The \ion{H}{I}-rich Ultra-diffuse Galaxies follow the Extended Schmidt Law

Abstract

The \ion{H}{I}-rich ultra-diffuse galaxies (HUDGs) offer a unique case for studies of star formation laws (SFLs) as they host low star formation efficiency (SFE) and low-metallicity environments where gas is predominantly atomic. We collect a sample of six HUDGs in the field and investigate their location in the extended Schmidt law($\Sigma_{\text {SFR }} \propto \left(\Sigma_{\text{star}}^{0.5} \Sigma_{\text{gas}}\right)^{1.09}$). They are consistent with this relationship well (with deviations of only 1.1 sigma). Furthermore, we find that HUDGs follow the tight correlation between the hydrostatic pressure in the galaxy mid-plane and the quantity on the x-axis ($\rm log(\Sigma_{star}^{0.5}\Sigma_{gas})$) of the extended Schmidt law. This result indicates that these HUDGs can be self-regulated systems that reach the dynamical and thermal equilibrium. In this framework, the stellar gravity compresses the disk vertically and counteracts the gas pressure in the galaxy mid-plane to regulate the star formation as suggested by some theoretical models.