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 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 and redshift bin size
Dz. 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, Dz and stellar mass
m*. We also provide tabulated values and a software tool. We find that for
GOODS at z=2 and with Dz=0.5 the relative cosmic variance of galaxies with
m*>10^11 Msun is ~38%, while it is ~27% for GEMS and ~12% for COSMOS. For
galaxies of m*~10^10 Msun the relative cosmic variance is ~19% for GOODS, ~13%
for GEMS and ~6% for COSMOS. This implies that cosmic variance is a significant
source of uncertainty at z=2 for small fields and massive galaxies, while for
larger fields and intermediate mass galaxies cosmic variance is less serious.
