Cosmic Ray Physics
Peter Mészáros
The same shocks which the electrons responsible for the non-thermal gamma-rays in GRB should also accelerate protons present in the shockis. Both the internal and the external reverse shocks are mildly relativistic, and are expected to lead to a power law proton energy distribution of the form E^{-2} via the Fermi mechanism. Using the same shock parameters inferred from broad-band photon spectral fits, one infers that protons can be accelerated up to Lorentz factors of ~ 10^{11} in the observer frame. The relativistic protons can interact with photons in the GRB environment (e.g. the gamma-rays produced by the electrons in the jet itself, and produce TeV neutrinos, which would thus be intimately connected with the accelerated protons. The maximum proton energies achievable in GRB shocks are ~ 10^{20} eV (Waxman, 1995, Vietri 1995), i.e. the so-called GZK limit energies expected in the diffuse cosmic ray flux being measured with large cosmic ray arrays, such as the AUGER Observatory, in which the Penn State particle and gravitational astrophysics group is involved. (One of Auger’s 1600 ground detectors is shown in the figure, in front of the Andes mountains in Mendoza, Argentina). To reach these particle energies, the acceleration time must be shorter than both the radiation or adiabatic loss time and the escape time from the acceleration region. The resulting constraints on the magnetic field and the bulk Lorentz factor are close to those required to obtain efficient gamma-ray emission at ~1 MeV. If the accelerated electrons which produce the gamma-rays and the protons carry a similar fraction of the total energy, the GRB cosmic ray energy production rate at 10^{20} eV throughout the universe is of order 10^{44} erg/Mpc^3/yr, comparable to the observationally required rate of gamma-rays from GRB and from the observed diffuse cosmic ray flux. These numbers depend to some extent on uncertainties in the burst total energy and beaming fraction, as well as on the poorly constrained burst rate evolution with redshift.
Direct confirmation of a GRB or another different origin of UHECRs will be difficult. Large cosmic ray arrays such as the Pierre Auger Observatory (see Figure above) and the Telescope Array (TA) have a large acceptance, which will greatly improve the cosmic ray count statistics. The current results favor the bottom-up scenario, and do in fact show a clear GZK feature (see figure on the left). The directional information is being used to try to test or constrain the AGN, GRB and other scenario, so far without significant correlations. Earlier results from the Pierre Auger Observatory did suggest a (weak) possible correlation with AGNs, but with moe data this correlation has not proven significant. The problem is that these AGNs are not good candidates for accelerating cosmic rays (typically blazar-type AGNs are though to be good candidates). The correlation, however, is good with the general large scale distribution of matter (i.e. all galaxies). One possibility is of course that GRBs located at random in the galaxies inside the GZK radius are responsible, as argued above. Another possibility is that radio-quiet AGNs , which are ten times more numerous than radio-loud blazars, may be the acceleration sites (Pe’er, Murase and Mészáros). If indeed UHECRs are largely heavy nuclei, then nearby radio quiet AGNs are in fact quite viable sources of UHECRs.
The question of why the spectrum of cosmic rays at EeV energies and higher is so flat and becomes even flatter above that (“ankle”) energy is an unsolved issue. One explanation that we have recently proposed (Katz, Mészáros and Waxman, 2010) is that it is due to the observed cosmic rays measured being those which just manage to escape the relativistic shock of the sources, at the upper end of the accelerated spectrum, which automatically yields an inverse squared law in energy or flatter spectrum
A factor which plays a role in formulating sources models is that CRs will interact with intra-source ambient photons or protons, leading to charged and neutral pions whose decay leads to VHE neutrinos and γ-rays (see neutrinos). However, IceCube has tested a possible spatial and temporal correlation between VHE neutrinos and the GRBs measured by Swift or Fermi GBM, useing as a template a simlplified standard internak shock model, an internal shock magnetic dissipation model and a photospehruc model, concluding (IceCUbe, 2015; IceCube, 2017) that less than ~1% of these EM-detected classical GRBs can be responsible for the observed VHE neutrinos. Of course there are a number of uncertanities, assumptions and approximations in these models used by IceCubei; in particular, they assumed that the observed photons and the CRs and neutrinos are produced in the same shocks or acceleration regions. This, however, need not be the case. A good case has been made for the MeV photon spectrum being produced in the jet photosphere (see, e.g., GRBs). However, the CRs could be mainly accelerated in shocks further out, including outer internal shocks or external reverse shocks ( Asano and Meszaros, 2016), where the target photon density for pγ interactions is much smaller, and a much lower neutrino production is expected. Such a model in fact fits well the Auger and TA data on the ultra-high energy CRs in the 10^{18.5} eV – 10^{20.5} eV range, while satisfying the IceCube neutrino limits, as shown in the figure on the left.
This research is partly sponsored by NASA
References:
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“Radio Quiet AGNs as Possible Sources of Ultra-high Energy Cosmic Rays” , Pe’er, A., Murase, K., and Meszaros, P., 2009, Phys.Rev, D, 80:123018 (arXiv:0911.1776)
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