Isothermal SelfSimilar Blast Wave Theory of Supernova Remnants Driven by Relativistic Gas Pressure
Abstract
We investigate the spherically symmetric, selfsimilar flow behind a blast wave from a point explosion in a medium whose density varies with distance asr ^{ω} with the assumption that the flow is both isothermal and contains a relativistic component of pressure. A selfsimilar solution is shown to exist only if both the blast wave speed,u _{ s },and the local sound speed,w, are constant. If Ω[≡ω(1w ^{2}/c ^{2})] lies in 1>Ω>0, there exists a critical point in the radial distanceflow 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 connection at the critical point has not been demonstrated. If Ω<0, a continuous singlevalued solution does not exist. If 2>Ω>1, the critical point is beyond the blast curve and the flow is subsonic everywhere. For 2<Ω<3, the critical point disappears, but a new one arises. To be physically acceptable, the flow must bypass this new critical point. It is shown that it does. The dependence of the solutions of Ω is nonanalytic for Ω<1, so that interpolation between neighboring values of Ω is not permitted. We investigate the stability of these isothermal blast waves to spherically symmetric but nonselfsimilar perturbations. If 3>Ω>3/2 or 0<Ω<1, the solutions are shown to be definitively linearly unstable against short wavelength disturbances near the blast front, they are also unstable there in 3/2>Ω>1 unless the flow meets the blast front atprecisely the velocity (normalized) of (2Ω1)^{1/2}/(32Ω)^{1/2}. The solutions are also unstable for all Ω in 1>Ω>0 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 selfsimilar form. We conclude that isothermal selfsimilar 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 selfsimilar 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 selfsimilar models.
 Publication:

Astrophysics and Space Science
 Pub Date:
 August 1977
 DOI:
 10.1007/BF00641740
 Bibcode:
 1977Ap&SS..50..323L
 Keywords:

 Astronomical Models;
 Detonation Waves;
 Gas Pressure;
 Relativistic Effects;
 Shock Wave Propagation;
 Supernova Remnants;
 Blasts;
 Gas Flow;
 Interstellar Gas;
 Isothermal Processes;
 Stellar Models;
 Stellar Winds;
 Astrophysics