Abstract

We report the first direct spectroscopicmeasurement of the velocity dispersion function (VDF) for the high-mass red sequence (RS) galaxy population at redshift z -0.55. We achieve high precision by using a sample of 600 000 massive galaxies with spectra from the Baryon Oscillation Spectroscopic Survey (BOSS) of the third Sloan Digital Sky Survey (SDSS-III), covering stellar masses M-* >= 10(11)M(circle dot). We determine the VDF by projecting the joint probability density function (PDF) of luminosity L and velocity dispersion sigma, i. e. p(L, sigma), defined by our previous measurements of the RS luminosity function and L-sigma relation for this sample. These measurements were corrected from red-blue galaxy population confusion, photometric blurring, incompleteness and selection effects within a forward-modelling framework that furthermore correctly accommodates the low spectroscopic signal-to-noise ratio of individual BOSS spectra. Our z -0.55 RS VDF is in overall agreement with the z -0 early-type galaxy (ETG) VDF at log(10) sigma >= 2.47; however, the number density of z = 0.55 RS galaxies that we report is larger than that of z = 0 ETG galaxies at 2.35 >= log10 sigma >= 2.47. The extrapolation of an intermediate-mass L-s relation towards the high-mass end in previous low-z works may be responsible for this disagreement. Evolutionary interpretation of this comparison is also subject to differences in the way the respective samples are selected; these differences can be mitigated in future work by analysing z = 0 SDSS data using the same framework presented in this paper. We also provide the sample PDF for the RS population (i. e. uncorrected for incompleteness), which is a key ingredient for gravitational lensing analyses using BOSS.