Leptonic and semi-leptonic neutrino interactions with muons in the proto-neutron star cooling

Abstract

It is known that muons are scarce just after the birth of a proto-neutron star via a supernova explosion but get more abundant as the proto-neutron star cools via neutrino emissions on the Kelvin-Helmholtz timescale. In this paper we evaluate all the relevant rates of the neutrino interactions with muons at different times in the proto-neutron star cooling. We are particularly interested in the late phase ($t\gtrsim 10s$), which will be accessible in the next Galactic supernova but has not been studied well so far. We calculate both leptonic and semi-leptonic processes, for the latter of which we pay attention also to the form factors with their dependence on the transferred momentum as well as to the modification of the dispersion relations for nucleons on the mean field level. We find that the flavor-exchange reactions ${\nu }_e+{\mu }^{-}\to {\nu }_{\mu }+e^{-}$ and ${\bar{\nu }}_{\mu }+{\mu }^{-}\to {\bar{\nu }}_e+e^{-}$ can be dominant, particularly at low energies, over the capture of ${\nu }_e$ on neutron and the scatterings of ${\bar{\nu }}_{\mu }$ on nucleons as the opacity sources for these species and that the inverse muon decay ${\bar{\nu }}_e+{\nu }_{\mu }+e^{-}\leftrightarrows {\mu }^{-}$ can overwhelm the scatterings of ${\bar{\nu }}_e$ and ${\nu }_{\mu }$ on nucleons again at low energies. At high energies, on the other hand, the corrections in the semi-leptonic processes mentioned above are more important. We also show the non-trivial energy- and angular dependences of the flavor-exchange reactions and the inverse muon decay. In the study of the diffusion coefficients from these reactions, we find that ${\bar{\nu }}_{\mu }$ is most affected. These pieces of information are indispensable for numerical computations and the interpretation of results thereof for the proto-neutron star cooling particularly at the very late phase.

53 pages, 19 Figures

References in corpus (6)

• Supernova Neutrino Detection
• Muon Creation in Supernova Matter Facilitates Neutrino-driven Explosions
• Supernova Neutrino Light Curves and Spectra for Various Progenitor Stars: From Core Collapse to Proto-neutron Star Cooling
• Observable signatures of enhanced axion emission from protoneutron stars
• Charged-Current Muonic Reactions in Core-Collapse Supernovae
• Cooling timescale for protoneutron stars and properties of nuclear matter: Effective mass and symmetry energy at high densities

Cited by in corpus (6)

• Universality of the Neutrino Collisional Flavor Instability in Core Collapse Supernovae
• Asymptotic states of fast neutrino-flavor conversions in the three-flavor framework
• Muon-induced collisional flavor instability in core-collapse supernova
• Neutrino-driven massive stellar explosions in 3D fostered by magnetic fields via turbulent $\alpha$-effect
• Detectability of Late-time Supernova Neutrinos with Fallback Accretion onto Protoneutron star
• Asymmetric emissions of neutrinos in the cooling of rotating proto-neutron stars