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The stellar mass - physical effective radius relation for dwarf galaxies in low-density environments
Daniel J. Prole
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The scaling relation between stellar mass (M_*) and physical effective radius (rₑ) 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_*-rₑ relation for late-type dwarfs ($10^{7}≤M_{*}$/$M_{\odot}≤10^{9}) using a sample of 188 isolated low surface brightness (LSB) galaxies, accounting for observational incompleteness. Surprisingly, the best-fitting model (\beta$=0.40±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_*-rₑ 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{[dex^{-1}]}\propto$$~r_{e}^{3.54\pm0.33}, 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.
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