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Dynamical model

We adopt the Sedov-Taylor dynamical model of an adiabatically expanding spherical blast wave (Taylor, 1950; Sedov, 1959) appropriate for middle-aged SNR's. In such a model the solution for the temperature and density has a self-similar form, and the radius of the shell and the shock velocity evolve with time as tex2html_wrap_inline736 and tex2html_wrap_inline738, respectively. The Sedov solution is a good approximation when the swept up interstellar mass exceeds the mass of the SN ejecta (tex2html_wrap_inline740, Woltjer 1972). The association between the Vela SNR and the old pulsar PSR0833-45 (Weiler & Panagia 1980, Weiler & Sramek 1988) suggests that the SNR is well in its adiabatic phase. To our purposes, a useful relation linking the shock temperature tex2html_wrap_inline742 with the shock wave velocity tex2html_wrap_inline744 is the following (McKee & Hollenbach 1980):
 equation53
In the following, we shall assume instantaneous energy equipartition between ions and electrons at the shock front. In this case, eq. 1 allows us to derive the shock speed from X-ray observations; in fact, the electron temperature derived from fitting the X-ray data is equal to tex2html_wrap_inline742 in equation 1.



Fabrizio Bocchino
Wed Jan 15 13:20:09 MET 1997