We present the occurrence rates for rocky planets in the habitable zones (HZs) of main-sequence dwarf stars based on the Kepler DR25 planet candidate catalog and Gaia-based stellar properties. We provide the first analysis in terms of star-dependent instellation flux, which allows us to track HZ planets. We define eta(circle plus) as the HZ occurrence of planets with radii between 0.5 and 1.5 R-circle plus orbiting stars with effective temperatures between 4800 and 6300 K. We find that eta(circle plus) for the conservative HZ is between 0.37(-0.21)(+0.48) (errors reflect 68% credible intervals) and 0.60(-0.36)(+0.90) planets per star, while the optimistic HZ occurrence is between 0.58(-0.33)(+0.73) and 0.88(-0.51)(+1.28) planets per star. These bounds reflect two extreme assumptions about the extrapolation of completeness beyond orbital periods where DR25 completeness data are available. The large uncertainties are due to the small number of detected small HZ planets. We find similar occurrence rates between using Poisson likelihood Bayesian analysis and using Approximate Bayesian Computation. Our results are corrected for catalog completeness and reliability. Both completeness and the planet occurrence rate are dependent on stellar effective temperature. We also present occurrence rates for various stellar populations and planet size ranges. We estimate with 95% confidence that, on average, the nearest HZ planet around G and K dwarfs is similar to 6 pc away and there are similar to 4 HZ rocky planets around G and K dwarfs within 10 pc of the Sun.

Observations support the hypothesis that gas disk gravitational instability might explain the formation of massive or wide-orbit gas giant exoplanets. The situation with regard to Jupiter-mass exoplanets orbiting within similar to 20 au is more uncertain. Theoretical models yield divergent assessments often attributed to the numerical handling of the gas thermodynamics. Boss used the beta cooling approximation to calculate three-dimensional hydrodynamical models of the evolution of disks with initial masses of 0.091 M-circle dot extending from 4 to 20 au around 1 M-circle dot protostars. The models considered a wide range (1-100) of beta cooling parameters and started from an initial minimum Toomre stability parameter of Q(i) = 2.7 (gravitationally stable). The disks cooled down from initial outer disk temperatures of 180 K to as low as 40 K as a result of the beta cooling, leading to fragmentation into dense clumps, which were then replaced by virtual protoplanets (VPs) and evolved for up to similar to 500 yr. The present models test the viability of replacing dense clumps with VPs by quadrupling the spatial resolution of the grid once dense clumps form, sidestepping in most cases VP insertion. After at least similar to 200 yr of evolution, the new results compare favorably with those of Boss: similar numbers of VPs and dense clumps form by the same time for the two approaches. The results imply that VP insertion can greatly speed disk instability calculations without sacrificing accuracy.

To fully constrain the orbits of low-mass circumstellar companions, we conduct combined analyses of the radial velocity data and the Gaia and Hipparcos astrometric data for eight nearby systems. Our study shows that companion-induced position and proper motion differences between Gaia and Hipparcos are significant enough to constrain orbits of low-mass companions to a precision comparable with previous combined analyses of direct imaging and radial velocity data. We find that our method is robust to whether we use Gaia Data Release 2 or Gaia Early Data Release 3, as well as whether we use all of the data or just proper motion differences. In particular, we fully characterize the orbits of HD 190360 b and HD 16160 C for the first time. With a mass of 1.8 +/- 0.2 M-Jup and an effective temperature of 123-176K and orbiting around a Sun-like star, HD 190360 b is the smallest Jupiter-like planet with well-constrained mass and orbit, belonging to a small sample of fully characterized Jupiter analogues. It is separated from its primary star by 0.25 arcsec and thus may be suitable for direct imaging by the coronagraph instrument of the Roman Space Telescope.