Expectations for the Hard X-ray Continuum and Gamma-ray Line Fluxes from the Type Ia supernova SN 2014J in M82

The hard X-ray continuum and gamma-ray lines from a Type Ia supernova dominate its integrated photon emissions and can provide unique diagnostics of the mass of the ejecta, the $^{56}$Ni yield and spatial distribution, its kinetic energy and expansion speed, and the mechanism of explosion. Such signatures and their time behavior "X-ray" the bulk debris field in direct fashion, and do not depend upon the oftimes problematic and elaborate UV, optical, and near-infrared spectroscopy and radiative transfer that have informed the study of these events for decades. However, to date no hard photons have ever been detected from a Type Ia supernova in explosion. With the advent of the supernova SN 2014J in M82, at a distance of $\sim$3.5 Mpc, this situation may soon change. Both NuSTAR and INTEGRAL have the potential to detect SN 2014J, and, if spectra and light curves can be measured, would usefully constrain the various explosion models published during the last $\sim$thirty years. In support of these observational campaigns, we provide predictions for the hard X-ray continuum and gamma-line emissions for fifteen Type Ia explosion models gleaned from the literature. The model set, containing as it does deflagration, delayed detonation, merger detonation, pulsational delayed detonation, and sub-Chandrasekhar helium detonation models, collectively spans a wide range of properties and, hence, signatures. We provide a brief discussion of various diagnostics (with examples), but importantly make the spectral and line results available electronically to aid in the interpretation of the anticipated data.Comment: Accepted to the Astrophysical Journal (March 31, 2014), with one additional figure and further discussion of techniqu

A Note on Near-factor-critical Graphs

A near-factor of a finite simple graph $G$ is a matching that saturates all vertices except one. A graph $G$ is said to be near-factor-critical if the deletion of any vertex from $G$ results in a subgraph that has a near-factor. We prove that a connected graph $G$ is near-factor-critical if and only if it has a perfect matching. We also characterize disconnected near-factor-critical graphs.Comment: 4 page