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 $f_{\cosΘ_{\rm SL}} \propto (1-\cos^2Θ_{\rm SL})^{-1/2}$. Though parameter studies, we determine the regime of validity for the analytical distributions of spin and obliquity. Since planetary mergers is a major outcome of planet-planet scatterings, observational search for the spin/obliquity signatures of exoplanets would provide important constraints on the dynamical history of planetary systems.
In the search for life beyond our Solar system, attention should be focused on those planets that have the potential to maintain habitable conditions over the prolonged periods of time needed for the emergence and expansion of life as we know it. The observable planetary architecture is one of the determinants for long-term habitability as it controls the orbital evolution and ultimately the stellar fluxes received by the planet. With an ensemble of n-body simulations and obliquity models of hypothetical planetary systems, we demonstrate that the amplitude and period of eccentricity, obliquity…
Planetary obliquity is a first order control on planetary climate and seasonal contrast, which has a number of cascading consequences for life. How moderately high obliquity (obliquities greater than Earth's current obliquity up to 45$^{\circ}$) affects a planet's surface physically has been studied previously, but we lack an understanding of how marine life will respond to these conditions. We couple the ROCKE-3D general circulation model to the cGENIE 3D biogeochemical model to simulate the ocean biosphere's response to various planetary obliquities, bioessential nutrient inventories, and bi…
Obliquity variability could play an important role in the climate and habitability of a planet. Orbital modulations caused by planetary companions and the planet's spin axis precession due to the torque from the host star may lead to resonant interactions and cause large-amplitude obliquity variability. Here we consider the spin axis dynamics of Kepler-62f and Kepler-186f, both of which reside in the habitable zone around their host stars. Using {\emph{N}}-body simulations and secular numerical integrations, we describe their obliquity evolution for particular realizations of the planetary sys…
We show that the existence of prograde equatorial satellites is consistent with a collisional tilting scenario for Uranus. In fact, if the planet was surrounded by a proto-satellite disk at the time of the tilting and a massive ring of material was temporarily placed inside the Roche radius of the planet by the collision, the proto-satellite disk would have started to precess incoherently around the equator of the planet, up to a distance greater than that of Oberon. Collisional damping would then have collapsed it into a thin equatorial disk, from which the satellites eventually formed. The f…
The Kepler mission and its successor K2 have brought forth a cascade of transiting planets. Many of these planetary systems exhibit multiple members, but a large fraction possess only a single transiting example. This overabundance of singles has lead to the suggestion that up to half of Kepler systems might possess significant mutual inclinations between orbits, reducing the transiting number (the so-called "Kepler Dichotomy"). In a recent paper, Spalding & Batygin (2016) demonstrated that the quadrupole moment arising from a young, oblate star is capable of misaligning the constituent orbits…
The obliquity of a terrestrial planet is an important clue about its formation and critical to its climate. Previous studies using simulated photometry of Earth show that continuous observations over most of a planet's orbit can be inverted to infer obliquity. However, few studies of more general planets with arbitrary albedo markings have been made and, in particular, a simple theoretical understanding of why it is possible to extract obliquity from light curves is missing. Reflected light seen by a distant observer is the product of a planet's albedo map, its host star's illumination, and th…
We constrain the angular momentum architecture of HD 106906, a 13 $\pm$ 2 Myr old system in the ScoCen complex composed of a compact central binary, a widely separated planetary-mass tertiary HD 106906 b, and a debris disk nested between the binary and tertiary orbital planes. We measure the orientations of three vectors: the companion spin axis, companion orbit normal, and disk normal. Using near-IR high-resolution spectra from Gemini/IGRINS, we obtain a projected rotational velocity of $v\sin{i_p}$ = 9.5 $\pm$ 0.2 km/s for HD 106906 b. This measurement together with a published photometric r…
Changes in planetary obliquity, or axial tilt, influence the climates on Earth-like planets. In the solar system, the Earth's obliquity is stabilized due to interactions with our moon and the resulting {small amplitude variations ($\sim$2.4\degree)} are beneficial for advanced life. Most Sun-like stars have at least one stellar companion and the habitability of circumstellar exoplanets is shaped by their stellar companion. We show that a stellar companion can dramatically change whether {Earth-like obliquity stability is} possible through planetary orbital precession relative to the binary orb…
We present a three-species (H$^+$, O$^+$ and e$^-$) multi-fluid magnetohydrodynamic (MHD) model, endowed with the requisite upper atmospheric chemistry, that is capable of accurately quantifying the magnitude of oxygen ion losses from "Earth-like" exoplanets in habitable zones, whose magnetic and rotational axes are roughly coincidental with one another. We apply this model to investigate the role of planetary obliquity in regulating atmospheric losses from a magnetic perspective. For Earth-like exoplanets orbiting solar-type stars, we demonstrate that the dependence of the total atmospheric i…
The spin-orbit obliquity of a planetary system constraints its formation history. A large obliquity may either indicate a primordial misalignment between the star and its gaseous disk or reflect the effect of different mechanisms tilting planetary systems after formation. Observations and statistical analysis suggest that system of planets with sizes between 1 and 4 R$_{\oplus}$ have a wide range of obliquities ($\sim0-30^{\circ}$), and that single- and multi-planet transiting have statistically indistinguishable obliquity distributions. Here, we revisit the ``breaking the chains'' formation m…
Small, rocky planets have been found orbiting in extreme proximity to their host stars, sometimes down to only $\sim 2$ stellar radii. These ultra-short-period planets (USPs) likely did not form in their present-day orbits, but rather migrated from larger initial separations. While tides are the probable cause of this migration, the tidal source has remained uncertain. Here we introduce planetary obliquity tides as a natural pathway for the production of USPs within close-in multi-planet systems. The crucial idea is that tidal dissipation generally forces planetary spin vectors to equilibrium …
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…
We explore the impact of obliquity variations on planetary habitability in hypothetical systems with high mutual inclination. We show that large amplitude, high frequency obliquity oscillations on Earth-like exoplanets can suppress the ice-albedo feedback, increasing the outer edge of the habitable zone. We restrict our exploration to hypothetical systems consisting of a solar-mass star, an Earth-mass planet at 1 AU, and 1 or 2 larger planets. We verify that these systems are stable for $10^8$ years with N-body simulations, and calculate the obliquity variations induced by the orbital evolutio…
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…
We present new transit observations of the hot Jupiter WASP-74 b ($T_\mathrm{eq} \sim$ 1860 K) using the high-resolution spectrograph HARPS-N and the multi-colour simultaneous imager MuSCAT2. We refine the orbital properties of the planet and its host star, and measure its obliquity for the first time. The measured sky-projected angle between the stellar spin-axis and the planet's orbital axis is compatible with an orbit well-aligned with the equator of the host star ($λ= 0.77\pm0.99 \mathrm{deg}$). We are not able to detect any absorption feature of H$α$, or any other atomic spectral features…
Detailed observational characterization of transiting exoplanet systems has revealed that the spin-axes of massive (M > ~1.2 solar masses) stars often exhibit substantial misalignments with respect to the orbits of the planets they host. Conversely, lower-mass stars tend to only have limited obliquities. A similar trend has recently emerged within the observational dataset of young stars' magnetic field strengths: massive T-Tauri stars tend to have dipole fields that are ~10 times weaker than their less-massive counterparts. Here we show that the associated dependence of magnetic star-disk tor…
We study the effects of planetary late migration on the gas giants obliquities. We consider the planetary instability models from Nesvorny & Morbidelli (2012), in which the obliquities of Jupiter and Saturn can be excited when the spin-orbit resonances occur. The most notable resonances occur when the $s_7$ and $s_8$ frequencies, changing as a result of planetary migration, become commensurate with the precession frequencies of Jupiter's and Saturn's spin vectors. We show that Jupiter may have obtained its present obliquity by crossing of the $s_8$ resonance. This would set strict constrains o…
We place the first constraints on the obliquity of a planetary-mass companion (PMC) outside of the Solar System. Our target is the directly imaged system 2MASS J01225093-2439505 (2M0122), which consists of a 120 Myr 0.4 M_sun star hosting a 12-27 M_J companion at 50 AU. We constrain all three of the system's angular momentum vectors: how the companion spin axis, the stellar spin axis, and the orbit normal are inclined relative to our line of sight. To accomplish this, we measure projected rotation rates (vsini) for both the star and the companion using new near-infrared high-resolution spectra…
We aim to revisit the system AB Pic which has a known companion at the exoplanet/ brown-dwarf boundary. We based this study on a rich set of observations to investigate the companion's orbit and atmosphere. We composed a spectrum of AB Pic b merging archival VLT/SINFONI K-band data, with published spectra at J and H-band (SINFONI) and Lp-band (Magellan-AO), and photometric measurements (HST and Spitzer). We modeled the spectrum with ForMoSA, based on two atmospheric models: ExoREM and BT-SETTL13. We determined the orbital properties of b fitting the astrometric measurements from NaCo (2003 and…
We consider the time-frequency analysis of a scattered light curve of a directly imaged exoplanet. We show that the geometric effect due to planetary obliquity and orbital inclination induce the frequency modulation of the apparent diurnal periodicity. We construct a model of the frequency modulation and compare it with the instantaneous frequency extracted from the pseudo-Wigner distribution of simulated light curves of a cloudless Earth. The model provides good agreement with the simulated modulation factor, even for the light curve with Gaussian noise comparable to the signal. Notably, the …
The stellar spin orientation relative to the orbital planes of multiplanet systems are becoming accessible to observations. For example, 55 Cancri is a system composed of 5 planets orbiting a member of a stellar binary for which a projected obliquity of 72+-12 deg relative to the orbit of the innermost planet has been reported (Bourrier & Hebrard 2014). This large obliquity has been attributed to the perturbation induced by the binary. Here we describe the secular evolution of similar systems and we discuss the case of the 55 Cancri system more deeply. We provide two different orbital configur…
We present seventeen high-precision light curves of five transits of the planet Qatar-2b, obtained from four defocussed 2m-class telescopes. Three of the transits were observed simultaneously in the SDSS griz passbands using the seven-beam GROND imager on the MPG/ESO 2.2-m telescope. A fourth was observed simultaneously in Gunn grz using the CAHA 2.2-m telescope with BUSCA, and in r using the Cassini 1.52-m telescope. Every light curve shows small anomalies due to the passage of the planetary shadow over a cool spot on the surface of the host star. We fit the light curves with the prism+gemc m…
Many Sun-like stars are observed to host close-in super-Earths (SEs) as part of a multi-planetary system. In such a system, the spin of the SE evolves due to spin-orbit resonances and tidal dissipation. In the absence of tides, the planet's obliquity can evolve chaotically to large values. However, for close-in SEs, tidal dissipation is significant and suppresses the chaos, instead driving the spin into various steady states. We find that the attracting steady states of the SE's spin are more numerous than previously thought, due to the discovery of a new class of "mixed-mode" high-obliquity e…
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 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…
A Hamiltonian model is constructed for the spin axis of a planet perturbed by a nearby planet with both planets in orbit about star. We expand the planet-planet gravitational potential perturbation to first order in orbital inclinations and eccentricities, finding terms describing spin resonances involving the spin precession rate and the two planetary mean motions. Convergent planetary migration allows the spinning planet to be captured into spin resonance. With initial obliquity near zero, the spin resonance can lift the planet's obliquity to near 90 or 180 degrees depending upon whether the…
Mapping the orbital obliquity distribution of young planets is one avenue towards understanding mechanisms that sculpt the architectures of planetary systems. TOI-942 is a young field star, with an age of ~60 Myr, hosting a planetary system consisting of two transiting Neptune-sized planets in 4.3- and 10.1-day period orbits. We observed the spectroscopic transits of the inner Neptune TOI-942b to determine its projected orbital obliquity angle. Through two partial transits, we find the planet to be in a prograde orbit, with a projected obliquity angle of |lambda| = 1/+41-33 deg. In addition, i…
We have detected the Rossiter-Mclaughlin effect during a transit of WASP-47b, the only known hot Jupiter with close planetary companions. By combining our spectroscopic observations with Kepler photometry, we show that the projected stellar obliquity is $λ= 0^\circ \pm 24^\circ$. We can firmly exclude a retrograde orbit for WASP-47b, and rule out strongly misaligned prograde orbits. Low obliquities have also been found for most of the other compact multiplanet systems that have been investigated. The Kepler-56 system, with two close-in gas giants transiting their subgiant host star with an obl…
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…
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…
Exoplanet discoveries over recent years have shown that terrestrial planets are exceptionally common. Many of these planets are in compact systems that result in complex orbital dynamics. A key step toward determining the surface conditions of these planets is understanding the latitudinally dependent flux incident at the top of the atmosphere as a function of orbital phase. The two main properties of a planet that influence the time-dependent nature of the flux are the obliquity and orbital eccentricity of the planet. We derive the criterion for which the flux variation due to obliquity is eq…
An Earth-analog orbiting within the habitable zone of $α$ Centauri B was shown to undergo large variations in its obliquity, or axial tilt, which affects the planetary climate by altering the radiative flux for a given latitude. We examine the potential implications of these obliquity variations for climate through Milankovitch cycles using an energy balance model with ice sheets. Similar to previous studies, the largest amplitude obliquity variations from spin-orbit resonances induce snowball states within the habitable zone, while moderate variations can allow for persistent ice caps or an i…
The stellar obliquity of a transiting planetary system can be constrained by combining measurements of the star's rotation period, radius, and projected rotational velocity. Here we present a hierarchical Bayesian technique for recovering the obliquity distribution of a population of transiting planetary systems, and apply it to a sample of 70 Kepler Objects of Interest. With ~95% confidence we find that the obliquities of stars with only a single detected transiting planet are systematically larger than those with multiple detected transiting planets. This suggests that a substantial fraction…
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…
The KPF-SLOPE Survey - Small, Compact Multi-Planet Systems Appear Spin-Orbit Aligned
California Institute of Technology（加州理工学院）；University of Hawai‘i（夏威夷大学）；Flatiron Institute（平顿研究所）；University of California Berkeley（加州大学伯克利分校）；University of Sydney（悉尼大学）
In transiting planetary systems, the angle between the orbital angular momentum and the stellar spin is usually constrained through the Rossiter-McLaughlin effect observed in radial velocity and can be subject to large uncertainties, especially for hot stars (T_eff > 6250 K). It is thus interesting to have an alternative method to constrain the value of the obliquity and to detect companions that might have disturbed the orbit of the planet. We show how the long-term variations in the transit duration (TDV) can be used to constrain the obliquity of the stellar rotation axis. We introduce a sim…
Recent analyses have revealed a mystery. The orbital period of the highly inflated hot Jupiter, WASP-12b, is decreasing rapidly. The rate of inspiral, however, is too fast to be explained by either eccentricity tides or equilibrium stellar tides. While dynamical stellar tides are possible, they require a subgiant structure for the star, whereas stellar models point toward a main sequence host. Here, we show that these hitherto irreconcilable observations might be explained by planetary obliquity tides if planet b's spin vector is trapped in a high-obliquity state maintained by a secular spin-o…
A General, Differentiable Transit Model for Ellipsoidal Occulters: Derivation, Application, and Forecast of Planetary Oblateness and Obliquity Constraints with JWST
Kepler-56 is a multi-planet system containing two coplanar inner planets that are in orbits misaligned with respect to the spin axis of the host star, and an outer planet. Various mechanisms have been proposed to explain the broad distribution of spin-orbit angles among exoplanets, and these theories fall under two broad categories. The first is based on dynamical interactions in a multi-body system, while the other assumes that disk migration is the driving mechanism in planetary configuration and that the star (or disk) is titled with respect to the planetary plane. Here we show that the lar…
Tidal coplanarization of circumbinary planetary systems through stellar Cassini states
School of Astronomy and Space Science, Nanjing University（南京大学天文与空间科学学院）；Key Laboratory of Modern Astronomy and Astrophysics in Ministry of Education, Nanjing University（南京大学现代天文与天体物理教育部重点实验室）
Scattered lights from terrestrial exoplanets provide valuable information about the planetary surface. Applying the surface reconstruction method proposed by Fujii et al. (2010) to both diurnal and annual variations of the scattered light, we develop a reconstruction method of land distribution with both longitudinal and latitudinal resolutions. We find that one can recover a global map of an idealized Earth-like planet on the following assumptions: 1) cloudless, 2) a face-on circular orbit, 3) known surface types and their reflectance spectra 4) no atmospheric absorption, 5) known rotation ra…
Direct-imaging techniques of exoplanets have made significant progress recently, and will eventually enable to monitor photometric and spectroscopic signals of earth-like habitable planets in the future. The presence of clouds, however, would remain as one of the most uncertain components in deciphering such direct-imaged signals of planets. We attempt to examine how the planetary obliquity produce different cloud patterns by performing a series of GCM (General Circulation Model) simulation runs using a set of parameters relevant for our Earth. Then we use the simulated photometric lightcurves…
We investigate the obliquity and spin period of Earth-Moon like systems after 4.5 Gyr of tidal evolution with various satellite masses and initial planetary obliquity and discuss their relations to the habitability of the planet. We find three possible outcomes: either i) the system is still evolving, ii) the system is double synchronous or iii) the satellite has collided with the planet. The transition between case i) and ii) is abrupt and occurs at slightly larger satellite mass ($m_s \sim 0.02m_p$) than the lunar mass. We suggest that cases ii) and iii) are less habitable than case i). Usin…
Inspired by the close-proximity pair of planets in the Kepler-36 system, we consider two effects that may have important ramifications for the development of life in similar systems where a pair of planets may reside entirely in the habitable zone of the hosting star. Specifically, we run numerical simulations to determine whether strong, resonant (or non-resonant) planet-planet interactions can cause large variations in planet obliquity---thereby inducing large variations in climate. We also determine whether or not resonant interactions affect the rate of lithopanspermia between the planet p…
Previous studies have shown that planets that rotate retrograde (backwards with respect to their orbital motion) generally experience less severe obliquity variations than those that rotate prograde (the same direction as their orbital motion). Here we examine retrograde-rotating planets on eccentric orbits and find a previously unknown secular spin-orbit resonance that can drive significant obliquity variations. This resonance occurs when the frequency of the planet's rotation axis precession becomes commensurate with an orbital eigenfrequency of the planetary system. The planet's eccentricit…
We introduce our new code, SMERCURY-T, which is based on existing codes SMERCURY (Lissauer et al. 2012) and Mercury-T (Bolmont et al. 2015). The result is a mixed-variable symplectic N-body integrator that can compute the orbital and spin evolution of a planet within a multi-planet system under the influence of tidal spin torques from its star. We validate our implementation by comparing our experimental results to that of a secular model. As we demonstrate in a series of experiments, SMERCURY-T allows for the study of secular spin-orbit resonance crossings and captures for planets within comp…
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 …
Using radial-velocity data from the Habitable-zone Planet Finder, we have measured the mass of the Neptune-sized planet K2-25b, as well as the obliquity of its M4.5-dwarf host star in the 600-800MYr Hyades cluster. This is one of the youngest planetary systems for which both of these quantities have been measured, and one of the very few M dwarfs with a measured obliquity. Based on a joint analysis of the radial velocity data, time-series photometry from the K2 mission, and new transit light curves obtained with diffuser-assisted photometry, the planet's radius and mass are $3.44\pm 0.12 \math…
