The Physics of the Neutrino Mechanism of Core-Collapse Supernovae

Abstract

(Abridged) Neutrino heating may drive core-collapse supernova explosions. Although it is known that the stalled accretion shock turns into explosion when the neutrino luminosity from the collapsed core exceeds a critical value (L_crit) (the "neutrino mechanism"), the physics of L_crit, as well as its dependence on the properties of the proto-neutron star (PNS) and changes to the microphysics has never been systematically explored. We solve the one-dimensional steady-state accretion problem between the PNS surface and the accretion shock. We quantify the deep connection between the solution space of steady-state accretion flows with bounding shocks and the neutrino mechanism. We show that there is a maximum, critical sound speed above which it is impossible to maintain accretion with a standoff shock, because the shock jump conditions cannot be satisfied. The physics of this critical sound speed is general and does not depend on a specific heating mechanism. For the simple model of pressure-less free-fall onto a shock bounding an isothermal accretion flow with sound speed c_T, we show that if c_T^2/v_escape^2 > 3/16 explosion results. We generalize this result to the more complete supernova problem, showing explicitly that the same physics determines L_crit. We find that the critical condition for explosion can be written as c_S^2/v_escape^2 = 0.19, where c_S is the adiabatic sound speed. This "antesonic" condition describes L_crit over a broad range in accretion rate and microphysics. We show that the addition of the accretion luminosity (L_acc) reduces L_crit non-trivially. As in previous work, we find that L_crit is always significantly higher than the maximum possible value of L_acc. Finally, we provide evidence that the reduction in L_crit seen in recent multi-dimensional simulations results from a reduction in the efficiency of cooling, rather than an increase in the heating rate.