An infrared census of R Coronae Borealis Stars II -- Spectroscopic classifications and implications for the rate of low-mass white dwarf mergers

We present results from a systematic infrared (IR) census of R Coronae Borealis (RCB) stars in the Milky Way, using data from the Palomar Gattini IR (PGIR) survey. R Coronae Borealis stars are dusty, erratic variable stars presumably formed from the merger of a He-core and a CO-core white dwarf (WD). PGIR is a 30 cm $J$-band telescope with a 25 deg$^{2}$ camera that surveys 18000 deg$^{2}$ of the northern sky ($\delta>-28^{o}$) at a cadence of 2 days. Using PGIR J-band lightcurves for $\sim$60 million stars together with mid-IR colors from WISE, we selected a sample of 530 candidate RCB stars. We obtained near-IR spectra for these candidates and identified 53 RCB stars in our sample. Accounting for our selection criteria, we find that there are a total of $\approx350^{+150}_{-100}$ RCB stars in the Milky Way. Assuming typical RCB lifetimes, this corresponds to an RCB formation rate of 0.8 - 5 $\times$ 10$^{-3}$ yr$^{-1}$, consistent with observational and theoretical estimates of the He-CO WD merger rate. We searched for quasi-periodic pulsations in the PGIR lightcurves of RCB stars and present pulsation periods for 16 RCB stars. We also examined high-cadenced TESS lightcurves for RCB and the chemically similar, but dustless hydrogen-deficient carbon (dLHdC) stars. We find that dLHdC stars show variations on timescales shorter than RCB stars, suggesting that they may have lower masses than RCB stars. Finally, we identified 3 new spectroscopically confirmed and 12 candidate Galactic DY Per type stars - believed to be colder cousins of RCB stars - doubling the sample of Galactic DY Per type stars.