An approximation to the likelihood function for band-power estimates of CMB anisotropies

Band-power estimates of cosmic microwave background fluctuations are now ro utinely used to place constraints on cosmological parameters. For this to b e done in a rigorous fashion, the full likelihood function of band power es timates must be employed. Even for Gaussian theories, this likelihood funct ion is not itself Gaussian, fur the simple reason that band-powers measure the variance of the random sky fluctuations. In the context of Gaussian sky fluctuations, we use an ideal situation to motivate a general form for the full likelihood function from a given experiment. Tills form contains only two free parameters, which can be determined if the 68% and 95% confidence intervals of the true likelihood function are known. The ansatz works rema rkably well when compared to the complete likelihood function for a number of experiments. For application of this kind of approach, we suggest that i n the future both 68% and 95% (and perhaps also the 99.7%) confidence inter vals be given when reporting experimental results.