Correlation between inner surface mass density and cold gas content in nearby galaxies

It is well known that the amount of cold gas in a galaxy is correlated with its star-formation rate, i.e. star-forming galaxies tend to host more gas. In addition, recent work has revealed tight correlations between star-formation rate and various structural parameters, notably the stellar surface mass density within the inner 1 kpc, Σ₁. Since cold gas is necessary for star formation, one would also expect correlations to exist between gas content and galaxy structure. To test this, we explore a number of these morphological parameters — velocity dispersion, Sérsic index, global stellar mass surface density, and Σ₁ — and their correlations with the molecular hydrogen (f_H2) and atomic hydrogen (f_HI) gas fractions. Our gas measurements are taken from the xCOLD GASS and ALFALFA surveys, yielding a sample of 227 galaxies with H₂ detections and 3,535 galaxies with HI detections within a redshift range of 0.01 ≤ z ≤ 0.05 and a stellar mass range of 10⁹ M_☉ ≤ M_* ≤ 10^11.5 M_☉. Structural parameters were obtained from publicly available catalogs based on Sloan Digital Sky Survey observations of these objects. By comparing Spearman correlation coefficients and analyzing the scatter in the data, we find that for both f_HI and f_H2, the strongest correlation is with Σ₁. Using only Σ₁, we can predict f_HI to within a factor of 1.8 and f_H2 to within a factor of 2.3. The larger residuals in the correlations involving H₂ may be due to the limited availability of H₂ measurements. Larger sample sizes would likely strengthen the correlation between f_H2 and Σ₁. Our findings highlight the predictive power of Σ₁ and offer a method to estimate cold gas content using readily available parameters for large samples of galaxies.