A physically motivated galaxy size definition across different state-of-the-art hydrodynamical simulations

Context. Galaxy sizes are a key parameter to distinguish between different galaxy types and morphologies, which in turn reflect distinct formation and assembly histories. Several methods have been proposed to define the boundaries of galaxies, often relying on light concentration or isophotal densities. However, these approaches are often constrained by observational limitations and do not necessarily provide a clear physical boundary for galaxy outskirts. Aims. With the advent of modern multi-wavelength deep imaging surveys, recent observational studies have introduced a new, physically motivated definition for determining galaxy sizes. This method takes the current or past radial position of the star formation threshold as the size of the galaxy. In practice, a proxy for measuring this position in the present-day Universe is the radial position of the stellar mass density contour at 1 M ⊙ pc −2 , defined as R 1 . In this study, we aim to test the validity of this new definition and assess its consistency across different redshifts and galaxy formation models. Methods. We analysed three state-of-the-art hydrodynamical simulation suites to explore the proposed size-stellar mass relation. For each simulation suite, we examined the stellar surface density profiles across a wide range of stellar masses and redshifts. We measured the galaxy sizes according to this new definition and compared them with the most traditional size metric, the stellar half-mass radius. Results. Our analysis demonstrates that the R 1 − M ⋆ relation exhibits consistent behaviour across both low and high stellar mass galaxies, with remarkably low scatter. This relation is independent of redshift and holds across the three different cosmological hydrodynamical simulation suites, highlighting its robustness to variations in galaxy formation models. Furthermore, we explore the connection between a galaxy’s total mass within R 1 and its stellar mass, finding very little scatter in this relation. This suggests that R 1 could serve as a reliable observational tracer for a galaxy’s dynamical mass. Conclusions. The size-stellar mass relation proposed provides a reliable and physically motivated method of defining the outskirts of galaxies. This method remains consistent not only at z = 0 but also throughout the evolutionary history of galaxies, offering a robust and meaningful framework for galaxy evolution studies.