deletions | additions       diff --git a/section_Modeling_the_Supernova_Shock__.tex b/section_Modeling_the_Supernova_Shock__.tex  index c8fa76e..ed308e3 100644  --- a/section_Modeling_the_Supernova_Shock__.tex  +++ b/section_Modeling_the_Supernova_Shock__.tex 
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\begin{itemize}  \item The variable radio emission from SN Ic encodes but does not directly yield the mass-loss history. To infer the mass-loss history, we must first model the radio emission from a supernova shock overtaking the CSM.  \item For relatively simple shock CSM interactions, Chavelier XXX and Chavelier XXX developed analytic solutions and set the language for shock-CSM interactions. However, it is very likely that the mass-loss history is more complicated and requires numerical simulations.  \item In principle, the evolution is radiative and hydrodynamic. However, we will be considering the radio emission from 10 days until 1000 days. During much of this time, one may simply evolve the shock and CSM interaction hydrodynamically, hydrodynamically  and post-process the radiation. In the spirit of building our knowledge, we will first consider spherically symmetric pre-explosion mass loss. There are plenty of examples of aspherical mass-loss, so we will also need to consider the signatures of aspherial ejection in the radio light curves.   \item But before we try to infer the aspherical character of the mass-loss from the radio lightcurves of SNe, we will first do forward modeling. We will take examples of observed aspherical ejections and model their radio light curves, exploring the systematics. It is unlikely that one can infer too many details about the asymmetry, so one goal is to characterize what broad aspherical characteristics one could infer.  \end{itemize}