1702.03004
Cross-correlating 2D and 3D galaxy surveys
Passaglia, et al
Galaxy surveys probe both structure formation and the expansion rate, making them promising avenues for understanding the dark universe. Photometric surveys accurately map the 2D distribution of galaxy positions and shapes in a given redshift range, while spectroscopic surveys provide sparser 3D maps of the galaxy distribution. Present a way to analyse overlapping 2D and 3D maps jointly and without loss of information. Represent 3D maps using spherical Fourier-Bessel (sFB) models, which preserve radial coverage while accounting for the spherical sky geometry, and decompose 2D maps in a spherical harmonic basis. In theses bases, a simple expression exists for the cross-correlation of the 2 fields. One very powerful application is the ability to simultaneously constrain the z distribution of the photometric sample, the sample biases, and cosmological parameters. Use the framework to show that combined analysis of DESI and LSST can improve cosmological constraints by factors of ~1.2 to ~1.8 on the region where they overlap relative to identically sized disjoint regions. Also show that in the overlap of DES and SDSS-III in Stripe 82, cross-correlating improves photo-z parameter constraints by factors of ~2 to ~12 over internal photo-z reconstructions.
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