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 L_X = 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 L_X of CVs to be 〈L_X〉 ≈ 4.6 × 10³⁰ erg s⁻¹, in contrast to previous surveys which yielded 〈L_X〉 ∼ 10³¹−10³² erg s⁻¹. We construct X-ray luminosity functions that, for the first time, flatten out at L_X ∼ 10³⁰ erg s⁻¹. We infer average number, mass, and luminosity densities of ρ_N,CV = (3.7 ± 0.7) × 10⁻⁶pc⁻³, ρM = ( 5.0 ± 1.0 ) × 1 0 − 5 M_⊙⁻¹ , and ρL_X = ( 2.3 ± 0.4 ) × 10²⁶ erg s⁻¹ M_⊙⁻¹ , respectively, in the solar neighborhood. Our uniform selection method also allows us to place meaningful estimates on the space density of AM CVns, ρ_{N,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.