Low Star Formation Efficiency in M31: Evidence for a Deficit of Bound Gas

The Andromeda galaxy (M31) exhibits a systematically low star formation efficiency (SFE) compared to other star-forming galaxies. Star formation is thought to be regulated by the mass of gravitationally bound gas. To investigate whether the low SFE in M31 originates from a scarcity of such bound gas, we analyze the dynamical state of its giant molecular cloud (GMC) population by estimating their virial parameters (${\alpha }_{\mathrm{v}\mathrm{i}\mathrm{r}}$). Using a JCMT-SCUBA2 850 micron dust-continuum GMC catalog as the parent sample, we combine it with IRAM 30 m CO(1-0) data to define a working sample of 173 GMCs and derive their kinematic properties. Most analyzed GMCs exhibit high ${\alpha }_{\mathrm{v}\mathrm{i}\mathrm{r}}$, indicating that they are predominantly gravitationally unbound at the approximately 86 pc resolution of our observations. While no statistically significant global correlation is found between SFE and ${\alpha }_{\mathrm{v}\mathrm{i}\mathrm{r}}$ for the full cloud sample, the upper quantiles of the SFE distribution show progressively stronger negative trends with increasing ${\alpha }_{\mathrm{v}\mathrm{i}\mathrm{r}}$. This upper-tail trend may arise from the combined effects of the virial parameter limiting the upper range of SFE values accessible to the GMC population and feedback-driven disruption reducing the number of high-SFE, high-${\alpha }_{\mathrm{v}\mathrm{i}\mathrm{r}}$ CO-bright clouds in the observed sample. The substantial scatter in the SFE-${\alpha }_{\mathrm{v}\mathrm{i}\mathrm{r}}$ plane likely reflects the diverse evolutionary stages of GMCs, the temporal mismatch between gas and star formation tracers, and the limitations of a cloud-averaged virial parameter as a tracer of internal dynamical structure, making a simple one-to-one correspondence between ${\alpha }_{\mathrm{v}\mathrm{i}\mathrm{r}}$ and instantaneous SFE difficult to recover for individual GMCs.