSeyfert galaxies are above the Eddington luminosity for 2MASX J16311554+2352577, 2MASXJ19471938+4449425, 2MASX J23272195+1524375. In case of Cygnus A, M bh and L Edd arean order of magnitude larger. The κ = 2 . cosmic-ray luminosities are more problematic. Theopacity for photomeson ( pγ ) interactions with (cid:15) X = 1 keV X-ray photons and the subsequent (cid:38) TeV neutrino production opacity is τ pγ ≈ L R − ( (cid:15) X / − .– 19 – hint of correlation that we found between the IceCube cosmic neutrino events andUHECRs with energy ≥ EeV should be investigated further by the experimental collabo-rations. Establishing a concrete correlation will be a ground-breaking discovery. Also a futureextension of IceCube to increase its sensitivity in the > PeV range will be very useful toprobe the cosmic neutrino spectrum and if there is a cutoff in the spectrum. A cutoff in thespectrum is not natural at the PeV scale if the same sources produce ≥ EeV cosmic raysand neutrinos. Whether the weak AGNs, which are plentiful in the nearby universe, are thesources of UHECRs and neutrinos or not is a question that will continued to be debated andinvestigated in the years to come.
Acknowledgments
We thank Paul Sommers for useful comments. We also thank an anonymous referee forhelpful suggestions to improve this work. This work was supported in part by the NationalResearch Foundation (South Africa) grants nos. 87823 (CPRR) and 91802 (Blue Skies). Thisresearch has made use of the VizieR catalog access tool, CDS, Strasbourg, France. Theoriginal description of the VizieR service was published in A&AS 143, 23.
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