Galaxy Correlation Function and Local Density from Photometric Redshifts Using the Stochastic Order Redshift Technique (SORT)

The stochastic order redshift technique (SORT) is a simple, efficient, and robust method to improve cosmological redshift
measurements. The method relies upon having a small (∼10 per cent) reference sample of high-quality redshifts. Within pencil-
beam-like sub-volumes surrounding each galaxy, we use the precise dN/dz distribution of the reference sample to recover new
redshifts and assign them one-to-one to galaxies such that the original rank order of redshifts is preserved. Preserving the rank
order is motivated by the fact that random variables drawn from Gaussian probability density functions with different means
but equal standard deviations satisfy stochastic ordering. This process is repeated for sub-volumes surrounding each galaxy in
the survey. This results in every galaxy being assigned multiple ‘recovered’ redshifts from which a new redshift estimate is
determined. An earlier paper applied SORT to a mock Sloan Digital Sky Survey at z 0.2 and accurately recovered the two-point
correlation function (2PCF) on scales > 4 h−1Mpc. In this paper, we test the performance of SORT in surveys spanning the
redshift range 0.75 < z < 2.25. We used two mock surveys extracted from the Small MultiDark–Planck and Bolshoi–Planck
N-body simulations with dark matter haloes that were populated by the Santa Cruz semi-analytic model. We find that SORT
overall improves redshift estimates, accurately recovers the redshift-space 2PCF ξ (s) on scales > 2.5 h−1Mpc, and provides
improved local density estimates in regions of average or higher density, which may allow for improved understanding of how
galaxy properties relate to their environments.