The probability that an exoplanet transits its host star is high for planets in close orbits, but drops off rapidly for increasing semimajor axes. This makes transit surveys for planets with large semimajor axes orbiting bright stars impractical, since one would need to continuously observe hundreds of stars that are spread out over the entire sky. One way to make such a survey tractable is to constrain the inclination of the stellar rotation axes in advance, and thereby enhance the transit probabilities. We derive transit probabilities for stars with stellar inclination constraints, considering a reasonable range of planetary system inclinations. We find that stellar inclination constraints can improve the transit probability by almost an order of magnitude for habitable-zone planets. When applied to an ensemble of stars, such constraints dramatically lower the number of stars that need to be observed in a targeted transit survey. We also consider multiplanet systems where only one planet has an identified transit, and derive the transit probabilities for the second planet assuming a range of mutual planetary inclinations.
This paper considers whether the population of known transiting exoplanets provides evidence for additional outer planets on inclined orbits, due to the perturbing effect of such planets on the orbits of inner planets. As such, we develop a semi-analytical method for calculating the probability that two mutually inclined planets are observed to transit. We subsequently derive a simplified analytical form to describe how the mutual inclination between two planets evolves due to secular interactions with a wide orbit inclined planet and use this to determine the mean probability that the two inn…
The Rossiter-McLaughlin (RM) effect has been widely used to estimate the sky-projected spin-orbit angle, $λ$, of transiting planetary systems. Most of the previous analysis assume that the host stars are rigid rotators in which the amplitude of the RM velocity anomaly is proportional to $v_\star \sin i_\star$. When their latitudinal differential rotation is taken into account, one can break the degeneracy, and determine separately the equatorial rotation velocity $v_\star$ and the inclination $i_{\star}$ of the host star. We derive a fully analytic approximate formula for the RM effect adoptin…
Early analyses of exoplanet statistics from the Kepler Mission revealed that a model population of multiple-planet systems with low mutual inclinations (${\sim1^{\circ}-2^{\circ}}$) adequately describes the multiple-transiting systems but underpredicts the number of single-transiting systems. This so-called "Kepler dichotomy" signals the existence of a sub-population of multi-planet systems possessing larger mutual inclinations. However, the details of these inclinations remain uncertain. In this work, we derive constraints on the intrinsic mutual inclination distribution by statistically expl…
The {\it Kepler} mission has detected thousands of planetary systems with 1-7 transiting planets packed within 0.7~au from their host stars. There is an apparent excess of single-transit planet systems that cannot be explained by transit geometries alone, when a single planetary mutual inclination dispersion is assumed. This suggests that the observed compact planetary systems have at least two different architectures. We present a scenario where the "Kepler dichotomy" may be explained by the action of an external giant planet or stellar companion misaligned with the inner multi-planet system.…
A large proportion of transiting planetary systems appear to possess only a single planet as opposed to multiple transiting planets. This excess of singles is indicative of significant mutual inclinations existing within a large number of planetary systems, but the origin of these misalignments is unclear. Moreover, recent observational characterization reveals that mutual inclinations tend to increase with proximity to the host star. These trends are both consistent with the dynamical influence of a strong quadrupolar potential arising from the host star during its early phase of rapid rotati…
Transiting Extrasolar Planet with a Companion: Effects of Orbital Eccentricity and Inclination
在早期的出版物[Sato and Asada，PASJ，61，L29（2009）]中开始的继续工作，我们考虑了光变曲线受轨道倾角和轨道偏心率的影响，该轨道围绕凌日系外行星（在行星-卫星系统或假设的真双星中）。我们表明，半长轴，偏心率和倾角的一个“月亮”围绕主行星的轨道可以确定由过境方法单独。为此目的，我们提出了一个配方的参数确定在一个小偏心率近似以及在确切的形式。因此，半长轴可以用亮度变化、渡越时间和光变曲线的间隔等可观测量来表示。我们还讨论了一个狭窄的参数区域，产生一个太阳系外的卫星相互过境。
对任意倾角的三体问题中的共振捕获进行了数值研究。无质量的粒子被设置为从1：5共振之外与一颗质量为1000的行星漂移，从而遇到行星的不同平均运动共振的网络。随机构造的样本探索0至180度倾角的参数空间，增量为5度，总计近6x10^5个数值模拟。30个共振内部和外部的行星的位置进行监测。我们发现，逆行共振是出乎意料的更有效的捕获比逆行共振，共振顺序不一定是一个很好的指标，在任意倾角的捕获效率。捕获概率显着下降，在中等样本偏心度的初始倾角范围内[10度，110度]。轨道反演是可能的初始圆形轨道与倾角范围[60度，130度]。在1：1共轨共振中的捕获在大的逆行倾角时很可能发生。如果行星的轨道偏心率大于0.1，则通过偏心Kozai-Lidov机制的作用降低捕获概率。捕获的不对称性出现在内部和外部共振之间，因为被捕获的轨道优先被捕获在内部共振中。逆行共振的相对俘获效率表明，逆行轨道上的达摩克洛和半人马座小行星的动力学寿命必须明显大于逆行轨道上的动力学寿命，这意味着最近发现的逆行共振小行星2006 BZ 8，2008 SO 218，2009 QY 6和1999 LE 31（Morais和Nynui，2013，MNRAS 436，L30）可能是在外部巨行星之间徘徊的最古老的小天体之一。
The outer architectures of Kepler's compact systems of multiple transiting planets remain poorly constrained and few of these systems have lower bounds on the orbital distance of any massive outer planets. We infer a minimum orbital distance and upper limits on the inclination of a hypothetical Jovian-mass planet orbiting exterior to the six transiting planets at Kepler-11. Our constraints are derived from dynamical models together with observations provided by the Kepler mission. Firstly, the lack of transit timing variations (TTV) in the outermost transiting planet Kepler-11 g imply that the…
$π$ Men hosts a transiting super Earth ($P\approx6.27$ d, $m\approx4.82$ $M_{\oplus}$, $R\approx2.04$ $R_{\oplus}$) discovered by TESS and a cold Jupiter ($P\approx2093$ d, $m \sin I\approx10.02$ $M_{\rm{Jup}}$, $e\approx0.64$) discovered from radial velocity. We use Gaia DR2 and Hipparcos astrometry to derive the star's velocity caused by the orbiting planets and constrain the cold Jupiter's sky-projected inclination ($I_b=41-65^{\circ}$). From this we derive the mutual inclination ($ΔI$) between the two planets, and find that $49^{\circ}< ΔI < 131^{\circ}$ (1$σ$), and $28^{\circ} < ΔI < 152^…
WASP-148 is a recently announced extra-solar system harbouring at least two giant planets. The inner planet transits its host star. The planets travel on eccentric orbits and are near the 4:1 mean-motion resonance, which implies significant mutual gravitational interactions. In particular, this causes transit-timing variations of a few minutes, which were detected based on ground-based photometry. This made WASP-148 one of the few cases where such a phenomenon was detected without space-based photometry. Here, we present a self-consistent model of WASP-148 that takes into account the gravitati…
It is possible to learn about the orientation of a star's rotation axis by combining measurements of the star's rotation velocity ($v$) and its projection onto our line of sight ($v\sin i$). This idea has found many applications, including the investigation of the obliquities of stars with transiting planets. Here, we present a method for the probabilistic inference of the inclination of the star's rotation axis based on independent data sets that constrain $v$ and $v\sin i$. We also correct several errors and misconceptions that appear in the literature.
Compact multi-planet systems containing super-Earths or sub-Neptunes, commonly found around solar-type stars, may be surrounded by external giant planet or stellar companions, which can shape the architechture and observability of the inner systems. We present a comprehensive study on the evolution of the inner planetary system subject to the gravitational influence of an eccentric, misaligned outer perturber. Analytic results are derived for the inner planet eccentricities ($e_i$) and mutual inclination ($θ_{12}$) of the "2-planet + perturber" system, calibrated with numerical secular and N-b…
The recent characterization of transiting close-in planets has revealed an intriguing population of sub-Neptunes with highly tilted and even polar orbits relative to their host star's equator. Any viable theory for the origin of these close-in, polar planets must explain (1) the observed stellar obliquities, (2) the substantial eccentricities, and (3) the existence of Jovian companions with large mutual inclinations. In this work, we propose a theoretical model that satisfies these requirements without invoking tidal dissipation or large primordial inclinations. Instead, tilting is facilitated…
The angular momentum deficit (AMD) of a planetary system is a measure of its orbital excitation and a predictor of long-term stability. We adopt the AMD-stability criteria to constrain the orbital architectures for exoplanetary systems. Previously, He, Ford, & Ragozzine (2019) (arXiv:1907.07773v2) showed through forward modelling (SysSim) that the observed multiplicity distribution can be well reproduced by two populations consisting of a low and a high mutual inclination component. Here, we show that a broad distribution of mutual inclinations arising from systems at the AMD-stability limit c…
The giant impact phase of terrestrial planet formation establishes connections between super-Earths' orbital properties (semimajor axis spacings, eccentricities, mutual inclinations) and interior compositions (the presence or absence of gaseous envelopes). Using N-body simulations and analytic arguments, we show that spacings derive not only from eccentricities, but also from inclinations. Flatter systems attain tighter spacings, a consequence of an eccentricity equilibrium between gravitational scatterings, which increase eccentricities, and mergers, which damp them. Dynamical friction by res…
