Since the discovery of the first exoplanets, those most adequate for life to begin and evolve have been sought. Due to observational bias, however, most of the discovered planets so far are gas giants, precluding their habitability. However, if these hot Jupiters are located in the habitable zones of their host stars, and if rocky moons orbit them, then these moons may be habitable. In this work, we present a model for planetary transit simulation considering the presence of moons and planetary rings around a planet. The moon's orbit is considered to be circular and coplanar with the planetary orbit. The other physical and orbital parameters of the star, planet, moon, and rings can be adjusted in each simulation. It is possible to simulate as many successive transits as desired. Since the presence of spots on the surface of the star may produce a signal similar to that of the presence of a moon, our model also allows for the inclusion of starspots. The result of the simulation is a light curve with a planetary transit. White noise may also be added to the light curves to produce curves similar to those obtained by the CoRoT and Kepler space telescopes. The goal is to determine the criteria for detectability of moons and/or ring systems using photometry. The results show that it is possible to detect moons with radii as little as 1.3 R$_{\oplus}$ with CoRoT and 0.3 R_{\oplus}$ with Kepler.
Gas giant planets in the Solar system host large satellite systems with multiple regular and irregular moons. Regular moons revolve around their host planet in circular, low inclination short period orbits, and are thought to form in-situ through coagulation processes. In contrast, irregular moons have highly inclined (and even retrograde), typically eccentric and long period orbits around their host planet. Irregular moons are therefore often thought to be unbound objects in helio-centric orbits that were later captured to their current orbits around the planet. Here we study the a different …
We examine the effects that planetary encounters have on the moon systems of ejected gas giant planets. We conduct a suite of numerical simulations of planetary systems containing three Jupiter-mass planets (with the innermost planet at 3 AU) up to the point where a planet is ejected from the system. The ejected planet has an initial system of 100 test-particle moons. We determine the survival probability of moons at different distances from their host planet, measure the final distribution of orbital elements, examine the stability of resonant configurations, and characterize the properties o…
A planetary mass scale and a system of composition codes are presented for describing the geophysical characteristics of exoplanets and Solar System planets, dwarf planets, and spherical moons. The composition classes characterize the rock, ice, and gas properties of planetary bodies. The planetary mass scale includes five mass classes with upper and lower mass limits derived from recent studies of the exoplanet mass radius and mass density relationships and the physical characteristics of planets, dwarf planets, and spherical moons in the Solar System. The combined mass and composition codes …
Tidal force plays an important role in the evolution of the planet-moon system. The tidal force of a moon can excite seismic waves in the planet it is orbiting. A tidal-seismic resonance is expected when a tidal force frequency matches a free-oscillation frequency of the planet. Here we show that when the moon is close to the planet, the tidal-seismic resonance can cause large-amplitude seismic waves, which can change the shape of the planet and in turn exert a negative torque on the moon to cause it to fall rapidly toward the planet. We postulate that the tidal-seismic resonance may be an imp…
We formulated tidal decay lifetimes for hypothetical moons orbiting extrasolar planets with both lunar and stellar tides. Previous work neglected the effect of lunar tides on planet rotation, and are therefore applicable only to systems in which the moon's mass is much less than that of the planet. This work, in contrast, can be applied to the relatively large moons that might be detected around newly-discovered Neptune-mass and super-Earth planets. We conclude that moons are more stable when the planet/moon systems are further from the parent star, the planets are heavier, or the parent stars…
We investigate the properties of microlensing events caused by planetary systems where planets with a moon are widely separated from their host stars. From this investigation, we find that the moon feature generally appears as an very short-duration perturbation on the smooth asymmetric light curve of the lensing event induced by the wide separation planet; thus it can be easily discriminated from the planet feature responsible for the overall asymmetric light curve. For typical Galactic lensing events with the Einstein radius of $\sim 2$ AU, the asymmetry of the light curves due to bound plan…
All 4 giant planets in the Solar System host systems of multiple moons, whereas the terrestrial planets only host up to 2 moons. The Earth can capture small asteroids as temporary satellites, which begs the question as to how many moons could stably orbit the Earth, or an Earth-mass exoplanet. We perform a series of N-body simulations of closely-spaced equal mass moons in nested orbits around an Earth-mass planet orbiting a Sun-like star. The innermost moon begins near the host planets Roche radius, and the system is packed until the outermost moon begins near the stability limit for single mo…
Planet-planet scattering is the leading mechanism to explain the broad eccentricity distribution of observed giant exoplanets. Here we study the orbital stability of primordial giant planet moons in this scenario. We use N-body simulations including realistic oblateness and evolving spin evolution for the giant planets. We find that the vast majority (80-90% across all our simulations) of orbital parameter space for moons is destabilized. There is a strong radial dependence, as moons past 0.1 Hill radii are systematically removed. Closer-in moons on Galilean-moon-like orbits (< 0.04 Hill radii…
The detectability of moons of extra-solar planets is investigated, focussing on the time-of-arrival perturbation technique, a method for detecting moons of pulsar planets, and the photometric transit timing technique, a method for detecting moons of transiting planets. Realistic thresholds are derived and analysed in the in the context of the types of moons that are likely to form and be orbitally stable for the lifetime of the system. For the case of the time-of-arrival perturbation technique, the analysis is conducted in two stages. First, a preliminary investigation is conducted assuming th…
Most of the exoplanets with known masses at Earth-like distances to Sun-like stars are heavier than Jupiter, which raises the question of whether such planets are accompanied by detectable, possibly habitable moons. Here we simulate the accretion disks around super-Jovian planets and find that giant moons with masses similar to Mars can form. Our results suggest that the Galilean moons formed during the final stages of accretion onto Jupiter, when the circumjovian disk was sufficiently cool. But in contrast to other studies, with our assumptions, we show that Jupiter was still feeding from the…
Irregular moons are a class of satellite found orbiting all of the Solar System's giant planets: as their orbits don't match those of their planets, they are theorised to have formed elsewhere in the Solar System and were subsequently captured into their observed orbits. Missions such as Cassini have contributed significant empirical data on irregular moons in the present day but this paper aims to develop our currently limited theoretical understanding of their origins and capture as it presents one of the first projects to connect moon capture with another feature common to all giant planets…
Beyond Earth-like planets, moons can be habitable, too. No exomoons have been securely detected, but they could be extremely abundant. Young Jovian planets can be as hot as late M stars, with effective temperatures of up to 2000 K. Transits of their moons might be detectable in their infrared photometric light curves if the planets are sufficiently separated ($\gtrsim10$ AU) from the stars to be directly imaged. The moons will be heated by radiation from their young planets and potentially by tidal friction. Although stellar illumination will be weak beyond 5 AU, these alternative energy sourc…
Compared to the giant planets in the solar system, exoplanets have many remarkable properties such as the prevalence of giant planets on eccentric orbits and the presence of hot Jupiters. Planet-planet scattering (PPS) between giant planets is a possible mechanism in interpreting above and other observed properties. If the observed giant planet architectures are indeed the outcomes of PPS, such drastic dynamical process must affect their primordial moon systems. In this Letter, we discuss the effect of the PPS on the survival of their regular moons. From the viewpoint of observations, some pre…
We show that the fate of moons of a close-in giant planet is mainly determined by the migration history of the planet in the protoplanetary disk. As the planet migrates in the disk from beyond the snow line towards a multi-day period orbit, the formed and forming moons become unstable as the planet's sphere of influence shrinks. Disk-driven migration is faster than the moons' tidal orbital evolution. Moons are eventually ejected from around close-in exoplanets or forced into collision with them before tides from the star affect their orbits. If moons are detected around close-in exoplanets, th…
Understanding the Moon's formation mechanism is necessary for studying not only the Moon itself, but also the evolution, formation, habitability, and structure of other planets and the moons in the Solar system and in extrasolar planetary systems. In this paper, I suggest a mechanism of the Moon formation. I posit that the Moon came into existence from the same gaseous cloud that the Earth originated from. The paper concludes that the moons can only form at the time of planet formation in a parallel and simultaneous process, and the new moons cannot form in a grown up Solar system. The Earth-M…
It has been previously shown that moons of extrasolar planets may be detectable with the Kepler Mission, for moon masses above ~0.2 Earth masses Kipping et al. 2009c. Transit timing effects have been formerly identified as a potent tool to this end, exploiting the dynamics of the system. In this work, we explore the simulation of transit light curves of a planet plus a single moon including not only the transit timing effects but also the light curve signal of the moon itself. We introduce our new algorithm, LUNA, which produces transit light curves for both bodies, analytically accounting for…
One of the primary surprises of exoplanet detections has been the discovery of compact planetary systems, whereby numerous planets reside within ~0.5 AU of the host star. Many of these kinds of systems have been discovered in recent years, indicating that they are fairly common orbital architecture. Of particular interest are those systems for which the host star is low-mass, thus potentially enabling one or more of the planets to lie within the Habitable Zone of the host star. One of the contributors to the habitability of the Earth is the presence of a substantial moon whose tidal effects ca…
The geometric arrangement of planet and moon orbits into a regularly spaced pattern of distances is the result of a self-organizing system. The positive feedback mechanism that operates a self-organizing system is accomplished by harmonic orbit resonances, leading to long-term stable planet and moon orbits in solar or stellar systems. The distance pattern of planets was originally described by the empirical Titius-Bode law, and by a generalized version with a constant geometric progression factor (corresponding to logarithmic spacing). We find that the orbital periods $T_i$ and planet distance…
Jupiter and Saturn play host to an impressive array of satellites, making it reasonable to suspect that similar systems of moons might exist around giant extrasolar planets. Furthermore, a significant population of such planets is known to reside at distances of several Astronomical Units (AU), leading to speculation that some moons thereof might support liquid water on their surfaces. However, giant planets are thought to undergo inward migration within their natal protoplanetary disks, suggesting that gas giants currently occupying their host star's habitable zone formed further out. Here we…
We demonstrate that habitable Earth-mass planets and moons can exist in the Kepler-16 system, known to host a Saturn-mass planet around a stellar binary, by investigating their orbital stability in the standard and extended habitable zone (HZ). We find that Earth-mass planets in satellite-like (S-type)orbits are possible within the standard HZ in direct vicinity of Kepler-16b, thus constituting habitable exomoons. However, Earth-mass planets cannot exist in planetary-like (P-type) orbits around the two stellar components within the standard HZ. Yet, P-type Earth-mass planets can exist superior…
The hydrostatic equilibrium of multi-layer bodies lacks a satisfactory theoretical treatment despite its wide range of applicability. Here we show that by using the exact analytical potential of homogeneous ellipsoids we can obtain recursive analytical solutions and an exact numerical method for the hydrostatic equilibrium shape problem of multi-layer planets and synchronous moons. The recursive solutions rely on the series expansion of the potential in terms of the polar and equatorial shape eccentricities, while the numerical method uses the exact potential expression. These solutions can be…
The four major satellites of Jupiter, known as the Galilean moons, and Saturn's most massive satellite, Titan, are believed to have formed in a predominantly gaseous circum-planetary disk, during the last stages of formation of their parent planet. Pebbles from the protoplanetary disk are blocked from flowing into the circumplanetary disk by the positive pressure gradient at the outer edge of the planetary gap, so the gas drag assisted capture of planetesimals should be the main contributor to the delivery of solids onto circum-planetary disks. However, a consistent framework for the subsequen…
[Abridged] We present an extensive suite of terrestrial planet formation simulations that allows quantitative analysis of the stochastic late stages of planet formation. We quantify the feeding zone width, Delta a, as the mass-weighted standard deviation of the initial semi-major axes of the planetary embryos and planetesimals that make up the final planet. The size of a planet's feeding zone in our simulations does not correlate with its final mass or semi-major axis, suggesting there is no systematic trend between a planet's mass and its volatile inventory. Instead, we find that the feeding …
Given the interest in future space missions devoted to the exploration of key moons in the solar system and that may involve libration point orbits, an efficient design strategy for transfers between moons is introduced that leverages the dynamics in these multi-body systems. The moon-to-moon analytical transfer (MMAT) method is introduced, comprised of a general methodology for transfer design between the vicinities of the moons in any given system within the context of the circular restricted three-body problem, useful regardless of the orbital planes in which the moons reside. A simplified …
The Earth's comparatively massive moon, formed via a giant impact on the proto-Earth, has played an important role in the development of life on our planet, both in the history and strength of the ocean tides and in stabilizing the chaotic spin of our planet. Here we show that massive moons orbiting terrestrial planets are not rare. A large set of simulations by Morishima et al., 2010, where Earth-like planets in the habitable zone form, provides the raw simulation data for our study. We use limits on the collision parameters that may guarantee the formation of a circumplanetary disk after a p…
We survey the methods proposed in the literature for detecting moons of extrasolar planets in terms of their ability to distinguish between prograde and retrograde moon orbits, an important tracer of moon formation channel. We find that most moon detection methods, in particular, sensitive methods for detecting moons of transiting planets, cannot observationally distinguishing prograde and retrograde moon orbits. The prograde and retrograde cases can only be distinguished where dynamical evolution of the orbit due to e.g. three body effects is detectable, where one of the two cases is dynamica…
Current lunar origin scenarios suggest that Earth's Moon may have resulted from the merger of two (or more) smaller moonlets. Dynamical studies of multiple moons find that these satellite systems are not stable, resulting in moonlet collision or loss of one or more of the moonlets. We perform Smoothed Particle Hydrodynamic (SPH) impact simulations of two orbiting moonlets inside the planetary gravitational potential and find that the classical outcome of two bodies impacting in free space is altered as erosive mass loss is more significant with decreasing distance to the planet. Depending on t…
We investigate how the variation of the obliquity (the axial tilt) of a hypothetical exo-Earth is effected by the presence of a satellite, an exo-Moon. Namely, we study analytically and numerically how the range of obliquity of the exo-Earth changes if an exo-Moon is added to a system comprised of exo-Sun, exo-Earth and exo-planets. We say that the impact of the exo-Moon is stabilising if upon the addition of the exo-Moon the range of obliquity decreases, while we call the impact destabilising if the range increases as the exo-Moon is added to the system. The problem is considered in a general…
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）
Large surface temperatures on the illuminated hemisphere of the Moon can lead it to contribute a significant amount of flux to spatially unresolved infrared (IR) observations of the Earth-Moon system, especially at wavelengths where Earth's atmosphere is absorbing. We have paired the NASA Astrobiology Institute's Virtual Planetary Laboratory three-dimensional spectral Earth model with a model of the phase dependent IR spectrum of a Moonlike satellite to investigate the effects of an unresolved companion on IR observations of Earthlike extrasolar planets. For an extrasolar twin Earth-Moon syste…
Most of the properties of the Earth-Moon system can be explained by a collision between a planetary embryo and the growing Earth late in the accretion process. Simulations show that most of the material that eventually aggregates to form the Moon originates from the impactor. However, analysis of the terrestrial and lunar isotopic composition show them to be highly similar. In contrast, the compositions of other solar system bodies are significantly different than the Earth and Moon. This poses a major challenge to the giant impact scenario since the Moon-forming impactor is then thought to al…
The co-planarity of solar-system planets led Kant to suggest that they formed from an accretion disk, and the discovery of hundreds of such disks around young stars as well as hundreds of co-planar planetary systems by the Kepler satellite demonstrate that this formation mechanism is extremely widespread. Many moons in the solar system, such as the Galilean moons of Jupiter, also formed out of the accretion disks that coalesced into the giant planets. We report here the discovery of an intermediate system OGLE-2013-BLG-0723LB/Bb composed of a Venus-mass planet orbiting a brown dwarf, which may…
The moons of giant planets are believed to form in situ in Circumplanetary Discs (CPDs). Here we present an N-body population synthesis framework for satellite formation around a Jupiter-like planet, in which the dust-to-gas ratio, the accretion rate of solids from the Protoplanetary Disc, the number, and the initial positions of protosatellites were randomly chosen from realistic distributions. The disc properties were from 3D radiative simulations sampled in 1D and 2D grids and evolved semi-analytically with time. The N-body satellitesimals accreted mass from the dust component of the disc, …
The Kepler space telescope has detected transits of objects as small as the Earth's Moon, and moons as small as 0.2 Earth masses can be detected in the Kepler data by transit timing and transit duration variations of their host planets. Such massive moons around giant planets in the stellar habitable zone (HZ) could serve as habitats for extraterrestrial life. We here assess the danger of exomoons to be in a runaway greenhouse (RG) state due to extensive heating from the planet. We apply pre-computed evolution tracks for giant planets to calculate the incident planetary radiation on the moon a…
We present two methods to determine an exomoon's sense of orbital motion (SOM), one with respect to the planet's circumstellar orbit and one with respect to the planetary rotation. Our simulations show that the required measurements will be possible with the European Extremely Large Telescope (E-ELT). The first method relies on mutual planet-moon events during stellar transits. Eclipses with the moon passing behind (in front of) the planet will be late (early) with regard to the moon's mean orbital period due to the finite speed of light. This "transit timing dichotomy" (TTD) determines an exo…
We evaluate gravitational lensing as a technique for the detection of extrasolar moons. Since 2004 gravitational microlensing has been successfully applied as a detection method for extrasolar planets. In principle, the method is sensitive to masses as low as an Earth mass or even a fraction of it. Hence it seems natural to investigate the microlensing effects of moons around extrasolar planets. We explore the simplest conceivable triple lens system, containing one star, one planet and one moon. From a microlensing point of view, this system can be modelled as a particular triple with hierarch…
The gas giant planets in the Solar System have a retinue of icy moons, and we expect giant exoplanets to have similar satellite systems. If a Jupiter-like planet were to migrate toward its parent star the icy moons orbiting it would evaporate, creating atmospheres and possible habitable surface oceans. Here, we examine how long the surface ice and possible oceans would last before being hydrodynamically lost to space. The hydrodynamic loss rate from the moons is determined, in large part, by the stellar flux available for absorption, which increases as the giant planet and icy moons migrate cl…
The Cassini spacecraft discovered a propeller-shaped structure in Saturn's A ring. This propeller structure is thought to be formed by gravitational scattering of ring particles by an unseen embedded moonlet. Self-gravity wakes are prevalent in dense rings due to gravitational instability. Strong gravitational wakes affect the propeller structure. Here, we derive the condition for formation of a propeller structure by a moonlet embedded in a dense ring with gravitational wakes. We find that a propeller structure is formed when the wavelength of the gravitational wakes is smaller than the Hill …
The fragility of the Uranian moons during the giant planet instability
Johns Hopkins APL（约翰斯·霍普金斯大学应用物理实验室）；Planetary Science Institute（行星科学研究所）；University of Oklahoma（俄克拉荷马大学）；Rice University（莱斯大学）；Southwest Research Institute（西南研究院）
Satellite formation is a natural by-product of planet formation. With the discovery of nu- merous extrasolar planets, it is likely that moons of extrasolar planets (exomoons) will soon be discovered. Some of the most promising techniques can yield both the mass and radius of the moon. Here, I review recent ideas about the formation of moons in our Solar System, and discuss the prospects of extrapolating these theories to predict the sizes of moons that may be discovered around extrasolar planets. It seems likely that planet-planet collisions could create satellites around rocky or icy planets …
The exquisite photometric precision of the Kepler space telescope now puts the detection of extrasolar moons at the horizon. Here, we firstly review observational and analytical techniques that have recently been proposed to find exomoons. Secondly, we discuss the prospects of characterizing potentially habitable extrasolar satellites. With moons being much more numerous than planets in the solar system and with most exoplanets found in the stellar habitable zone being gas giants, habitable moons could be as abundant as habitable planets. However, satellites orbiting planets in the habitable z…
Moons orbiting rocky exoplanets in compact orbits about other stars experience an accelerated tidal evolution, and can either merge with their parent planet or reach the limit of dynamical instability within a Hubble time. We review the parameter space over which moons become unbound, including the effects of atmospheric tides on the planetary spin. We find that such tides can change the final outcome from merger to escape, albeit over a limited parameter space. We also follow the further evolution of unbound moons, and demonstrate that the overwhelmingly most likely long-term outcome is that …
Each of the giant planets within the Solar System has large moons but none of these moons have their own moons (which we call ${\it submoons}$). By analogy with studies of moons around short-period exoplanets, we investigate the tidal-dynamical stability of submoons. We find that 10 km-scale submoons can only survive around large (1000 km-scale) moons on wide-separation orbits. Tidal dissipation destabilizes the orbits of submoons around moons that are small or too close to their host planet; this is the case for most of the Solar System's moons. A handful of known moons are, however, capable …
The field of exoplanetary science has experienced a recent surge of new systems that is largely due to the precision photometry provided by the Kepler mission. The latest discoveries have included compact planetary systems in which the orbits of the planets all lie relatively close to the host star, which presents interesting challenges in terms of formation and dynamical evolution. The compact exoplanetary systems are analogous to the moons orbiting the giant planets in our Solar System, in terms of their relative sizes and semi-major axes. We present a study that quantifies the scaled sizes …
The (yet-to-be confirmed) discovery of a Neptune-sized moon around the ~3.2 Jupiter-mass planet in Kepler 1625 puts interesting constraints on the formation of the system. In particular, the relatively wide orbit of the moon around the planet, at ~40 planetary radii, is hard to reconcile with planet formation theories. We demonstrate that the observed characteristics of the system can be explained from the tidal capture of a secondary planet in the young system. After a quick phase of tidal circularization, the lunar orbit, initially much tighter than 40 planetary radii, subsequently gradually…
Many exoplanets have been found in orbits close to their host stars and thus they are subject to the effects of photo-evaporation. Previous studies have shown that a large portion of exoplanets detected by the Kepler mission have been significantly eroded by photo-evaporation. In this paper, we numerically study the effects of photo-evaporation on the orbital evolution of a hypothesized moon system around a planet. We find that photo-evaporation is crucial to the stability of the moon system. Photo-evaporation can erode the atmosphere of the planet thus leading to significant mass loss. As the…
Satellites of giant planets thought to form in gaseous circumplanetary disks (CPDs) during the late planet-formation phase, but it was unknown so far whether smaller mass planets, such as the ice giants could form such disks, thus moons there. We combined radiative hydrodynamical simulations with satellite population synthesis to investigate the question in the case of Uranus and Neptune. For both ice giants we found that a gaseous CPD is created at the end of their formation. The population synthesis confirmed that Uranian-like, icy, prograde satellite-system could form in these CPDs within a…
Despite numerous attempts, no exomoon has firmly been confirmed to date. New missions like CHEOPS aim to characterize previously detected exoplanets, and potentially to discover exomoons. In order to optimize search strategies, we need to determine those planets which are the most likely to host moons. We investigate the tidal evolution of hypothetical moon orbits in systems consisting of a star, one planet and one test moon. We study a few specific cases with ten billion years integration time where the evolution of moon orbits follows one of these three scenarios: (1) "locking", in which the…
Material from the surface of a planet can be ejected into space by a large impact, and could carry primitive life forms with it. We performed n-body simulations of such ejecta to determine where in the Solar System rock from Earth and Mars may end up. We find that, in addition to frequent transfer of material among the terrestrial planets, transfer of material from Earth and Mars to the moons of Jupiter and Saturn is also possible, but rare. We expect that such transfer is most likely during the Late Heavy Bombardment or during the next one or two billion years. At this time, the icy moons wer…
From analytical studies of tidal heating, eclipses and planetary illumination, it is clear that the exomoon habitable zone (EHZ) - the set of moon and host planet orbits that permit liquid water on an Earthlike moon's surface - is a manifold of higher dimension than the planetary HZ. This paper outlines the first attempt to produce climate models of exomoons which possess all the above sources and sinks of energy. We expand on our previous 1D latitudinal energy balance models (LEBMs), which follow the evolution of the temperature on an Earthlike moon orbiting a Jupiterlike planet, by adding pl…
The Kepler mission found hundreds of planet candidates within the habitable zones (HZ) of their host star, including over 70 candidates with radii larger than 3 Earth radii ($R_\oplus$) within the optimistic habitable zone (OHZ) (Kane et al. 2016). These giant planets are potential hosts to large terrestrial satellites (or exomoons) which would also exist in the HZ. We calculate the occurrence rates of giant planets ($R_p =$~3.0--25~$R_\oplus$) in the OHZ and find a frequency of $(6.5 \pm 1.9)\%$ for G stars, $(11.5 \pm 3.1)\%$ for K stars, and $(6 \pm 6)\%$ for M stars. We compare this with p…
