The shell type supernova remnant Cassiopeia A is the brightest and one of the best studied radio sources in our Galaxy. The synchrotron radiation of this source continues to submillimeter wavelengths, and perhaps even further to the infrared (Tuffs et al., 1997) and hard X-rays (Allen et al., 1997). The estimates of the mean magnetic field and the energy content in radio emitting electrons based on simple equipartition arguments give 0.16 mG and 5 x 1049 erg, respectively (Anderson et al., 1991). Assuming a larger field, of about 0.3 mG, and taking into account the propagation effects one may reduce the total energy in relativistic electrons to a more comfortable level of about 3 x 1048 erg compared to the estimate of 1.5 x 1050 erg in the kinetic energy of diffuse ejecta of Cas A (Braun, 1987). On the other hand, the TeV Y-ray observations by HEGRA constrain the total amount of accelerated protons to 1049 erg (see below). Thus, the content of electrons in accelerated particles in this source is significantly enhanced compared to the ratio e/p ~ 1/100 observed in local CRs. This implies that Cas A cannot be representative of the source population which provides the bulk of the observed CR fluxes. To a large extent this is not a surprise because Cas A is a unique source in our Galaxy in general, and among SNRs, in particular.
Although most of the radiation of Cas A of both thermal and nonther-mal origin comes from a shell enclosed between two spheres with angular radii of 100 arcsec and 150 arcsec, corresponding to spatial radii R = 1.7 pc and R = 2.5 pc for a distance to the source of d = 3.4 km (Reed et al., 1995), the bulk of nonthermal energy may originate not in the shell, through the diffusive shock acceleration of particles (as in most of SNRs), but in the numerous hot spots which appear to be fast moving knots (Scott and Chevalier, 1975) or compact, steep-spectrum radio structures (e.g. Bell, 1977; Cowsik and Sarkar, 1984). The radio structures are of special interest because it is likely that their bright radio emission is not just the result of an enhanced magnetic field, but is (also) caused by the local enhancement of relativistic electrons. In other words, these regions can be the sites of particle acceleration. The calculations of the spectral and temporal evolution of the synchrotron radiation of Cas A within a two-zone model which distinguishes between compact, bright steep-spectrum radio knots and the diffuse "plateau" (Atoyan et al., 2000a), provide further support for this hypothesis. In particular, it has been shown that the energy distributions of electrons in these compact structures becomes significantly steeper than the acceleration spectrum on timescales of the energy-dependent escape of electrons into the surrounding diffuse plateau region.
A possible fit to the broad band synchrotron fluxes of Cas A is shown in Fig. 5.11. Magnetic fields Bi = 1.2 mG and B2 = 0.3 mG in the compact bright radio structures and in the diffuse plateau region, respectively, are assumed. The total magnetic field energy in the shell is then WB2 = 3.8 x 1048 erg. In the compact zone-1 regions it is significantly less, WBi = 2x 1047 erg. On the other hand, the contents of relativistic electrons in zones 1 and 2 are comparable – Wei = 1.6 x 1048 erg and We2 = 1.8 x 1048 erg, respectively.
By comparing the bremsstrahlung flux of radio emitting electrons with the flux upper limit
set by the SAS-2 and COS B detectors, Cowsik and Sarkar (1980) derived a lower limit to the mean magnetic field in the shell of Cas
Such a meaningful constraint on the magnetic field is possible because of the high radio flux of Cas A and effective production of high energy Y-rays via electron bremsstrahlung. This is actually quite an unusual situation compared with other shell type "isolated" SNRs (i.e. remnants in regions free of massive clouds) for which bremsstrahlung is generally a less effective Y-ray production mechanism. The reasons are twofold: a very large amount of electrons with energy extending to at least 10 GeV (the electrons which produce synchrotron radiation at mm wavelengths), and an unusually large density of the gas in the nebula,
In addition, in the heavy,oxygen-rich gas in Cas A, the electron bremsstrahlung is amplified
1)/A) by a large factor of about 4 compared to bremsstrahlung in a pure hydrogen gas.
Fig. 5.11 Synchrotron fluxes calculated in the framework of two-zone model for Cas A (from Atoyan et al., 2000a). The acceleration spectrum of the electrons in the zone 1, which is modelled as being composed of 150 compact structures with a mean radius R = 0.06 pc, is assumed to be a power-law with an index of 2.2 and exponential cutoff at Eo = 18 TeV; the escape time of electrons from knots is assumed as
The magnetic fields in the knots (zone-1) and in the plateau region (zone-2) are B1 = 1.2 mG and B2 = 0.3 mG, respectively. Dashed and dot-dashed curves show contributions of zone 1 and zone 2 to the overall synchrotron radiation flux (solid curve).the inverse Compton component is dominated by scattering of electrons on far infrared dust emission with T ~ 100 K (Atoyan et al., 2002). For other SNRs, the 2.7 K CMBR dominates over all other seed photon fields. Even so, because of severe synchrotron energy losses of the electrons in the strong magnetic field, exceeding 100 ^G, the IC component of radiation in Cas A is significantly suppressed, and only at TeV energies it may become comparable with the bremsstrahlung flux.
The expected Y-ray fluxes produced by the electrons responsible for the broad-band synchrotron emission presented in Fig. 5.11, are shown in Fig. 5.12. The thin solid line corresponds to the total flux of the bremsstrahlung Y-rays, and the dashed and dot-dashed lines represent the bremsstrahlung fluxes from zone-1 and zone-2, respectively.
Because of the steep decline of the energy distribution of radio electrons in the compact radio structures (zone-1), the intensity of the Y-ray flux at E — 1 GeV is dominated by the flat-spectrum bremsstrahlung of the plateau region (see Fig. 5.12). It is also important that the contribution of other Y-ray production mechanisms at this energy is not yet significant. Therefore, future measurements of the differential flux of high energy Y-rays from Cas A by GLAST should allow rather accurate determinations of a number of important parameters in Cas A.
If the fluxes of hard X-rays observed at E > 10 keV have indeed a synchrotron origin (Allen et al., 1997), relativistic electrons in Cas A should be accelerated to energies up to tens of TeV. These electrons should then produce TeV Y-rays. Along with bremsstrahlung, at these energies the principal mechanism for Y-ray production is the inverse Compton (IC) scattering of electrons in the field of thermal dust emission with T = 97 K (Mezger et al., 1986).
The fluxes of IC Y-rays expected from Cas A depend very sensitively on the mean magnetic field B2 in zone-2 (the shell). In particular, in the VHE regime, Fic – B2-(5+a2)/2, where «2 > 3 is the spectral index of TeV electrons in the shell. Thus, the flux of IC Y-rays could be significantly increased assuming smaller values of B2, and hence also of B1 fields, since the radio data require the ratio of magnetic fields in two zones to be approximately at the level of B1/B2 — 4. On the other hand, B2 cannot be significantly less than 0.3 mG, otherwise bremsstrahlung would lead to overproduction of X- and Y-rays, in contradiction with the OSSE/RXTE and EGRET data (see Fig. 5.12).
Formally, the IC Y-ray flux can be increased assuming a more structured model for the magnetic field distribution in the shell. Namely, one may assume that the magnetic field in the shell of Cas A is reduced from the highest value B1 in the compact zone-1 (the acceleration sites) to a lower value B2 in the surrounding zone-2, and further on to some B3 < B2 in zone 3. The latter would then represent the regions of the shell with relatively low magnetic field or the regions adjacent to the shell. Relativistic electrons could then escape from zone-2 into zone-3, as they do from zone-1 into zone-2. Because the shell is significantly larger than the compact zone-1 structures, the characteristic timescales for the electron escape from zone-2 into zone-3 should be significantly larger than that the escape time from zone-1 into zone-2.
In Fig. 2.11 the fluxes of IC Y-rays, calculated in the framework of the 3-zone model with B3 = 0.1 mG, are shown. Two different values for the magnetic field in zone-1, B1 = 1 mG (solid line) and B1 = 1.6 mG (dashed line) are assumed. The magnetic field in the zone-2 for both cases is fixed to B2 = B1/4. Although B1 (and B2) in these 2 cases change only by a factor of 1.6, the fluxes of TeV Y-rays drop significantly, by a factor of 6.
Fig. 5.12 The fluxes of synchrotron (dotted line), inverse Compton (3-dot—dashed line), and bremsstrahlung (solid line) radiations calculated in the framework of the two-zone model of Cas A for the same model parameters as in Fig. 5.11. The broad band overall spectral energy distribution consisting of these three components of radiation is shown by the curve marked as "total". The bremsstrahlung fluxes produced in zone-1 and zone-2 are shown separately by the dashed and dot-dashed curves, respectively. The hatched region shows the expected flux sensitivity of GLAST. The X-ray/soft Y-ray fluxes measured by RXTE and OSSE detectors, as well as the flux upper limit from EGRET, are also shown.
For the given magnetic fields B1 and B2 in the zones 1 and 2, the 3-zone model allows an increase (compared to the 2-zone model) of the Y-ray fluxes at energies above 1 TeV by a factor of 3. The assumption of the magnetic field B3 smaller than 0.1 mG does not result in a further increase of TeV Y-ray fluxes, because for such low magnetic fields all electrons up to several TeV are not in the "saturation" regime, therefore variations of B3 do not affect the electron energy distribution in zone 3.
Thus, the IC fluxes, shown in Fig. 2.11, should be treated as strict upper limits . This is an important conclusion which should be taken into account in interpretations of TeV radiation. In this regard, the original interpretation of hard X-rays as synchrotron radiation from multi-TeV electrons (Allen et al., 1997) needs more solid observational support, and deserves further theoretical studies. In particular, this radiation could be explained also in terms of the nonthermal bremsstrahlung of electrons accelerated by plasma waves to subrelativistic energies (Laming, 2001). If so, the need of TeV electrons would disappear, and correspondingly the IC interpretation of the TeV signal from Cas A would become rather shaky and, in fact, somewhat redundant, especially if one takes into account the fact that the TeV flux can be quite comfortably explained by interactions of accelerated protons with the ambient gas. As it can seen from Fig. 2.11, the interpretation of the TeV flux in terms of n0-decay Y-rays requires only 1049 erg in accelerated protons which is only factor of 10 more than the energy in rela-tivistic electrons, and, at the same time, constitutes only < 7% of the total kinetic energy available in Cas A. Note that the n0-decay Y-ray flux shown in Fig. 2.11 corresponds to a rather modest, from the point of view of the total energy budget, assumption concerning the proton energy distribution with a spectral index ap = 2.15 and E0 ^ 1 TeV. But "economically" less attractive proton spectra, e.g. with ap = 2.4, which would require a factor of 4 larger total energy in protons, are still acceptable.
Actually, the nonlinear diffusive shock-acceleration model applied to Cas A faces just opposite problem. This model, based on parameters adopted to fit the X-ray data in terms of synchrotron radiation, predicts a flat Y-ray flux significantly exceeding the observed TeV flux (Berezhko et al., 2001). Such a discrepancy can be removed assuming that the X-rays are not of synchrotron origin. Then, an alternative (to the diffusive shock-acceleration in the shell) could be proton acceleration in the bright radio structures, e.g. by the second-order Fermi mechanism as discussed by Chevalier et al. (1978) and Cowsik and Sarkar (1984).
The predictions of the 3-zone model, which was introduced above to estimate the maximum (theoretically possible) flux contributed through the IC channel, just marginally match the TeV flux (see Fig. 2.11). Therefore, at this stage the leptonic origin of the TeV radiation cannot be ruled out. The crucial test for the origin of TeV radiation of Cas A can be provided by future detailed spectroscopic Y-ray measurements in the energy interval between 100 GeV and several TeV. The spectrum predicted by the leptonic model at energies above 1 TeV is very steep, with a photon index r > 3. Therefore the detection of a differential Y-ray spectrum harder than E-3 at TeV energies, would be a strong argument in favour of the hadronic origin of radiation. At the same time, the detection of a steep TeV spectrum cannot be uniquely interpreted, because introducing an "early" energy cutoff E0 in the proton spectrum around several TeV one may easily reproduce a flat high energy Y-ray spectrum with strong steepening above 1 TeV. An additional piece of information is contained at low energies. The bremsstrahlung Y-ray fluxes expected above 100 MeV are almost two orders of magnitude above the GLAST sensitivity, unless the magnetic field in the shell does not significantly exceed 1 mG. This, however, seems unlikely, because otherwise it would require an unrealistically large energy, WB2 > 3 x 1050 erg, to be deposited in the magnetic field of the shell. Thus, we may conclude that GLAST as well as sub-100 GeV threshold IACT arrays should detect Y-ray signals from Cas A. The spectrum of Y-radiation of leptonic origin, which at these energies is dominated by electron bremsstrahlung, can be predicted (from radio data) very robustly. It should be close to a flat power-law, <x E-2. This makes the identification of radiation mechanisms quite difficult, because the proton spectrum (and, consequently, the n0-decay y-ray spectrum), cannot be significantly steeper than E-2 2, otherwise the hadronic mechanism would require an unacceptably large energy in accelerated particles. In this regard, more promising is the energy region below 100 MeV, where the n0-decay as well as the IC components are strongly suppressed, and thus the flux measured at low energies would provide an important "calibration point" for extrapolation of the bremsstrahlung contribution to higher energies.
In summary, the Y-ray spectrometry of Cas A with GLAST and future IACT arrays will give definite answers about the energy distribution between the magnetic field and accelerated electrons and protons, and thus will provide a crucial insight into the nature of acceleration processes in one of the most prominent nonthermal objects in our Galaxy.
