Speaker
Description
Kilonovae light-curves depend on the efficiency with which beta decay e$^\pm$ deposit their energy in the expanding ejecta. We show that the time $t_{\rm e}$, at which the deposited energy fraction drops to $1/e$, depends mainly on ejecta density and velocity, and only weakly on the initial electron fraction $Y_e$ and entropy $s_0$: $t_{\rm e} = t_0 \times (\rho t^3/(\rho t^3)_0)^{s_{\rm e}}$ days, where $(\rho t^3)_0 = \frac{0.025 M_{\odot}}{4 \pi (0.2c)^3}$ and $t_0 \approx 16, (19), [19] \text{ days}$ , $s_{\rm e} = 0.37, (0.42), [0.5]$ for $Y_e< 0.22 , \forall s_0$ ; ($ Y_e> 0.22 , \frac{s_0}{k_b/ \text{baryon}} > 55$) ; [$ Y_e < 0.22 , \frac{s_0}{k_b/ \text{baryon}} < 55$]. The accuracy of the analytic approximation is within $\sim 20 \%$, which is comparable to the uncertainty due to nuclear mass model and reaction rates uncertainties. The shallower than square-root dependence on $\rho t^3$, $s_{\rm e} \leq 1/2$, results from an increase with time of the characteristic e$^\pm$ energy $\langle E_{\rm e} \rangle$ (in contrast with the commonly used $\langle E_{\rm e} \rangle \propto t^{-1/3}$). This occurs due to the activity of "inverted decay-chains" in which a slow, low-energy decay is followed by a fast, high-energy one. Our results imply that the identification of "thermalization breaks" in bolometric kilonova light-curves may be used to determine the ratio $M/v^3$ of ejecta mass and velocity, as is done for Ia SNe using the $\gamma$-ray thermalization break. We provide an analytic description of the time dependent electron deposition efficiency that may be straightforwardly implemented in kilonovae light-curve calculations, and is accurate to within a factor $\sim 2$ over $3-4$ orders of magnitude in energy deposition evolution. Finally, we show that our results are weakly dependent on nuclear physics uncertainties.
