Most Hot Jupiters Were Cool Giant Planets for More Than 1 Gyr

TL;DR

The study investigates how hot Jupiters form by comparing the ages of three subpopulations split by their orbital periods around the debiased peak at $P_{orb} = 3.92$ d, using a calibrated solar-neighborhood age–velocity dispersion relation to infer absolute ages. It finds that inside-peak and near-peak hosts are about 3.1–3.3 Gyr old, while outside-peak hosts are ~2.2–2.36 Gyr old, suggesting a substantial late-time high-eccentricity migration component (>1.5 Gyr delay) alongside early in situ/disk-formation channels. A forward population model with three formation pathways and tidal evolution reproduces the observed age pattern when the late-population fraction $f_{LP}$ lies roughly between 0.4 and 0.8 and the stellar tidal quality factor $Q'_igstar$ falls in the $10^{6.5}$ to $10^{7}$ range, implying that 40–70% of hot Jupiters are late arrivals. The results have broad implications for hot Jupiter demographics, predicting a weaker orbital-period peak for younger systems and motivating follow-up surveillance for wide companions, while helping reconcile previous conflicting claims about their formation histories.

Abstract

The origin of hot Jupiters is the oldest problem in exoplanet astrophysics. Hot Jupiters formed in situ or via disk migration should be in place just a few Myr after the formation of their host stars. On the other hand, hot Jupiters formed via eccentricity excitation and tidal damping as a result of planet--planet scattering or Kozai-Lidov oscillations may take 1 Gyr or more to arrive at their observed locations. We propose that the relative ages of hot Jupiters inside, near, and outside the bias-corrected peak of the observed hot Jupiter period distribution can be used to distinguish between these possibilities. Though the lack of precise and accurate age inferences for isolated hot Jupiter host stars makes this test difficult to implement, comparisons between the Galactic velocity dispersions of the hot Jupiter subpopulations enable this investigation. To transform relative age offsets into absolute age offsets, we calibrate the monotonically increasing solar neighborhood age--velocity dispersion relation using an all-sky sample of subgiants with precise ages and a metallicity distribution matched to that of hot Jupiter hosts. We find that the inside-peak and near-peak subpopulations are older than the outside-peak subpopulation, with the inside-peak subpopulation slightly older than the near-peak subpopulation. We conclude that at least 40\% but not more than 70\% of the hot Jupiter population must have formed via a late-time, peak-populating process like high-eccentricity migration that typically occurs more than 1.5 Gyr after system formation.

Figures (10)

• Figure 1: Cartoon of the characteristic mean ages expected for four different hot Jupiter formation scenarios: disk migration, disk migration plus tidal evolution, disk migration plus a late-time peak-populating mechanism, and disk migration plus a late-time peak-populating mechanism both affected by tidal evolution. The light blue, dark blue, and light green rectangles correspond to the inside-, near-, and outside-peak subpopulations, while we indicate with gray shading the scenarios for which tidal dissipation is important. In the two scenarios on the left, hot Jupiters form almost entirely from an early-time process that results in an approximately uniform distribution in orbital period (e.g., disk migration). In the two scenarios on the right, however, a large fraction of hot Jupiters form via a late-time process that results in a peaked orbital period distribution (e.g., high-eccentricity migration). Each scenario results in different age orderings for the three subpopulations, so we argue that characteristic mean age measurements should differentiate between them.
• Figure 2: Solar neighborhood age--velocity dispersion relations as a function of metallicity. We subdivide the subgiant sample presented in Nataf24 into four equal-size metallicity bins. We then order each subsample in age and calculate velocity dispersion in consecutive windows of 3000 stars. We plot the result of these calculations as overlapping colored points: light purple for the first quartile, dark purple for the second quartile, light orange for the third quartile, and dark orange for the fourth quartile. We plot as solid colored lines a smoothing spline of the respective data and as transparent polygons the 16th/84th interquantile ranges of the subsample's velocity dispersion distribution suggested by bootstrap resampling. Though they exhibit noticeable differences in velocity dispersion at older ages, there is no significant metallicity dependence on velocity dispersion between 2 and 4 Gyr, the characteristic mean ages of our hot Jupiter subpopulations.
• Figure 3: Solar neighborhood age--velocity dispersion relation for the metallicity interval $-0.06 < \text{[Fe/H]} < +0.36$ appropriate for hot Jupiter hosts as explained in Section \ref{['sec:methods']}. We follow the same procedure we use to generate Figure \ref{['fig:metalcomp']} and plot as the black line the resulting smoothed age--velocity dispersion relation and as the gray polygon its 16th/84th interquantile range. We calculate the debiased median period of the hot Jupiter period distribution by weighting hot Jupiter systems' orbital periods by their scaled semimajor axes $a/R_\ast$ to account for the observational biases present in the transit technique that has discovered most hot Jupiters. The near-peak subpopulation comprises one third of the overall sample with orbital periods closest to this debiased median period. We then create two additional subpopulations: one inside the debiased peak with orbital periods shorter than the near-peak subpopulation and one outside the debiased peak with orbital periods longer than the near-peak subpopulation. We plot as light blue, dark blue, and light green horizontal lines the velocity dispersions of the inside-, near-, and outside-peak hot Jupiter subpopulations. The inside-peak and near-peak subpopulations have characteristic mean ages $\tau \approx 3.2$ Gyr, with the inside-peak subpopulation slightly older than the near-peak subpopulation. On the other hand, the outside-peak subpopulation has a characteristic mean age $\tau \approx 2.3$ Gyr. The distinctly younger age of the outside-peak subpopulation relative to the inside- and near-peak subpopulations supports the fourth scenario in Figure \ref{['fig:scenarios']}. In that scenario, the combination of (1) an early-time formation channel that produces a uniform period distribution, (2) a late-time formation channel that produces a peaked period distribution, and (3) subsequent tidal evolution have all contributed to the formation and evolution of the hot Jupiter population.
• Figure 4: Illustration of the three hot Jupiter subpopulations and their characteristic mean ages. We plot as the gray histogram the orbital period distribution of our solar neighborhood transiting hot Jupiter sample. We mark with vertical black lines the boundaries of the three subpopulations we have identified and shade the inside-, near-, and outside-peak subpopulations in light blue, dark blue, and light green. We plot the characteristic mean age ranges as the black error bars in each region. We find that the inside-peak subpopulation is older, but still statistically consistent with, the characteristic mean age of the near-peak subpopulation. In contrast, the outside-peak subpopulation is younger than both shorter-period subpopulations. We argue that this ordering in age plus the statistically younger characteristic mean age of the outside-peak subpopulation is best explained by a late-time, peak-populating formation mechanism that is responsible for placing most hot Jupiters near and inside the debiased orbital period peak. Subsequent tidal evolution would then move some of these hot Jupiters to shorter orbital periods over billions of years.
• Figure 5: The same age--velocity dispersion relation as in Figure \ref{['fig:thirdscomp']}. To emphasize the effect of observational biases on the characteristic mean ages of exoplanet systems, we plot as horizontal lines the velocity dispersions of all known giant planet systems with orbital periods $P>10$ d (light purple), the subset of these systems discovered via the Doppler technique (dark purple), and the subset of these systems discovered via the transit technique (orange). Because by itself the Doppler technique is only sensitive to long-period giant planets orbiting quiescent stars, Doppler surveyors have usually avoided stars with chromospheric emission indicative of youth. This bias against young stars in the population of Doppler-discovered exoplanet systems makes comparing the mean ages of the Doppler- and transit-discovered exoplanet populations challenging. We caution against combining populations of planets detected via more than one technique for system age-related analyses without first accounting for biases incurred by each detection method.