Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An exact integral relation between the Ni56 mass and the bolometric
  light curve of a type Ia supernova   An exact relation between the Ni56 mass and the bolometric light curve of a
type Ia supernova can be derived as follows, using the following excellent
approximations: 1. the emission is powered solely by Ni56-> Co56 ->Fe56; 2.
each mass element propagates at a non-relativistic velocity which is constant
in time (free coasting); and 3. the internal energy is dominated by radiation.
Under these approximations, the energy E(t) carried by radiation in the ejecta
satisfies: dE/dt=-E(t)/t-L(t)+Q(t), where Q(t) is the deposition of energy by
the decay which is precisely known and L(t) is the bolometric luminosity. By
multiplying this equation by time and integrating over time we find:
E(t)*t=\int_0^t Q(t')t'dt' -\int_0^t L(t')t'dt'. At late time, t>> t_peak, the
energy inside the ejecta decreases rapidly due to its escape, and thus we have
\int_0^t Q(t')t'dt'=\int_0^t L(t')t'dt'. This relation is correct regardless of
the opacities, density distribution or Ni56 deposition distribution in the
ejecta and is very different from "Arnett's rule", L_peak ~ Q(t_peak). By
comparing \int_0^t Q(t')t'dt' with \int_0^t L(t')t'dt' at t~40 day after the
explosion, the mass of Ni56 can be found directly from UV, optical and infrared
observations with modest corrections due to the unobserved gamma-rays and due
to the small residual energy in the ejecta, E(t)*t>0.

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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: math
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci