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tokens: of the CSM density profile and the forward shock evolution together determine the temporal behavior of the optically thin radio flux density. For s = 0 and , the flux density rises with time as once , the flux density evolution steepens to (visible as a kink in the model light curve of Figure 1 with cm −3 around 100 days after explosion; such a kink was also noted by Pérez-Torres et al. 2014 ). Meanwhile for s = 2, the optically thin scaling is when later, when bottoms out at unity, then . Therefore, the temporal evolution of the optically thin flux density can be used to estimate the density profile of the CSM. 4.5. Caveats and Complexities As discussed by Horesh et al. ( 2012 , 2013 ), the most significant uncertainty in converting radio luminosity to a density of the CSM is the efficiency of magnetic field acceleration, . In the case of uniform density CSM and optically thin synchrotron emission, the density derived from a given flux density will depend on as when , and when . For s = 2 and , we find , and when converges to unity then . In addition, as seen by comparing Figures 3 with 4 , and Figures 5 with 6 , the synchrotron emission becomes optically thin faster for lower values of . Figure 3. Each panel shows a set of radio light curve models at a distinct frequency (marked top left), assuming , , , , and s = 2. The model grids span a range of values () with spacing of 1 dex, with purple-blue models corresponding to low values and red models to high . Observed 3 σ upper limits at each frequency are overplotted as black triangles. Figure 4. Each panel shows a set of radio light curve models at a distinct frequency (marked top left), assuming a more conservative (compared to in Figure 3 ) and retaining , , , and s = 2. The model grid and color scheme represent the same range of values as in Figure 3 . Observed 3 σ upper limits at each frequency are overplotted as black triangles. Figure 5. Each panel shows a set of radio light curve models at a distinct frequency (marked top left), assuming , , , , and s = 0. The model grids span a range of n 0 values ( cm −3 ) with resolution of 1 dex, with purple-blue models corresponding to low n 0 values and red models to high n 0 . Observed 3 σ upper limits at each frequency are overplotted as black triangles. Figure 6. Each panel shows a set of radio light curve models at a distinct frequency (marked top left), assuming a more conservative (compared to in Figure 5 ) and retaining , , , and s = 0. The model grid and color scheme represent the same range of n 0 values as in Figure 5 . Observed 3 σ upper limits at each frequency are overplotted as black triangles. Radio light curve models are also affected by the assumed values of SN ejecta mass and explosion energy. If we take conservatively low values of and , we find forward shock velocities of and at t = 10 days since explosion for and , respectively. These blast wave velocities are high enough that synchrotron self absorption still dominates over