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tokens: as different catalogs cover different redshift ranges. We compile a set of small-scale rejection masks (bright stars, bad imaging tracks, and small regions without spectroscopic coverage) provided by these surveys and generate a joint rejection mask by taking the union. 8 8 The masks are available at 10.5281/zenodo.4012781 . Table 1 summarizes the basic parameters of the spectroscopic reference sources that we use after applying the joint SDSS rejection mask, the 60% Galactic mask, and the infrared point-source mask described in Section 3.1.1 . Table 1 Spectroscopic Redshift Reference Notes. a Effective unmasked sky area in deg 2 . b Number of sources in the effective area. c Fraction of the sources in the Northern Galactic Hemisphere. d Median and 68% CL range of the redshift distribution. References. (1) Strauss et al. ( 2002 ), (2) Blanton et al. ( 2005 ), (3) Reid et al. ( 2016 ), (4) Bautista et al. ( 2018 ), (5) Schneider et al. ( 2010 ), (6) Pâris et al. ( 2017 ), (7) Ata et al. ( 2018 ). 3.2. Clustering Redshifts We apply the clustering-based or cross-correlation-based redshift estimation following Ménard et al. ( 2013 ) for both the channel intensity and Planck's Compton y maps. The technique is based on the simple ansatz that all matter tracers appear spatially clustered on the sky if their redshift distributions overlap. One can thus take a “reference” sample of galaxies or quasars with known redshifts and propagate the redshift information into a “test” data set with an unknown redshift distribution. This is achieved by cross-correlating the reference and test samples as a function of redshift of the former. The first applications to large data sets are done in the regime of discrete objects as the test sample to estimate source redshift distributions in photometric surveys (e.g., Rahman et al. 2015 , 2016a , 2016b ; Scottez et al. 2016 ; Hildebrandt et al. 2017 ; Davis et al. 2018 ; Gatti et al. 2018 ; Kitanidis et al. 2020 ; Krolewski et al. 2019 ). It is straightforward to generalize the method and redshift inference to diffuse fields simply by replacing the notion of objects with pixels on a set of predetermined grids (Schmidt et al. 2015 ; Chiang Ménard 2019 ; Chiang et al. 2019 ). Our implementation in this work is largely based on that in Chiang et al. ( 2019 ); here we briefly describe the key steps and minor modifications made for the tSZ tomography. We denote the overdensity field of the 2D test intensity map as (where T = I ν i in the multichannel analysis and T = y for the direct y map tomography) and that for the 3D reference sources as . As both are, in general, biased tracers of the underlying matter density field with the angular correlation function at some effective scale, we can write down a linear expression for their cross-correlation amplitudes evaluated in bins of the reference redshift z i aswhere b T and b R are the effective linear-clustering bias for the test and reference data at the scales considered.