Planet Across Space and Time (PAST). VII. The origin and tidal evolution of hot Jupiters constrained by a broken age-frequency relation

Abstract

The discovery of hot Jupiters has challenged the classical planet formation theory. Although various formation mechanisms have been proposed, the dominant channel and relative contributions remain unclear. Furthermore, hot Jupiters offer a unique opportunity to test tidal theory and measure the fundamental tidal quality factor, which is yet to be well-constrained. In this work, based on a hot Jupiter sample around single Sun-like stars with kinematic properties, {we find that the declining trend of their frequency is broken with a ridge at about 2 Gyr, providing direct evidence that hot Jupiters are formed with multiple origins of different timescales. By fitting with the theoretical expectations, we provide a constraint of tidal factor for Sun-like stars, which aligns well with the detected number of hot Jupiters with orbital decay. Moreover, we simultaneously constrain the relative importance of different channels: although the majority of hot Jupiters are formed early, within several tenths of Gyr via 'Early' models (e.g., in-situ formation, disk migration, planet-planet scattering and Kozai-Lidov interaction), a significant portion (about 40%) should be formed late on a relatively long timescale extending up to several Gyr mainly via the secular chaos mechanism, further supported by the obliquity distribution of 'late-arrived' hot Jupiters. Our findings provide a unified framework that reconciles hot Jupiter demographics and long-term evolution with multichannel formation.

Figures (29)

• Figure 1: The observed age-frequency relation of hot Jupiters. Frequency of hot Jupiters as a function of kinematic age for the entire hot Jupiter sample (Top), and separately for the two populations: 'late-arrived' (Middle) and 'early-arrived' (Bottom). The vertical and horizontal errorbars represent the uncertainties of Frequencies of hot Jupiters and kinematic ages, respectively.
• Figure 1: The probability density distribution for the typical timescale of planet-star Kozai cycles. To overcome general relativity pericenter precession, we only keep these Kozai–Lidov oscillations with timescales shorter than the pericenter precession timescales.
• Figure 2: Fitting the observed age-frequency relation of hot Jupiters with a hybrid model. Left panel: The frequency of hot Jupiters $F_{\rm HJ}$ as a function of age. The observation data is plotted as solid black points and line segments denote the 1-$\sigma$ interval. The solid line denotes best-fit of the hybrid model with 38% hot Jupiter contributed from the 'Late' model (red dashed) and 62% from the 'Early' models (blue dashed). Right panel: Relative likelihood in logarithm as a function of $Q^{'}_{*}$ and $f_{\rm Late}$. The blue, green, and red lines indicate the boundary of the 1-$\sigma$, 2-$\sigma$, and 3-$\sigma$ confidence levels.
• Figure 2: The cumulative distribution of the difference between the kinematic ages and tidal evolution timescales $t-t_{\rm tide}$. The results from the observed and synthetic hot Jupiter sample that can be classified as 'Late-arrived' are plotted as solid black line and dashed red line, respectively. We print the two-sample KS test $p-$value. The solid orange line denotes the arrival timescale of hot Jupiters via the secular models derived from simulations 2017MNRAS.464..688H.
• Figure 3: Additional supporting evidence for the secular chaos as the 'Late' model. The cumulative distributions of the sky-projected stellar obliquities $\lambda$ for the 'early-arrived’ (blue) and 'late-arrived’ (red) hot Jupiter systems with long-alignment timescales and young kinematic ages. The dashed lines represent the predicted $\lambda$ distributions inferred from the stellar obliquity distributions predicted by different mechanisms and the aligned distribution randomly in $0-20 ^\circ$.