Deriving Thermonuclear Supernova Properties from Gamma-Ray Line Measurements

We illustrate methods for deriving properties of thermonuclear, or Type Ia, supernovae, including synthesized $^{56}$Ni mass, total ejecta mass, ejecta kinetic energy, and $^{56}$Ni distribution in velocity, from gamma-ray line observations. We simulate data from a small number of published SN Ia models for a simple gamma-ray instrument, and measure their underlying properties from straightforward analyses. Assuming spherical symmetry and homologous expansion, we calculate exact line profiles for all $^{56}$Co and $^{56}$Ni lines at all times, requiring only the variation of mass density and $^{56}$Ni mass fraction with expansion velocity as input. By parameterizing these quantities, we iterate the parameters to fit the simulated data. We fit the full profiles of multiple lines, or we integrate over the lines and fit line fluxes only versus time. Line profile fits are more robust, but in either case, we can recover accurately the values of the aforementioned properties of the models simulated, given sufficient signal-to-noise in the lines. A future gamma-ray mission with line sensitivity approaching 10$^{-6}$ photons cm$^{-2}$ s$^{-1}$ would measure these properties for many SN Ia, and with unprecedented precision and accuracy for a few per year. Our analyses applied to the reported $^{56}$Co lines from SN 2014J favor a low $^{56}$Ni mass and low ejecta mass, relative to other estimates.