HdC and EHe stars through the prism of Gaia DR3: Evolution of RV amplitude and dust formation rate with effective temperature

The Gaia DR3 release includes heliocentric radial velocity measurements and velocity variability indices for tens of millions of stars observed over 34 months.In this study, we utilise these indices to investigate the intrinsic radial velocity variations of Hydrogen-deficient Carbon (HdC) stars and Extreme Helium (EHe) stars across their large ranges of temperature and brightness. Taking advantage of the newly defined HdC temperature classes, we examine the evolution of the total velocity amplitude with effective temperature. Additionally, we analyse the variation in the dust production rate of R Coronae Borealis (RCB) stars with temperature using two different proxies for the photometric state of RCB stars: one from Gaia and another from the 2MASS survey. Our observations revealed a trend in the evolution of the maximum radial velocity amplitude across each HdC temperature class. Similarly, we also observed a correlation between stellar temperature and the dust production rate. Interestingly, we possibly observed for the first time some variations of the intrinsic radial velocity amplitude and the dust production rate with HdC temperature class. If confirmed, these variations would indicate that the helium shell-burning giant stage starts with strong atmospheric motions that decrease in strength, up to $\sim$6000 K, before picking up again as the HdC star atmosphere shrinks further in size and reaches warmer temperatures. Moreover, the dust formation rate appears to be much higher in colder RCB stars compared to warmer ones.