Velocity Dispersion σ aper Aperture Corrections as a Function of Galaxy Properties from Integral-field Stellar Kinematics of 10,000 MaNGA Galaxies

Abstract

The second moment of the stellar velocity within the effective radius, denoted by , is a crucial quantity in galaxy studies, as it provides insight into galaxy properties and their mass distributions. However, large spectroscopic surveys typically do not measure σ e directly, instead providing σ aper, the second moment of the stellar velocity within a fixed fiber aperture. In this paper, we derive an empirical aperture correction formula, given by , using spatially resolved stellar kinematics extracted from approximately 10,000 Sloan Digital Sky Survey–Mapping Nearby Galaxies at Apache Point Observatory integral field unit observations. Our analysis reveals a strong dependence of α on the r-band absolute magnitude M r, g–i color, and Sérsic index n Ser, where α values are lower for brighter, redder galaxies with higher Sérsic indices. Our results demonstrate that the aperture correction derived from previous literature on early-type galaxies cannot be applied to predict the aperture corrections for galaxies with intermediate Sérsic indices. We provide a lookup table of α values for different galaxy types, with parameters in the ranges of −18 > M r > −24, 0.4 < g–i < 1.6, and 0 < n Ser < 8. A Python script is provided to obtain the correction factors from the lookup table.