Velocity Dispersion $\ddot{I}{ƒ}_{\mathrm{aper}}$ 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 $\ddot{I}{ƒ}_{\mathrm{e}}^2$, 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 $\ddot{I}{ƒ}_{\mathrm{e}}$ directly, instead providing $\ddot{I}{ƒ}_{\mathrm{aper}}$, the second moment of the stellar velocity within a fixed fiber aperture. In this paper, we derive an empirical aperture correction formula, given by $\ddot{I}{ƒ}_{\mathrm{aper}}/\ddot{I}{ƒ}_{\mathrm{e}}=(R_{\mathrm{aper}}/R_{\mathrm{e}}{)}^{\hat{I}}\pm$, using spatially resolved stellar kinematics extracted from approximately 10,000 Sloan Digital Sky Survey-Mapping Nearby Galaxies at Apache Point Observatory (SDSS-MaNGA) integral field unit observations. Our analysis reveals a strong dependence of $\hat{I}\pm$ on the $r$-band absolute magnitude $M_{\mathrm{r}}$, $g-i$ color, and Sersic index $n_{\mathrm{Ser}}$, where $\hat{I}\pm$ values are lower for brighter, redder galaxies with higher Sersic 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 Sersic indices. We provide a lookup table of $\hat{I}\pm$ values for different galaxy types, with parameters in the ranges of $-18>M_{\mathrm{r}}>-24$, $0.4<g-i<1.6$, and $0<n_{\mathrm{Ser}}<8$. A Python script is provided to obtain the correction factors from the lookup table.

12 pages, 10 figures, 1 table, published in Research in Astronomy and Astrophysics