Testing the Momentum-driven Supernova Feedback Paradigm in M31

Momentum feedback from isolated supernova remnants (SNRs) have been increasingly recognized by modern cosmological simulations as a resolution-independent means to implement the effects of feedback in galaxies, such as turbulence and winds. However, the integrated momentum yield from SNRs is uncertain due to the effects of SN clustering and interstellar medium (ISM) inhomogeneities. In this paper, we use spatially-resolved observations of the prominent 10-kpc star-forming ring of M31 to test models of mass-weighted ISM turbulence driven by momentum feedback from isolated, non-overlapping SNRs. We use a detailed stellar-age distribution (SAD) map from the Panchromatic Hubble Andromeda Treasury (PHAT) survey, observationally-constrained SN delay-time distributions, and maps of the atomic and molecular hydrogen to estimate the mass-weighted velocity dispersion using the Martizzi et al. ISM turbulence model. Our estimates are within a factor of 2 of the observed mass-weighted velocity dispersion in most of the ring, but exceed observations at densities $\lesssim 0.2$ cm$^{-3}$ and SN rates $>2.1\times 10^{-4}$ SN yr$^{-1}$ kpc$^{-2}$, even after accounting for plausible variations in stellar-age distribution models and ISM scale height assumptions. We conclude that at high SN rates the momentum deposited is most likely suppressed by the non-linear effects of SN clustering, while at low densities, SNRs reach pressure equilibrium before the cooling phase. These corrections should be introduced in models of momentum-driven feedback and ISM turbulence.