Oxygen Isotope Ratios in Hydrogen-Deficient Carbon Stars: A Correlation with Effective Temperature and Implications for White Dwarf Merger Outcomes

Hydrogen-deficient Carbon (HdC) stars are a class of supergiants with anomalous chemical compositions, suggesting that they are remnants of CO-He white dwarf (WD) mergers. This class comprises two spectroscopically similar subclasses - dusty R Coronae Borealis (RCB) and dustless Hydrogen-deficient Carbon (dLHdC) stars. Both subclasses have a stark overabundance of $^{18}\textrm{O}$ in their atmospheres, but spectroscopic differences between them remain poorly studied. We present high-resolution ($R \approx 75000$) K-band spectra of six RCB and six dLHdC stars, including four newly discovered dLHdC stars, making this the largest sample to date. We develop a semi-automated fitting routine to measure $^{16}\textrm{O}/^{18}\textrm{O}$ ratios for this sample, tripling the number of dLHdC stars with oxygen isotope ratios measured from high resolution spectra. All six dLHdC stars have $^{16}\textrm{O}/^{18}\textrm{O}<1$, while the RCB stars have $^{16}\textrm{O}/^{18}\textrm{O}>4$. Additionally, for the first time, we find a trend of decreasing $^{16}\textrm{O}/^{18}\textrm{O}$ ratios with increasing effective temperature for HdC stars, consistent with predictions of theoretical WD merger models. However, we note that current models overpredict the low $^{16}\textrm{O}/^{18}\textrm{O}$ ratios of dLHdC stars by two orders of magnitude. We also measure abundances of C, N, O, Fe, S, Si, Mg, Na, and Ca for these stars. We observe a correlation between the abundances of $^{14}\textrm{N}$ and $^{18}\textrm{O}$ in our sample, suggesting that a fixed fraction of the $^{14}\textrm{N}$ is converted to $^{18}\textrm{O}$ in these stars via $\alpha$-capture. Our results affirm the emerging picture that the mass ratio/total mass of the WD binary determine whether an RCB or dLHdC is formed post-merger.