Modeling of Radio Emission from Supernovae : Application to Type Ia

Abstract: The interaction of supernova (SN) ejecta with the circumstellar medium (CSM) drives a strong shock wave into the CSM. These shocks are ideal places where effective particle acceleration and magnetic field amplification can take place. The accelerated relativistic particles, in the presence of magnetic field, could emit a part of their energy via synchrotron radiation in radio wavelengths. The flux of this radiation, when compared with observations, gives an estimate of the CSM density. This could either be the particle density ($\rm n_{ISM}$) in case of the SN exploding in a constant density medium, characteristic of interstellar medium, or pre-SN mass loss rate ($\mdot$) of the progenitor system for a wind medium. In this work we have modeled the synchrotron luminosities and compared that with the radio upper limits measured for the Type Ia SNe 2011fe and 2014J. Assuming equipartition of energy between electric and magnetic fields, with 10$\%$ of the thermal shock energy in each field, we found a very low density medium, having $\rm n_{ISM} < \sim $ 0.35 $\ccc$,around both the SNe. In terms of $\mdot$ this implies an upper limit of $10^{-9}$ \msunyr for a wind velocity of 100 \kms. From the measurements of H I column density it could be expected that $\rm n_{ISM} \sim $ 1 $\ccc$ around both the SNe. If this is the true value close to the SNe, this would indicate that the energy density in magnetic field is less than that presumed for energy equipartition. The progenitors of both SNe 2011fe and 2014J are not clear. However previous studies have pointed toward a few potential  channels. Here, we have compared the CSM densities estimated by our models with that predicted by those different plausible formation channels and have tried to constrain the amplification of magnetic fields in SN shocks.