Survival of satellites during the migration of a Hot Jupiter

TL;DR

This study examines whether satellites can survive the inward Type-II migration of a Jupiter-mass planet in a protoplanetary disk. It couples a Posidonius N-body code with both equilibrium and dynamical tide models for the star and planet, plus disk-driven migration, to track a satellite’s fate as the host planet moves inward to close-in orbits. The results show that satellite survival is unlikely for final planet distances below about $0.1$ AU, with outer satellites commonly disrupted dynamically and inner satellites tidally disrupted; survival is favored by low satellite dissipation and higher satellite mass, though even then the surviving configuration occupies a narrow region of parameter space. Including dynamical tides in both the star and planet increases the likelihood of survival relative to equilibrium tides alone, but long-term stability remains uncertain, and the putative WASP-49 A b satellite is unlikely to have endured planetary migration under the modeled conditions.

Abstract

We investigate the origin and stability of extrasolar satellites orbiting close-in gas giants, focusing on whether these satellites can survive planetary migration within a protoplanetary disk. To address this question, we used Posidonius, an N-Body code with an integrated tidal model, which we expanded to account for the migration of a gas giant within a disk. Our simulations include tidal interactions between a $1M_\odot$ star and a $1M_{Jup}$ planet, as well as between the planet and its satellite, while neglecting tides raised by the star on the satellite. We adopt a standard equilibrium tide model for the satellite, planet, and star, and additionally explore the impact of dynamical tides in the convective regions of both the star and planet on satellite survival. We examine key parameters, including the initial satellite-planet distance, disk lifetime (proxy for the planet's final orbital distance), satellite mass, and satellite tidal dissipation. For simulations incorporating dynamical tides, we explore three different initial stellar rotation periods. We find that satellite survival is rare if the satellite has nonzero tidal dissipation. Survival is only possible for initial orbital distances of at least 0.6 times the Jupiter-Io separation and for planets orbiting beyond about 0.1 AU. Satellites that fail to survive are either 1) tidally disrupted, as they experience orbital decay and cross the Roche limit, or 2) dynamically disrupted, where eccentricity excitation drives their periastron within the Roche limit. Satellite survival is more likely for low tidal dissipation and higher satellite mass. Given that satellites around close-in planets appear unlikely to survive planetary migration, our findings suggest that if such satellites do exist, another process should be invoked. In that context, we also discuss the claim of the existence of a putative satellite around WASP-49 A b.

Figures (13)

• Figure 1: Schema of the simulation set-up: A Io-like satellite orbits around a Jupiter-like planet with a solar-like host star.
• Figure 2: Evolution of the disk surface density $\Sigma_g(r,~t)$.
• Figure 3: Evolution of the semi-major axis and eccentricity of a Jupiter-mass planet due to type-II migration for different disk lifetimes $\tau_{\rm disk}$ and different assumptions on the stellar tide. The dashed lines corresponds to the case where only the equilibrium tide in the star is accounted for, the solid lines corresponds to cases where both the equilibrium tide and dynamical tide are taken into account (initial fast stellar rotation period of 1 day). Note that the rotation of the star is evolving, here mainly due to the contraction of the radius, and its evolution is encoded in the corotation radius curve (i.e. where the orbital frequency is equal to the stellar spin). For clarity, we only plot 2 cases in the bottom panel ($\tau_{\rm disk} = 2\times10^4$ yr and $5\times10^4$ yr). Equilibrium tide is still represented with dashed lines but also with transparency to ease identification.
• Figure 4: Evolution of a $1~M_{\rm Io}$ satellite orbiting a migrating Jupiter-mass planet for different initial distances of the satellite. Here, the disk lifetime is $3\times10^4$ yr, the initial rotation period of the star is 1 day and the dissipation in the satellite is taken to be 0. The top left panel shows the evolution of the semi-major axis of the satellite (full colored lines), the shaded colored lines represent the periastron and apoastron. The gray dotted line represents the radius of the planet, the black dash-dotted line represents the Roche radius, the black dashed line the corotation radius (where the satellite's mean motion is equal to the spin of the planet) and the grey dashed line represents the half of the Hill radius of the planet. The bottom left panel shows the evolution of the satellite's eccentricity. The top right panel shows the evolution of the semi-major axis of the planet (full colored lines). The black dashed line represents the corotation radius (where the planet's mean motion is equal to the spin of the star). The bottom left panel shows the evolution of the planet's eccentricity.
• Figure 5: Same as the right column of Figure \ref{['Fig5']} but for a disk lifetime of $5\times10^3$ yr (left column) and $5\times10^4$ yr (right column). The top row shows the evolution of the orbital distance of the satellites and the bottom row shows the evolution of their eccentricities. For the left column, the final semi-major axis of the planet is 0.125 AU and for the right column, it is 0.035 AU. This difference can be visualized thanks to the grey dashed lines corresponding to half the Hill radius of the planet, which comes much closer to the planet when the $\tau_{\rm disk} = 5\times10^4$ yr.