Possible sources of ultrahigh-energy cosmic protons A. V. Uryson

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1 Possible sources of ultrahigh-energy cosmic protons A. V. Uryson P. N. Lebedev Physics Institute, Russian Academy of Sciences, /17924 Moscow, Russia (Submitted 17 June 1996) Pis'ma Zh. Eksp. Teor. Fiz. 64, No. 2, (25 July 1996) The arrival directions of showers with energies above ev, recorded by the Akeno and AGASA detectors, are analyzed. Their distributions over the celestial sphere are compared with the distributions of possible sources of protons of such high energies. An analysis using three standard deviations of uncertainty in the determination of the arrival directions of the showers shows that the sources of the protons initiating the showers are nuclei of active galaxies with red shifts z , i.e. their distance from us does not exceed 40 Mpc, assuming the Hubble constant is H= 75 km/s - Mpc American Institute of Physics. [S (96) ] PACS numbers: pq; Dh The origin of cosmic protons with ultrahigh energies E> 1017 CV is still unclear. From the standpoint of energetics, acceleration mechanisms, and trapping of particles by galactic magnetic fields, the most likely sources of such protons in the Galaxy could be pulsars. Outside the Galaxy the most likely sources could be the nuclei of active galaxies or quasars/-3 and/or hot spots of radio galaxies. 4 (In the explosion of supernovae, the maximum energy of accelerated protons is 1015 ev.s) The experimental data attest to the fact that wide atmospheric showers with energies E> ev arrive predominantly from high galactic latitude S.6,7 This indicates that they could be of extragalactic origin. The spectrum of extragalactic protons can possess a characteristic feature-an abrupt steepening at E ev due to the interaction of the protons with the cosmic background radiation, so that the flux of particles with energy E ev decreases twice as fast as the power-law extrapolation. 8,9 However, if the sources of such protons are mainly objects located comparatively close to us, then there will be no blackbody cutoff: The effective mean free path of particles with energies of 5 - IOt9 and 102 ev in the cosmic background photon field is 1000 and 200 Mpc, respectively, and protons with any energy, right up to E = 1022 ev, traverse practically freely distances of the order of Mpc.l Therefore if the proton sources are located at distances of the order of tens of Mpc from us, then the spectrum will not have a blackbody cutoff. Estimates of the distances to possible sources of cosmic rays with E> ev can be found in Refs. 4 and 11. In Ref. 4 it was assumed, based on an analysis of the chemical composition and spectrum of cosmic rays obtained by different groups, that the sources are powerful radio galaxies and distances of the order of 50 Mpc were obtained. In Ref. 11 it is shown that approximately 30% of the protons detected arrive from the plane of the Local Supercluster, i.e. from distances of the order of Mpc /96/ $ American Institute of Physics 77

2 In the present work, we compared the distribution given in Refs. 11 and 12 for the arrival directions of showers with energies E> ev with the distributions of the nuclei of active (and radio) galaxies and x-ray pulsars (as the most powerful pulsars) over the celestial sphere. We assumed that protons propagate in the intergalactic space along straight lines and that their deflection in the Galactic magnetic fields can be neglected. (The Galactic magnetic field equals approximately (3-5) Oe over a distance of the order of 20 kpc.l) The distribution of the arrival directions of showers over the sky can be determined from the Akeno and AGASA data (the arrival data recorded on other setups have not been published): These are the arrival directions of 12 showers with E > ev in the equatorial coordinates (a, S) from Ref. 12 and the Galactic coordinates (l,b) of three pairs of showers with E_ ev, which, to within the limits of error, have the same coordinates, from Ref. 11. Since the shower of Ref. 12 appears in one of these pairs, there were a total of 17 showers. The rms error in determining the coordinates of the showers is a-,rh = V in Ref. 11 and 0-,h--3 in Ref. 12. The optical coordinates of galaxies and pulsars are determined to within seconds, so that in identifying possible proton sources the search region was determined by a circle with radius Sash=7, 8, and 9. According to statistics, for a random distribution of the errors in the coordinates the probability that a proton falls within the 3 Osh range equals 99.8%. The search for radio galaxies and galaxies with active nuclei was made in the catalogs in Refs. 13 and 14-all galaxies from Ref. 13 and the galaxies from Ref. 14 which were not contained in Ref. 13 were studied. The search for x-ray pulsars was made in the catalog in Ref. 15. We examine first the search for galaxies. The showers were divided into groups: showers arriving from sections of the sky with galactic latitude I b I % 30 a) six showers from Ref. 12; b) 10 showers from Refs. 11 and 12; c) 12 showers, irrespective of latitude Ibl, from Ref. 12; and, d) all 17 showers, irrespective of latitude Ib1, from Refs. 11 and 12. As a rule, more than one galaxy was present in the error range of a shower, but within each range there was at least one galaxy with red shift z The arrival directions of the showers in the coordinates (a, 8), the group they belong to and also the coordinates and red shifts of galaxies with z , which fell within the error range of the showers, are presented in Table I. (The enumeration of the showers is ours.) The total number K of showers in a group and the number N of showers in a group in which at least one galaxy fell within the search field are presented in Table II. Next, we determined the probabilities that galaxies with different z fall within the error range of N out of K showers. Groups of fictitious showers whose arrival coordinates were determined randomly were studied. The groups consisted of 6 and 10 showers arriving from sections of the sky with b j % 30 and 12 and 17 showers with no limits on b. In each group, the coordinates of the fictitious showers were determined with the aid of a random number generator 16 in the field of view a=0 to 24 h, 8=-10 to 80. The 78 JETP Lett., Vol. 64, No. 2, 25 July 1996 A. V. Uryson 78

3 TABLE 1. Arrival directions of showers, groups to which they belong, and coordinates and red shifts of galaxies falling within the error range of a shower. Coordinates with z in No. Avalanche Reference Group the 3 ash=9 error range of a shower a 8 coordinates 13 z (Ref. 13) 1 1 h42m c,d c,d c,d a,b,c,d 11'37"' b,d b,d b,d b,d a,b,c,d a,b,c,d a,b,c,d a,b,c,d d ,12 c,d c,d c,d a,b,c,d artificial groups contained Nsim showers in which at least one galaxy with z --z, = 0.022, , and and arbitrary z was present within the 3 o-sh error range. The quantity Ns;, took on the values O--NS;,,,--K. In the group consisting of K showers, the probability P that a galaxy falls randomly within the error range of a given number Ns;,, of showers was determined as P=1"'=_ t(ns;,n); IM, where M is the number of tests performed for each group. The resulting probabilities P that a galaxy falls randomly within the error range of TABLE 11. Total number K of showers in groups, number of showers N whose error range contains at least one galaxy with z , and probability P of a random occurrence in the error range 3o-Sh for N showers. Probability P, Shower group Number of showers Number of showers 3 (sn K N a b < c d < 10-5 < JETP Lett., Vol. 64, No. 2, 25 July 1996 A. V. Uryson 79

4 Pr C 1~ 4 d to b ,-z I FIG. 1. Calculated values of the probability that at least one galaxy with arbitrary z and z--zi=0.022, , and falls within the error range 3 Q,,,h=7 for N of K showers. The curves through the computed points were drawn as a visual aid: a-k=n=6; b-k=n= 10; c-k= 12, N=8; d-k= 17, N= 13. a shower are shown in Fig. 1 for M= and different values of z in the groups (a,b,c,d). In addition, the probabilities for z and 30-Sh=7, 8, and 9 are presented in Table II. It is evident from the values of P presented that the random occurrence of galaxies with z in the search field of a fixed number N of showers is an unlikely event for groups with N%6 if 3ffsh=7 and N>6 if 3a-sh=8 and 9. The search for x-ray pulsars gave the following results. The pulsar A (X ) fell within the error range of shower No. 3. The probability that one pulsar falls accidentally within the search field of any of 12 showers equals Therefore, according to the theory of probability, this coincidence could be accidental. No galaxy listed in Table I emits significant fluxes in the radio or x-ray ranges. 13,14 This means that the presence of powerful radiation in these ranges apparently is not a necessary condition for sources of ultrahigh-energy protons. Possible sources are galaxies with active nuclei, located at distances R _- 40 Mpc from us, assuming the Hubble constant H=75 km/s.mpc. If this is so, then the spectrum of extragalactic protons will not possess a black-body cutoff. The conclusions obtained here can be checked in investigations which are just beginning. 17 In these investigations, a larger statistical sample of ultrahigh-energy showers, whose coordinates will be determined to within approximately 0.2, will be obtained. I am deeply grateful to G. B. Christiansen for his interest in this work and to A. V. 80 JETP Lett., Vol. 64, No. 2, 25 July 1996 A. V. Uryson 80

5 Zasov and A. 1. Nikishov for a discussion. I thank A. G. Gorshkov, V. K. Konnikova, and O. K. Sil'chenko for a discussion of the catalogs of galaxies and selection criteria for sources. 1 V. S. BerezinskiT, S. V. Bulanov, V. L. Ginzburg et al., Astrophysics of Cosmic Rays [in Russian], Nauka, Moscow (1990). 2 R. J. Protheroe and A. P. Szabo, Phys. Rev. Lett. 69, 2885 (1992). 3M. H. Salamon and F. W. Stecker, Phys. Rev. Lett. 73, 35 (1994). J. Rachen, T. Stanev, and P. Biermann, Astron. Astrophys. 273, 377 (1993). SE. G. Berezhko in Proc. 24th ICRC, Rome (1995), Vol. 3, p M. N. D'yakonov, T. A. Egorov, N. N. Efimov et al., Ultrahigh-Energy Cosmic Rays [in Russian], Nauka, Siberian Branch, Novosibirsk (1991). 7B. N. Afanasiev, M. N. Dyakonov, T. A. Egorov et al., in Proc. 24th ICRC, Rome (1995), Vol. 2, p $G. T. Zatsepin and V. A. Kuz'min, JETP Lett. 4, 78 (1966). 9K. Greisen, Phys. Rev. Lett. 16, 748 (1966). ' F. W. Stecker, Phys. Rev. Lett. 21, 1016 (1968). 11N. Hayashida, K. Honda, M. Honda et al., ICRR Report , Tokyo (1996). 12 N. Hayashida, K. Honda, M. Honda et al., in Proc. 22nd ICRC, Dublin (1991), Vol. 2, p V. A. LipovetskiT, S. N. Neizvestnyi, and O. M. Neizvesmaya, Soob. SAO, No. 55, SAO Akad. Nauk SSSR (1987). 1 M. P. Veron-Cetty and P. Veron, ESO Scientific Report N10 (1991). 15 S. B. Popov, (1996). 16 G. E. Forsythe, M. A. Malcolm, and C. B. Moler, Computer Methods for Mathematical Computations, Prentice-Hall, Englewood Cliffs, N. J. (1977). 17M. Teshima et al., Nucl. Phys. B 28, 169 (1992). Translated by M. E. 81 JETP Lett., Vol. 64, No. 2, 25 July 1996 A. V. Uryson 81