Other
Scientific paper
Aug 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977ap%26ss..50..323l&link_type=abstract
Astrophysics and Space Science, vol. 50, no. 2, Aug. 1977, p. 323-342.
Other
Astronomical Models, Detonation Waves, Gas Pressure, Relativistic Effects, Shock Wave Propagation, Supernova Remnants, Blasts, Gas Flow, Interstellar Gas, Isothermal Processes, Stellar Models, Stellar Winds
Scientific paper
We investigate the spherically symmetric, self-similar flow behind a blast wave from a point explosion in a medium whose density varies with distance as r°' with the assumption that the flow is both isothermal and contains a relativistic component of pressure. A self-similar solution is shown to exist oniy if both the blast wave speed, u~, and the local sound speed, w, are constant. If Q[~co(1 - w2/c2)] lies in 1 > Q>O, there exists a critical point in the radial distance-flow velocity plane. To be physically acceptable, the solution must pass through the origin and through the critical point and then through to the blast front; solution branches between these points exist, although a proper coimection at the critical point has not been demonstrated. If Q <0, a continuous single-valued solution does not exist. If 2> Q> 1, the critical point is beyond the blast curve and the flow is subsonic everywhere. For 2 < Q <3, the critical point disappears, but a new one arises. To be physically acceptable, the flow must by-pass this new critical point. It is shown that it does. The dependence of the solutions on Q is non-analytic for Q < 1, so that interpolation between neighboring values of Q is not permitted. We investigate the stability of these isothermal blast waves to spherically symmetric but non-self-similar perturbations. If 3> Q > or 0< Q <1, the solutions are shown to be definitively linearly unstable against short wavelength disturbances near the blast front, they are also unstable there in ~> Q> 1 unless the flow meets the blast front at precisely the velocity (normalized) of (2Q- 1)1/2/(3 - 2Q)"2. The solutions are also unstable for all Q in 1 > Q>O near the critical point. Since there is no characteristic time scale in the system, all the instabilities grow as a power law in time rather than exponentially. The existence of these instabilities implies that initial deviations do not decay and the system does not tend to a self-similar form. We conclude that isothermal self-similar blast waves do not provide a valid model for a supernova remnant driven by a relativistic gas pressure. Since the validity of the adiabatic blast wave models has elsewhere been shown to be questionable, it is doubtful whether the self-similar property can be involved at all in the case of supernova remnants. This raises serious questions of interpretation of quantities deduced for supernova remnants on the basis of the use of self-similar models
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