The impact of rotation on turbulent tidal friction in stellar and planetary convective regions

The impact of rotation on turbulent tidal friction in stellar and planetary convective regions

Authors:

Mathis et al

Abstract:

Turbulent friction in convective regions in stars and planets is one of the key physical mechanisms that drive the dissipation of the kinetic energy of tidal flows in their interiors and the evolution of their systems. This friction acts both on the equilibrium/non-wave like tide and on tidal inertial waves in these layers. It is thus necessary to obtain a robust prescription for this friction. In the current state-of-the-art, it is modeled by a turbulent eddy-viscosity coefficient, based on mixing-length theory, applied on velocities of tides. However, none of the current prescriptions take into account the action of rotation that can strongly affects turbulent convection. Therefore, we use theoretical scaling laws for convective velocities and characteristic lengthscales in rotating stars and planets that have been recently confirmed by 3-D high-resolution nonlinear Cartesian numerical simulations to derive a new prescription. A corresponding local model of tidal waves is used to understand the consequences for the linear tidal dissipation. Finally, new grids of rotating stellar models and published values of planetary convective Rossby numbers are used to discuss astrophysical consequences. The action of rotation on convection deeply modifies the turbulent friction applied on tides. In the regime of rapid rotation (with a convective Rossby number below 0.25), the eddy-viscosity may be decreased by several ordres of magnitude. It may lead to a loss of efficiency of the viscous dissipation of the equilibrium tide and to a more efficient complex and resonant dissipation of tidal inertial waves in the bulk of convective regions. Therefore, it is necessary to have a completely coupled treatment of the tidal/rotational evolution of star-planet systems and multiple stars with a coherent treatment of the variations of tidal flows and of their dissipation as a function of rotation.

Are Tidal Effects the Root Cause for Exoplanetary Spin-orbit Alignment?

ARE TIDAL EFFECTS RESPONSIBLE FOR EXOPLANETARY SPIN–ORBIT ALIGNMENT?

Authors:

Li et al

Abstract:

The obliquities of planet-hosting stars are clues about the formation of planetary systems. Previous observations led to the hypothesis that for close-in giant planets, spin–orbit alignment is enforced by tidal interactions. Here, we examine two problems with this hypothesis. First, Mazeh and coworkers recently used a new technique—based on the amplitude of starspot-induced photometric variability—to conclude that spin–orbit alignment is common even for relatively long-period planets, which would not be expected if tides were responsible. We re-examine the data and find a statistically significant correlation between photometric variability and planetary orbital period that is qualitatively consistent with tidal interactions. However it is still difficult to explain quantitatively, as it would require tides to be effective for periods as long as tens of days. Second, Rogers and Lin argued against a particular theory for tidal re-alignment by showing that initially retrograde systems would fail to be re-aligned, in contradiction with the observed prevalence of prograde systems. We investigate a simple model that overcomes this problem by taking into account the dissipation of inertial waves and the equilibrium tide, as well as magnetic braking. We identify a region of parameter space where re-alignment can be achieved, but it only works for close-in giant planets, and requires some fine tuning. Thus, while we find both problems to be more nuanced than they first appeared, the tidal model still has serious shortcomings.

Tidal Effects Disputed as Source of Exoplanet Spin Orbit Misalignment

Are Tidal Effects Responsible for Exoplanetary Spin-Orbit Alignment?

Authors:

Li et al

Abstract:

The obliquities of planet-hosting stars are clues about the formation of planetary systems. Previous observations led to the hypothesis that for close-in giant planets, spin-orbit alignment is enforced by tidal interactions. Here, we examine two problems with this hypothesis. First, Mazeh and coworkers recently used a new technique -- based on the amplitude of starspot-induced photometric variability -- to conclude that spin-orbit alignment is common even for relatively long-period planets, which would not be expected if tides were responsible. We re-examine the data and find a statistically significant correlation between photometric variability and planetary orbital period that is qualitatively consistent with tidal interactions. However it is still difficult to explain quantitatively, as it would require tides to be effective for periods as long as tens of days. Second, Rogers and Lin argued against a particular theory for tidal re-alignment by showing that initially retrograde systems would fail to be re-aligned, in contradiction with the observed prevalence of prograde systems. We investigate a simple model that overcomes this problem by taking into account the dissipation of inertial waves and the equilibrium tide, as well as magnetic braking. We identify a region of parameter space where re-alignment can be achieved, but it only works for close-in giant planets, and requires some fine tuning. Thus, while we find both problems to be more nuanced than they first appeared, the tidal model still has serious shortcomings.

Could a hot Jupiter Bleed out its Atmosphere to Necome a hot Mini Neptune?

Tidally-driven Roche-Lobe Overflow of Hot Jupiters with MESA

Authors:

Valsecchi et al

Abstract:

Many exoplanets have now been detected in orbits with ultra-short periods, very close to the Roche limit. Building upon our previous work, we study the possibility that mass loss through Roche lobe overflow (RLO) may affect the evolution of these planets, and could possibly transform a hot Jupiter into a lower-mass planet (hot Neptune or super-Earth). We focus here on systems in which the mass loss occurs slowly ("stable mass transfer" in the language of binary star evolution) and we compute their evolution in detail with the binary evolution code MESA. We include the effects of tides, RLO, irradiation and photo-evaporation of the planet, as well as the stellar wind and magnetic braking. Our calculations all start with a hot Jupiter close to its Roche limit, in orbit around a sun-like star. The initial orbital decay and onset of RLO are driven by tidal dissipation in the star. We confirm that such a system can indeed evolve to produce lower-mass planets in orbits of a few days. The RLO phase eventually ends and, depending on the details of the mass transfer and on the planetary core mass, the orbital period can remain around a few days for several Gyr. The remnant planets have a rocky core and some amount of envelope material, which is slowly removed via photo-evaporation at nearly constant orbital period; these have properties resembling many of the observed super-Earths and sub-Neptunes. For these remnant planets we also predict an anti-correlation between mass and orbital period; very low-mass planets (Mpl≲5M⊕) in ultra-short periods (Porb less than 1d) cannot be produced through this type of evolution.

Tidal Tails From SU Aur's Protoplanetary Disk Caused by Unseen Brown Dwarf?

Near-IR High-Resolution Imaging Polarimetry of the SU Aur Disk: Clues for Tidal Tails?

Authors:

de Leon et al

Abstract:

We present new high-resolution (∼0\farcs09) H-band imaging observations of the circumstellar disk around the T Tauri star SU Aur. Our observations with Subaru-HiCIAO have revealed the presence of scattered light as close as 0\farcs15 (∼20 AU) to the star. Within our image, we identify bright emission associated with a disk with a minimum radius of ∼90 AU, an inclination of ∼35$\degr$ from the plane of the sky, and an approximate P.A. of 15$\degr$ for the major axis. We find a brightness asymmetry between the northern and southern sides of the disk due to a non-axisymmetric disk structure. We also identify a pair of asymmetric tail structures extending east and west from the disk. The western tail extends at least 2\farcs5 (350 AU) from the star, and is probably associated with a reflection nebula previously observed at optical and near-IR wavelengths. The eastern tail extends at least 1\arcsec (140 AU) at the present signal-to-noise. These tails are likely due to an encounter with an unseen brown dwarf, but our results do not exclude the explanation that these tails are outflow cavities or jets.

Tidal Truncation of Inclined Circumstellar and Circumbinary Disks

Tidal Truncation of Inclined Circumstellar and Circumbinary Discs in Young Stellar Binaries

Authors:

Miranda et al

Abstract:

Recent observations have shown that circumstellar and circumbinary discs in young stellar binaries are often misaligned with respect to the binary orbital plane. We analyze the tidal truncation of such misaligned discs due to torques applied to the disc at the Lindblad resonances from the tidal forcings of the binary. We consider eccentric binaries with arbitrary binary-disc inclination angles. We determine the dependence of the tidal forcing strengths on the binary parameters and show that they are complicated non-monotonic functions of eccentricity and inclination. We adopt a truncation criterion determined by the balance between resonant torque and viscous torque, and use it to calculate the outer radii of circumstellar discs and the inner radii of circumbinary discs. Misaligned circumstellar discs have systematically larger outer radii than aligned discs, and are likely to fill their Roche lobes if inclined by more than 45∘−90∘, depending on the binary mass ratio and disc viscosity parameter. Misaligned circumbinary discs generally have smaller inner radii than aligned discs, but the details depend sensitively on the binary and disc parameters.

Deforming Exoplanets Through Tidal Forces

The flattenings of the layers of rotating planets and satellites deformed by a tidal potential

Authors:

Folonier et al

Abstract:

We consider the Clairaut theory of the equilibrium ellipsoidal figures for differentiated non-homogeneous bodies in non-synchronous rotation adding to it a tidal deformation due to the presence of an external gravitational force. We assume that the body is a fluid formed by n homogeneous layers of ellipsoidal shape and we calculate the external polar flattenings and the mean radius of each layer, or, equivalently, their semiaxes. To first order in the flattenings, the general solution can be written as ϵk=k∗ϵh and μk=k∗μh, where k is a characteristic coefficient for each layer which only depends on the internal structure of the body and ϵh,μh are the flattenings of the equivalent homogeneous problem. For the continuous case, we study the Clairaut differential equation for the flattening profile, using the Radau transformation to find the boundary conditions when the tidal potential is added. Finally, the theory is applied to several examples: i) a body composed of two homogeneous layers; ii) bodies with simple polynomial density distribution laws and iii) bodies following a polytropic pressure-density law.

Comparing Gyrochronological and Isochronal Age For Transiting Exoplanet Host Stars

A comparison of gyrochronological and isochronal age estimates for transiting exoplanet host stars

Authors:

Maxted et al

Abstract:

Previous studies suggest that tidal interactions may be responsible for discrepancies between the ages of exoplanet host stars estimated using stellar models (isochronal ages) and age estimates based on the stars' rotation periods (gyrochronological ages). We have compiled a sample of 28 transiting exoplanet host stars with measured rotation periods. We use a Bayesian Markov chain Monte Carlo method to determine the joint posterior distribution for the mass and age of each star in the sample, and extend this method to include a calculation of the posterior distribution of the gyrochronological age. The gyrochronological age (τgyro) is significantly less than the isochronal age for about half of the stars in our sample. Tidal interactions between the star and planet are a reasonable explanation for this discrepancy in some cases, but not all. The distribution of τgyro values is evenly spread from very young ages up to a maximum value of a few Gyr. There is no clear correlation between τgyro and the strength of the tidal force on the star due to the innermost planet. There is clear evidence that the isochronal ages for some K-type stars are too large, and this may also be the case for some G-type stars. This may be the result of magnetic inhibition of convection. There is currently no satisfactory explanation for the discrepancy between the young age for CoRoT-2 estimated from either gyrochronology or its high lithium abundance, and the extremely old age for its K-type stellar companion inferred from its very low X-ray flux. There is now strong evidence that the gyrochronological ages of some transiting exoplanet host stars are significantly less than their isochronal ages, but it is not always clear that this is good evidence for tidal interactions between the star and the planet.

Binary Stellar System RW Aurigae's Disk Explained by Tidal Encounter

A tidal encounter caught in the act: modelling a star-disc fly-by in the young RW Aurigae system

Authors:

Dai et al

Abstract:

RW Aurigae (RW Aur) is a binary star system with a long molecular arm trailing the primary star. Cabrit et al. (2006) noted the resemblance between this extended structure and the tidal arm stripped from the primary star in the simulations of star-disc encounters by Clarke & Pringle (1993). In this paper we use new hydrodynamical models and synthetic observations to fit many of the parameters of RW Aur. Using hydrodynamic models we find that the morphological appearance of RW Aur can be indeed explained by a tidal encounter with the secondary star. We reproduce all the major morphological and kinematic features of the system. Using radiative transfer calculations, we find that synthetic CO and dust continuum observations of our hydrodynamic models agree well with observations. We reproduce all the main features of the line profiles, from emission fluxes to the optical depth of the different components of the system. The agreement between observations and simulations thus lends strong support to the hypothesis of a tidal encounter scenario. Finally, we propose a possible solution for the origin of the dimming of the primary star observed in 2010/2011 by Rodriguez et al. (2013).

Tidal Torques on Misaligned Protoplanetary Disks in Binary Systems

Tidal Torques on Misaligned Disks in Binary Systems

Authors:

Lubow et al

Abstract:

We extend previous studies of the tidal truncation of coplanar disks in binary systems to the more general case of noncoplanar disks. As in the prograde coplanar case, Lindblad resonances play a key role in tidal truncation. We analyze the tidal torque acting on a misaligned nearly circular disk in a circular orbit binary system. We concentrate on the 2:1 inner Lindblad resonance associated with the m=2 tidal forcing (for azimuthal wavenumber m) that plays a major role in the usual coplanar case. We determine the inclination dependence of this torque, which is approximately cos^8(i/2) for misalignment angle i. Compared to the prograde coplanar case (i=0), this torque decreases by a factor of about 2 for i = pi/6 and by a factor of about 20 for i=pi/2. The Lindblad torque decreases to zero for a tilt angle of pi (counter-rotation), consistent with previous investigations. The effects of higher order resonances associated with m greater than 2 tidal forcing may contribute somewhat, but are much more limited than in the i=0 case. These results suggest that misaligned disks in binary systems can be significantly extended compared to their coplanar counterparts. In cases where a disk is sufficiently inclined and viscous, it can overrun all Lindblad resonances and overflow the Roche lobe of the disk central object.

On the Road to Jinx: Detecting Tidally Distorted Solid Exoplanets Around M Dwarfs

The observational effects and signatures of tidally distorted solid exoplanets

Authors:

Saxena et al

Abstract:

Our work examines the detectability of tidally distorted solid exoplanets in synchronous rotation. Previous work has shown that tidally distorted shapes of close-in gas giants can give rise to radius underestimates and subsequently density overestimates for those planets. We examine the assumption that such an effect is too minimal for rocky exoplanets and find that for smaller M Class stars there may be an observationally significant tidal distortion effect at very close-in orbits. We quantify the effect for different stellar types and planetary properties using some basic assumptions. Finally, we develop a simple analytic expression to test if there are detectable bulge signatures in the photometry of a system. We find that close in for smaller M Class stars there may be an observationally significant signature that may manifest itself in both in-transit bulge signatures and ellipsoidal variations.

Modeling a Close-in Exoplanet as a Maclaurin Spherioid

Tidal interactions of a Maclaurin spheroid. II: Resonant excitation of modes by a close, misaligned orbit

Authors:

Braviner et al

Abstract:

We model a tidally forced star or giant planet as a Maclaurin spheroid, decomposing the motion into the normal modes found by Bryan (1889). We first describe the general prescription for this decomposition and the computation of the tidal power. Although this formalism is very general, forcing due to a companion on a misaligned, circular orbit is used to illustrate the theory. The tidal power is plotted for a variety of orbital radii, misalignment angles, and spheroid rotation rates. Our calculations are carried out including all modes of degree l≤4, and the same degree of gravitational forcing. Remarkably, we find that for close orbits (a/R∗≈3) and rotational deformations that are typical of giant planets (e≈0.4) the l=4 component of the gravitational potential may significantly enhance the dissipation through resonance with surface gravity modes. There are also a large number of resonances with inertial modes, with the tidal power being locally enhanced by up to three orders of magnitude. For very close orbits (a/R∗≈3), the contribution to the power from the l=4 modes is roughly the same magnitude as that due to the l=3 modes.

A Novel Method of Modeling the Evolution of Close-in Planets

Deformation and tidal evolution of close-in planets and satellites using a Maxwell viscoelastic rheology

Authors:

Correia et al

Abstract:

In this paper we present a new approach to tidal theory. Assuming a Maxwell viscoelastic rheology, we compute the instantaneous deformation of celestial bodies using a differential equation for the gravity field coefficients. This method allows large eccentricities and it is not limited to quasi-periodic perturbations. It can take into account an extended class of perturbations, including chaotic motions and transient events. We apply our model to some already detected eccentric hot Jupiters and super-Earths in planar configurations. We show that when the relaxation time of the deformation is larger than the orbital period, spin-orbit equilibria arise naturally at half-integers of the mean motion, even for gaseous planets. In the case of super-Earths, these equilibria can be maintained for very low values of eccentricity. Our method can also be used to study planets with complex internal structures and other rheologies.

Tidal Evolution of Multiple Exoplanetary Systems Such as Kepler-62 & Kepler-186

Tidal evolution in multiple planet systems: application to Kepler-62 and Kepler-186

Authors:

Bolmont et al

Abstract:

A large number of observed exoplanets are part of multiple planet systems. Most of these systems are sufficiently close-in to be tidally evolving. In such systems, there is a competition between the excitation caused by planet-planet interactions and tidal damping. Using as an example two multiple planet systems, which host planets in the surface liquid water habitable zone (HZ): Kepler-62 and Kepler-186, we show the importance and effect of both planetary and stellar tides on the dynamical evolution of planets and on the climate of the HZ planets.

Thermal Atmospheric Tides are Important for Considering Habitability

Spin evolution of Earth-sized exoplanets, including atmospheric tides and core-mantle friction

Authors:

Cunha et al

Abstract:

Planets with masses between 0.1 - 10 M_earth are believed to host dense atmospheres. These atmospheres can play an important role on the planet's spin evolution, since thermal atmospheric tides, driven by the host star, may counterbalance gravitational tides. In this work we study the long-term spin evolution of Earth-sized exoplanets. We generalize previous works by including the effect of eccentric orbits and obliquity. We show that under the effect of tides and core-mantle friction, the obliquity of the planets evolve either to 0 or 180 degrees. The rotation of these planets is also expected to evolve into a very restricted number of equilibrium configurations. In general, none of this equilibria is synchronous with the orbital mean motion. The role of thermal atmospheric tides becomes more important for Earth-sized planets in the habitable zones of their systems, so they cannot be neglected when we search for their potential habitability.

Tidal Heating of Multilayered Terrestrial Exoplanets

TIDAL HEATING IN MULTILAYERED TERRESTRIAL EXOPLANETS

Authors:

Henning et al

Abstract:

The internal pattern and overall magnitude of tidal heating for spin-synchronous terrestrial exoplanets from 1 to 2.5 RE is investigated using a propagator matrix method for a variety of layer structures. Particular attention is paid to ice-silicate hybrid super-Earths, where a significant ice mantle is modeled to rest atop an iron-silicate core, and may or may not contain a liquid water ocean. We find multilayer modeling often increases tidal dissipation relative to a homogeneous model, across multiple orbital periods, due to the ability to include smaller volume low viscosity regions, and the added flexure allowed by liquid layers. Gradations in parameters with depth are explored, such as allowed by the Preliminary Earth Reference Model. For ice-silicate hybrid worlds, dramatically greater dissipation is possible beyond the case of a silicate mantle only, allowing non-negligible tidal activity to extend to greater orbital periods than previously predicted. Surface patterns of tidal heating are found to potentially be useful for distinguishing internal structure. The influence of ice mantle depth and water ocean size and position are shown for a range of forcing frequencies. Rates of orbital circularization are found to be 10-100 times faster than standard predictions for Earth-analog planets when interiors are moderately warmer than the modern Earth, as well as for a diverse range of ice-silicate hybrid super-Earths. Circularization rates are shown to be significantly longer for planets with layers equivalent to an ocean-free modern Earth, as well as for planets with high fractions of either ice or silicate melting.

Tidal Damping in Compact Planetary Systems

Secular Effects of Tidal Damping in Compact Planetary Systems

Authors:

Hansen et al

Abstract:

We describe the long-term evolution of compact systems of terrestrial planets, using a set of simulations that match the statistical properties of the observed exoplanet distribution. The evolution is driven by tidal dissipation in the planetary interiors, but the systems evolve as a whole due to secular gravitational interactions. We find that, for Earth-like dissipation levels, planetary orbits can be circularised out to periods of order 100 days, an order of magnitude larger than is possible for single planets. The resulting distribution of eccentricities is a qualitative match to that inferred from transit timing variations, with a minority of non-zero eccentricities maintained by particular secular configurations. The coupling of the tidal and secular processes enhance the inward migration of the innermost planets in these systems, and can drive them to short orbital periods. Resonant interactions of both the mean motion and secular variety are observed, although the interactions are not strong enough to drive systemic instability in most cases. However, we demonstrate that these systems can easily be driven unstable if coupled to giant planets on longer period orbits.

WASP-19b is the First Example of a Tidally Distorted Exoplanet

Tidally Distorted Exoplanets: Density Corrections for Short-Period Hot-Jupiters based solely on Observable Parameters

Authors:

Burton et al

Abstract:

The close proximity of short period hot-Jupiters to their parent star means they are subject to extreme tidal forces. This has a profound effect on their structure and, as a result, density measurements that assume that the planet is spherical can be incorrect. We have simulated the tidally distorted surface for 34 known short period hot-Jupiters, assuming surfaces of constant gravitational equipotential for the planet, and the resulting densities have been calculated based only on observed parameters of the exoplanet systems. Comparing these results to the density values assuming the planets are spherical shows that there is an appreciable change in the measured density for planets with very short periods (typically less than two days). For one of the shortest-period systems, WASP-19b, we determine a decrease in bulk density of 12% from the spherical case and, for the majority of systems in this study, this value is in the range of 1-5%. On the other-hand, we also find cases where the distortion is negligible (relative to the measurement errors on the planetary parameters) even in the cases of some very short period systems, depending on the mass ratio and planetary radius. For high-density gas-planets requiring apparently anomalously large core masses, density corrections due to tidal deformation could become important for the shortest-period systems.

POET: A Model for (P)lanetary (O)rbital (E)volution due to (T)ides on Evolving Stars

POET: A Model for (P)lanetary (O)rbital (E)volution due to (T)ides on Evolving Stars

Authors:

Penev et al

Abstract:

We make publicly available an efficient, versatile, easy to use and extend tool for calculating the evolution of circular aligned planetary orbits due to the tidal dissipation in the host star. This is the first model to fully account for the evolution of the angular momentum of the stellar convective envelope by the tidal coupling, the transfer of angular momentum between the stellar convective and radiative zones, the effects of the stellar evolution on the tidal dissipation efficiency and stellar core and envelope spins, the loss of stellar convective zone angular momentum to a magnetically launched wind and frequency dependent tidal dissipation. This is only a first release and further development is under way to allow calculating the evolution of inclined and eccentric orbits, with the latter including the tidal dissipation in the planet and its feedback on planetary structure. Considerable effort has been devoted to providing extensive documentation detailing both the usage and the complete implementation details, in order to make it as easy as possible for independent groups to use and/or extend the code for their purposes. POET represents a significant improvement over some previous models for planetary tidal evolution and so has many astrophysical applications. In this article, we describe and illustrate several key examples.

They ought to have named it POETESS:  (P)lanetary (O)rbital (E)volution due to (T)ides on (E)volving (S)tar (S)ystems.