A survey of ultra-compact high-state AM CVn binaries with ZTF and Gaia: New discoveries and observational constraints on Galactic space density

Ultra-compact AM CVn binaries in the high-state of stable mass transfer (10-9M/) are expected to be among the loudest persistent sources for upcoming space-based GW observatories. These systems typically have orbital periods P 30 minutes. We present a systematic search for high-state AM CVn binaries in the Milky Way by targeting a region within the Gaia color-magnitude diagram, combined with ZTF time-domain photometry. We focus on variable targets within that sample with 5-30 minute periods. Our survey discovered three new high-state AM CVn binaries (ZTF J1840-1742, ZTF J2007-0527 and ZTF J2111+3158) with orbital periods of 16.86, 18.63, and 16.71 minutes, and recovered three known systems. We obtain high-speed photometry and phase-resolved spectroscopy to confirm their nature. Their spectra show helium emission lines with no detectable hydrogen. In two targets, the lines are double-peaked, and Doppler tomograms confirm an accretion disk. We estimate mass accretion rates of about10-9M/, and 3 sigma X-ray luminosity upper limits of about10 33. Based on this sample, we infer a local space density of high-state AM CVn population in the Milky Way of about(1.0-2.7) times10-8-3 (for disk scale heights h z=300-200 pc), representing 2-5% of the total Galactic AM CVn density. Their birth rate, about(2.4-4.3) times10-4-1 (for h z=300-200 pc), is consistent with the total AM CVn birth rate, implying most systems entering the high-state phase survive and evolve to longer orbital periods. This local space density suggests LISA and TianQin will detect about 36% and 19% of the total Galactic population, respectively, during their nominal 4-yr missions (S/N 5). The Vera C. Rubin Observatory's LSST will detect about 34-44% of these systems over its 10-yr survey (m r 26.9 mag).