Cataclysmic variables and AM CVn binaries in SRG/eROSITA + Gaia: Volume limited samples, X-ray luminosity functions, and space densities We present volume-limited samples of cataclysmic variables (CVs) and AM CVn binaries jointly selected from SRG/eROSITA eRASS1 and Gaia DR3 using an X-ray + optical color–color diagram (the "X-ray Main Sequence"). This tool identifies all CV subtypes, including magnetic and low-accretion rate systems, in contrast to most previous surveys. We find 23 CVs, 3 of which are AM CVns, out to 150 pc in the Western Galactic Hemisphere. Our 150 pc sample is spectroscopically verified and complete down to LX = 1.3 × 1029 erg s−1 in the 0.2–2.3 keV band, and we also present CV candidates out to 300 pc and 1000 pc. We discovered two previously unknown systems in our 150 pc sample: the third nearest AM CVn and a magnetic period bouncer. We find the mean LX of CVs to be 〈LX〉 ≈ 4.6 × 1030 erg s−1, in contrast to previous surveys which yielded 〈LX〉 ∼ 1031−1032 erg s−1. We construct X-ray luminosity functions that, for the first time, flatten out at LX ∼ 1030 erg s−1. We infer average number, mass, and luminosity densities of ρN,CV = (3.7 ± 0.7) × 10−6pc−3, (math formular), and (math formular), respectively, in the solar neighborhood. Our uniform selection method also allows us to place meaningful estimates on the space density of AM CVns, ρN,AM CVn = (5.5 ± 3.7) × 10−7 pc−3. Magnetic CVs and period bouncers make up 35% and 25% of our sample, respectively. This work, through a novel discovery technique, shows that the observed number densities of CVs and AM CVns, as well as the fraction of period bouncers, are still in tension with population synthesis estimates. 137 1 IOP Publishing application/pdf