When deriving information about the accelerated protons one has to subtract a possibly non-negligible "contamination" caused by directly accelerated electrons that upscatter photons of the 2.7 K CMBR (which is the dominant target photon field in most of SNRs) to Y-ray energies. The same multi-TeV electrons responsible for IC Y-rays of TeV energies produce also synchrotron UV/X-ray radiation. The typical energies EY and ex of the IC and synchrotron photons produced by an electron are related by
This relation neglects the Klein-Nishina effect which however becomes important at energies
The ratio of the synchrotron and IC fluxes
at these energies does not practically depend on the shape of the spectrum of parent relativistic electrons, but strongly depends on the magnetic field:
For a flat X-ray spectrum with photon index ~ 2, the energy flux fX is almost energy-independent. Therefore fX at a typical energy of 1 keV could serve as a good indicator of the IC Y-ray fluxes expected at TeV energies, although for magnetic fields B < 100 ^G the energy of synchrotron photons (produced by the same parent electrons) relevant to ~ 1 TeV Y-rays is in the soft X-ray domain.
The contribution of n0-decay Y-rays dominates over the contribution of the IC component when
where S1keV is the flux of nonthermal synchrotron radiation at 1 keV normalised to
(the corresponding energy
which is a typical level of nonthermal X-ray fluxes reported from shell-type supernova remnants SN 1006 and RX J1713.7-3946.
In Fig. 5.1 the integral fluxes of
and inverse Compton Y-rays from a SNR of age 103 yr are shown. The
flux corresponds to the scaling factor A = 1. The IC fluxes are calculated by normalising the synchrotron X-ray fluxes to
for ambient magnetic fields of 3yU,G, 10yU,G, and 30^G. For both electrons and protons we assume continuous acceleration over 103 years with a time-independent injection spectrum with r = 2 and E0 = 100 TeV. Note that for the normalisations used, the results presented in Fig. 5.1 only slightly depend on the source age, unless it is larger than the synchrotron cooling time of multi-TeV electrons,
Examination of the condition given by Eq.(5.7) is of particular interest. If it could be shown that the TeV signals, reported by the CANGAROO collaboration from two shell type SNRs, SN 1006 (Tanimori et al., 1998b) and RX J1713.7-3946 (Muraishi et al., 2000) cannot be explained by IC scattering, this would be observational evidence of shock-acceleration of protons in a SNR, because the only alternative for the explanation of TeV emission of these objects are Y-rays of nucleonic origin produced in interactions of accelerated protons with the ambient gas.
Generally, with the exception of Cas, and perhaps a few other specific objects, the IC radiation of SNRs in the TeV region is dominated by the 2.7 K CMBR seed photons. As long as the gas number density does not significantly exceed 10 cm-3, in this energy regime we can safely ignore the contribution from electron bremsstrahlung. The relative contributions of these radiation components can be estimated from Fig. 5.3 where the electron energy-loss timescales due to different cooling processes are shown. This is true, however, for the stationary (continuous) electron accelerator. After the electron accelerator turns off, the number of electrons with E > 20 TeV producing > 1 TeV inverse Compton Y-rays diminishes, and bremsstrahlung then may dominate even in the TeV regime. It is interesting to compare also the bremsstrahlung and n0-decay Y-ray fluxes. The cooling times of both processes slightly (logarithmically) depend on particle energy. The cooling time of electrons due to relativistic bremsstrahlung is comparable with the p — p cooling time of protons, but it is shorter, by a factor of 3 to 5, than the characteristic cooling time of protons through the n0-decay channel. Therefore the n0-decay Y-ray flux would dominate over the bremsstrahlung Y-ray flux (at energies above 100 MeV), if the overall energy in accelerated protons exceeds the energy in relativistic electrons by a factor of 10 or more.
Fig. 5.3 The electron-energy-loss timescales,
, due to synchrotron emission, bremsstrahlung, Compton scattering of the 2.7 CMBR and Coulomb collisions for the case of
(it is assumed that the interstellar gas with
is compressed by a strong shock by a factor of 4). For these parameters, Compton losses dominate below 100 MeV, bremsstrahlung losses dominate near 1 GeV, and the synchrotron losses dominate above 10 GeV. On each radiative loss curve the typical photon energy emitted by an electron with the given kinetic energy is indicated. This shows that the radio synchrotron and the relativistic bremsstrahlung (as well as n0-decay) emission components will endure for the longest time after the electron source has turned off, and the X-ray synchrotron, TeV inverse Compton and non-relativistic (sub-MeV) bremsstrahlung emission components will decrease fastest.
