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We propose a second-order statistic parameter ε, the relative occurrence rate between hot Jupiters (HJs) and cold Jupiters (CJs) (ε = η HJ/η CJ), to probe the migration of gas giants. Since the planet occurrence rate is the combined outcome of the formation and migration processes, a joint analysis of HJ and CJ frequency may shed light on the dynamical evolution of giant planet systems. We first investigate the behavior of ε as the stellar mass changes observationally. Based on the occurrence rate measurements of HJs (η HJ) from the Transiting Exoplanet Survey Satellite survey and CJs (η CJ) from the California Legacy Survey, we find a tentative trend (97% confidence) that ε drops when the stellar mass rises from 0.8 to 1.4 M ⊙, which can be explained by different giant planet growth and disk migration timescales around different stars. We carry out planetesimal and pebble accretion simulations, both of which can reproduce the results of η HJ, η CJ, and ε. Our findings indicate that the classical core accretion + disk migration model can explain the observed decreasing trend of ε. We propose two ways to increase the significance of the trend and verify the anticorrelation. Future works are required to better constrain ε, especially for M dwarfs and for more massive stars.

In 2017, the California-Kepler Survey (CKS) published its first data release (DR1) of high-resolution optical spectra of 1305 planet hosts. Refined CKS planet radii revealed that small planets are bifurcated into two distinct populations, super-Earths (smaller than 1.5 R ⊕) and sub-Neptunes (between 2.0 and 4.0 R ⊕), with few planets in between (the “radius gap”). Several theoretical models of the radius gap predict variation with stellar mass, but testing these predictions is challenging with CKS DR1 due to its limited M ⋆ range of 0.8–1.4 M ⊙. Here we present CKS DR2 with 411 additional spectra and derived properties focusing on stars of 0.5–0.8 M ⊙. We found that the radius gap follows R p ∝ P m with m = −0.10 ± 0.03, consistent with predictions of X-ray and ultraviolet- and core-powered mass-loss mechanisms. We found no evidence that m varies with M ⋆. We observed a correlation between the average sub-Neptune size and M ⋆. Over 0.5–1.4 M ⊙, the average sub-Neptune grows from 2.1 to 2.6 R ⊕, following Rp∝M⋆α with α = 0.25 ± 0.03. In contrast, there is no detectable change for super-Earths. These M ⋆–R p trends suggest that protoplanetary disks can efficiently produce cores up to a threshold mass of M c , which grows linearly with stellar mass according to M c ≈ 10 M ⊕(M ⋆/M ⊙). There is no significant correlation between sub-Neptune size and stellar metallicity (over −0.5 to +0.5 dex), suggesting a weak relationship between planet envelope opacity and stellar metallicity. Finally, there is no significant variation in sub-Neptune size with stellar age (over 1–10 Gyr), which suggests that the majority of envelope contraction concludes after ∼1 Gyr.

One possible formation mechanism for Hot Jupiters is that high-eccentricity gas giants experience tidal interactions with their host star that cause them to lose orbital energy and migrate inwards. We study these types of tidal interactions in an eccentric Hot Jupiter called HAT-P-2 b, which is a system where a long-period companion has been suggested and hints of orbital evolution were detected. Using 5 additional years of radial velocity (RV) measurements, we further investigate these phenomena. We investigated the long-period companion by jointly fitting RVs and Hipparcos-Gaia astrometry and confirmed this long-period companion, significantly narrowed down the range of possible periods ( P2=8500−1500+2600 days), and determined that it must be a substellar object ( 10.7−2.2+5.2 M j). We also developed a modular pipeline to simultaneously model rapid orbital evolution and the long-period companion. We find that the rate and significance of evolution are highly dependent on the long-period companion modeling choices. In some cases the orbital rates of change reached de/dt=3.28−1.72+1.75×10−3 yr−1, d ω/dt = 1.12° ± 0.22° yr−1, which corresponds to a ∼321 yr apsidal precession period. In other cases, the data is consistent with de/dt = 7.67 ± 18.6 × 10−4 yr−1, d ω/dt = 0.76° ± 0.24° yr−1. The most rapid changes found are significantly larger than the expected relativistic precession rate and could be caused by transient tidal planet–star interactions. To definitively determine the magnitude and significance of potential orbital evolution in HAT-P-2 b, we recommend further monitoring with RVs and precise transit and eclipse timings.

We present the discovery of a Jupiter-like planet, HD 73344 d ( md=2.55−0.46+0.56MJ , ad=6.70−0.26+0.25 au, ed=0.18−0.12+0.14 ) based on 27 yr radial velocity (RV) observations from ELODIE, Lick/Hamilton, SOPHIE, APF, and HIRES. HD 73344 also hosts a compact inner planetary system, including a transiting sub-Neptune, HD 73344 b (Pb = 15.61 days, rb=2.88−0.07+0.08R⊕ ), and a nontransiting Saturn-mass planet (Pc = 65.936 days, mcsinic=0.367−0.021+0.022MJ ). By analyzing TESS light curves, we identified a stellar rotation period of 9.03 ± 1.3 days. Combining this with vsini* measurements from stellar spectra, we derived a stellar inclination of 63.6∘−16.5+17.4 . Furthermore, by combining RVs and Hipparcos–Gaia astrometric acceleration, we characterized the three-dimensional orbit of the outer giant planet and constrained its mutual inclination relative to the innermost transiting planet to be 46° < ΔIbd < 134° (1σ) and 20° < ΔIbd < 160° (2σ), strongly disfavoring coplanar architectures. Our analytical calculations and N-body simulations reveal that the two inner planets are strongly coupled with each other and undergo nodal precession together around the orbital axis of the giant planet. During nodal precession, the orbital inclinations of inner planets oscillate with time and therefore become misaligned relative to the stellar spin axis. The formation of such systems suggests a history of planet–planet scattering or misalignment between the inner and outer components of protoplanetary disks. The upcoming release of Gaia Data Release 4 will uncover more systems similar to HD 73344, and enable the study of the flatness of exoplanet systems with a mixture of inner and outer planetary systems on a statistical level.

We measure the true obliquity of TOI-2364, a K dwarf with a sub-Saturn-mass (Mp = 0.18 MJ) transiting planet on the upper edge of the hot-Neptune desert. We used new Rossiter–McLaughlin observations gathered with the Keck Planet Finder to measure the sky-projected obliquity λ = 7° + 10°–11°. Combined with a stellar rotation period of 23.47 ± 0.29 days measured with photometry from the Tierras Observatory, this yields a stellar inclination of 90° ± 13° and a true obliquity ψ = 15 .° 6 + 7 .° 7–7 .° 3, indicating that the planet’s orbit is well aligned with the rotation axis of its host star. The determination of ψ is important for investigating a potential bimodality in the orbits of short-period sub-Saturns around cool stars, which tend to be either aligned with or perpendicular to their host stars’ spin axes.