Saving Doomed Planets: Mass Loss and Angular Momentum Return Boost Hot Jupiter Survival Rates

Abstract

The existence of giant extrasolar planets on short-period orbits ("hot Jupiters") represents a challenge to theories of planet formation. A leading explanation invokes perturbations from distant companions, i.e., the Eccentric Kozai-Lidov (EKL) mechanism, which can excite the eccentricities of initially wide-orbiting planets to values of order unity. The resulting tidal dissipation at periastron shrinks and circularizes the orbits to their observed configurations. While observations of orbital misalignment and distant companions support this scenario, theoretical models have struggled to reproduce the observed hot Jupiter occurrence rate. Population synthesis studies often predict that many source "cold Jupiters" are destroyed by tidal disruption during highly eccentric passages. We revisit this question with improved treatments of the mass loss and angular momentum return experienced by tidally perturbed planets. Numerical studies are performed by combining secular dynamical evolution with planetary structural evolution using Modules for Experiments in Stellar Astrophysics (MESA). We also use an analytical approach to estimate rates of tidal disruption and hot Jupiter survival. Our new population synthesis studies of giant planets in stellar binaries show that improved treatment of tidal mass loss enhances hot Jupiter survival by a factor of $\sim2-3$, yielding occurrence rates ($\gtrsim 0.5\%$ around FGK stars) consistent with observations. Angular momentum return from mass accreted onto the star may also produce a pileup of hot Jupiters near three-day orbital periods that is in statistical agreement with observations. These results suggest that EKL-driven high-eccentricity migration, when combined with realistic planetary mass loss, may be a dominant channel for hot Jupiter formation.

Figures (10)

• Figure 1: Time evolutions of $e_p$ (top left), $a_p$ (bottom left), $m_p$ (top right), and $R_p$ (bottom right) for an example system that forms a hot Jupiter through one quadrupole cycle. Evolutions with varying fractions of angular momentum return are shown, including $f_{\rm ret} = 0$ (orange curves), $f_{\rm ret} = 0.5$ (blue curves), and $f_{\rm ret} = 1$ (gray curves). The $a_p$ panel (bottom left) shows a zoomed-in view of the final circularization locations of the hot Jupiter (inset panel corresponds to the gray rectangle), with the dashed black lines corresponding to analytical predictions from Eq. (\ref{['eq:final_a']}). This system initially has $m_* = 1.427 M_{\odot}$, $m_p = 0.857 M_J$, $m_c = 0.838 M_{\odot}$, $a_p = 1.621$ au, $a_c = 82.846$ au, $e_p = 0.077$, $e_c = 0.084$, $\omega_1 = 46.075^{\circ}$, $\omega_2 = 212.893^{\circ}$, and $i = 84.210^{\circ}$.
• Figure 2: Comparison of the hot Jupiter occurrence rate from the observations of Mayor+11 (shaded blue region) and those estimated from the simulations in this work. To obtain the simulated occurrence rates, we use the fraction of FGK stars in wide binaries from Raghavan+10 and the fraction of systems that harbor cold Jupiters as a source population in Fulton+21, then multiply by the fraction of cold Jupiters that become hot Jupiters in our simulations (given in Table \ref{['tab:sims']}). We show the rates for the varying mass loss prescriptions of low loss (blue points), moderate loss (orange points), and high loss (gray points), as a function of varied angular momentum return $f_{\rm ret}$. The occurrence rate estimate from the NoLoss run is also plotted (dashed red line), which uses the approach taken in previous studies of removing planets that graze $q/r_t = 2.7$Petrovich15bWeldon+25.
• Figure 3: Top row: Mass loss fractions as a function of initial $a_p$ and $a_c$ in the moderate loss simulations for $f_{\rm ret} =0$ (left), $f_{\rm ret} =0.5$ (middle), and $f_{\rm ret} =1$ (right). Surviving hot Jupiters are shown with circles and tidal disruptions with an orange "X". The color code corresponds to the fraction of mass lost, with darker points indicating lower amounts of loss. Bottom row: Mass loss fractions as a function of initial $\epsilon$ and $i$. The color code is the same as in the top row.
• Figure 4: Mass loss fractions as a function of initial planetary mass. We show surviving hot Jupiters (HJ) with blue dots and tidal disruptions (TD) with an orange "X". The angular momentum return fraction is varied from $f_{\rm ret} =0$ (top), $f_{\rm ret} =0.5$ (middle), to $f_{\rm ret} =1$ (bottom).
• Figure 5: Mass-period distribution for observed hot Jupiters (black stars) that are relatively circularized (measured eccentricities $e<0.1$), along with the final state of surviving hot Jupiters in the simulations (gray dots have $f_{\rm ret} = 0$, blue open circles have $f_{\rm ret} = 0.5$, and orange open squares have $f_{\rm ret} = 1$). The top row corresponds to the low-loss case, the middle row corresponds to moderate loss, and the bottom row corresponds to high loss. The threshold for inspiral and merger with the host star from stellar tidal dissipation is shown with a black line, calculated using the calibration from Hansen10.