Large planetary spin-orbit misalignments (obliquities) may strongly influence atmospheric circulation and tidal heating in the planet. A promising avenue to generate obliquities is via spin-orbit resonances, where the spin and orbital precession frequencies of the planet cross each other as the system evolves in time. One such mechanism involves a dissipating (mass-losing) protoplanetary disk that drives orbital precession of an interior planet. We study this scenario analytically in this paper, and obtain the mapping between the general initial spin orientation and the final obliquity. We show that (i) under adiabatic evolution (i.e. the disk dissipates at a sufficiently slow rate), the final planetary obliquity as a function of the initial spin orientation bifurcates into distinct tracks governed by interactions with the resonance; (ii) under nonadiabatic evolution, a broad range of obliquities can be excited. We obtain analytical expressions for the final obliquities for various regimes of parameter space. The dynamical system studied in this paper is an example of "Colombo's top", and our analysis and results can be adapted to other applications.
The next generation of exoplanet space photometry missions proposed by both NASA and ESA promise to discover small transiting planets around the nearest and brightest main-sequence stars. The physical and rotational properties of these stars, in conjunction with Gaia-precision distances, can be used to determine the inclination of the stellar rotation axis. Given edge-on orbital paths for transiting planets, stellar inclinations can be interpreted as obliquities projected into the line of sight, which can be used to more clearly reveal the system architectures of small planets and the factors …
We recommend an intensive effort to survey and understand the obliquity distribution of small close-in extrasolar planets over the coming decade. The orbital obliquities of exoplanets--i.e., the relative orientation between the planetary orbit and the stellar rotation--is a key tracer of how planets form and migrate. While the orbital obliquities of smaller planets are poorly explored today, a new generation of facilities coming online over the next decade will make such observations possible en masse. Transit spectroscopic observations with the extremely large telescopes will enable us to mea…
We present a comprehensive theoretical study on the spin evolution of a planet under the combined effects of tidal dissipation and gravitational perturbation from an external companion. Such a "spin + companion" system (called Colombo's top) appears in many [exo]planetary contexts. The competition between the tidal torque (which drives spin-orbit alignment and synchronization) and the gravitational torque from the companion (which drives orbital precession of the planet) gives rise to two possible spin equilibria ("Tidal Cassini Equilibria", tCE) that are stable and attracting: the "simple" tC…
Obliquity measurements for stars hosting relatively long-period giant planets with weak star-planet tidal interactions may play a key role in distinguishing between formation theories for shorter-period hot Jupiters. Few such obliquity measurements have been made to date due to the relatively small sample of known wide-orbiting, transiting Jovian-mass planets and the challenging nature of these targets, which tend to have long transit durations and orbit faint stars. We report a measurement of the Rossiter-McLaughlin effect across the transit of K2-140 b, a Jupiter-mass planet with period $P=6…
Results on the obliquity of exoplanet host stars -- the angle between the stellar spin axis and the planetary orbital axis -- provide important diagnostic information for theories describing planetary formation. Here we present the first application of asteroseismology to the problem of stellar obliquity determination in systems with transiting planets and Sun-like host stars. We consider two systems observed by the NASA Kepler Mission which have multiple transiting small (super-Earth sized) planets: the previously reported Kepler-50 and a new system, Kepler-65, whose planets we validate in th…
Models are developed to simulate lightcurves of stars dimmed by transiting exoplanets with and without rings. These models are then applied to \textit{Kepler} photometry to search for planetary rings in a sample of 21 exoplanets, mostly hot Jupiters, chosen to offer the best observational opportunity for discovering potential rings. We also examine what kinds of rings might be expected for these planets, in terms of both size and orientation, based on arguments involving the host planet's equilibrium temperature, its likely obliquities, and the formation and stability of possible ring systems.…
The rotation of a star and the revolutions of its planets are not necessarily aligned. This article reviews the measurement techniques, key findings, and theoretical interpretations related to the obliquities (spin-orbit angles) of planet-hosting stars. The best measurements are for stars with short-period giant planets, which have been found on prograde, polar, and retrograde orbits. It seems likely that dynamical processes such as planet-planet scattering and secular perturbations are responsible for tilting the orbits of close-in giant planets, just as those processes are implicated in exci…
HAT-P-11 is a mid-K dwarf that hosts one of the first Neptune-sized planets found outside the solar system. The orbit of HAT-P-11b is misaligned with the star's spin --- one of the few known cases of a misaligned planet orbiting a star less massive than the Sun. We find an additional planet in the system based on a decade of precision radial velocity (RV) measurements from Keck/HIRES. HAT-P-11c is similar to Jupiter in its mass ($M_P \sin{i} = 1.6\pm0.1$ $M_J$) and orbital period ($P = 9.3^{+1.0}_{-0.5}$ year), but has a much more eccentric orbit ($e=0.60\pm0.03$). In our joint modeling of RV …
We present observations of the Rossiter-McLaughlin effect for two exoplanetary systems, revealing the orientations of their orbits relative to the rotation axes of their parent stars. HAT-P-4b is prograde, with a sky-projected spin-orbit angle of lambda = -4.9 +/- 11.9 degrees. In contrast, HAT-P-14b is retrograde, with lambda = 189.1 +/- 5.1 degrees. These results conform with a previously noted pattern among the stellar hosts of close-in giant planets: hotter stars have a wide range of obliquities and cooler stars have low obliquities. This, in turn, suggests that three-body dynamics and tid…
Thermal light-curve analysis is a powerful approach to probe the thermal structures of exoplanetary atmospheres, which are greatly influenced by the planetary obliquity and eccentricity. Here we investigate the thermal light curves of eccentric-tilted exoplanets across various radiative timescales, eccentricities, obliquities, and viewing geometries using results of shallow-water simulations presented in Ohno $\&$ Zhang (2019). We also achieve an analytical theory of the thermal light curve that can explain general trends in the light curves of tilted exoplanets. For tilted planets in circular…
Relatively long-period nonsynchronized planets---such as warm Jupiters---potentially retain the primordial rotation, eccentricity, and obliquity that might encapsulate information on planetary climate and formation processes. To date, there has not been a systematic study on climate patterns on these planets that will significantly influence their observations. Here we investigate the atmospheric dynamics of nonsynchronized, fast-rotating exoplanets across various radiative timescales, eccentricities, and obliquities using a shallow water model. The dynamical pattern can be demarcated into fiv…
Identifying liquid water on the surface of planets is a high priority, as this traditionally defines habitability. One proposed signature of oceans is specular reflection ("glint"), which increases the apparent albedo of a planet at crescent phases. We post-process a global climate model of an Earth-like planet to simulate reflected lightcurves. Significantly, we obtain glint-like phase variations even though we do not include specular reflection in our model. This false positive is the product of two generic properties: 1) for modest obliquities, a planet's poles receive less orbit-averaged s…
The Coupled Tidal Evolution of the Moons and Spins of Warm Exoplanets
Princeton University（普林斯顿大学）；Canadian Institute for Theoretical Astrophysics（加拿大理论天体物理研究所）；Observatoire de Paris, Université PSL, Sorbonne Université, Université de Lille, LNE, CNRS（巴黎天文台，巴黎文理研究大学，索邦大学，里尔大学，LNE，法国国家科学研究中心）
We present observations of the Rossiter-McLaughlin effect for the transiting exoplanet systems WASP-1, WASP-24, WASP-38 and HAT-P-8, and deduce the orientations of the planetary orbits with respect to the host stars' rotation axes. The planets WASP-24b, WASP-38b and HAT-P-8b appear to move in prograde orbits and be well aligned, having sky-projected spin orbit angles consistent with zero: λ = -4.7 \pm 4.0°, λ = 15 + 33°/-43° and λ = -9.7 +9.0°/-7.7°, respectively. The host stars have Teff < 6250 K and conform with the trend of cooler stars having low obliquities. WASP-38b is a massive planet o…
Planetary climates are strongly affected by planetary orbital parameters such as obliquity, eccentricity, and precession. In exoplanetary systems, exo-terrestrial planets should have various obliquities. High-obliquity planets would have extreme seasonal cycles due to the seasonal change of the distribution of the insolation. Here, we introduce the Non-hydrostatic ICosahedral Atmospheric Model(NICAM), a global cloud-resolving model, to investigate the climate of high-obliquity planets. This model can explicitly simulate a three-dimensional cloud distribution and vertical transports of water va…
The tilt of a planet's spin axis off its orbital axis ("obliquity") is a basic physical characteristic that plays a central role in determining the planet's global circulation and energy redistribution. Moreover, recent studies have also highlighted the importance of obliquities in sculpting not only the physical features of exoplanets but also their orbital architectures. It is therefore of key importance to identify and characterize the dominant processes of excitation of non-zero axial tilts. Here we highlight a simple mechanism that operates early on and is likely fundamental for many extr…
We observed with the SOPHIE spectrograph (OHP, France) the transit of the HAT-P-6b exoplanet across its host star. The resulting stellar radial velocities display the Rossiter-McLaughlin anomaly and reveal a retrograde orbit: the planetary orbital spin and the stellar rotational spin point towards approximately opposite directions. A fit to the anomaly measures a sky-projected angle lambda = 166 +/- 10 degrees between these two spin axes. All seven known retrograde planets are hot jupiters with masses M_p < 3 M_Jup. About two thirds of the planets in this mass range however are prograde and al…
The orientation between a star's spin axis and a planet's orbital plane provides valuable information about the system's formation and dynamical history. For non-transiting planets at wide separations, true stellar obliquities are challenging to measure, but lower limits on spin-orbit orientations can be determined from the difference between the inclination of the star's rotational axis and the companion's orbital plane ($Δi$). We present results of a uniform analysis of rotation periods, stellar inclinations, and obliquities of cool stars (SpT $\gtrsim$ F5) hosting directly imaged planets an…
Planetary obliquity and eccentricity influence climate by shaping the spatial and temporal patterns of stellar energy incident at a planet's surface, affecting both the annual mean climate and magnitude of seasonal variability. Previous work has demonstrated the importance of both planetary obliquity and eccentricity for climate and habitability, but most studies have not explicitly modeled the response of life to these parameters. While exaggerated seasons may be stressful to some types of life, a recent study found an increase in marine biological activity for moderately high obliquities <45…
The angle between the spin axis of the host star and the orbit of its planets (i.e., the stellar obliquity) is precious information about the formation and evolution of exoplanetary systems. Measurements of the Rossiter-McLaughlin effect revealed that many stars that host a hot-Jupiter have high obliquities, suggesting that hot-Jupiter formation involves excitation of orbital inclinations. In this contribution we show how the passage of the planet over starspots can be used to measure the obliquity of exoplanetary systems. This technique is used to obtain - for the first time - the obliquity o…
Over the past decade asteroseismology has become a powerful method to systematically characterize host stars and dynamical architectures of exoplanet systems. In this contribution I review current key synergies between asteroseismology and exoplanetary science such as the precise determination of planet radii and ages, the measurement of orbital eccentricities, stellar obliquities and their impact on hot Jupiter formation theories, and the importance of asteroseismology on spectroscopic analyses of exoplanet hosts. I also give an outlook on future synergies such as the characterization of sub-…
Recent work suggests that many short-period extrasolar planets may have spin obliquities that are significantly tilted with respect to their orbital planes. These large obliquities are a natural outcome of ``secular spin-orbit resonance'', a configuration in which the planetary spin precession frequency matches the frequency of orbit nodal regression, or a Fourier component thereof. While exoplanet spin obliquities have not yet been measured directly, they may be detectable indirectly through their signatures in various observations, such as photometric measurements across the full phase of a …
Planetary rotation rates and obliquities provide information regarding the history of planet formation, but have not yet been measured for evolved extrasolar planets. Here we investigate the theoretical and observational perspective of the Rossiter-McLauglin effect during secondary eclipse (RMse) ingress and egress for transiting exoplanets. Near secondary eclipse, when the planet passes behind the parent star, the star sequentially obscures light from the approaching and receding parts of the rotating planetary surface. The temporal block of light emerging from the approaching (blue-shifted) …
The outflowing magnetized wind from a host star shapes planetary and exoplanetary magnetospheres dictating the extent of its impact. We carry out three-dimensional (3D) compressible magnetohydrodynamic (MHD) simulations of the interactions between magnetized stellar winds and planetary magnetospheres corresponding to a far-out star-planet system, with and without planetary dipole obliquity. We identify the pathways that lead to the formation of a dynamical steady-state magnetosphere and find that magnetic reconnection plays a fundamental role in the process. The magnetic energy density is foun…
We report photometric and radial velocity observations of the XO-4 transiting planetary system, conducted with the FLWO 1.2m telescope and the 8.2m Subaru Telescope. Based on the new light curves, the refined transit ephemeris of XO-4b is $P = 4.1250828 \pm 0.0000040$ days and $T_c [BJD_TDB] = 2454485.93323 \pm 0.00039$. We measured the Rossiter-McLaughlin effect of XO-4b and estimated the sky-projected angle between the stellar spin axis and the planetary orbital axis to be $λ= -46.7^{\circ} ^{+8.1^{\circ}}_{-6.1^{\circ}}$. This measurement of $λ$ is less robust than in some other cases becau…
Variations in the axial tilt, or obliquity, of terrestrial planets can affect their climates and therefore their habitability. Kepler-62f is a 1.4 R$_\oplus$ planet orbiting within the habitable zone of its K2 dwarf host star (Borucki et al. 2013). We perform N-body simulations that monitor the evolution of obliquity of Kepler-62f for 10 million year timescales to explore the effects on model assumptions, such as the masses of the Kepler-62 planets and the possibility of outer bodies. Significant obliquity variation occurs when the rotational precession frequency overlaps with one or more of t…
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 s…
The obliquity of the Earth, which controls our seasons, varies by only ~2.5 degrees over ~40,000 years, and its eccentricity varies by only ~0.05 over 100,000 years. Nonetheless, these small variations influence Earth's ice ages. For exoplanets, however, variations can be significantly larger. Previous studies of the habitability of moonless Earth-like exoplanets have found that high obliquities, high eccentricities, and dynamical variations can extend the outer edge of the habitable zone by preventing runaway glaciation (snowball states). We expand upon these studies by exploring the orbital …
We find the orbit of the Neptune-sized exoplanet HAT-P-11b to be highly inclined relative to the equatorial plane of its host star. This conclusion is based on spectroscopic observations of two transits, which allowed the Rossiter-McLaughlin effect to be detected with an amplitude of 1.5 m/s. The sky-projected obliquity is 103_{-10}^{+26} degrees. This is the smallest exoplanet for which spin-orbit alignment has been measured. The result favors a migration scenario involving few-body interactions followed by tidal dissipation. This finding also conforms with the pattern that the systems with t…
NASA's Kepler mission revealed that $\sim 30\%$ of Solar-type stars harbor planets with sizes between that of Earth and Neptune on nearly circular and co-planar orbits with periods less than 100 days. Such short-period compact systems are rarely found with planet pairs in mean-motion resonances (MMRs) -- configurations in which the planetary orbital periods exhibit a simple integer ratio -- but there is a significant overabundance of planet pairs lying just wide of the first-order resonances. Previous work suggests that tides raised on the planets by the host star may be responsible for forcin…
Important clues on the formation and evolution of planetary systems can be inferred from the stellar obliquity $ψ$. We study the distribution of obliquities using the California-Kepler Survey and the TEPCat Catalog of Rossiter-MacLaughlin (RM) measurements, from which we extract, respectively, 275 and 118 targets. We infer a "best fit" obliquity distribution in $ψ$ with a single parameter $κ$. Large values of $κ$ imply that $ψ$ is distributed narrowly around zero, while small values imply approximate isotropy. Our findings are: (1) The distribution of $ψ$ in Kepler systems is narrower than fou…
We present three-dimensional atmospheric circulation models of a hypothetical "warm Jupiter" planet, for a range of possible obliquities from 0-90 degrees. We model a Jupiter-mass planet on a 10-day orbit around a Sun-like star, since this hypothetical planet sits at the boundary between planets for which we expect that tidal forces should have aligned their rotation axes with their orbital axes (i.e., ones with zero obliquity) and planets whose timescale for tidal alignment is longer than the typical age of an exoplanet system. In line with observational progress, which is pushing atmospheric…
We present photometric and spectroscopic observations of the 2009 Feb. 2 transit of the exoplanet XO-3b. The new data show that the planetary orbital axis and stellar rotation axis are misaligned, as reported earlier by Hebrard and coworkers. We find the angle between the sky projections of the two axes to be 37.3 +/- 3.7 deg, as compared to the previously reported value of 70 +/- 15 deg. The significance of this discrepancy is unclear because there are indications of systematic effects. XO-3b is the first exoplanet known to have a highly inclined orbit relative to the equatorial plane of its …
In planetary systems with sufficiently small inter-planet spacing, close encounters can lead to planetary collisions/mergers or ejections. We study the spin property of the merger products of two giant planets in a statistical manner using numerical simulations and analytical modeling. Planetary collisions lead to rapidly rotating objects and a broad range of obliquities. We find that, under typical conditions for two-planet scatterings, the distributions of spin magnitude $S$ and obliquity $Θ_{\rm SL}$ of the merger products have simple analytical forms: $f_{S} \propto S$ and $f_{\cosΘ_{\rm S…
The obliquity of a planet is the tilt between its equator and its orbital plane. Giant planets are expected to form with near-zero obliquities. After its formation, some dynamical mechanism must therefore have tilted Saturn up to its current obliquity of 26.7°. This event is traditionally thought to have happened more than 4 Gyrs ago during the late planetary migration because of the crossing of a resonance between the spin-axis precession of Saturn and the nodal orbital precession mode of Neptune. Here, we show that the fast tidal migration of Titan measured by Lainey et al. (2020) is incompa…
Detached circumplanetary disks are unstable to tilting as a result of the stellar tidal potential. We examine how a tilted circumplanetary disk affects the evolution of the spin axis of an oblate planet. The disk is evolved using time-dependent equations for linear wave-like warp evolution, including terms representing the effect of the tidal potential and planetary oblateness. For a disk with a sufficiently large mass, we find that the planet spin quickly aligns to the misaligned disk. The tilt of the planetary spin axis then increases on the same timescale as the disk. This can be an efficie…
The Sun's equator and the planets' orbital planes are nearly aligned, which is presumably a consequence of their formation from a single spinning gaseous disk. For exoplanetary systems this well-aligned configuration is not guaranteed: dynamical interactions may tilt planetary orbits, or stars may be misaligned with the protoplanetary disk through chaotic accretion, magnetic interactions or torques from neighbouring stars. Indeed, isolated 'hot Jupiters' are often misaligned and even orbiting retrograde. Here we report an analysis of transits of planets over starspots on the Sun-like star Kepl…
Many exoplanets in close-in orbits are observed to have relatively high eccentricities and large stellar obliquities. We explore the possibility that these result from planet-planet scattering by studying the dynamical outcomes from a large number of orbit integrations in systems with two and three gas-giant planets in close-in orbits (0.05 AU < a < 0.15 AU). We find that at these orbital separations, unstable systems starting with low eccentricities and mutual inclinations ($e\lesssim0.1$, $i\lesssim0.1$) generally lead to planet-planet collisions in which the collision product is a planet on…
We present Rossiter-McLaughlin observations of WASP-13b and WASP-32b and determine the sky-projected angle between the normal of the planetary orbit and the stellar rotation axis ($λ$). WASP-13b and WASP-32b both have prograde orbits and are consistent with alignment with measured sky-projected angles of $λ={8^{\circ}}^{+13}_{-12}$ and $λ={-2^{\circ}}^{+17}_{-19}$, respectively. Both WASP-13 and WASP-32 have $T_{\mathrm{eff}}<6250$K and therefore these systems support the general trend that aligned planetary systems are preferentially found orbiting cool host stars. A Lomb-Scargle periodogram …
