Observability of neutron events above the Greisen-Zatsepin-Kuzmin cut-off due to violation of Lorentz invariance

The clustering of ultra high energy cosmic ray events suggests that they have originated from compact sources. One of the possible physical mechanisms by which ultra high energy nuclei reach the Earth from far away astrophysical sources (quasars or BL Lac objects) evading the Greisen-Zatsepin-Kuzmin (GZK) cut-off is by violation of Lorentz invariance. Assuming that there is violation of Lorentz invariance, we calculate the expected number of neutron events from some of the EGRET sources (including $\gamma$-ray loud BL Lac objects) which can be correlated in direction with ultra high energy cosmic ray events observed by AGASA above energy $4\times10^{19}$eV. We present in this paper what AGASA should see in future if violation of Lorentz invariance is responsible for the propagation of ultra high energy cosmic rays having energies above the GZK cut-off when there is a correlation of EGRET sources with the ultra high energy cosmic ray events.

magnetic field are at present exciting fields of study. References [12,13,14] discuss different suggestions on these issues. The Greisen-Zatsepin-Kuzmin(GZK) cut-off [15] will prevent nucleons of energy greater than 4 × 10 19 eV from travelling more than about 50 Mpc, but most of the suitable astrophysical acceleration sites are located at greater distances. AGASA experiment [3] has recorded about 8 events above 10 20 eV, whereas data recorded by HiRes fluorescence detector [16] seem to be in agreement with the GZK-cutoff [17]. Since currently the experimental data are not convincing enough for accepting the presence of the GZK cut-off, theoretical suggestions for observability of cosmic rays above the GZK cut-off remain of interest to us. The Physics involving the formation and annhilation of topological defects (TDs) has been studied as a possible explanation of observing UHECR. However TD annhilation has unique observational consequences such as, copious production of particles like neutrinos and γ-rays [18]. The experimental signatures of the Z-burst scenario has been discussed in [19]. Gamma ray bursts have also been identified as a possible explanation of observing UHECR above the GZK cut-off [20,21].
If the highest energy cosmic rays have a neutral component then that will come to the Earth from the direction of its source. Elbert and Sommers [22] identified radio-loud quasar 3C147 as an ideal source within 10 • of the highest energy event observed by Fly's Eye experiment [1] at energy 3.2 × 10 20 eV. Later another quasar PG0117 + 213 was identified by Biermann [23] within the error cone of the second highest energy event observed by AGASA [24]. In the last few years a lot of work has been done by different groups [25,26,27,28] in correlating UHECR events with radio quasars and BL Lac objects. It was pointed out by Dubovsky et al. [29] that the statistics of clustering of ultra high energy cosmic ray events suggests their correlation with compact sources. In [30] the authors have pointed out that there is no significant correlation between quasars or BL Lac objects and ultra high energy cosmic ray events. They have used data from Haverah Park [5] and Volcano Ranch experiments [6] for their statistical analysise. However, the authors of [26] have shown that there is a significant correlation between compact sources and observed ultra high energy cosmic ray events using the data from AGASA [3] and Yakutsk [4] experiments. The probability of positional coincidence between BL Lac objects and UHECR events to occur by chance in a random distribution is of the order of 10 −4 . The still unknown data from HiRes experiment [2] and the accumulating data from AUGER experiment [31] will enable us to carry out statistical analysis with a bigger set of data in the near future.
Since, as of now it is not clear whether the UHECR events are statistically uncorrelated with compact sources at high redshifts, the physical mechanisms by which neutral component of UHECR may come to the Earth evading the GZK cut-off from high redshifts are still exciting fields of study for us. In the Z-burst scenario [32] or in models of hypothetical "immune messengers" [33] neutral particles can come to the Earth from the direction of the source evading the GZK cut-off. It has been suggested by Coleman and Glashow [34] that if there is violation of Lorentz invariance (VLI) then protons and neutrons of energies above the GZK cut-off will reach the Earth without interacting with the cosmic microwave background. In the present work we show that one can test whether VLI is responsible for the observability of the UHECR events above the GZK cut-off using the data from AGASA experiment and certainly with the data from AUGER [31] experiment in future. We have predicted what AGASA should see in future if VLI is the underlying physical mechanism for propagation of cosmic rays with energies above the GZK cut-off from compact sources at high redshifts.
We consider the ultra high energy cosmic ray events observed by AGASA above the GZK cut-off. Among this set of events we find that some of them can be correlated in direction with EGRET sources from the third EGRET catalog [36]. In [27] the authors have suggested that the sources of UHECR are high energy peaked BL Lac objects. Our set of correlated EGRET sources also include γ-ray loud BL Lac objects. If the radiation energy density is sufficiently high in a source, photo-pion production leads to the generation of a sufficient number of neutrons which can escape from the system. If there is VLI the neutrons having an energy above a certain energy will not decay. The energy above which the neutrons become stable depends on the degree of VLI. In [35] the authors have obtained a limit on the energy above which neutrons become stable, using observational data from the Yakutsk experiment [4]. These neutrons can travel through the cosmic microwave background with energy above the GZK cut-off when there is VLI and in that case we expect to detect them from the direction of the compact source. For clusters of UHECR events we consider sources within 4 • of the events and for a single event we correlate with a source within 2.5 • . In our correlated data set we have eight EGRET sources, among which three (3EG J0433+2908, 3EG J1052+5718 and 3EG J1424+3734) are confirmed BL Lac objects from the Véron 2001 catalog [37,27]. Among the remaining five, 3EG J1744-0310 is a quasar [38]. The four unidentified EGRET sources i.e. 3EG J1824+3441, 3EG J1903+0550, 3EG J0429+0337 and 3EG J0215+1123 may be BL Lac objects that have not yet been confirmed. Two of these four unidentified EGRET sources are also present in Table 3 of [27]. In the first row of TABLE I we note that the redshift of the EGRET source 3EG J0433+2908 is more than 0.3 [39]. The fourth and fifth columns of TABLE I give longitudes and latitudes of the sources in Galactic coordinates and the seventh and eighth columns display longitudes and latitudes of the UHECR events in Galactic coordinates.
We consider the sources of TABLE I whose redshifts are known and calculate the number of neutron events from them expected to be detected by AGASA in 30 years. We calculate the expected number of neutron events from the source 3EG J0433+2908 assuming its redshift to be 0.3. In future we will come to know the redshifts of the other EGRET sources and then it will also be possible to calculate the expected number of neutron events from them. There are both theoretical [40] and observational [41] reasons to believe that when proton acceleration is being limited by energy losses, the luminosity of the object in very high energy cosmic rays L CR is approximately equal to its luminosity in gamma rays. The cosmic ray luminosity L CR in the energy range 1 × 10 19 eV< E < 4 × 10 20 eV can be assumed to be emitted equally in each decade of energy E. In that case, in each decade of energy we expect the power emitted in UHECR in the energy range of 1 × 10 19 eV to 4 × 10 20 eV to be approximately L CR /10. Let 'A' be the area of AGASA detector which is 10 12 cm 2 [3]. Here we mention that the exposure of the AGASA detector is energy independent in the energy range in which we are interested. One can see the plot of exposure against energy of the UHECRs for AGASA detector in [42]. The expected number of neutron events in a time interval dt o in AGASA within the source energy interval of E 1 and E 2 can be expressed as where d is the luminosity distance of the source from the Earth. N n s and N n o are respectively the number of neutrons emitted at the source and observed by the detector. E s , E o are the source energy and observed energy of the neutrons respectively. If the redshift of the source is z then E o = E s /(1 + z). Similary the correction to be applied to observed time t o due to redshift of the source is t o = t s (1 + z), where t s is the time at which the neutron is emitted from the source.
We have assumed there is VLI and that the lower limit of the above integration is such that neutrons are stable above this energy.
We define F ob γ as the energy received in gamma rays per second per cm 2 on the surface of the Earth from an EGRET source and this quantity can be calculated from [36]. ǫ n is the efficiency of neutron production in the source. When the photon density in a source is sufficiently high then the efficiency of neutron and proton production become comparable near the end of the UHECR spectrum [43]. Hence it is not unreasonable to assume ǫ n = 1/2 in our calculation. If we assume the luminosity of the source in gamma rays of energy more than 100MeV L γ to be a fraction x times the luminosity of the source in UHECR L CR , then eqn.(1) can be written as An almost similar procedure has been followed in ref. [43] in calculating number of neutron events from Centaurus A but without the assumption of VLI. Using eqn. (2) we calculate the expected number of neutron events between observed energy intervals of 1 × 10 20 eV and 2 × 10 20 eV in AGASA from the sources of TABLE I whose redshifts are known. The second column of TABLE II displays the photon flux in 10 −8 photon cm −2 sec −1 above 100 MeV energy for the EGRET sources in the first column [36]. The third column shows the photon spectral indices from [36] of the EGRET sources displayed in the first column. The fourth and fifth columns present the expected number of neutron events in a time interval of 30 years in AGASA for case (1) ǫ n = 1/2, x = 1 and for case(2) ǫ n = 1/2, x = 1/2 respectively. In the last 10 years data from AGASA there is no event above 10 20 eV energy from the direction of the sources of first column of TABLE II. If VLI is the underlying mechanism for UHECR propagation then we can expect to see UHECR events above 10 20 eV from the direction of the sources presented in TABLE II in future. If we increase the area of the detector or the time of data collection then of course we would detect more neutron events than that presented in TABLE II. The number of neutron events will increase linearly with increasing area or time of data collection by the detector. Since the area of AUGER is 30 times larger than AGASA, we can expect such neutron events in a much shorter interval of time in AUGER.

Conclusion
In this paper we have presented how the UHECR data above the GZK cut-off can tell us whether VLI is the underlying mechanism for the propagation of these cosmic rays from quasars or BL Lac objects at high redshifts.