For more than 40 years, the galactic SNRs have been believed to be the sites of production of the bulk of the observed CR flux. The strong shocks in SNRs may provide – through the diffusive shock acceleration mechanism – very effective, up to 10 to 30 per cent, conversion of the total SN explosion into relativistic protons and nuclei, as well as explaining the hard, 
type, source spectra, as it follows from the CR propagation studies in the galactic disk.Although quite plausible, these arguments still remain as a theoretical conjecture, and thus cannot supersede direct evidence. The detection and identification of n0-decay Y-rays from SNRs, primarily at TeV energies, would be the first straightforward proof of the acceleration of protons by SNR shocks. On the other hand, the failure to detect
r Y-ray signals from several selected SNRs would impose strong constraints on the energy in accelerated protons, 
This would indicate an inability of the ensemble of galactic SNRs to explain the observed CR fluxes.
For a standard "power-law with exponential cutoff" energy distribution of protons,
the flux of Y-rays produced in the interactions of CR protons with the ambient gas is basically determined by the scaling parameter
where WCR is the total energy in accelerated protons, n is the ambient gas density, and d is the distance to the source. The Y-ray spectrum at high energies repeats the spectral shape of parent protons – a power-law with approximately the same power-law index r and a cutoff at E ~ 0.1E0. For a given energy density of accelerated protons , the integral flux of Y-rays above 300 MeV is almost independent of the proton spectral index,
Fig. 5.1 Fluxes of
(heavy solid line) and IC (thin lines) Y-rays from a 103 year old SNR. The
Y-rays are calculated for the scaling parameter A = 1. The IC
Y-ray fluxes are calculated for 3 different values of the magnetic field B = 3 (solid curve), 10 (dashed curve), and
(dot-dashed curve), assuming that the electrons produce the same flux of synchrotron radiation
For the protons and electrons we assume the same acceleration spectrum with r = 2 and Eo = 100 TeV.
At energies
and for the standard chemical composition of CRs and the ambient gas,
where fr « 1 and 0.2 for the the proton spectral indices r = 2 and 2.3, respectively. The integral fluxes of n0-decay Y-rays from a 103 yr old SNR for the scaling parameter A =1 are shown in Fig. 5.1. The Y-ray fluxes are calculated for a proton spectrum with r = 2 and E0 = 100 TeV.
Within the diffusive shock acceleration model, the amount of relativistic particles increases with time as the remnant passes through its free expansion phase, and reaches the maximum when the SNR enters the so-called Sedov phase – the phase when the mass of the swept-up matter becomes comparable with the mass of the ejecta. Correspondingly the peak luminosity of Y-rays appears at the early Sedov phase (Drury et al., 1994, Berezhko and Volk, 1997), typically 103 – 104 years after the SN explosion. At this stage the radius of the shell exceeds several parsecs which implies an angular size of about 1° for relatively close (d < 1 kpc) SNRs. The conflict between the angular size (^ <x 1/d) and the Y-ray flux (JY <x 1/d2) significantly limits the number of SNRs which could be detected in Y-rays by the current generation of IACTs. The best candidates would be young SNR at distances of a few kpc or less, which have already entered their Sedov phase, show nonthermal synchrotron radiation, and are expanding into regions of enhanced gas density. An additional criterion would be the possible association of these SNRs with Y-ray sources detected by EGRET. The Whipple collaboration has chosen for observations 6 SNRs which more or less satisfy these condition. No positive signal from any of these SNR has been detected (Buckley et al., 1998). The corresponding upper limits on the fluxes above 300 GeV are shown in Fig. 2.8 along with the EGRET integral fluxes or upper limits (Esposito et al., 1996).
These points are compared with the theoretical expectations normalised to the EGRET data points as well as with a range of fluxes based on conservative estimates of the scaling parameter A. Although being very important and meaningful, these upper limits cannot be used as an evidence against the SNRs as sites of acceleration of galactic cosmic rays, especially if one takes into account large, typically up to a factor of 10, uncertainties in the scaling parameter A. For example, even for the most stringent constraint on the TeV flux set so far, the upper limit obtained by the HEGRA collaboration for the Tycho SNR at the 33 mCrab level is still above the prediction of the "nominal theory" . The model predictions in Fig. 2.9 assume that Tycho has progressed well into the Sedov phase. In fact this young supernova remnant could still be in the pre-Sedov phase. If so, the fraction of the mechanical energy converted into relativistic particles could be below 10 percent (0 = 0.1), and correspondingly lower Y-ray fluxes would be expected.
The TeV upper limits become uncomfortable only if we assume that the MeV/GeV fluxes detected by EGRET are dominated by interactions of accelerated protons with the ambient nebular gas. However, due to the poor angular resolution of EGRET, the association of most of the "excess GeV" regions with SNRs is questionable and needs further observational evidence. For example, in the case of Y Cygni, the GeV data are not consistent with the spatial extent of the remnant, and can be associated with a weak X-ray source, RX J2020.2+4026 (Brazier et al, 1996). The theoretical predictions do not unconditionally support the associations of GeV sources with SNRs either. Drury et al.(1994) argued that EGRET could not detect GeV Y-rays from standard SNRs, because even for the best candidates the parameter A is less than 1, with the flux level determined by A =1 being only marginally compatible with the EGRET sensitivity. Only special configurations like dense molecular clouds overtaken by supernova shells may provide detectable Y-radiation at both GeV and TeV energies at the level of sensitivities of EGRET and current ground-based instruments.
If we nevertheless accept that the EGRET detections have physical links to SNRs, i.e. assume that the GeV radiation is produced at interactions of accelerated particles with ambient gas, there are at least 3 possible reasons that could explain the lack of TeV Y-rays from the same SNRs.
Large contributions of the electron bremsstrahlung. Assuming that only 20 percent (or less) of the observed fluxes below 1 GeV from IC 433, Y Cygni and W44 is contributed by protons, the flux of n0-decay Y-rays at TeV energies would be correspondingly reduced by a factor of 5, i.e. to the level which does not contradict the TeV upper limits shown in Fig. 2.8. If so, the major fraction of GeV radiation should be attributed to electrons, most likely of bremsstrahlung origin. This would require the electron-to-proton ratio of accelerated particles close to 1, i.e. strong, up to a factor of 100, enhancement of electrons in the total energy budget of accelerated particles compared to their relative content in the locally observed CRs. If true, this would imply that SNRs cannot be responsible for the bulk of observed cosmic ray protons and nuclei.
Cutoffs in the proton spectrum below 1 TeV. This assumption can be tightly connected with the requirement of dense ambient gas. In order to provide the observed absolute fluxes of GeV Y-rays by interactions of accelerated electrons and/or protons we should assume high density environments, otherwise it is difficult to keep the total energy budget in accelerated particles within reasonable limits. Indeed, the EGRET fluxes above 300 MeV shown in Fig. 2.8 are close to 10-7 ph/cm2s, which implies that the parameter A in Eq.(5.2) should be as large as 3. For the maximum available content of CRs in a SNR, WCR — 1050 erg, the density of the ambient hydrogen gas should exceed 10 cm-3, given the > 2 kpc distances to the SNRs in the Whipple selection list. If particle acceleration takes place in the same region, a variety of new effects, in particular the role of wave damping on the maximum energy to which particles can be accelerated (Drury et al., 1996), should be included in theoretical treatments. For example, Baring et al. (1999) have argued, based on their study of nonlinear shock acceleration, that SNRs expanding into high density regions cannot effectively accelerate particles beyond 1 TeV. Another mechanism for "early cutoffs" in the SNR spectra, associated with a feedback effect in the highly turbulent plasma, has been suggested by Malkov et al. (2002). Although the cutoffs below 1 TeV in the spectra of accelerated protons could be the simplest solution to the problem of lack of Y-rays from the "EGRET SNRs", it leaves unanswered the question of whether it should be treated as an argument against the SNR paradigm of galactic cosmic rays in general, or it simply implies that another type of SNRs should be invoked for explanation of the spectrum of GCRs extending to 1015 eV.
Steep acceleration spectra. For a fixed scaling parameter A, a proton spectrum with r = 2.3 results in a factor of 5 lower Y-ray flux above 1 TeV than one with a harder spectrum of r ~ 2. Thus, a steeper acceleration spectrum of protons would be another simple way to avoid TeV Y-rays at the flux levels exceeding the Whipple and HEGRA upper limits, even if the observed fluxes around 1 GeV are entirely due to the n0-decay component of radiation. In this regard we note that the presently favoured source spectrum < E-r with r < 2.1, derived from the observed energy dependence of the ratio of secondary to primary cosmic rays (e.g. Swordy, 2001), implies negligible reacceleration of CRs in the ISM. Otherwise softer source spectra, as steep as E-2 4, should be expected. This actually agrees with the so-called Kolmogorov type spectrum for the interstellar turbulence which predicts CR propagation with a diffusion coefficient < E-1/3. Although CR source spectra with r — 2.3 — 2.4 seem to be in conflict with models of the nonlinear diffusive shock acceleration, such relatively steep source spectra do not rule out SNRs as major contributors to the galactic cosmic rays.
An example of a good fit to the Y-ray data from the supernova remnant IC 443, based on the above assumptions to avoid high TeV fluxes, is shown in Fig. 5.2. In accordance with this phenomenological study (Gaisser et al., 1998), for a specific set of parameters it is possible to accommodate both the EGRET fluxes and TeV Y-ray upper limits.
Fig. 5.2 Interpretation of Y-ray fluxes from IC 433. The solid, dashed and dotted lines correspond to the contributions from bremsstrahlung,
decay, and inverse Compton processes, calculated for the following model parameters:
In all Y-ray production scenarios in SNRs the inverse Compton component does not noticeably contribute to the overall flux of low energy 
Y-rays (see e.g. Gaisser et al., 1998). Therefore, the absolute EGRET fluxes require quite a large density of ambient gas which in turn could be the reason for the large power-law indices of r ^2.3 2.4 or "early cutoffs"
in the proton spectra, if the particle acceleration and Y-ray production regions coincide. In this context one may conclude that the SNRs in low density and homogeneous environments may appear as more effective TeV emitters. The scaling factors A of such SNRs are, however, small,
thus the integral Y-ray fluxes of hadronic origin at 1 TeV could be below
In addition to the low fluxes, the detection of TeV radiation of hadronic origin from such objects is not a easy task because of the extended character of radiation (1° or so) and the significant "contamination" induced by inverse Compton Y-rays of directly accelerated electrons.
