The C/N ratio from FUV spectroscopy as a constraint on evolution of the dwarf nova HS 0218 + 3229

<jats:title>ABSTRACT</jats:title>
<jats:p>White dwarfs that accrete from non-degenerate companions show anomalous carbon and nitrogen abundances in the photospheres of their stellar components have been postulated to be descendants of supersoft X-ray binaries. Measuring the carbon-to-nitrogen abundance ratio may provide constraints on their past evolution. We fit far-ultraviolet spectroscopy of the cataclysmic variable HS 0218 + 3229 taken with the Cosmic Origins Spectrograph using Markov chain Monte Carlo methods, and found the carbon-to-nitrogen ratio is about one tenth of the Solar value $(\rm{\log \mathrm{[C/N]}}=-0.56\pm 0.15)$. We also provide estimates of the silicon and aluminium abundances, and upper limits for iron and oxygen. Using the parameters we derived for HS 0218 + 3229 we reconstruct its past. We calculated a grid of mesa models and implemented Gaussian process fits in order to determine its most likely initial binary configuration. We found that an initial mass of the donor of $M_{\rm donor;i}=0.90-0.98,\rm{\mathrm{M}_{\odot }}$ and an initial orbital period of Porb; i = 2.88 d (Porb; i = 3.12–3.16 d) for an assumed initial white dwarf mass of $\rm{M_{\mathrm{WD}}}_\mathrm{;i}=0.83\, \rm{\mathrm{M}_{\odot }}$$(\rm{M_{\mathrm{WD}}}_{\rm ;i}=0.60\, \rm{\mathrm{M}_{\odot }})$ can replicate the measured parameters. The low mass ratio, $M_{\rm donor;i} / \rm{M_{\mathrm{WD}}}_{\rm ;i} =1.08-1.18\, (1.5-1.63)$, suggests that the system did not go through a phase of hydrogen-burning on the white dwarf’s surface. However, we can not exclude a phase of thermal time-scale mass transfer in the past. We predict that HS 0218 + 3229 will evolve below the ≃ 76.2 ± 1 min period minimum for normal cataclysmic variables.</jats:p>