THE PHYSICS OF THE NEUTRINO MECHANISM OF CORE-COLLAPSE SUPERNOVAE

Although it is known that the stalled accretion shock in models of core-collapse supernovae turns into explosion when the neutrino luminosity from the proto-neutron star (PNS) exceeds a critical value (L-nu,L- (crit)(core)) (the "neutrino mechanism"), the physics of L-nu,L- (crit)(core) has never been systematically explored. We solve the accretion problem between the PNS surface and the accretion shock. We quantify the deep connection between the general problem of accretion flows with bounding shocks and the neutrino mechanism. In particular, we show that there is a maximum, critical sound speed above which the shock jump conditions cannot be satisfied and steady-state accretion is impossible. This physics 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, we show that shock solutions are possible only for sound speed c(T) < c(T)(crit) and that c(T)(2)/v(esc)(2) = 3/16 = 0.1875 at c(T)(crit). We generalize this result to the supernova problem, showing that the same physics determines L-nu,L- (crit)(core). The critical condition for explosion can be written as c(S)(2)/v(esc)(2) similar or equal to 0.19, where c(S) is the adiabatic sound speed. This "antesonic" condition describes L-nu,L- (crit)(core) over a broad range of parameters, and other criteria proposed in the literature fail to capture this physics. We show that the accretion luminosity reduces L-nu,L- (crit)(core) non-trivially. A larger PNS radius decreases L-nu,L- (crit)(core), implying that a stiff high-density equation of state may be preferred. Finally, using an analytic model, we provide evidence that the reduction of L-nu,L- (crit)(core) seen in recent multi-dimensional simulations results from reduced cooling efficiency, rather than an increased heating rate.