A Steep Slope and Small Scatter for the High-Mass End of the L-$sigma$ Relation at $zsim0.55$

We measure the intrinsic relation between velocity dispersion ($sigma$) and luminosity ($L$) for massive, luminous red galaxies (LRGs) at redshift $z sim 0.55$. We achieve unprecedented precision by using a sample of 600,000 galaxies with spectra from the Baryon Oscillation Spectroscopic Survey (BOSS) of the third Sloan Digital Sky Survey (SDSS-III), covering a range of stellar masses $M_* gtrsim 10^{11} M_{odot}$. 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-$sigma$ relation of the form $L propto sigma^{beta}$, we find $beta = 7.8 pm 1.1$ for $sigma$ corrected to the effective radius, and a very small intrinsic scatter of $s = 0.047 pm 0.004$ in $log_{10} sigma$ 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-$sigma$ relation at $zsim0.55$ is consistent with the one measured at $z=0.1$. Our results, in combination with those presented in Montero-Dorta et al. (2014), provide a detailed description of the high-mass end of the red sequence (RS) at $zsim0.55$. This characterization, in the light of previous literature, suggest that the high-mass RS distribution corresponds to the core elliptical population.

The High-Mass End of the Red Sequence at z~0.55 from SDSS-III/BOSS: completeness, bimodality and luminosity function

We have developed an analytical method based on forward-modeling techniques to characterize the high-mass end of the red sequence (RS) galaxy population at redshift $zsim0.55$, from the DR10 BOSS CMASS spectroscopic sample, which comprises $sim600,000$ galaxies. The method, which follows an unbinned maximum likelihood approach, allows the deconvolution of the intrinsic CMASS colour-colour-magnitude distributions from photometric errors and selection effects. This procedure requires modeling the covariance matrix for the i-band magnitude, g-r colour and r-i colour using Stripe 82 multi-epoch data. Our results indicate that the error-deconvolved intrinsic RS distribution is consistent, within the photometric uncertainties, with a single point ($<0.05~{rm{mag}}$) in the colour-colour plane at fixed magnitude, for a narrow redshift slice. We have computed the high-mass end ($^{0.55}M_i lesssim -22$) of the $^{0.55}i$-band RS Luminosity Function (RS LF) in several redshift slices within the redshift range $0.52<z<0.63$. In this narrow redshift range, the evolution of the RS LF is consistent, within the uncertainties in the modeling, with a passively-evolving model with $Phi_* = (7.248 pm 0.204) times10^{-4}$ Mpc$^{-3}$ mag$^{-1}$, fading at a rate of $1.5pm0.4$ mag per unit redshift. We report RS completeness as a function of magnitude and redshift in the CMASS sample, which will facilitate a variety of galaxy-evolution and clustering studies using BOSS. Our forward-modeling method lays the foundations for future studies using other dark-energy surveys like eBOSS or DESI, which are affected by the same type of photometric blurring/selection effects.