Quantifying cosmic variance

• Published in: Monthly notices of the Royal Astronomical Society 2010-10, Vol.407 (4), p.2131-2140
• Main Authors: Driver, Simon P., Robotham, Aaron S. G.
• Format: Article
• Language: English
• Subjects: Astronomy; Cosmology; Earth, ocean, space; Exact sciences and technology; galaxies: general; galaxies: luminosity function; galaxies: luminosity function, mass function; galaxies: statistics; large-scale structure of Universe; mass function; Stars & galaxies
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1111/j.1365-2966.2010.17028.x

We determine an expression for the cosmic variance of any ‘normal’ galaxy survey based on examination of M*± 1 mag galaxies in the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) data cube. We find that cosmic variance will depend on a number of factors principally: total survey volume, survey aspect ratio and whether the area surveyed is contiguous or comprising independent sightlines. As a rule of thumb cosmic variance falls below 10 per cent once a volume of 107 h−30.7 Mpc3 is surveyed for a single contiguous region with a 1:1 aspect ratio. Cosmic variance will be lower for higher aspect ratios and/or non-contiguous surveys. Extrapolating outside our test region we infer that cosmic variance in the entire SDSS DR7 main survey region is ∼7 per cent to z < 0.1. The equation obtained from the SDSS DR7 region can be generalized to estimate the cosmic variance for any density measurement determined from normal galaxies (e.g. luminosity densities, stellar mass densities and cosmic star formation rates) within the volume range 103–107 h−30.7 Mpc3. We apply our equation to show that two sightlines are required to ensure that cosmic variance is