# A Parametric Study of the Acoustic Mechanism for Core-Collapse Supernovae

## TL;DR

This study examines the conditions under which acoustic waves can revive stalled shock waves in core-collapse supernovae, revealing that a combination of neutrino heating and acoustic power is crucial for successful explosions.

## Contribution

It introduces a parametric framework with a critical surface to evaluate the acoustic mechanism's effectiveness in supernova shock revival, extending previous models.

## Key findings

- Large acoustic powers are needed in 1D to revive shocks due to neutrino cooling effects.
- In 2D, the required acoustic powers align with previous estimates by Burrows et al.
- Shock revival depends on the combined effect of neutrino heating and acoustic wave power.

## Abstract

We investigate the criterion for the acoustic mechanism to work successfully in core-collapse supernovae. The acoustic mechanism is an alternative to the neutrino-heating mechanism. It was proposed by Burrows et al., who claimed that acoustic waves emitted by $g$-mode oscillations in proto-neutron stars (PNS) energize a stalled shock wave and eventually induce an explosion. Previous works mainly studied to which extent the $g$-modes are excited in the PNS. In this paper, on the other hand, we investigate how strong the acoustic wave needs to be if it were to revive a stalled shock wave. By adding the acoustic power as a new axis, we draw a critical surface, an extension of the critical curve commonly employed in the context of neutrino heating. We perform both 1D and 2D parametrized simulations, in which we inject acoustic waves from the inner boundary. In order to quantify the power of acoustic waves, we use the extended Myers theory to take neutrino reactions into proper account. We find for the 1D simulations that rather large acoustic powers are required to relaunch the shock wave, since the additional heating provided by the secondary shocks developed from acoustic waves is partially canceled by the neutrino cooling that is also enhanced. In 2D, the required acoustic powers are consistent with those of Burrows et al. Our results seem to imply, however, that it is the sum of neutrino heating and acoustic powers that matters for shock revival.