SIMBAD references

The second moment of the stellar velocity within the effective radius, denoted by ${\sigma }_{{\rm{e}}}^{2}$, 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 ${\sigma }_{\mathrm{aper}}/{\sigma }_{{\rm{e}}}={({R}_{\mathrm{aper}}/{R}_{{\rm{e}}})}^{\alpha }$, 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.