In the model problem of steady spherical pressure-less free-fall onto a standing shockwave around an accreting central mass, the “antesonic” condition limits the regime of stable accretion to ${c_T^2/v_{\rm esc}^2\leq3/16}$, where $c_T$ is the isothermal sound speed in the subsonic post-shock flow, and $v_{\rm esc}$ is the escape velocity at the shock radius. Above this limit, it is impossible to simultaneously satisfy both the time-steady Euler equation and the strong shock jump conditions, and the system undergoes a time-dependent transition to a thermal wind. This physics has been shown to explain the existence of a critical neutrino luminosity in steady-state models of proto-neutron star accretion 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. We show that 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 multi-dimensional supernova simulations can greatly impact the critical antesonic ratio. Specifically, a core angular velocity corresponding to a millisecond rotation period after contraction of the proto-neutron star results in only a $\sim5$ per-cent reduction of the critical curve. In contrast, near-sonic isotropic or anisotropic turbulence described by 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 $\sim20-40$ per-cent. We further show that there is a maximum on the specific turbulent kinetic energy of $\simeq v_{\rm esc}^2/4$ above which accretion with any finite value of $c_T$ is impossible. 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.

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Publication

Monthly Notices of the Royal Astronomical Society