"Sample Variance" in Small-Scale CMB Anisotropy Experiments

Details "Sample Variance" in Small-Scale CMB Anisotropy Experiments "Sample Variance" in Small-Scale CMB Anisotropy Experiments

1993-05-25

arxiv.org/abs/astro-ph/9305030v2

Astrophys.J.421:L5,1994

Astronomy and Astrophysics

Astrophysics

6 pages in Plain TeX with 1 postscript figure appended

Scientific paper

10.1086/187173

We discuss the effects of finite sky coverage and the uncertainty in extracting information about the power spectrum from experiments on small angular scales. In general the cosmic variance is enhanced by a factor of $4\pi/A$, where $A$ is the solid angle sampled by the experiment. As a rough guide, an experiment with sensitivity peaking at the $\ell$th multipole has to cover $\simgt\ell$ independent patches to have a lower ``sample variance'' than for a whole-sky measurement of the quadrupole. Our approach gives a relatively simple way of attaching an error bar to the theoretical prediction for a particular experiment, and thereby comparing theories with experimental results, without the need for computationally-intensive Maximum Likelihood or Monte Carlo calculations.

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