The stellar mass - physical effective radius relation for dwarf galaxies in low-density environments

Abstract

The scaling relation between stellar mass ($M_{\ast }$) and physical effective radius ($r_e$) has been well-studied using wide spectroscopic surveys. However, these surveys suffer from severe surface brightness incompleteness in the dwarf galaxy regime, where the relation is poorly constrained. In this study, I use a Bayesian empirical model to constrain the power-law exponent $\beta$ of the $M_{\ast }$-$r_e$ relation for late-type dwarfs ($10^7$$\le$$M_{\ast }$/$M_{\odot }$$\le$$10^9$) using a sample of 188 isolated low surface brightness (LSB) galaxies, accounting for observational incompleteness. Surprisingly, the best-fitting model ($\beta$=0.40$\pm$0.07) indicates that the relation is significantly steeper than would be expected from extrapolating canonical models into the dwarf galaxy regime. Nevertheless, the best fitting $M_{\ast }$-$r_e$ relation closely follows the distribution of known dwarf galaxies. These results indicate that extrapolated canonical models over-predict the number of large dwarf (i.e. LSB) galaxies, including ultra-diffuse galaxies (UDGs), explaining why they are over-produced by some semi-analytic models. The best-fitting model also constrains the power-law exponent of the physical size distribution of UDGs to $n[\mathrm{de}{\mathrm{x}}^{-1}]\propto$$r_e^{3.54\pm 0.33}$, consistent to within 1$\sigma$ of the corresponding value in cluster environments and with the theoretical scenario in which UDGs occupy the high-spin tail of the normal dwarf galaxy population.

Accepted in MNRAS letters

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