HOW TO MAKE MAPS FROM COSMIC MICROWAVE BACKGROUND DATA WITHOUT LOSINGINFORMATION

The next generation of cosmic microwave background (CMB) experiments c an measure cosmological parameters with unprecedented accuracy-in prin ciple. To achieve this in practice when faced with such gigantic data sets, elaborate data analysis methods are needed to make it computatio nally feasible. An important step in the data pipeline is to make a ma p, which typically reduces the size of the data set by orders of magni tude. We compare 10 map-making methods and find that for the Gaussian case, both the method used by the COBE Differential Microwave Radiomet er (DMR) team and various forms of Wiener filtering are optimal in the sense that the map retains all cosmological information that was pres ent in the time-ordered data (TOD). Specifically, one obtains just as small error bars on cosmological parameters when estimating them from the map as one could have obtained by estimating them directly from th e TOD. The method of simply averaging the observations of each pixel ( for total-power detectors), on the contrary, is found generally to des troy information, as does the maximum entropy method and most other no nlinear map-making techniques. Since it is also numerically feasible, the COBE method is the natural choice for large data sets. Other lossl ess (e.g., Wiener-filtered) maps can then be computed directly from th e COBE method map.