The continuing search for evidence of tidal orbital decay of hot Jupiters
Kishore C. Patra, Joshua N. Winn, Matthew J. Holman, Michael Gillon, Artem Burdanov, Emmanuel Jehin, Laetitia Delrez, Francisco J. Pozuelos, Khalid Barkaoui, Zo… 展开作者
Kishore C. Patra, Joshua N. Winn, Matthew J. Holman, Michael Gillon, Artem Burdanov, Emmanuel Jehin, Laetitia Delrez, Francisco J. Pozuelos, Khalid Barkaoui, Zouhair Benkhaldoun, Norio Narita, Akihiko Fukui, Nobuhiko Kusakabe, Kiyoe Kawauchi, Yuka Terada, L. G. Bouma, Nevin N. Weinberg, Madelyn Broome
备注：
16 pages, 26 figures, accepted for publication in AJ
Many of the known hot Jupiters are formally unstable to tidal orbital decay. The only hot Jupiter for which orbital decay has been directly detected is WASP-12, for which transit timing measurements spanning more than a decade have revealed that the orbital period is decreasing at a rate of $dP/dt\approx 10^{-9}$, corresponding to a reduced tidal quality factor of about $2\times 10^5$. Here, we present a compilation of transit-timing data for WASP-12 and eleven other systems which are especially favorable for detecting orbital decay: KELT-16; WASP-18, 19, 43, 72, 103, 114, and 122; HAT-P-23; HATS-18; and OGLE-TR-56. For most of these systems we present new data that extend the time baseline over which observations have been performed. None of the systems besides WASP-12 displays convincing evidence for period changes, with typical upper limits on $dP/dt$ on the order of $10^{-9}$ or $10^{-10}$, and lower limits on the reduced tidal quality factor on the order of $10^5$. One possible exception is WASP-19, which shows a statistically significant trend, although it may be a spurious effect of starspot activity. Further observations are encouraged.
For most hot Jupiters around main-sequence Sun-like stars, tidal torques are expected to transfer angular momentum from the planet's orbit to the star's rotation. The timescale for this process is difficult to calculate, leading to uncertainties in the history of orbital evolution of hot Jupiters. We present evidence for tidal spin-up by taking advantage of recent advances in planet detection and host-star characterization. We compared the projected rotation velocities and rotation periods of Sun-like stars with hot Jupiters and spectroscopically similar stars with (i) wider-orbiting giant pla…
Hot stars with hot Jupiters have a wide range of obliquities, while cool stars with hot Jupiters tend to have low obliquities. An enticing explanation for this pattern is tidal realignment of the cool host stars, although this explanation assumes that obliquity damping occurs faster than orbital decay, an assumption that needs further exploration. Here we revisit this tidal realignment problem, building on previous work identifying a low-frequency component of the time-variable tidal potential that affects the obliquity but not the orbital separation. We adopt a recent empirically-based model …
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 para…
Tidal heating is often used to interpret "radius anomaly" of hot Jupiters (i.e. radii of a large fraction of hot Jupiters are in excess of 1.2 Jupiter radius which cannot be interpreted by the standard theory of planetary evolution). In this paper we find that tidal heating induces another phenomenon "runaway inflation" (i.e. planet inflation becomes unstable and out of control when tidal heating rate is above its critical value). With sufficiently strong tidal heating, luminosity initially increases with inflation, but across its peak it decreases with inflation such that heating is stronger …
Observations of hot Jupiters around solar-type stars with very short orbital periods (~day) suggest that tidal dissipation in such stars is not too efficient so that these planets can survive against rapid orbital decay. This is consistent with recent theoretical works, which indicate that the tidal Q of planet-hosting stars can indeed be much larger than the values inferred from stellar binaries. On the other hand, recent measurements of Rossiter-McLaughlin effects in transiting hot Jupiter systems not only reveal that many such systems have misaligned stellar spin with respect to the orbital…
WASP-12b stands out among the planets of its class of hot Jupiters because of the observed fast orbital decay attributed to tidal dissipation. The measured rate of the orbital period is $\stackrel{\bf\centerdot}{\textstyle{P}}_{\rm orb}\,=\,-\,29\pm3\;\mbox{ms/yr}\;$=$\;(9.2\pm1.0)\times10^{-10}\;\mbox{s/s}$. In the literature heretofore, all attempts to explain this high rate were based on the assumption that the orbital evolution is dominated by the tides in the star. Since the modified tidal quality factor in yellow dwarfs is insufficient to warrant such a decay rate, a hypothesis was put f…
Constraining Tidal Migration with the Hot Jupiter Population
Princeton University（普林斯顿大学）；University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；Canadian Institute for Theoretical Astrophysics（加拿大理论天体物理研究所）；University of California Los Angeles（加州大学洛杉矶分校）
Hot Jupiters orbiting rapidly rotating stars on inclined orbits undergo tidally induced nodal precession measurable over several years of observations. The Hot Jupiters WASP-33 b and KELT-9 b are particularly interesting targets as they are among the hottest planets found to date, orbiting relatively massive stars. Here, we analyze archival and new data that span 11 and 5 years for WASP-33 b and KELT-9 b, respectively, in order to to model and improve upon their tidal precession parameters. Our work confirms the nodal precession for WASP-33 b and presents the first clear detection of the prece…
We calculate the conversion from non-adiabatic, non-radial oscillations tidally induced by a hot Jupiter on a star to observable spectroscopic and photometric signals. Models with both frozen convection and an approximation for a perturbation to the convective flux are discussed. Observables are calculated for some real planetary systems to give specific predictions. Time-dependent line broadening and the radial velocity signal during transit are both investigated as methods to provide further insight into the nature of the stellar oscillations. The photometric signal is predicted to be propor…
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 …
In anticipation of improved observational data for Jupiter's gravitational field from the Juno spacecraft, we predict the static tidal response for a variety of Jupiter interior models based on ab initio computer simulations of hydrogen-helium mixtures. We calculate hydrostatic-equilibrium gravity terms using the non-perturbative concentric Maclaurin Spheroid (CMS) method that eliminates lengthy expansions used in the theory of figures. Our method captures terms arising from the coupled tidal and rotational perturbations, which we find to be important for a rapidly-rotating planet like Jupiter…
While cooler giant planets are often observed with non-zero eccentricities, the short-period circular orbits of hot Jupiters suggest that they lose orbital energy and angular momentum due to tidal interactions with their host stars. However, orbital decay has never been unambiguously observed. We use data from Gaia Data Release 2 to show that hot Jupiter host stars have a smaller Galactic velocity dispersion than a similar population of stars without hot Jupiters. Since Galactic velocity dispersion is correlated with age, this observation implies that the population of hot Jupiter host stars i…
We calculate small amplitude gravitational and thermal tides of uniformly rotating hot Jupiters composed of a nearly isentropic convective core and a geometrically thin radiative envelope. We treat the fluid in the convective core as a viscous fluid and solve linearized Navier Stokes equations to obtain tidal responses of the core, assuming that the Ekman number ${\rm Ek}$ is a constant parameter. In the radiative envelope, we take account of the effects of radiative dissipations on the responses. The properties of tidal responses depend on thermal timescales $τ_*$ in the envelope and Ekman nu…
We study the migration of hot Jupiters orbiting solar-type pre-main sequence and main sequence stars under the effect of tidal dissipation. The explored range of stellar mass extends from 0.6 to 1.3 $M_{\odot}$. We apply recently developed prescriptions which allow us to explore the orbital evolution over the wide parameter space. Three types of tides are considered: equilibrium tide, inertial waves, and gravity waves. We combine the results of our simulations with the observed distribution of stellar and planetary parameters to evaluate the infall rate of hot Jupiters in the Milky Way galaxy.…
A significant fraction of the hot Jupiters with final circularized orbital periods of less than 5 days are thought to form through the channel of high-eccentricity migration. Tidal dissipation at successive periastron passages removes orbital energy of the planet, which has the potential for changes in semi-major axis of a factor of ten to a thousand. In the equilibrium tide approximation we show that, in order for high-eccentricity migration to take place, the relative level of tidal dissipation in Jupiter analogues must be at least 10 times higher than the upper-limit attributed to the Jupit…
We investigate tidal dissipation of obliquity in hot Jupiters. Assuming an initial random orientation of obliquity and parameters relevant to the observed population, the obliquity of hot Jupiters does not evolve to purely aligned systems. In fact, the obliquity evolves to either prograde, retrograde or 90^{o} orbits where the torque due to tidal perturbations vanishes. This distribution is incompatible with observations which show that hot jupiters around cool stars are generally aligned. This calls into question the viability of tidal dissipation as the mechanism for obliquity alignment of h…
We provide evidence that the obliquities of stars with close-in giant planets were initially nearly random, and that the low obliquities that are often observed are a consequence of star-planet tidal interactions. The evidence is based on 14 new measurements of the Rossiter-McLaughlin effect (for the systems HAT-P-6, HAT-P-7, HAT-P-16, HAT-P-24, HAT-P-32, HAT-P-34, WASP-12, WASP-16, WASP-18, WASP-19, WASP-26, WASP-31, Gl 436, and Kepler-8), as well as a critical review of previous observations. The low-obliquity (well-aligned) systems are those for which the expected tidal timescale is short, …
Context. The Juno spacecraft has obtained highly accurate tidal Love numbers, which provide important constraints on the tidal response and interior structure of Jupiter. Aims. In order to exploit these observations, it is necessary to develop an approach for accurately calculating the tidal response of Jupiter for a given interior model and to investigate the role of interior structure. Methods. We directly solve the linearized tidal equations of a compressible, self-gravitating, rotating and viscous fluid body using a pseudo-spectral method. The Coriolis force is fully taken into account but…
Two formation scenarios have been proposed to explain the tight orbits of hot Jupiters. They could be formed in orbits with a small inclination (with respect to the stellar spin) via disk migration, or in more highly inclined orbits via high-eccentricity migration, where gravitational interactions with a companion and tidal dissipation are at play. Here we target hot Jupiter systems where the misalignment $λ$ has been inferred observationally and we investigate whether their properties are consistent with high-eccentricity migration. Specifically, we study whether stellar tides can be responsi…
Transiting hot Jupiters occupy a wedge-shaped region in the mass ratio-orbital separation diagram. Its upper boundary is eroded by tidal spiral-in of massive, close-in planets and is sensitive to the stellar tidal dissipation parameter $Q_s'$. We develop a simple generative model of the orbital separation distribution of the known population of transiting hot Jupiters, subject to tidal orbital decay, XUV-driven evaporation and observational selection bias. From the joint likelihood of the observed orbital separations of hot Jupiters discovered in ground-based wide-field transit surveys, measur…
The origin of warm Jupiters (gas giant planets with periods between 10 and 200 days) is an open question in exoplanet formation and evolution. We investigate a particular migration theory in which a warm Jupiter is coupled to a perturbing companion planet that excites secular eccentricity oscillations in the warm Jupiter, leading to periodic close stellar passages that can tidally shrink and circularize its orbit. If such companions exist in warm Jupiter systems, they are likely to be massive and close-in, making them potentially detectable. We generate a set of warm Jupiter-perturber populati…
The Juno Orbiter is measuring the three-dimensional gravity field perturbation of Jupiter induced by its rapid rotation, zonal flows, and tidal response to its major natural satellites. This paper aims to provide the contributions to the tesseral harmonics coefficients Cnm, Snm, and the Love numbers knm to be expected from static tidal response in the gravity field of rotating Jupiter. For that purpose, we apply the method of Concentric Maclaurin Ellipsoids (CMS). As we are interested in the variation of the tidal potential with the longitudes of the moons, we take into account the simultaneou…
Recent Kepler observations revealed an unexpected abundance of "hot" Earth-size to Neptune-size planets in the inner ~0.02-0.2 AU from their parent stars. Another "oddity" of recent observations is the discovery of a hot jupiter planet around a very metal poor star of extragalactic origin. We point out that these observations have natural explanations in the framework of the Tidal Downsizing hypothesis, a new and an alternative model for planet formation. We show that disassociation of molecular hydrogen leads to the "second collapse" of the giant planet embryos. The collapse forms much denser…
The tidal evolution of hot Jupiters may change the efficiency of transit surveys of stellar clusters. The orbital decay that hot Jupiters suffer may result in their destruction, leaving fewer transiting planets in older clusters. We calculate the impact tidal evolution has for different assumed stellar populations, including that of 47~Tuc, a globular cluster that was the focus of an intense HST search for transits. We find that in older clusters one expects to detect fewer transiting planets by a factor of two for surveys sensitive to Jupiter-like planets in orbits out to 0.5~AU, and up to a …
We study the interaction between stellar irradiation and tidal heating in gaseous planets with short orbital periods. The intentionally simplified atmospheric model we employ makes the problem analytically tractable and permits the derivation of useful scaling relations. We show that many tidal models provide thermal feedback, producing interior radiative zones and leading to enhanced g-mode dissipation with a wide spectrum of resonances. These resonances are dynamically tuned by the thermal feedback, and so represent a novel form of thermomechanical feedback, coupling vibrational modes to the…
The inner moons of Jupiter and Saturn migrate outwards due to tidal energy dissipation within the planets, the details of which remain poorly understood. We demonstrate that resonance locking between moons and internal oscillation modes of the planet can produce rapid tidal migration. Resonance locking arises due to the internal structural evolution of the planet and typically produces an outward migration rate comparable to the age of the solar system. Resonance locking predicts a similar migration timescale but a different effective tidal quality factor $Q$ governing the migration of each mo…
At mid-mission perijove 17, NASA's Juno mission has revealed a $7σ$ discrepancy between Jupiter's observed high-degree tidal response and the theoretical equilibrium tidal response, namely the Love number $k_{42}$. Here, we propose an interpretation for this puzzling disagreement based on an interior-orbital resonance between internal gravity waves trapped in Jupiter's dilute core and the orbital motion of Io. We use simple Jupiter models to calculate a fractional correction $Δk_{42}$ to the equilibrium tidal response that comes from the dynamical tidal response of a $g$-mode trapped in Jupite…
Although warm jupiters are generally too far from their stars for tides to be important, the presence of an inner planetary companion to a warm jupiter can result in tidal evolution of the system. Insight into the process and its effects comes form classical secular theory of planetary perturbations. The lifetime of the inner planet may be shorter than the age of the system, because the warm jupiter maintains its eccentricity and hence promotes tidal migration into the star. Thus a warm jupiter observed to be alone in its system might have previously cleared away any interior planets. Before i…
Thermal tides can torque the atmosphere of hot Jupiters into asynchronous rotation, while these planets are usually assumed to be locked into spin-orbit synchronization with their host star. In this work, our goal is to characterize the tidal response of a rotating hot Jupiter to the tidal semidiurnal thermal forcing of its host star, by identifying the structure of tidal waves responsible for variation of mass distribution, their dependence on the tidal frequency and their ability to generate strong zonal flows. We develop an ab initio global modeling that generalizes the early approach of Ar…
We study the possibility of tidal dissipation in the solid cores of giant planets and its implication for the formation of hot Jupiters through high-eccentricity migration. We present a general framework by which the tidal evolution of planetary systems can be computed for any form of tidal dissipation, characterized by the imaginary part of the complex tidal Love number, ${\rm Im}[{\tilde k}_2(ω)]$, as a function of the forcing frequency $ω$. Using the simplest viscoelastic dissipation model (the Maxwell model) for the rocky core and including the effect of a nondissipative fluid envelope, we…
Tidal transfer of angular momentum is expected to cause hot Jupiters to spiral into their host stars. Although the timescale for orbital decay is very uncertain, it should be faster for systems with larger and more evolved stars. Indeed, it is well established that hot Jupiters are found less frequently around subgiant stars than around main-sequence stars. However, the interpretation of this finding has been ambiguous, because the subgiants are also thought to be more massive than the F- and G-type stars that dominate the main-sequence sample. Consequently it has been unclear whether the abse…
Stars with hot Jupiters sometimes have high obliquities, which are possible relics of hot Jupiter formation. Based on the characteristics of systems with and without high obliquities, it is suspected that obliquities are tidally damped when the star has a thick convective envelope, as is the case for main-sequence stars cooler than ~6100K, and the orbit is within ~8 stellar radii. A promising theory for tidal obliquity damping is the dissipation of inertial waves within the star's convective envelope. Here, we consider the implications of this theory for the timing of hot Jupiter formation. Sp…
Via the Rossiter-McLaughlin effect, it is possible to measure the sky-projected angle between the stellar spin and a planet's orbital spin. Observed orbital inclinations have been found to range over all possible angles. A tentative detection of a correlation between the dispersion in spin/orbit angle and the youth of the system is revealed, using spin/orbit measurements for hot Jupiters around stars with masses larger than 1.2 Solar Masses for which age estimates are more accurately determined. The chance of this pattern arising by chance has been computed to 7%. This appears in accordance wi…
Various interactions affect the population of close-in planets. Among them, the tidal and magnetic interactions drive orbital decay and star-planet angular momentum exchange, leading to stellar spin-up. As a result of the above processes, a planet may initiate the mass transfer to the host star once it encounters the Roche limit. Another mechanism providing substantial mass loss is associated with the atmospheric escape caused by photoevaporation followed by orbital expansion, which is thought to be important for hot Neptunes and super-Earths. Thus, the fraction of the initial number of hot Ju…
An observation of Jupiter's tidal response is anticipated for the on-going Juno spacecraft mission. We combine self-consistent, numerical models of Jupiter's equilibrium tidal response with observed Doppler shifts from the Juno gravity science experiment to test the sensitivity of the spacecraft to tides raised by the Galilean satellites and the Sun. The concentric Maclaurin spheroid (CMS) method finds the equilibrium shape and gravity field of a rotating, liquid planet with the tide raised by a satellite, expanded in Love numbers ($k_{nm}$). We present improvements to CMS theory that eliminat…
Close-in extrasolar gas giants -- the hot Jupiters -- display departures in radius above the zero-temperature solution, the radius excess, that are anomalously high. The radius excess of hot Jupiters follows a relatively close relation with thermal tidal tidal torques and holds for ~ 4-5 orders of magnitude in a characteristic thermal tidal power in such a way that is consistent with basic theoretical expectations. The relation suggests that thermal tidal torques determine the global thermodynamic and spin state of the hot Jupiters. On empirical grounds, it is shown that theories of hot Jupite…
Transit Timing Variation (TTV) of hot Jupiters provides direct observational evidence of planet tidal dissipation. Detecting tidal dissipation through TTV needs high precision transit timings and long timing baselines. In this work, we predict and discuss the potential scientific contribution of SiTian Survey in detecting and analyzing exoplanet TTV. We develop a tidal dissipation detection pipeline for SiTian Survey that aims at time-domain astronomy with 72 1-meter optical telescopes. The pipeline includes the modules of light curve deblending, transit timing obtaining, and TTV modeling. SiT…
It is debated whether the two hot Jupiter populations --- those on orbits misaligned from their host star's spin axis and those well-aligned --- result from two migration channels or from two tidal realignment regimes. Here I demonstrate that equilibrium tides raised by a planet on its star can account for three observed spin-orbit alignment trends: the aligned orbits of hot Jupiters orbiting cool stars, the planetary mass cut-off for retrograde planets, and the stratification by planet mass of cool host stars' rotation frequencies. The first trend can be caused by strong versus weak magnetic …
We present a simplified model to study the orbital evolution of a young hot Jupiter inside the magnetospheric cavity of a proto-planetary disk. The model takes into account the disk locking of stellar spin as well as the tidal and magnetic interactions between the star and the planet. We focus on the orbital evolution starting from the orbit in the 2:1 resonance with the inner edge of the disk, followed by the inward and then outward orbital migration driven by the tidal and magnetic torques as well as the Roche-lobe overflow of the tidally inflated planet. The goal in this paper is to study h…
Gas giants orbiting their host star within the ice line are thought to have migrated to their current locations from farther out. Here we consider the origin and dynamical evolution of observed Jupiters, focusing on hot and warm Jupiters with outer friends. We show that the majority of the observed Jupiter pairs (twenty out of twenty-four) will be dynamically unstable if the inner planet was placed at >~1AU distance from the stellar host. This finding is at odds with formation theories that invoke the migration of such planets from semi-major axes >~1AU due to secular dynamical processes (e.g.…
Observed hot Jupiter (HJ) systems exhibit a wide range of stellar spin-orbit misalignment angles. The origin of these HJs remains unclear. This paper investigates the inward migration of giant planets due to Lidov-Kozai (LK) oscillations induced by a distant (100-1000 AU) stellar companion. We conduct a large population synthesis study, including the octupole gravitational potential from the stellar companion, mutual precession of the host stellar spin axis and planet orbital axis, tidal dissipation in the planet, and stellar spin-down in the host star due to magnetic braking. We consider a ra…
We study the orbital evolution of hot Jupiters due to the excitation and damping of tidally driven $g$-modes within solar-type host stars. Linearly resonant $g$-modes (the dynamical tide) are driven to such large amplitudes in the stellar core that they excite a sea of other $g$-modes through weakly nonlinear interactions. By solving the dynamics of large networks of nonlinearly coupled modes, we show that the nonlinear dissipation rate of the dynamical tide is several orders of magnitude larger than the linear dissipation rate. We find stellar tidal quality factors $Q \approx 10^5-10^6$ for s…
We study tidal dissipation in stars with masses in the range $0.1-1.6 M_\odot$ throughout their evolution, including turbulent effective viscosity acting on equilibrium tides and inertial waves in convection zones, and internal gravity waves in radiation zones. We consider a range of stellar evolutionary models and incorporate the frequency-dependent effective viscosity acting on equilibrium tides based on the latest simulations. We compare the tidal flow and dissipation obtained with the conventional equilibrium tide, which is strictly invalid in convection zones, finding that the latter typi…
Gas giant planets orbiting within 0.1 AU of their host stars, unlikely to have formed in situ, are evidence for planetary migration. It is debated whether the typical hot Jupiter smoothly migrated inward from its formation location through the proto-planetary disk or was perturbed by another body onto a highly eccentric orbit, which tidal dissipation subsequently shrank and circularized during close stellar passages. Socrates and collaborators predicted that the latter class of model should produce a population of super-eccentric proto-hot Jupiters readily observable by Kepler. We find a pauci…
Tidal friction is thought to be important in determining the long-term spin-orbit evolution of short-period extrasolar planetary systems. Using a simple model of the orbit-averaged effects of tidal friction Eggleton, Kiseleva & Hut (1998), we analyse the effects of the inclusion of stellar magnetic braking on the evolution of such systems. A phase-plane analysis of a simplified system of equations, including only the stellar tide together with a model of the braking torque proposed by Verbunt & Zwaan (1981), is presented. The inclusion of stellar magnetic braking is found to be extremely impor…
We investigate the constraints on the formation of, and tidal dissipation processes in, hot Jupiters (HJs) that can be inferred based on reliable knowledge of the age of a system or population. Particular attention is paid to the role of young systems (such as those in open clusters or star-forming regions) in such studies. For an ensemble of coeval HJ (or proto-HJ) systems, we quantify the effect of age on the distribution of orbital eccentricities with respect to orbital periods as well as the location of the observed "pile-up" feature. We expect the effects of pre-main-sequence stellar evol…
We report the discovery of WTS-2 b, an unusually close-in 1.02-day hot Jupiter (Mp=1.12MJ, Rp=1.363RJ) orbiting a K2V star, which has a possible gravitationally-bound M-dwarf companion at 0.6 arcsec separation contributing ~20 percent of the total flux in the observed J-band light curve. The planet is only 1.5 times the separation from its host star at which it would be destroyed by Roche lobe overflow, and has a predicted remaining lifetime of just ~40 Myr, assuming a tidal dissipation quality factor of Q'*=10^6. Q'* is a key factor in determining how frictional processes within a host star a…
I consider a Jovian planet on a highly eccentric orbit around its host star, a situation produced by secular interactions with its planetary or stellar companions. The tidal interactions at every periastron passage exchange energy between the orbit and the planet's degree-2 fundamental-mode. Starting from zero energy, the f-mode can diffusively grow to large amplitudes if its one-kick energy gain > 10^-5 of the orbital energy. This requires a pericentre distance of < 4 tidal radii (or 1.6 Roche radii). If the f-mode has a non-negligible initial energy, diffusive evolution can occur at a lower …
The sunspot record since 1749 is made of three major cycles (9.98, 10.9 and 11.86 yr). The side frequencies are related to the spring tidal period of Jupiter and Saturn (9.93 yr) and to the tidal sidereal period of Jupiter (11.86 yr). A simplified harmonic constituent model based on the above two planetary tidal frequencies and on the exact dates of Jupiter and Saturn planetary tidal phases, plus a theoretically deduced 10.87-year central cycle reveals complex quasi-periodic interference/beat patterns at about 115, 61 and 130 years, plus a quasi-millennial large beat cycle around 983 years. We…
Observed transit timing variation (TTV) potentially reveals the period decay caused by star-planet tidal interaction which can explain the orbital migration of hot Jupiters. We report the TTV of XO-3b, using TESS observed timings and archival timings. We generate a photometric pipeline to produce light curves from raw TESS images and find the difference between our pipeline and TESS PDC is negligible for timing analysis. TESS timing presents a shift of 17.6 minutes (80 $σ$), earlier than the prediction from the previous ephemeris. The best linear fit for all timings available gives a Bayesian …
We calculate tidal torque due to semi-diurnal thermal tides in rotating hot Jupiters, taking account of the effects of radiative cooling in the envelope and of the planets rotation on the tidal responses. We use a simple Jovian model composed of a nearly isentropic convective core and a thin radiative envelope. To represent the tidal responses of rotating planets, we employ series expansions in terms of spherical harmonic functions $Y_l^m$ with different $l$s for a given $m$. For low forcing frequency, there occurs frequency resonance between the forcing and the $g$- and $r$-modes in the envel…
The origin of Jupiter-mass planets with orbital periods of only a few days is still uncertain. It is widely believed that these planets formed near the water-ice line of the protoplanetary disk, and subsequently migrated into much smaller orbits. Most of the proposed migration mechanisms can be classified either as disk-driven migration, or as excitation of a very high eccentricity followed by tidal circularization. In the latter scenario, the giant planet that is destined to become a hot Jupiter spends billions of years on a highly-eccentric orbit, with apastron near the water-ice line. Event…
