BL Lacertae are probable sources of the observed ultrahigh energy cosmic rays
Abstract
We calculate angular correlation function between ultrahigh energy cosmic rays (UHECR) observed by Yakutsk and AGASA experiments, and most powerful BL Lacertae objects. We find significant correlations which correspond to the probability of statistical fluctuation less than , including penatly for selecting the subset of brightest BL Lacs. We conclude that some of BL Lacs are sources of the observed UHECR and present a list of most probable candidates.
BL Lacertae are probable sources of … \sodtitleBL Lacertae are probable sources of the observed ultrahigh energy cosmic rays \rauthorP. G. Tinyakov and I. I. Tkachev \sodauthorTinyakov, Tkachev \PACS98.70.Sa
Introduction.
Identification of sources of ultrahigh energy cosmic rays (UHECR) is extremely important. Knowing production sites of UHECR will help to explain the apparent absence of the GreisenZatsepinKuzmin (GZK) cutoff [1] by selecting a particular class of models. In the case of astrophysical origin it will give an invaluable information on physical conditions and mechanisms which may lead to acceleration of particles to energies of order eV. In the case of extragalactic origin, it will provide a direct information about poorly known parameters which influence propagation of UHECR, such as extragalactic magnetic fields and universal radio background.
There are observational reasons to believe that UHECR are produced by compact sources. It has been known for quite a while that the observed highest energy cosmic rays contain doublets and triplets of events coming from close directions [2, 3, 4]. Our recent analysis [5] based on the calculation of angular correlation function shows that explanation of clusters by chance coincidence is highly improbable: the correlation function for Yakutsk events [6] with energies eV has an excess at which would occur with probability for the uniform distribution, while the correlation function for AGASA events [3, 7] with energies eV has an excess at corresponding to chance probability . The combined probability of the fluctuation in both sets is . So significant autocorrelations should imply also large correlation of these events with their actual sources. It is a purpose of the present paper to identify these sources.
The clustering of UHECR by itself imposes certain constraints on possible source candidates. With the observed fraction of events in clusters, the total number of sources can be estimated along the lines of Ref. [8] to be of order several hundred. If the GZK cutoff is absent (or at energies below the cutoff), this estimate gives the number of sources in the entire Universe. Thus, to produce observed clustering, the extragalactic sources have to be extremely rare as compared to ordinary galaxies. Taking uniformly distributed sources for an estimate, the closest one is at .
Various astrophysical candidates such as neutron stars, supernovae, gammaray bursts, colliding galaxies, active galactic nuclei (AGN), lobes of radiogalaxies, dead quasars and others (for a review see Refs.[9] and references therein) have been proposed as sources of UHECR. Possible connection of highestenergy cosmic rays with these objects was considered in Refs. [3, 4, 10]. In this paper we study correlations of UHECR with BL Lacertae (BL Lac) objects which comprise a subclass of AGN. Our motivations for selecting BL Lacs are as follows. If AGNs are sources, only those which have jets directed along the line of sight, or blazars, can correlate with observed UHECR events (regardless of the distance to a blazar in a world without GZK cutoff), since particles accelerated in a relativistic jet are strongly beamed. Blazars include BL Lacs and violently variable quasars with flat and highly polarized spectra. These spectral features give direct indication of seeing a relativistically beamed jet very close to the line of sight. BL Lacs is a subclass of blazars characterized, in addition to the above spectral features which they share, by the (near) absence of emission lines in the spectra. This very important distinction indicates low density of ambient matter and radiation and, therefore, more favorable conditions for acceleration to highest energies.
The most recent catalog of AGNs and quasars contains 306 confirmed BL Lacs [11]. While this is the richest catalog we are aware of, it still may be incomplete. However, this is not crucial for establishing correlations between BL Lacs and UHECR events. Correlations of BL Lacs with UHECR were not studied before. We show that these correlations do exist and are statistically significant.
Method and results.
Our method is based on calculation of the angular correlation function and is similar to the one we have used in Ref. [5]. For each BL Lac, we divide the sphere into concentric rings (bins) with fixed angular size. We count the number of events falling into each bin and then sum over all BL Lacs, thus obtaining the numbers (data counts). We repeat the same procedure for a large number (typically ) of randomly generated sets of UHECR events. This gives the mean MonteCarlo counts , the variance and the probability to match or exceed the data count observed in the first bin. This probability is a function of the bin size . Peaks of or minima of with respect to show angular scales at which correlations are most significant.
The MonteCarlo events are generated in the horizon reference frame with the geometrical acceptance
where is the zenith angle. Coordinates of the events are then transformed into the equatorial frame assuming random arrival time. This transformation depends on the latitude of the experiment, so events simulating different experiments are generated separately. The distribution of the generated MonteCarlo events in declination and right ascension reproduces well that of the experimental data.
We have shown in Ref. [5] that autocorrelations are most significant for the two sets of UHECR events: 26 Yakutsk events with energy eV and 39 AGASA events with energy eV. If BL Lacs are sources of UHECR, their correlations with UHECR should be particularly large for these two sets. Assuming that energies of the events are not important for correlations at small angles, we combine them together in one set of 65 events.
Since acceleration of particles to energies of order eV typically requires extreme values of parameters, probably not all BL Lacs emit UHECR of required energy. We assume that this ability is correlated with optical and radio emissions, and select the most powerful BL Lacs by imposing cuts on redshift, apparent magnitude and 6 cm radio flux. For more than a half of BL Lacs the redshift is not known. It is generally expected that these BL Lacs are at . We include them in the set. The cuts
(1) 
leave 22 BL Lacs which are shown in Fig. 1 together with 65 cosmic rays from the combined set. The dependence on cuts is discussed below.
As one can see from Fig. 1, two of 22 BL Lacs coincide with the two triplets of UHECR events, one coincides with a doublet and two BL Lacs lie close to single events. This is reflected in the correlation function, which is plotted in Fig. 2 for the bin size . It has 8 events in the first bin while 1.25 is expected for the uniform distribution. The probability of such an excess is . BL Lacs and UHECR events which contribute to this correlation are listed in Table 1. Note that at large angles the correlation function fluctuates around zero, which shows that the acceptance in the MonteCarlo simulation is chosen correctly.
Name  l  b  z  E/ eV 

1ES 0806+524  166.25  32.91  0.138  3.4; 2.8; 2.5 
RX J10586+5628  149.59  54.42  0.144  7.76; 5.35 
2EG J0432+2910  170.52    5.47; 4.89  
OT 465  74.22  31.4    4.88 
TEX 1428+370  63.95  66.92  0.564  4.97 
The probability as a function of the angular separation is shown in Fig. 3. It has a minimum at . For comparison, smooth curve shows the behavior expected when 9 events out of 65 come from BL Lacs (assuming that accuracy of angle determination is and distribution of errors is Gaussian ).
The small angular size of the peak in the correlation function, compatible with the experimental angular resolution, suggests that UHECR events responsible for these correlations are produced by neutral primary particles. Indeed, if the primaries were charged they would have been deflected in the Galactic magnetic field by depending on arrival direction, particle energy and the model of the magnetic field, and correlations at would be destroyed.
Discussion.
We have seen that 22 bright BL Lacs and 65 cosmic rays from the combined set are strongly correlated: the probability to find 8 or more out of 65 randomly generated cosmic rays within of any of the BL Lacs is . Should one conclude that BL Lacs are sources of UHECR, or the above correlation may be an artifact of our selection procedure? Let us discuss possible loopholes.
First potential source of problem is incompleteness of the BL Lac catalog and nonuniform coverage of the sky. Indeed, 22 BL Lacs selected by cuts (1) almost all lie in the Northen hemisphere due to observational bias. However, it is easy to understand that, unlike for many other astrophysical problems, for establishing the fact of correlations with UHECR the incompleteness of BL Lac catalog is not essential. The method we use works for any set of potential sources regardless of their distribution over the sky (including such extreme cases as just one source, or a compact group of several sources). This is guaranteed by using the same set of sources with real data and with each MonteCarlo configuration.
Second potential problem is related to the fact that there exist strong autocorrelations in the UHECR set, while MonteCarlo events are not correlated. One may wonder if the observed correlation with BL Lacs is (partially) due to autocorrelations of UHECR. To see that this effect is negligible in our case, we performed test MonteCarlo simulations with configurations containing the same number of doublets and triplets as the real data, and random in other respects. We found practically no difference between the two methods.
Finally, there is an issue of cuts and related issue of selection of catalogs. One may worry that by adjusting several cuts and searching in several catalogs the probability as small as can be found with any set of astrophysical objects, even with those which have nothing to do with UHECR. So, the question is how easily the low values of can be obtained within the adopted procedure of cuts. This question can be studied quantitatively by assigning a proper penalty for each try in such a way that resulting probability gives true measure for the correlations in question to be a statistical fluctuation. For the case at hand we have found that when proper penalties are assigned, the resulting probability is larger than by about an order of magnitude. In other words, one would have to try thousands of catalogs to find correlation as significant as we have found for BL Lacs. We present the procedure of penalty calculation and resulting significance of correlations below.
In fact, we did not search for correlations with other catalogs of astrophysical objects. Thus, no penalty is associated with that. Similarly, we did not adjust the set of cosmic rays (as explained before, it was selected in Ref. [5] on the basis of most significant autocorrelations). But we do adjust cuts in the BL Lac catalog. Therefore, we should assign a penalty factor to this adjustment.
It is clear that some cuts have to be made because 65 events may have at most 65 sources among 306 BL Lacs in the catalog (probably much less). In our calculations we imposed cuts on redshift, magnitude and 6 cm radioflux. The cut on redshift is motivated by the expected total number of sources; we did not adjust this cut to minimize the probability. Cuts on magnitude and radioflux were adjusted. Corresponding penalty can be calculated in the following way (cf. Ref [5]). A random set of cosmic rays should be generated and treated as real data, i.e. minimum probability is searched for by adjusting the cuts in the BL Lac catalog in exactly the same way as it was done for the real data. This should be repeated many times, giving different each time. The number of occurrences of a given value of is then calculated as a function of . This gives the probability (we call it ) that the adjustment of the cuts in BL Lac catalog produces with a random set of cosmic rays. The probability is a correct measure of the significance of correlations. We define as the penalty factor.
We calculated with random sets of cosmic rays. We have found that the penalty grows at small and approaches a constant value in the limit (for this reason it is more convenient to define the penalty factor than to work in terms of ). For the real set of UHECR and is reached with the cuts
(2) 
They leave 5 BL Lacs two of which coincide with triplets. (In the previous section different cuts are presented because, with similar significance, they include more potential sources.) This probability should be multiplied by the penalty factor. We found that the penalty factor is at [12]. This gives , which is the probability that the correlation we have found is a statistical fluctuation.
Conclusions.
The significant correlations between UHECR and BL Lacs imply that at least some of BL Lacs are sources of UHECR. Most probable candidates can be seen in Fig. 1 and are listed in Table 1. Two BL Lacs, 1ES 0806+524 and RX J10586+5628, coincide with triplets of UHECR events (in the second case the third event of a triplet is at and is not listed in the table). Both of them are at the distance of Mpc from the Earth. The nextprobable candidate 2EG J0432+2910 has unknown redshift.
The correlations at small angles are difficult to explain by charged primary particles. Within the Standard Model the only two neutral candidates are photon and neutrino. Photon attenuation length at eV is much smaller (see e.g. [9]) than the distance to even the closest BL Lac. However, photons can not be ruled out yet if one assumes sources at Mpc and “extreme” astrophysical conditions: primary particles accelerated to eV with “hard” spectrum and , and extragalactic magnetic fields G [13]. Neutrino models [14] require similar assumptions except that constraints on the magnetic filed are relaxed for “pure” neutrino sources and there is no constraint on the distance to the sources. However, if “pure” neutrino sources cannot be arranged, the model effectively becomes “photonic” [13]. If astrophysical difficulties can be overcome, these models will be appealing candidates for the solution of the UHECR puzzle. Alternatively, one may resort to a new physics, e.g., violation of the Lorentz invariance [15].
Independent crosschecks are necessary to determine whether particular objects are sources of UHECR. One of these crosschecks could be coincidence of arrival time of events contributing to small angle correlations with periods of activity of candidate BL Lacs. Dedicated monitoring of these BL Lac may be suggested. It is also important to analyze possible specific properties of air showers initiated by these events.
Acknowledgments
We are grateful to S.L. Dubovsky, K.A. Postnov, M.E. Shaposhnikov and D.V. Semikoz for valuable comments and discussions. This work is supported by the Swiss Science Foundation, grant 2158947.99, and by INTAS grant 991065.
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