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.