Long-term tidal evolution of short-period planets with companions

Of the fourteen transiting extrasolar planetary systems for which radii have been measured, at least three appear to be considerably larger than theoretical estimates suggest. It has been proposed by Bodenheimer, Lin & Mardling that undetected companions acting to excite the orbital eccentricity are responsible for these oversized planets, as they find new equilibrium radii in response to being tidally heated. In the case of HD 209458, this hypothesis has been rejected by some authors because there is no sign of such a companion at the 5 m/s level, and because it is difficult to say conclusively that the eccentricity is non-zero. Transit timing analysis [...]. Whether or not a companion is responsible for the large radius of HD 209458b, almost certainly some short-period systems have companions which force their eccentricities to nonzero values. This paper is dedicated to quantifying this effect. The eccentricity of a short-period planet will only be excited as long as its (non-resonant) companion's eccentricity is non-zero. Here we show that the latter decays on a timescale which depends on the structure of the interior planet, a timescale which is often shorter than the lifetime of the system. This includes Earth-mass planets in the habitable zones of some stars. We determine which configurations are capable of sustaining significant eccentricity for at least the age of the system, and show that these include systems with companion masses as low as a fraction of an Earth mass. The orbital parameters of such companions are consistent with recent calculations which show that the migration process can induce the formation of low mass planets external to the orbits of hot Jupiters. Systems with inflated planets are therefore good targets in the search for terrestrial planets.Comment: 25 pages, 19 figures. Accepted for publication in MNRA

Dynamical Interactions Make Hot Jupiters in Open Star Clusters

Explaining the origin and evolution of exoplanetary "hot Jupiters" remains a significant challenge. One possible mechanism for their production is planet-planet interactions, which produces hot Jupiters from planets born far from their host stars but near their dynamical stability limits. In the much more likely case of planets born far from their dynamical stability limits, can hot Jupiters can be formed in star clusters? Our N-body simulations of planetary systems inside star clusters answer this question in the affirmative, and show that hot Jupiter formation is not a rare event. We detail three case studies of the dynamics-induced births of hot Jupiters on highly eccentric orbits that can only occur inside star clusters. The hot Jupiters' orbits bear remarkable similarities to those of some of the most extreme exoplanets known: HAT-P-32 b, HAT-P-2 b, HD 80606 b and GJ 876 d. If stellar perturbations formed these hot Jupiters then our simulations predict that these very hot, inner planets are often accompanied by much more distant gas giants in highly eccentric orbits.Comment: 18 pages, 4 figure

The Formation and Evolution of Multiple Star Systems

Multiple systems play an important role in the evolution of star clusters. First we discuss several formation mechanisms which depend on the presence of binaries, either primordial or of dynamical origin. Hierarchical configurations are often stable over long times and yet may experience evolution of the internal orbital parameters. We describe an attempt to model the eccentricity change induced by the outer component using an averaging method, together with the effects due to tidal dissipation and apsidal motion acting on the inner binary. This treatment is adopted for systems with high induced eccentricity which gives rise to some interesting outcomes of significant period shrinkage

Tidal Heating of Extra-Solar Planets

Extra-solar planets close to their host stars have likely undergone significant tidal evolution since the time of their formation. Tides probably dominated their orbital evolution once the dust and gas had cleared away, and as the orbits evolved there was substantial tidal heating within the planets. The tidal heating history of each planet may have contributed significantly to the thermal budget that governed the planet's physical properties, including its radius, which in many cases may be measured by observing transit events. Typically, tidal heating increases as a planet moves inward toward its star and then decreases as its orbit circularizes. Here we compute the plausible heating histories for several planets with measured radii, using the same tidal parameters for the star and planet that had been shown to reconcile the eccentricity distribution of close-in planets with other extra-solar planets. Several planets are discussed, including for example HD 209458 b, which may have undergone substantial tidal heating during the past billion years, perhaps enough to explain its large measured radius. Our models also show that GJ 876 d may have experienced tremendous heating and is probably not a solid, rocky planet. Theoretical models should include the role of tidal heating, which is large, but time-varying.Comment: Accepted for publication to Ap

Long Term Evolution of Close Planets Including the Effects of Secular Interactions

This paper studies the long term evolution of planetary systems containing short-period planets, including the effects of tidal circularization, secular excitation of eccentricity by companion planets, and stellar damping. For planetary systems subject to all of these effects, analytic solutions (or approximations) are presented for the time evolution of the semi-major axes and eccentricities. Secular interactions enhance the inward migration and accretion of hot Jupiters, while general relativity tends to act in opposition by reducing the effectiveness of the secular perturbations. The analytic solutions presented herein allow us to understand these effects over a wide range of parameter space and to isolate the effects of general relativity in these planetary systems.Comment: 14 pages, 2 figures, accepted to Ap

On the Radii of Extrasolar Giant Planets

We have computed evolutionary models for extrasolar planets which range in mass from 0.1 to 3.0 Jovian Masses, and which range in equilibrium temperature from 113 K to 2000 K. We present four sequences of models, designed to show the structural effects of a solid core and of internal heating due to the conversion of kinetic to thermal energy at pressures of tens of bars. The model planetary radii are intended for comparisons with radii derived from observations of transiting extrasolar planets. To provide such comparisons, we expect that of order 10 transiting planets with orbital periods less than 200 days can be detected around bright (V<10) main-sequence stars for which accurate, well-sampled radial velocity measurements can be readily accumulated. Through these observations, structural properties of the planets will be derivable, particularly for low-mass, high-temperature planets. Implications regarding the transiting companion to OGLE-TR-56 recently announced by Konacki et al. are discussed. With regard to the confirmed transiting planet, HD 209458b, we find, in accordance with other recent calculations, that models without internal heating predict a radius that is 35 percent smaller than the observed radius. We explore the possibility that HD 209458b owes its large size to dissipation of energy arising from ongoing tidal circularization of the orbit. We show that residual scatter in the current radial velocity data set for HD 209458b is consistent with the presence of an as-of-yet undetected second companion, and that further radial velocity monitoring of the star is indicated.Comment: 23 pages, 3 figures, accepted by Astrophysical Journa

Effects of Secular Interactions in Extrasolar Planetary Systems

This paper studies the effects of dynamical interactions among the planets in observed extrasolar planetary systems, including hypothetical additional bodies, with a focus on secular perturbations. These interactions cause the eccentricities of the planets to explore a distribution of values over time scales that are long compared to observational time baselines, but short compared to the age of the systems. The same formalism determines the eccentricity forcing of hypothetical test bodies (terrestrial planets) in these systems and we find which systems allow for potentially habitable planets. Such planets would be driven to nonzero orbital eccentricity and we derive the distribution of stellar flux experienced by the planets over the course of their orbits. The general relativistic corrections to secular interaction theory are included in the analysis and such effects are important in systems with close planets ($\sim$4 day orbits). Some extrasolar planetary systems (e.g., Upsilon Andromedae) can be used as a test of general relativity, whereas in other systems, general relativity can be used to constrain the system parameters (e.g., \sin i \gta 0.93 for HD160691). For the case of hot Jupiters, we discuss how the absence of observed eccentricity implies the absence of companion planets.Comment: 32 pages, 11 figures, accepted for publication in Ap

Characterizing the Orbital Eccentricities of Transiting Extrasolar Planets with Photometric Observations

The discovery of over 200 extrasolar planets with the radial velocity (RV) technique has revealed that many giant planets have large eccentricities, in striking contrast with most of the planets in the solar system and prior theories of planet formation. The realization that many giant planets have large eccentricities raises a fundamental question: ``Do terrestrial-size planets of other stars typically have significantly eccentric orbits or nearly circular orbits like the Earth?'' Here, we demonstrate that photometric observations of transiting planets could be used to characterize the orbital eccentricities for individual transiting planets, as well the eccentricity distribution for various populations of transiting planets (e.g., those with a certain range of orbital periods or physical sizes). Such characterizations can provide valuable constraints on theories for the excitation of eccentricities and tidal dissipation. We outline the future prospects of the technique given the exciting prospects for future transit searches, such as those to be carried out by the CoRoT and Kepler missions.Comment: 32 pages, 10 figures, accepted to Ap

Theoretical Radii of Extrasolar Giant Planets: the Cases of TrES-4, XO-3b, and HAT-P-1b

To explain their observed radii, we present theoretical radius-age trajectories for the extrasolar giant planets (EGPs) TrES-4, XO-3b, and HAT-P-1b. We factor in variations in atmospheric opacity, the presence of an inner heavy-element core, and possible heating due to orbital tidal dissipation. A small, yet non-zero, degree of core heating is needed to explain the observed radius of TrES-4, unless its atmospheric opacity is significantly larger than a value equivalent to that at 10$\times$solar metallicity with equilibrium molecular abundances. This heating rate is reasonable, and corresponds for an energy dissipation parameter ($Q_p$) of $\sim10^{3.8}$ to an eccentricity of $\sim$0.01, assuming 3$\times$solar atmospheric opacity and a heavy-element core of $M_c = 30$ $M_{\oplus}$. For XO-3b, which has an observed orbital eccentricity of 0.26, we show that tidal heating needs to be taken into account to explain its observed radius. Furthermore, we reexamine the core mass needed for HAT-P-1b in light of new measurements and find that it now generally follows the correlation between stellar metallicity and core mass suggested recently. Given various core heating rates, theoretical grids and fitting formulae for a giant planet's equilibrium radius and equilibration timescale are provided for planet masses $M_p=$ 0.5, 1.0, and 1.5 $M_J$ with $a =$ 0.02-0.06 AU, orbiting a G2V star. When the equilibration timescale is much shorter than that of tidal heating variation, the ``effective age'' of the planet is shortened, resulting in evolutionary trajectories more like those of younger EGPs. Motivated by the work of \citet{jackson08a,jackson08b}, we suggest that this effect could indeed be important in better explaining some observed transit radii.Comment: 11 pages; references added; ApJ accepted versio