Neutrino quantum kinetics in three flavors

The impact of neutrino flavor conversion on the supernova mechanism is yet to be fully understood. We present multi-energy and multi-angle solutions of the neutrino quantum kinetic equations in three flavors, without employing any attenuation term for the neutrino self-interaction strength and taking into account neutrino advection and non-forward collisions with the background medium. Flavor evolution is explored within a spherically symmetric shell surrounding the region of neutrino decoupling in the interior of a core-collapse supernova, relying on the output of a spherically symmetric core-collapse supernova model with a progenitor mass of $18.6 M_\odot$. We select two representative post-bounce times: $t_{\rm pb} = 0.25$ s (no angular crossings are present and flavor conversion is triggered by slow collective effects) and $t_{\rm pb} = 1$ s (angular crossings trigger fast flavor instabilities). We find that flavor equipartition is achieved for the late post-bounce time ($t_{\rm pb} = 1$ s), where the (anti)neutrino emission properties among different flavors tend to approach each other. In this case, $\bar\nu_e$ tends to $\bar\nu_x = (\bar\nu_\mu + \bar\nu_\tau)/2$ and a similar trend holds for neutrinos. However, flavor equipartition does not occur for our early post-bounce time ($t_{\rm pb} = 0.25$ s). Accounting for weak-magnetism corrections, crossings in the $\mu$ and $\tau$ lepton number angular distributions arise; however, such crossings have a magnitude smaller than the one occurring in the electron sector and negligibly affect flavor evolution. Because of flavor conversion, the neutrino heating rate increases up to $30\%$ with respect to the case where flavor conversion is neglected.