The Occurrence Rate of Nearby Planetary Companions to Hot Jupiters

TL;DR

This work delivers the largest uniform search for transiting inner companions to hot Jupiters using five years of TESS data, carefully accounting for false positives and detection completeness. Through a detailed BLS-based pipeline, signal vetting, and injection--recovery calibration, it derives a posterior occurrence rate of $\eta = 7.6^{+5.5}_{-3.8}\%$ for $0.25\,\text{d} \le P < 10\,\text{d}$ and $1 \le R_p/R_\oplus < 4$ around hot Jupiters, with the rate highly sensitive to the assumed mutual inclination distribution. The results support a predominantly disk-migration or in-situ formation for hot Jupiters (as indicated by low mutual inclinations) yet allow for a non-negligible quiet-formation fraction; a comparison to TTV-based rates suggests limited evidence for maximal misalignment. The findings imply that hot Jupiters with close companions may still commonly host cold outer companions, reinforcing a nuanced view of hot Jupiter formation channels and highlighting the need for comprehensive RV+transit studies to fully map system architectures. Overall, the work constrains the relative prevalence of formation pathways and clarifies the dynamical histories of hot Jupiter systems.

Abstract

Of the > 500 confirmed transiting hot jupiters and approximately 2000 additional candidates today, only ten are known to have nearby companion planets. The survival of nearby companions means that these hot jupiters cannot have migrated to their present location via dynamically disruptive high-eccentricity migration but instead have undergone disk migration or formed in situ. The occurrence rate for these nearby companions, therefore, constrains the relative efficiency of different hot jupiter formation pathways. Here, we perform a uniform box least-squares search for nearby transiting companions to hot jupiters in the first five years of TESS data. Accounting for observational completeness and detection efficiency, we arrive at an occurrence rate of $(7.6^{+5.5}_{-3.8})\%$, which is a lower limit on the fraction of hot jupiters that underwent disk migration or in situ formation. Comparing this rate with that derived from transit-timing variation searches suggests that hot jupiters are likely mostly aligned with their nearby companions, but their apparently higher incidence of grazing transits may point to a slight preferential misalignment. We also synthesize evidence that hot jupiters with nearby companions may have cold companions at a rate similar to that of other hot jupiters. Comprehensive transit, radial velocity, and stellar obliquity measurements in hot jupiter systems with nearby companions will be necessary to fully account for the relative prevalence of proposed hot jupiter formation pathways.

Figures (7)

• Figure 1: The distribution of the host stars of the selected hot jupiters. Left: The histogram of stellar mass. Right: The color--magnitude diagram.
• Figure 2: A scatter plot of $\sigma_P$ versus $\sigma_T$ for the detection of injected transit signals, similar to Figure 2 by 2014AJ....147..119C. The thin blue lines denote the chosen significance levels for ephemeris matching in equation \ref{['eqn:sigma_pt_levels']} and divides the plane into four quadrants. The cluster of points in the upper right quadrant corresponds to true ephemeris matches, while the cluster of points in the lower left are random false matches.
• Figure 3: Detection fraction as a function of transit S/N. The blue marks are the recovery fraction of injected planets within each S/N bin with error bars representing the Agresti--Coull confidence interval of binomial proportion, and the orange curve is a scaled gamma distribution CDF. The detection fraction asymptotically approaches $\approx 0.95$ as the transit $\mathrm{S}/\mathrm{N} \to \infty$.
• Figure 4: Transiting planetary systems hosting nearby planetary companions to hot jupiters ($P < 10\,\text{d}$). Non-transiting planets are omitted. The leftmost circle in each row represent the host star, with the mark's size indicating the stellar radius and fill color the stellar effective temperature 2019AJ....158..138S. The other circles represent the transiting planets in each system, with their sizes proportional to planet radii and fill colors indicating a giant planet (orange) or a small planet (gray). The relative mark sizes among either the stars or the planets are to scale, but not between a star and its planets. The translucent marks are planet candidates not yet published in the literature. Systems which are counted as detected (\ref{['sec:results']}) for the occurrence rate calculation (\ref{['sec:occurrence']}) have their names highlighted in magenta. The systems are sorted in ascending order of the period of the largest planet. This figure and its caption are adapted from Figure 10 by 2023MNRAS.524.1113S.
• Figure 5: Overall observational completeness of simulated nearby companions to hot jupiters in bins of the orbital periods and planet radii of the companions (\ref{['sec:completeness']}), expressed as percentages. The observational completeness takes account of both transit probability and detection efficiency.