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Register a new userEmpirical Tidal Dissipation in Exoplanet Hosts From Tidal Spin-Up
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Stars with hot Jupiters tend to be rotating faster than other stars of the same age and mass. This trend has been attributed to tidal interactions between the star and planet. A constraint on the dissipation parameter $Q_star$ follows from the assumption that tides have managed to spin up the star to the observed rate within the age of the system. This technique was applied previously to HATS-18 and WASP-19. Here we analyze the sample of all 188 known hot Jupiters with an orbital period $< 3.5$ days and a cool host star ($T_{eff} < 6100$ K). We find evidence that the tidal dissipation parameter ($Q_star$) increases sharply with forcing frequency, from $10^5$ at 0.5 day$^{-1}$ to $10^7$ at 2 day$^{-1}$. This helps to resolve a number of apparent discrepancies between studies of tidal dissipation in binary stars, hot Jupiters, and warm Jupiters. It may also allow for a hot Jupiter to damp the obliquity of its host star prior to being destroyed by tidal decay.
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We introduce two new features to REBOUNDx, an extended library for the N-body integrator REBOUND. The first is a convenient parameter interpolator for coupling different physics and integrators using numerical splitting schemes. The second implements a constant time lag model for tides (without evolving spins) from Hut (1981). We demonstrate various examples of these features using post-main sequence stellar evolution data from MESA (Modules for Experiments in Stellar Astrophysics). These additional effects are publicly available as of REBOUNDxs latest release.
WASP-12 is a hot Jupiter system with an orbital period of $P= 1.1textrm{ day}$, making it one of the shortest-period giant planets known. Recent transit timing observations by Maciejewski et al. (2016) and Patra et al. (2017) find a decreasing period with $P/|dot{P}| = 3.2textrm{ Myr}$. This has been interpreted as evidence of either orbital decay due to tidal dissipation or a long term oscillation of the apparent period due to apsidal precession. Here we consider the possibility that it is orbital decay. We show that the parameters of the host star are consistent with either a $M_ast simeq 1.3 M_odot$ main sequence star or a $M_ast simeq 1.2 M_odot$ subgiant. We find that if the star is on the main sequence, the tidal dissipation is too inefficient to explain the observed $dot{P}$. However, if it is a subgiant, the tidal dissipation is significantly enhanced due to nonlinear wave breaking of the dynamical tide near the stars center. The subgiant models have a tidal quality factor $Q_astsimeq 2times10^5$ and an orbital decay rate that agrees well with the observed $dot{P}$. It would also explain why the planet survived for $simeq 3textrm{ Gyr}$ while the star was on the main sequence and yet is now inspiraling on a 3 Myr timescale. Although this suggests that we are witnessing the last $sim 0.1%$ of the planets life, the probability of such a detection is a few percent given the observed sample of $simeq 30$ hot Jupiters in $P<3textrm{ day}$ orbits around $M_ast>1.2 M_odot$ hosts.
Tidal interactions in close star-planet or binary star systems may excite inertial waves (their restoring force is the Coriolis force) in the convective region of the stars. The dissipation of these waves plays a prominent role in the long-term orbital and rotational evolution of the bodies involved. If the primary star rotates as a solid body, inertial waves have a Doppler-shifted frequency restricted to the range $[-2Omega, 2Omega]$ ($Omega$ being the angular velocity of the star), and they can propagate in the entire convective region. However, turbulent convection can sustain differential rotation with an equatorial acceleration (as in the Sun) or deceleration that modifies the frequency range and propagation domain of inertial waves and allows corotation resonances for non-axisymmetric oscillations. In this work, we perform numerical simulations of tidally excited inertial waves in a differentially rotating convective envelope with a conical (or latitudinal) rotation profile. The tidal forcing that we adopt contains spherical harmonics that correspond to the case of a circular and coplanar orbit. We study the viscous dissipation of the waves as a function of tidal frequency for various stellar masses and differential rotation parameters, as well as its dependence on the turbulent viscosity coefficient. We compare our results with previous studies assuming solid-body rotation and point out the potential key role of corotation resonances in the dynamical evolution of close-in star-planet or binary systems.
The architecture of many exoplanetary systems is different from the solar system, with exoplanets being in close orbits around their host stars and having orbital periods of only a few days. We can expect interactions between the star and the exoplanet for such systems that are similar to the tidal interactions observed in close stellar binary systems. For the exoplanet, tidal interaction can lead to circularization of its orbit and the synchronization of its rotational and orbital period. For the host star, it has long been speculated if significant angular momentum transfer can take place between the planetary orbit and the stellar rotation. In the case of the Earth-Moon system, such tidal interaction has led to an increasing distance between Earth and Moon. For stars with Hot Jupiters, where the orbital period of the exoplanet is typically shorter than the stellar rotation period, one expects a decreasing semimajor axis for the planet and enhanced stellar rotation, leading to increased stellar activity. Also excess turbulence in the stellar convective zone due to rising and subsiding tidal bulges may change the magnetic activity we observe for the host star. Here I review recent observational results on stellar activity and tidal interaction in the presence of close-in exoplanets, and discuss the effects of enhanced stellar activity on the exoplanets in such systems.
We use the distribution of extrasolar planets in circular orbits around stars with surface convective zones detected by ground based transit searches to constrain how efficiently tides raised by the planet are dissipated on the parent star. We parameterize this efficiency as a tidal quality factor (Q*). We conclude that the population of currently known planets is inconsistent with Q*<10^7 at the 99% level. Previous studies show that values of Q* between 10^5 and 10^7 are required in order to explain the orbital circularization of main sequence low mass binary stars in clusters, suggesting that different dissipation mechanisms might be acting in the two cases, most likely due to the very different tidal forcing frequencies relative to the stellar rotation frequency occurring for star--star versus planet--star systems.
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