Cosmic Ray Physics

Peter Mészáros, Soebur Razzaque, XiangYu Wang

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 astrophysics group is involved. AUGER-ANDES (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.

When ultra-high energy cosmic rays (UHECR) in the range above ~10^{18} eV (or EeV) enter the Earth's upper atmosphere they collide with atmospheric nuclei and initiate hadronic (pions) and electromagnetic cascades (muon pairs, electron pairs, gamma-rays). The muons showers eventually reach the surface and can be detected with ground detectors, while the electromagnetic showers excite atmospheric nitrogen fluorescence (and also radiate via the Cherenkov effect) whose optical light can be detected with telescopes (see Figure on the left). SHOWER The decay of the charged pions and muons also produce neutrinos in the EeV range, whose showers at high inclination can be measured by surface detectors. The Pierre Auger Cosmic Ray Observatory (picture above) is a large international collaboration, in which Penn State plays a significant role. It uses a hybrid technique exploiting both surface detectors (1600 water Cherenkov tanks, covering a 3000 km^2 area, measuring the muons reaching the surface) and atmospheric fluorescence (24 Fly's Eye-type wide-angle telescopes monitoring the fluorescent trace of the developing electromagnetic showers through the atmosphere). Auger is more than half complete and is scheduled for completion in early 2007. It already has been taking data, which addresses various issues such as photon fraction, isotropy and spectrum.

Cosmic ray flux from AGASA and HIRES Discussions of GRB or AGN as cosmic ray sources are mainly oriented at exploring their contribution to the energy range above EeV (10^{18} - 10^{20} eV). (A model where GRB are responsible for CRs ranging from PeV to GZK is Wick et al, 2004). At EeV and higher energies the observed UHECR isotropy and the small expected magnetic deflection suggests an extra-galactic origin. The requirement that they are not attenuated by the cosmic microwave background through photomeson interactions constrains that they are originated within a volume inside a radius of 50-100 Mpc, the so-called ``GZK'' volume (e.g. Cronin 2005). The spectrum is expected to show such a GZK cutoff at about the GZK energy of 10^{20} eV. However, two previous cosmic ray experiments, AGASA and HiRes, reported conflicting results, at the 3-sigma level (see spectrum on the right). AGASA used a ground detector technique, while HiRes used an atmospheric fluorescence technique, and the two experiments were difficult to cross-calibrate (they were also in different locations). It is expected that Auger, using at the same location both techniques together in a hybrid scheme, will be able to resolve this question in a few years of observation.

Two broad classes of UHECR production models have been suggested. One of them, the ``top-down'' scenarios, attribute UHECR to the decay of fossil Grand Unification defects, and no GZK cutoff is expected. In the other, the ``bottom-up'' scenarios, it is assumed that UHECRs are accelerated in astrophysical sources, and these should exhibit a GZK cutoff. One of the most prominent candidate sources for the bottom-up scenario is GRBs (Waxman, 1995; 2004). Two other possibilities are AGNs, e.g. Berezinsky 2005, Rachen and Biermann 1997; and galaxy cluster shocks, e.g. Inoue 2005. The most commonly discussed version of the GRB scenario considers the UHECR to be protons accelerated in GRB internal shocks. The GRB contribution to the cosmic ray spectrum is plotted on the figure in the left, showing the GZK cutoff (from Waxman, 2004). GRB-CR SPECTRUM

Direct confirmation of a GRB (or other) origin of UHECRs will be difficult. The next generation cosmic ray detectors such as the Pierre Auger Observatory (see Figure above) will have a substantially enhanced effective target area, which will greatly improve the cosmic ray count statistics. This will help to disentangle the two scenarios (top-down or bottom-up) and will reveal whether a GZK feature indeed exists. Within the bottom-up scenario, the directional information may either prove or significantly constrain the alternative AGN scenario, and may eventually shed light on whether GRBs are indeed the sources of UHECRs.

In fact, recent results from the Pierre Auger Observatory have suggested a (weak) possible correlation with AGNs. 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 quite 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.

Alternatively, a peculiar type of supernovae, called hypernovae, are associated with sub-energetic GRBs, such as SN1998bw/GRB980425 and SN2003lw/GRB031203. Such hypernovae appear to have high (up to mildly relativistic) velocity ejecta, which may be linked to the sub-energetic GRBs. Wang, Razzaque, Meszaros and Dai (2008) find that the external shock produced by the high velocity ejecta of a hypernova can accelerate protons up to energies as high as 1E19 eV, and the cosmological hypernova rate is sufficient to account for the energy flux above the second knee. In addition, Wang, Razzaque and Meszaros find that hypernova can accelerate heavy nuclei up to 1E20 eV. This is interesting, in view of recent (2010) reports by the Auger group that the composition in the GZK range may be increasingly weighted towards heavy elements.

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

This research is partly sponsored by NSF

References:

``The spectrum of cosmic rays escaping from relativistic shocks", Katz, B., Meszaros, P. and Waxman, E., 2010, JCAP, 210:012

``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)

``On the Origin and Survival of Ultra-High-Energy Cosmic-Ray Nuclei in Gamma-Ray Bursts and Hypernovae", Wang, X-Y, Razzaque, S. and Meszaros, P. (2008), ApJ 677 432

``High-energy Cosmic Rays and Neutrinos from Semi-relativistic Hypernovae", Wang, X-Y, Razzaque, S, Meszaros, P and Dai, Z-G, 2007, Phys.Rev.D, 76:083009 (astro-ph/0705.0027)

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