Exercise 3: We can approximately estimate the peak time of the associated transient by taking the geometric mean of the expansion time of the ejecta (assumed to be homologous) and the diffusion time for a static medium.  Using values derived from the numerical simulations above (M ~ 0.01 solar masses, v ~ 0.2c) and an opacity analogous to type Ia supernovae (~ 0.2), what is the characteristic peak time scale for a kilonova?  Can you guess at any limitations in this back of the envelope calculation?