Physics of Luminous Transient Light Curves: A New Relation Between Peak Time and Luminosity. (arXiv:1812.06522v1 [astro-ph.HE])

Physics of Luminous Transient Light Curves: A New Relation Between Peak Time and Luminosity. (arXiv:1812.06522v1 [astro-ph.HE])
<a href="http://arxiv.org/find/astro-ph/1/au:+Khatami_D/0/1/0/all/0/1">David K. Khatami</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Kasen_D/0/1/0/all/0/1">Daniel N. Kasen</a>

Simplified analytic methods are frequently used to model the light curves of
supernovae and other energetic transients and to extract physical quantities,
such as the ejecta mass and amount of radioactive heating. The applicability
and quantitative accuracy of these models, however, have not been clearly
delineated. Here we carry out a systematic study comparing certain analytic
models to numerical radiation transport calculations. We show that the neglect
of time-dependent diffusion limits the accuracy of common Arnett-like analytic
models, and that the widely-applied Arnett’s rule for inferring radioactive
mass does not hold in general, with an error that increases for models with
longer diffusion times or more centralized heating. We present new analytic
relations that accurately relate the peak time and luminosity of an observed
light curve to the physical ejecta and heating parameters. We further show that
recombination and mixing modify the peak of the light curve and that these
effects can be accounted for by varying a single dimensionless parameter in the
new relations. The results presented should be useful for quickly and robustly
inferring the physical properties of a wide variety of transient phenomena.

Simplified analytic methods are frequently used to model the light curves of
supernovae and other energetic transients and to extract physical quantities,
such as the ejecta mass and amount of radioactive heating. The applicability
and quantitative accuracy of these models, however, have not been clearly
delineated. Here we carry out a systematic study comparing certain analytic
models to numerical radiation transport calculations. We show that the neglect
of time-dependent diffusion limits the accuracy of common Arnett-like analytic
models, and that the widely-applied Arnett’s rule for inferring radioactive
mass does not hold in general, with an error that increases for models with
longer diffusion times or more centralized heating. We present new analytic
relations that accurately relate the peak time and luminosity of an observed
light curve to the physical ejecta and heating parameters. We further show that
recombination and mixing modify the peak of the light curve and that these
effects can be accounted for by varying a single dimensionless parameter in the
new relations. The results presented should be useful for quickly and robustly
inferring the physical properties of a wide variety of transient phenomena.

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