The evolutionary history of ultra-compact accreting binaries. I. Chemical abundances and formation channel of the eclipsing AM CVn system ZTF J225237.05-051917.4 from HST spectroscopy
AM Canum Venaticorum (AM CVn) stars are ultra-compact binary systems composed of a white dwarf (WD) primary accreting from a H-deficient donor. They are important as potential progenitors of Type Ia supernovae and laboratories for gravitational-wave studies, yet their evolutionary history remains unsolved. Three formation channels have been proposed: the WD channel, the He-star channel, and the cataclysmic variable (CV) channel. We aim to provide the first accurate measurements of the fundamental parameters of the accretor in ZTFJ225237.05-051917.4, including the abundances of key elements such as C, N, and Si, by analysing UV spectra obtained with the Hubble Space Telescope. These measurements provide new insight into the system's evolutionary history and establish it as a benchmark to develop our pipeline for application to a larger sample of AM CVns. We determine the binary parameters from photometric modelling and constrain the atmospheric parameters of the WD accretor, including Teff, logg, and chemical abundances, by fitting the UV spectrum with synthetic spectral models. We then infer the system's formation channel by comparing our results with theoretical evolutionary models. We measure a Teff=23300$\pm$600K and a surface gravity of logg=8.4$\pm$0.3, which implies an accretor mass of 0.86$\pm$0.16 solar masses. We find a high N/C abundance ratio by mass of >153. The accretor is significantly hotter than previous estimates based on simplified blackbody fits to the spectral energy distribution, underscoring the importance of detailed spectral modelling for determining accurate system parameters. Our results show that UV spectroscopy is well-suited to constraining the formation channels of AM CVn systems. We conclude that the He-star channel can be excluded based on the high N/C ratio, while the WD and CV channels remain consistent with the observations.