What are the hot R coronae borealis stars?

We investigate the evolutionary status of four stars: V348 Sgr, DY Cen, and MV Sgr in the Galaxy and HV 2671 in the LMC. These stars have in common random deep declines in visual brightness, which are characteristic of R Coronae Borealis (RCB) stars. RCB stars are typically cool hydrogen-deficient supergiants. The four stars studied in this paper are hotter (Teff = 15-20 kK) than the majority of RCB stars (Teff = 5000-7000 K). Although these are commonly grouped together as the hot RCB stars they do not necessarily share a common evolutionary history. We present new observational data and an extensive collection of archival and previously published data that is reassessed to ensure internal consistency. We find temporal variations of various properties on different timescales that will eventually help us to uncover the evolutionary history of these objects. DY Cen and MV Sgr have typical RCB helium abundances, which exclude any currently known post-asymptotic giant branch (post-AGB) evolutionary models. Moreover, their carbon and nitrogen abundances present us with further problems for their interpretation. V348 Sgr and HV 2671 are in general agreement with a born-again post-AGB evolution, and their abundances are similar to Wolf-Rayet central stars of planetary nebulae (PNs). The three Galactic stars in the sample have circumstellar nebulae, which produce forbidden line radiation (for HV 2671 we have no information). V348 Sgr and DY Cen have low-density, low-expansion velocity nebulae (resolved in the case of V348 Sgr), while MV Sgr has a higher density, higher expansion velocity nebula. All three stars, on the other hand, have split emission lines, which indicate the presence of an equatorial bulge but not of a Keplerian disk. In addition, the historical light curves for the three Galactic hot RCB stars show evidence for a significant fading in their maximum-light brightnesses of ∼1 mag over the last 70 yr. From this we deduce that their effective temperatures increased by a few thousand degrees. If V348 Sgr is a born-again star, as we presume, this means that the star is returning from the born-again AGB phase to the phase of a central star of PN. Spectroscopically, no dramatic change is observed over the last 50 years for V348 Sgr and MV Sgr. However, there is some evidence that the winds of V348 Sgr and DY Cen have increased in strength in the last decade. HV 2671, located in the LMC, has not been analyzed in detail but at 5 Å resolution is almost identical to V348 Sgr. Through the bolometric correction derived for V348 Sgr and the known distance, we can estimate the absolute V magnitude of HV 2671 (MV = -3.0 mag) and its bolometric luminosity (∼6000 L ̇)