We introduce xCOLD GASS, a legacy survey providing a census of molecular gas in the local Universe. Building upon the original COLD GASS survey, we present here the full sample of 532 galaxies with CO(1-0) measurements from the IRAM-30m telescope. The sample is mass-selected in the redshift interval $0.01<z<0.05$ from SDSS, and therefore representative of the local galaxy population with M$_{ast}>10^9$M$_{odot}$. The CO(1-0) flux measurements are complemented by observations of the CO(2-1) line with both the IRAM-30m and APEX telescopes, HI observations from Arecibo, and photometry from SDSS, WISE and GALEX. Combining the IRAM and APEX data, we find that the CO(2-1) to CO(1-0) luminosity ratio for integrated measurements is $r_{21}=0.79pm0.03$, with no systematic variations across the sample. The CO(1-0) luminosity function is constructed and best fit with a Schechter function with parameters {$L_{mathrm{CO}}^* = (7.77pm2.11) times 10^9,mathrm{K,km,s^{-1}, pc^{2}}$, $phi^{*} = (9.84pm5.41) times 10^{-4} , mathrm{Mpc^{-3}}$ and $alpha = -1.19pm0.05$}. With the sample now complete down to stellar masses of $10^9$M$_{odot}$, we are able to extend our study of gas scaling relations and confirm that both molecular gas fraction and depletion timescale vary with specific star formation rate (or offset from the star-formation main sequence) much more strongly than they depend on stellar mass. Comparing the xCOLD GASS results with outputs from hydrodynamic and semi-analytic models, we highlight the constraining power of cold gas scaling relations on models of galaxy formation.
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