The Effect of Tidal Inflation Instability on the Mass and Dynamical Evolution of Extrasolar Planets with Ultrashort Periods

By Pin-Gao Gu, D. Lin, P. Bodenheimer. 2003

165 citations recorded by the source corpus.

We investigate the possibility of substantial inflation of short-period Jupiter-mass planets, as a result of their internal tidal dissipation associated with the synchronization and circularization of their orbits. We employ the simplest prescription based on an equilibrium model with a constant lag angle for all components of the tide. We show the following: (1) In the low-eccentricity limit, the synchronization of the planets' spin with their mean motion is established before tidal dissipation can significantly modify their internal structure. (2) However, above a critical eccentricity, which is a function of the planets' semimajor axis, tidal dissipation of energy during the circularization process can induce planets to inflate in size before their eccentricity is damped. (3) For moderate eccentricities, the planets adjust to stable thermal equilibria in which the rate of their internal tidal dissipation is balanced by the enhanced radiative flux associated with their enlarged radii. (4) For sufficiently large eccentricities, the planets swell beyond two Jupiter radii and their internal degeneracy is partially lifted. Thereafter, their thermal equilibria become unstable and they undergo runaway inflation until their radii exceed the Roche radius. (5) We determine the necessary and sufficient condition for this tidal inflation instability. (6) These results are applied to study short-period planets. We show that for young Jupiter-mass planets, with a period of less than 3 days, an initial radius of about 2RJ, and an orbital eccentricity greater than 0.2, the energy dissipated during the circularization of their orbits is sufficiently intense and protracted to inflate their sizes up to their Roche radii. (7) We estimate the mass-loss rate, the asymptotic planetary masses, and the semimajor axes for various planetary initial orbital parameters. The possibility of gas overflow through both inner (L1) and outer (L2) Lagrangian points for the planets with short periods or large eccentricities is discussed. (8) Planets with more modest eccentricity (<0.3) and semimajor axis (>0.03-0.04 AU) lose mass via Roche lobe overflow mostly through the inner Lagrangian (L1) point. As a result of the conservation of total angular momentum, these mass-losing planets migrate outward, such that their semimajor axes and Roche radii increase while their mass, eccentricity, and tidal dissipation rate decrease until the mass loss is quenched. (9) Based on these results, we suggest that the combined effects of self-regulated mass loss and tidally driven orbital evolution may be responsible for the apparent lack of giant planets with ultrashort periods ≲3 days. (10) Mass loss during their orbital circularization may also have caused the planets with periods in the range ~3-7 days to be less massive than long-period planets, which are not affected by the star-planet tidal interaction. (11) The accretion of the short-period planets' tidal debris can also lead to the surface layer contamination and metallicity enhancement of their host stars. (12) Among the planets with periods of 1-3 weeks today, some may have migrated outward and attained circular orbits while others may have preserved their initial eccentricity and semimajor axis. Therefore, planets with circular orbits are expected to coexist with those with eccentric orbits in this period range. (13) Gross tidal inflation of planets occurs on the timescale ~106 yr after their formation for a brief interval of ~105 yr. The relatively large sizes of their classical and weak-line T Tauri host stars increase the planets' transit probability. The inflated sizes of the tidally heated planets also increase the eclipse depth of such transit events. Thus, the tidal inflation and disruption of planets may be directly observable around classical and weak-line T Tauri stars.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/46925e849f766778220e13d0b2c6c7e5ab7bcf1c

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In Astronomy and Astrophysics

1. Jon Fortney
2. C. Mordasini
3. Gregory Laughlin
4. G. Chabrier
5. M. Perryman
6. D. Lai
7. D. Lin
8. M. Marley

Citations in the corpus

• Is tidal heating sufficient to explain bloated exoplanets? Consistent calculations accounting for finite initial eccentricity (2010, background): “Following Bodenheimer et al. (2001) and Gu et al. (2003), attempts have been made to explain the observed large radius of some transiting close-in gas giant exoplanets - the so-called ”Hot Jupiters” - by means of tidal heating (Jackson et al. 2008; Miller et al. 2009; Ibgui et al. 2009).”
• Toward a Deterministic Model of Planetary Formation. IV. Effects of Type I Migration (2008, background): “In reality, a large fraction of the giant planets that have migrated to small disk radii may either be consumed (e.g., Sandquist et al. 1998) or tidally disrupted (e.g., Trilling et al. 1998; Gu et al. 2003) by their host stars.”
• Toward a Deterministic Model of Planetary Formation. III. Mass Distribution of Short-Period Planets around Stars of Various Masses (2005, background): “The effect of post formation star-planet tidal interaction, which has not been taken into account in our model, may have caused the demise of a majority of the close-in planets, in particular massive planets (Gu et al. 2003, Paper II).”
• MASS TRANSFER, TRANSITING STREAM, AND MAGNETOPAUSE IN CLOSE-IN EXOPLANETARY SYSTEMS WITH APPLICATIONS TO WASP-12 (2010, background): “The suggested energy source was tidal dissipation due to an assumed eccentricity of the orbit (see also Gu et al. 2003).”
• Tidal Dissipation in Stars and Giant Planets (2014, background): “Gu et al. (2003) identified a tidal inflation instability that may lead to the disruption of gas giants.”
• Formation of Hot Planets by a Combination of Planet Scattering, Tidal Circularization, and the Kozai Mechanism (2008, unknown): “We also need to take into account the relativity precession and J2 potential of the central star, which prevent the Kozai mechanism, as well as the long-term tidal disruption process (e.g., Gu et al. 2003).”
• The TRAPPIST survey of southern transiting planets. I. Thirty eclipses of the ultra-short period planet WASP-43 b (2012, background): “…with the host star that should lead in most cases to a slow spiral-in of the planet and to a transfer of angular momentum to the star (e.g. Barker & Ogilvie 2009, Jackson et al. 2009, Mastumura et al. 2010), the end result being the planet’s disruption at its Roche limit (Gu et al. 2003).”
• Two Classes of Hot Jupiters (2007, background): “Tidal Heating Another scenario that has been suggested for stopping the inward migration of planets is Roche lobe overflow (Trilling et al. 1998), possibly aided by tidal heating (Gu et al. 2003).”
• THE MASS OF KOI-94d AND A RELATION FOR PLANET RADIUS, MASS, AND INCIDENT FLUX (2013, unknown): “Coupled tidal and planetary structure evolution has been calculated by a number of authors (Bodenheimer et al. 2001; Gu et al. 2003; Ibgui & Burrows 2009; Miller et al. 2009; Ibgui et al. 2010; Leconte et al. 2010).”
• Toward a Deterministic Model of Planetary Formation. I. A Desert in the Mass and Semimajor Axis Distributions of Extrasolar Planets (2003, background): “These planets have either formed with relatively low masses (see §4) or lost some of their initial mass through Roche lobe overflow (Trilling et al. 1998; Gu et al. 2003).”
• Tidal Dissipation in Rotating Giant Planets (2003, background): “Enhancement of the tidal dissipation rate implies a more rapid synchronization of the planet’s spin with its orbit, a faster circularization of the orbit, and a more intense heating of the planet, which may lead in turn to inflation and even Roche lobe overflow (Gu et al. 2003).”
• Toward a Deterministic Model of Planetary Formation. II. The Formation and Retention of Gas Giant Planets around Stars with a Range of Metallicities (2004, background): “This discrepancy suggests that more than 90% of the hot Jupiters that migrated to the stellar vicinity are either consumed (Sandquist et al. 1998) or tidally disrupted (Gu et al. 2003) by their host stars.”