A steep slope and small scatter for the high-mass end of the L-σ relation at z ∼ 0.55

We measure the intrinsic relation between velocity dispersion (σ) and luminosity (L) for massive, luminous red galaxies at redshift z ∼ 0.55. We achieve unprecedented precision by using a sample of 600 000 galaxies with spectra from the Baryon Oscillation Spectroscopic Survey of the third Sloan Digital Sky Survey (SDSS-III), covering a range of stellar masses M_* ≳ 10¹¹ M_⊙. We deconvolve the effects of photometric errors, limited spectroscopic signal-to-noise ratio, and red-blue galaxy confusion using a novel hierarchical Bayesian formalism that is generally applicable to any combination of photometric and spectroscopic observables. For an L-σ relation of the form L ∝ σ^β, we find β = 7.8 ± 1.1 for σ corrected to the effective radius, and a very small intrinsic scatter of s = 0.047 ± 0.004 in log₁₀σ at fixed L. No significant redshift evolution is found for these parameters. The evolution of the zero-point within the redshift range considered is consistent with the passive evolution of a galaxy population that formed at redshift z = 2-3, assuming single stellar populations. An analysis of previously reported results seems to indicate that the passively evolved high-mass L-σ relation at z ∼ 0.55 is consistent with the one measured at z = 0.1. Our results, in combination with those presented in the LF work of Montero-Dorta et al., provide a detailed description of the high-mass end of the red sequence (RS) at z ∼ 0.55. This characterization, in the light of previous literature, suggest that the high-mass RS distribution corresponds to the `core' elliptical population.