Orbital relaxation and excitation of planets tidally interacting with white dwarfs

Observational evidence of white dwarf planetary systems is dominated by the remains of exo-asteroids through accreted metals, debris discs, and orbiting planetesimals. However, exo-planets in these systems play crucial roles as perturbing agents, and can themselves be perturbed close to the white dwarf Roche radius. Here, we illustrate a procedure for computing the tidal interaction between a white dwarf and a near-spherical solid planet. This method determines the planet’s inward and/or out-ward drift, and whether the planet will reach the Roche radius and be destroyed. We avoid constant tidal lag formulations and instead employ the self-consistent secular Darwin-Kaula expansions from Boué & Efroimsky (2019), which feature an arbitrary frequency dependence on the quality functions. We adopt wide ranges of dynamic viscosities and spin rates for the planet in order to straddle many possible outcomes, and provide a foundation for the future study of individual systems with known or assumed rheologies. We find that: (i) massive Super-Earths are destroyed more readily than minor planets (such as the ones orbiting WD 1145+017 and SDSSJ1228+1040),(ii) low-viscosity planets are destroyed more easily than high-viscosity planets, and(iii) the boundary between survival and destruction is likely to be fractal and chaotic

Precise radial velocities of giant stars XVI. Planet occurrence rates from the combined analysis of the Lick, EXPRESS, and PPPS giant star surveys

Context. Radial velocity surveys of evolved stars allow us to probe a higher stellar mass range, on average, compared to main-sequence samples. Hence, differences between the planet populations around the two target classes can be caused by either the differing stellar mass or stellar evolution. To properly disentangle the effects of both variables, it is important to characterize the planet population around giant stars as accurately as possible. Aims. Our goal is to investigate the giant planet occurrence rate around evolved stars and determine its dependence on stellar mass, metallicity, and orbital period. Methods. We combine data from three different radial velocity surveys targeting giant stars: The Lick giant star survey, the radial velocity program EXoPlanets aRound Evolved StarS (EXPRESS), and the Pan-Pacific Planet Search (PPPS), yielding a sample of 482 stars and 37 planets. We homogeneously rederived the stellar parameters of all targets and accounted for varying observational coverage, precision and stellar noise properties by computing a detection probability map for each star via injection and retrieval of synthetic planetary signals. We then computed giant planet occurrence rates as a function of period, stellar mass, and metallicity, corrected for incompleteness. Results. Our findings agree with previous studies that found a positive planet-metallicity correlation for evolved stars and identified a peak in the giant planet occurrence rate as a function of stellar mass, but our results place it at a slightly smaller mass of (1.68 ± 0.59) M⊙. The period dependence of the giant planet occurrence rate seems to follow a broken power-law or log-normal distribution peaking at (718 ± 226) days or (797 ± 455) days, respectively, which roughly corresponds to 1.6 AU for a 1 M⊙star and 2.0 AU for a 2 M⊙star. This peak could be a remnant from halted migration around intermediate-mass stars, caused by stellar evolution, or an artifact from contamination by false positives. The completeness-corrected global occurrence rate of giant planetary systems around evolved stars is 10.7%1.6%+2.2% for the entire sample, while the evolutionary subsets of RGB and HB stars exhibit 14.2%2.7%+4.1% and 6.6%1.3%+2.1%, respectively. However, both subsets have different stellar mass distributions and we demonstrate that the stellar mass dependence of the occurrence rate suffices to explain the apparent change of occurrence with the evolutionary stage