An Analytical Density Profile of Dense Circumstellar Medium in Type II Supernovae

Observations of Type II supernovae imply that a large fraction of its progenitors experience enhanced mass loss years to decades before core collapse, creating a dense circumstellar medium (CSM). Assuming that the CSM is produced by a single mass eruption event, we analytically model the density profile of the resulting CSM. We find that a double power-law profile, where the inner (outer) power-law index has a characteristic value of -1.5 (-10 to -12), gives a good fit to the CSM profile obtained using radiation hydrodynamical simulations. With our profile the CSM is well described by just two parameters, the transition radius $r_{\ast }$ and density at $r=r_{\ast }$ (alternatively $r_{\ast }$ and the total CSM mass). We encourage future studies to include this profile, if possible, when modelling emission from interaction-powered transients.