A COSMIC VARIANCE COOKBOOK

Deep pencil beam surveys (< 1 deg(2)) are of fundamental importance for studying the high-redshift universe. However, inferences about galaxy population properties (e. g., the abundance of objects) are in practice limited by cosmic variance. This is the uncertainty in observational estimates of the number density of galaxies arising from the underlying large-scale density fluctuations. This source of uncertainty can be significant, especially for surveys which cover only small areas and for massive high-redshift galaxies. Cosmic variance for a given galaxy population can be determined using predictions from cold dark matter theory and the galaxy bias. In this paper, we provide tools for experiment design and interpretation. For a given survey geometry, we present the cosmic variance of dark matter as a function of mean redshift (z) over bar and redshift bin size Delta z. Using a halo occupation model to predict galaxy clustering, we derive the galaxy bias as a function of mean redshift for galaxy samples of a given stellar mass range. In the linear regime, the cosmic variance of these galaxy samples is the product of the galaxy bias and the dark matter cosmic variance. We present a simple recipe using a fitting function to compute cosmic variance as a function of the angular dimensions of the field, (z) over bar, Delta z, and stellar mass m(+). We also provide tabulated values and a software tool. The accuracy of the resulting cosmic variance estimates (delta sigma(nu)/sigma(nu)) is shown to be better than 20%. We find that for GOODS at (z) over bar = 2 and with Delta z = 0.5, the relative cosmic variance of galaxies with m(*) > 10(11)M(circle dot) is similar to 38%, while it is similar to 27% for GEMS and similar to 12% for COSMOS. For galaxies of m(*) similar to 10(10) M-circle dot, the relative cosmic variance is similar to 19% for GOODS, similar to 13% for GEMS, and similar to 6% for COSMOS. This implies that cosmic variance is a significant source of uncertainty at (z) over bar = 2 for small fields and massive galaxies, while for larger fields and intermediate mass galaxies, cosmic variance is less serious.