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

The scaling relation between stellar mass (M_∗) 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 β of the M_∗–r_e relation for late-type dwarfs (10⁷ ≤ M_∗/M_⊙ ≤ 10⁹) using a sample of 188 isolated low surface brightness (LSB) galaxies, accounting for observational incompleteness. Surprisingly, the best-fitting model (β = 0.40 ± 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_∗–r_e relation closely follows the distribution of known dwarf galaxies. These results indicate that extrapolated
canonical models overpredict the number of large dwarf (i.e. LSB) galaxies, including ultra-diffuse galaxies (UDGs), explaining why they are overproduced by some semi-analytic models. The best-fitting model also constrains the power-law exponent of the physical size distribution of UDGs to n[dex⁻¹] ∝ r^3.54±0.33_e , consistent to within 1σ 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.