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

The second moment of the stellar velocity within the effective radius,denoted by σ^(2)_(e),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 byσ_(aper)/σ_(e)=(R_(aper)/R_(e))^(α),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 ofαon the r-band absolute magnitude M_(r),g-i color,and Sérsic index nSer,whereαvalues 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 ofαvalues 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.

Systematic Errors Induced by the Elliptical Power-law model in Galaxy–Galaxy Strong Lens Modeling

The elliptical power-law model of the mass in a galaxy is widely used in strong gravitational lensing analyses.However,the distribution of mass in real galaxies is more complex.We quantify the biases due to this model mismatch by simulating and then analyzing mock Hubble Space Telescope imaging of lenses with mass distributions inferred from SDSS-Ma NGA stellar dynamics data.We find accurate recovery of source galaxy morphology,except for a slight tendency to infer sources to be more compact than their true size.The Einstein radius of the lens is also robustly recovered with 0.1%accuracy,as is the global density slope,with 2.5%relative systematic error,compared to the 3.4%intrinsic dispersion.However,asymmetry in real lenses also leads to a spurious fitted"external shear"with typical strengthγext=0.015.Furthermore,time delays inferred from lens modeling without measurements of stellar dynamics are typically underestimated by~5%.Using such measurements from a sub-sample of 37 lenses would bias measurements of the Hubble constant H0 by~9%.Although this work is based on a particular set of Ma NGA galaxies,and the specific value of the detected biases may change for another set of strong lenses,our results strongly suggest the next generation cosmography needs to use more complex lens mass models.