The Antesonic Condition for the Explosion of Core-Collapse Supernovae II: Rotation and Turbulence

In the problem of steady free-fall onto a standing shockwave around acentral mass, the "antesonic" condition limits the regime of stable accretion to $c_T^2/v_\mathrm{esc}^2\leq3/16$, where $c_T$ is the isothermal sound speed in the subsonic post-shock flow, and $v_\mathrm{esc}$ is the escape velocity at the shock radius. Above this limit, it is impossible to satisfy both the Euler equation and theshock jump conditions, and the system transitions to a wind. This physics explains the existence of a critical neutrino luminosity in steady-state models ofaccretion in the context of core-collapse supernovae. Here, we extend the antesonic condition to flows with rotation and turbulence using a simple one-dimensional formalism. Both effects decrease the critical post-shock sound speed required for explosion. While quite rapid rotation is required for a significant change to the critical condition, we show that the level of turbulence typically achieved in supernova simulations can greatly impact the critical value of $c_T^2/v_\mathrm{esc}^2$. A core angular velocity corresponding to a millisecond rotation period after contraction of the proto-neutron star results in only a $\sim\!5$ per-cent reduction of the critical curve. In contrast, near-sonic turbulence with specific turbulent kinetic energy $K/c_T^2=0.5-1$, leads to a decrease in the critical value of $c_T^2/v_{\rm esc}^2$ by $\sim\!20-40$ per-cent. This analysis provides a framework for understanding the role of post-shock turbulence in instigating explosions in models that would otherwise fail and helps explain why multi-dimensional simulations explode more easily than their one-dimensional counterparts.