The featureless energy spectrum of cosmic rays, extending as a single power-law up to the knee around 1015 eV, indicates that the flux of galactic CRs is dominated by a single source population. If so, the representatives of this source population should be sources of nonthermal synchrotron X-rays and very high energy Y-rays. Since both radiation components have been reported from 3 prominent SNRs – SN 1006, RX J1713.7-39, and Cas A -one may interpret this as strong evidence of close association of this hypothetical source population with SNRs. On the other hand, the requirement of a single source population to dominate in production of the bulk of galactic CRs would then imply that the SNRs should be able to accelerate particles to at least 1015 eV (= 1 PeV). Although the "standard" diffusive shock acceleration theory applied to SNRs does not guarantee effective acceleration of protons beyond 1014 eV, particle accelerations to > 1015 eV is possible, at least in principle, in those SNRs (hereafter "PeV SNRs") where the magnetic field exceeds 0.1 mG. Remarkably, the CRs themselves may provide the necessary magnetic field through amplification of the ambient interstellar field by large-amplitude plasma waves (Lucek and Bell, 2000). The increased magnetic field reduces the diffusion coefficient, and correspondingly increases, by an order of magnitude or more, the maximum achievable energy (Bell and Lucek, 2001).
The most straightforward search for sites of such extreme "PeV SNRs" can be performed by ground-based detectors operating effectively in the energy regime > 100 TeV. In Fig. 5.13 are shown the fluxes of X- and Y-rays of hadronic origin expected from a "PeV SNR". Both radiation components are initiated by interactions of accelerated protons with the ambient medium with a gas number density n =1 cm-3 and magnetic field B = 0.2 G. While the Y-rays arise directly from the decay of n0-mesons, the X-rays are result of synchrotron radiation of secondary electrons, the products of
The lifetime of electrons producing X-rays,
in a magnetic field exceeding 0.1 mG is very short
compared to the age of the source. Therefore the synchrotron X-radiation actually could be considered as an unavoidable "prompt" radiation component of hadronic interactions, emitted simultaneously with n0-decay Y-rays. Consequently, both the X- and Y-ray fluxes depend on the total amount of high energy protons currently accumulated in the source, and the rate of p-p interactions, i.e. on the density of the ambient matter. Although approximately the same fraction of energy of the parent protons is transferred to secondary electrons and Y-rays, because the energy of relatively low energy (sub-TeV) electrons is not radiated away effectively, the n0-decay Y-ray luminosity exceeds the synchrotron luminosity. The Lx/Ly ratio depends on the proton spectrum as well as on the history of particle injection, but for any reasonable proton spectrum extending to ^ 100 TeV, the energy release through the X-ray channel exceeds 20-30 percent of the energy released through the n0-decay channel. The broadband spectra of hadronic radiation of a "PeV" SNR shown in Fig. 5.13 are calculated for a proton accelerator at a distance d =1 kpc operating during 103 yr with a constant rate Lp = 3 x 1038 erg/s; the total energy accelerated in protons is about Wp = Lp • T ~ 1049 erg. The power-law spectrum of protons is assumed to be ap = 2.1. The solid, dashed, and dot-dashed curves correspond to 3 different cutoff energies in the proton spectrum – E0 = 1015, 3 x 1015, and E0 = 1016 eV, respectively. Remarkably, the spectrum of n0-decay Y-rays in the corresponding cutoff region at — (1/10)E0 almost repeats the shape of the proton spectrum around E0. Thus the search for ultra-high energy Y-rays from SNR in the energy domain > 100 TeV would lead to the discovery and identification of galactic sources responsible for the CR spectrum up to the knee. Moreover, accurate Y-ray spectroscopic measurements at highest energies would provide extremely important information about the shape of the source (acceleration) spectra of protons. Needless to say, this information could be crucial for identification of the acceleration mechanisms in SNRs, as well as for understanding of the role of different processes (e.g. acceleration versus propagation) which are responsible for the formation of the knee in the CR spectrum.
Unfortunately, the prospects of realizing this exciting method in practical terms is quite limited due to the lack of projects of Y-ray detectors with an adequate sensitivity in the energy interval 1014 — 1016 eV. The deep survey by the large PeV air-shower array CASA-MIA, with sensitivity — 10-14 ph/cm2s above 100 TeV did not reveal any source across a large fraction of the northern sky (McKay et al., 1993). The fluxes shown in Fig. 5.13 require an order of magnitude better detector sensitivity, unless the total energy in accelerated protons exceeds 1050 erg and/or the sources are located in dense environments. Unfortunately, an improvement of the CASA-MIA sensitivity by an order of magnitude seems quite unrealistic, given the limited experimental interest in this energy interval, at least at present.
In such circumstances, the search for "PeV SNRs" via hard synchrotron radiation of secondary
electrons is an alternative, and perhaps an even more powerful tool, given the superior potential of X-ray detectors. In particular, Chandra and XMM-Newton have sufficient sensitivity to perform such studies. Remarkably, the spectrum of this radiation in the cutoff region is much smoother that the corresponding cutoff in the Y-ray spectrum. For example, while the energy distribution in the form of an exponential cutoff in the proton spectrum is directly transferred to electrons (but shifted by a factor of 10 to lower energies), the synchrotron radiation in the corresponding cutoff region behaves as
This important feature, which is seen in Fig. 5.13, should allow a more comprehensive study of the highest energy part of the spectrum of accelerated protons via X-rays – the third generation products of p-p interactions.
An apparent difficulty in this method is connected with the separation and identification of the "hadronic" synchrotron X-rays from other X-ray radiation components, in particular from the "nominal" synchrotron radiation of directly accelerated electrons. These two components can be distinguished if the magnetic field in the X-ray production region exceeds 0.1 mG and the proton spectrum extends to
In the case of a high magnetic field the position of the cutoff of the synchrotron radiation of directly accelerated electrons does not depend on the magnetic field and typically appears in the soft X-ray domain,
(see Eq.(5.14)).
Fig. 5.13 The broad-band spectra of radiation from a "PeV SNR" initiated by interactions of accelerated protons with the ambient gas.
On the other hand, the position of the spectral cutoff of the synchrotron radiation produced by secondary electrons,
, is very sensitive to the magnetic field. For example, in the Bohm diffusion regime, the proton cutoff energy is proportional to the strength of the magnetic field, thus 
Thus, for extreme SNRs, with very large magnetic fields and proton cutoff energies, the synchrotron radiation of secondary electrons may have a relatively hard X-ray-spectrum compared with the synchrotron spectrum of directly accelerated electrons. The search for such a component in the nonthermal X-ray spectra of young SNRs is of great interest. If we are lucky, this may result in the discovery of "PeV SNRs" !
