Canceling Out Intensity Mapping Foregrounds

Intensity mapping of the 21 cm line has arisen as a powerful probe of the high-redshift Universe, but its potential is limited by extremely bright foregrounds and high source confusion. We propose a new analysis which can help solve both problems. From the combination of an intensity map with an overlapping galaxy survey, we construct a new one-point statistic which is unbiased by foregrounds and contains information left out of conventional analyses. We show that our method can measure the HI mass function with unprecedented precision using observations similar to recent 21 cm detections.