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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 itprovides insight into galaxy properties and their mass distributions. However,large spectroscopic surveys typically do not measure $\sigma_{\rm e}$ directly,instead providing $\sigma_{\rm aper}$, the second moment of the stellarvelocity within a fixed fiber aperture. In this paper, we derive an empiricalaperture correction formula, given by $\sigma_{\rm aper}/\sigma_{\rm e}=(R_{\rmaper}/R_{\rm e})^{\alpha}$, using spatially resolved stellar kinematicsextracted from approximately 10,000 Sloan Digital Sky Survey-Mapping NearbyGalaxies at Apache Point Observatory (SDSS-MaNGA) integral field unitobservations. Our analysis reveals a strong dependence of $\alpha$ on the$r$-band absolute magnitude $M_{\rm r}$, $g-i$ color, and Sersic index $n_{\rmSer}$, where $\alpha$ values are lower for brighter, redder galaxies withhigher Sersic indices. Our results demonstrate that the aperture correctionderived from previous literature on early-type galaxies cannot be applied topredict the aperture corrections for galaxies with intermediate Sersic indices.We provide a lookup table of $\alpha$ values for different galaxy types, withparameters in the ranges of $-18>M_{\rm r}>-24$, $0.4<g-i<1.6$, and $0<n_{\rmSer}<8$. A Python script is provided to obtain the correction factors from thelookup table.

research in astronomy and astrophysics/research in astronomy and astrophysics

Velocity Dispersion $\sigma_{\rm aper}$ Aperture Corrections as a  Function of Galaxy Properties from Integral-field Stellar Kinematics of  10,000 MaNGA Galaxies