Astronomy and Astrophysics – Astrophysics
Scientific paper
Jul 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993a%26a...274..775b&link_type=abstract
Astronomy and Astrophysics, Vol. 274, p. 775 (1993)
Astronomy and Astrophysics
Astrophysics
5
Scientific paper
Analytic models for supernovae with an envelope, in which density decreases proportionally to a power of radius, are considered and the solution for the evolution of temperature is found, which is expressed through elementary functions when the power is $k=-2$, $k=-4$ or $k=-8$. Together with the Arnett's solution for a uniform density core ($k=0$) this allows to construct a simple description of supernova light curves which is rather realistic when the opacity may be assumed constant. We generalize the elementary solution for the case of piecewise constant opacity (one constant value in the uniform core and another in the power-law envelope). We point out that the correct approach to the subject is not the usual eigenvalue formulation, but it belongs to the class of the moving boundary problems, and actually the task is equivalent to the famous Stefan problem. A comparison with detailed numerical calculations by Blinnikov and Bartunov for the same parameters of supernova models is carried out. The approximate analytic solutions are found to be good for a qualitative estimate of light curve parameters.
Blinnikov Sergei I.
Popov V. D.
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