The discovery of terrestrial exoplanets is uncovering increasingly diverse architectures. Of particular interest are those systems that contain exoplanets at a variety of star-planet separations, allowing direct comparison of exoplanet evolution (comparative planetology). The Kepler-1649 system contains two terrestrial planets similar both in size and insolation flux to Venus and Earth, although their eccentricities remain largely unconstrained. Here we present results of dynamical studies of the system and the potential effects on climate. The eccentricities of the Kepler-1649 system are poorly constrained, and we show that there are dynamically viable regions for further terrestrial planets in between the two known planets for a limited range of eccentricities. We investigate the effect of eccentricity of the outer planet on the dynamics of both planets and show that this results in high-frequency (1000-3000 year) eccentricity oscillations in long-term stable configurations. We calculate the resulting effect of these eccentricity variations on insolation flux and present the results of 3D climate simulations for the habitable zone planet. Our simulations demonstrate that, despite large eccentricity variations, the planet can maintain stable climates with relatively small temperature variations on the substellar hemisphere for a variety of initial climate configurations. Such systems thus provide key opportunities to explore alternative Venus/Earth climate evolution scenarios.
The eccentricity distribution of exoplanets is known from radial velocity surveys to be divergent from circular orbits beyond 0.1 AU. This is particularly the case for large planets where the radial velocity technique is most sensitive. The eccentricity of planetary orbits can have a large effect on the transit probability and subsequently the planet yield of transit surveys. The Kepler mission is the first transit survey that probes deep enough into period-space to allow this effect to be seen via the variation in transit durations. We use the Kepler planet candidates to show that the eccentr…
Kepler-1656b is a 5 $R_E$ planet with an orbital period of 32 days initially detected by the prime Kepler mission. We obtained precision radial velocities of Kepler-1656 with Keck/HIRES in order to confirm the planet and to characterize its mass and orbital eccentricity. With a mass of $48 \pm 4 M_E$, Kepler-1656b is more massive than most planets of comparable size. Its high mass implies that a significant fraction, roughly 80%, of the planet's total mass is in high density material such as rock/iron, with the remaining mass in a low density H/He envelope. The planet also has a high eccentric…
Hot Jupiters may have formed in situ, or been delivered to their observed short periods through one of two categories of migration mechanisms: disk migration or high-eccentricity migration. If hot Jupiters were delivered by high-eccentricity migration, we would expect to observe some "super-eccentric" Jupiters in the process of migrating. We update a prediction for the number of super-eccentric Jupiters we would expect to observe in the Kepler sample if all hot Jupiters migrated through high-eccentricity migration and estimate the true number observed by Kepler. We find that the observations f…
We characterize the eccentricity distribution of a sample of ~50 short-period planet candidates using transit and occultation measurements from NASA's Kepler Mission. First, we evaluate the sensitivity of our hierarchical Bayesian modeling and test its robustness to model misspecification using simulated data. When analyzing actual data assuming a Rayleigh distribution for eccentricity, we find that the posterior mode for the dispersion parameter is $σ=0.081 \pm^{0.014}_{0.003}$. We find that a two-component Gaussian mixture model for $e \cos ω$ and $e \sin ω$ provides a better model than eith…
Highly eccentric orbits are one of the major surprises of exoplanets relative to the Solar System and indicate rich and tumultuous dynamical histories. One system of particular interest is Kepler-1656, which hosts a sub-Jovian planet with an eccentricity of 0.8. Sufficiently eccentric orbits will shrink in semi-major axis due to tidal dissipation of orbital energy during periastron passage. Here our goal was to assess whether Kepler-1656b is currently undergoing such high-eccentricity migration, and to further understand the system's origins and architecture. We confirm a second planet in the …
Characterizing the dependence of the orbital architectures and formation environments on the eccentricity distribution of planets is vital for understanding planet formation. In this work, we perform statistical eccentricity studies of transiting exoplanets using transit durations measured via Kepler combined with precise and accurate stellar radii from the California-Kepler Survey and Gaia. Compared to previous works that characterized the eccentricity distribution from transit durations, our analysis benefits from both high precision stellar radii ($\sim$3%) and a large sample of $\sim$1000 …
Eccentricity is an important orbital parameter. Understanding its effect on planetary climate and habitability is critical for us to search for a habitable world beyond our solar system. The orbital configurations of M-dwarf planets are always tidally-locked at resonance states, which are quite different from those around Sun-like stars. M-dwarf planets need to be investigated separately. Here we use a comprehensive three-dimensional atmospheric general circulation model to systematically investigate how eccentricity influences climate and habitability of M-dwarf exoplanets. The simulation res…
If the exomoon candidate orbiting Kepler-1625b truly exists, it is much more massive than the moons observed in the Solar system (Teachey et al. 2017; Teachey & Kipping 2018). This exomoon would be sufficiently large to stably host its own satellite. This has sparked discussion of a new category of celestial object - a moon-moon (Forgan 2018) or submoon (Kollmeier & Raymond 2018). In this Note, I describe initial results of climate modelling of a hypothetical moon-moon in the Kepler-1625b system, calculated using the OBERON code, which jointly computes 1D latitudinal energy balance models for …
We test the high-eccentricity tidal migration scenario for Kepler-419b, a member of the eccentric warm Jupiter class of planets whose origin is debated. Kepler-419 hosts two known planets (b,c). However, in its current configuration, planet c cannot excite the eccentricity of planet b enough to undergo high-eccentricity tidal migration. We investigate whether the presence of an undiscovered fourth body could explain the orbit of Kepler-419b. We explore the parameter space of this potential third giant planet using a suite of N-body simulations with a range of initial conditions. From the resul…
Although our solar system features predominantly circular orbits, the exoplanets discovered so far indicate that this is the exception rather than the rule. This could have crucial consequences for exoplanet climates, both because eccentric terrestrial exoplanets could have extreme seasonal variation, and because giant planets on eccentric orbits could excite Milankovitch-like variations of a potentially habitable terrestrial planet,Äôs eccentricity, on timescales of thousands-to-millions of years. A particularly interesting implication concerns the fact that the Earth is thought to have gone …
Most planet pairs in the Kepler data that have measured transit time variations (TTV) are near first-order mean-motion resonances. We derive analytical formulae for their TTV signals. We separate planet eccentricity into free and forced parts, where the forced part is purely due to the planets' proximity to resonance. This separation yields simple analytical formulae. The phase of the TTV depends sensitively on the presence of free eccentricity: if the free eccentricity vanishes, the TTV will be in phase with the longitude of conjunctions. This effect is easily detectable in current TTV data. …
The Kepler era of exoplanetary discovery has presented the Astronomical community with a cornucopia of planetary systems very different from the one which we inhabit. It has long been known that Jupiter plays a major role in the orbital parameters of Mars and it's climate, but there is also a long-standing belief that Jupiter would play a similar role for Earth if not for its large moon. Using a three dimensional general circulation model (3-D GCM) with a fully-coupled ocean we simulate what would happen to the climate of an Earth-like world if Mars did not exist, but a Jupiter-like planet was…
Simulation of the spin evolution of some selected exoplanets and inferences on their climate
Università di Padova（帕多瓦大学）；Università di Bari（巴里大学）；Istituto Nazionale di Fisica Nucleare（意大利国家核物理研究所）；Università del Salento（萨伦托大学）；Istituto Nazionale di Astrofisica（意大利国家天体物理研究所）
Inferring planetary parameters from transit timing variations is challenging for small exoplanets because their transits may be so weak that determination of individual transit timing is difficult or impossible. We implement a useful combination of tools which together provide a numerically fast global photodynamical model. This is used to fit the TTV-bearing light-curve, in order to constrain the masses of transiting exoplanets in low eccentricity, multi-planet systems - and small planets in particular. We present inferred dynamical masses and orbital eccentricities in four multi-planet syste…
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…
As lower-mass stars often host multiple rocky planets, gravitational interactions among planets can have significant effects on climate and habitability over long timescales. Here we explore a specific case, Kepler-62f, a potentially habitable planet in a five-planet system with a K2V host star. N-body integrations reveal the stable range of initial eccentricities for Kepler-62f is $0.00 \leqslant e \leqslant 0.32$, absent the effect of additional, undetected planets. We simulate the tidal evolution of Kepler-62f in this range and find that, for certain assumptions, the planet can be locked in…
Solar system planets move on almost circular orbits. In strong contrast, many massive gas giant exoplanets travel on highly elliptical orbits, whereas the shape of the orbits of smaller, more terrestrial, exoplanets remained largely elusive. Knowing the eccentricity distribution in systems of small planets would be important as it holds information about the planet's formation and evolution, and influences its habitability. We make these measurements using photometry from the Kepler satellite and utilizing a method relying on Kepler's second law, which relates the duration of a planetary trans…
Orbital eccentricity is one of the basic planetary properties, whose distribution may shed light on the history of planet formation and evolution. Here, in a series of works on Planetary Orbit Eccentricity Trends (dubbed POET), we study the distribution of planetary eccentricities and their dependence on stellar/planetary properties. In this paper, the first work of the POET series, we investigate whether and how the eccentricities of small planets depend on stellar metallicities (e.g., [Fe/H]). Previous studies on giant planets have found a significant correlation between planetary eccentrici…
Doppler planet searches have discovered that giant planets follow orbits with a wide range of orbital eccentricities, revolutionizing theories of planet formation. The discovery of hundreds of exoplanet candidates by NASA's Kepler mission enables astronomers to characterize the eccentricity distribution of small exoplanets. Measuring the eccentricity of individual planets is only practical in favorable cases that are amenable to complementary techniques (e.g., radial velocities, transit timing variations, occultation photometry). Yet even in the absence of individual eccentricities, it is poss…
We analyze the transit timing variations obtained by the Kepler mission for 22 sub-jovian planet pairs (17 published, 5 new) that lie close to mean motion resonances. We find that the TTV phases for most of these pairs lie close to zero, consistent with an eccentricity distribution that has a very low RMS value of e ~ 0.01; but about a quarter of the pairs possess much higher eccentricities, up to 0.1 - 0.4. For the low-eccentricity pairs, we are able to statistically remove the effect of eccentricity to obtain planet masses from TTV data. These masses, together with those measured by radial v…
Planets on eccentric orbits have a higher geometric probability of transiting their host star. By application of Bayes' theorem, we reverse this logic to show that the eccentricity distribution of transiting planets is positively biased. Adopting the flexible Beta distribution as the underlying prior for eccentricity, we derive the marginalized transit probability as well as the a-priori joint probability distribution of eccentricity and argument of periastron, given that a planet is known to transit. These results allow to demonstrate that most planet occurrence rate calculations using Kepler…
The Kepler mission's discovery of a number of circumbinary planets orbiting close (a_p < 1.1 au) to the stellar binary raises questions as to how these planets could have formed given the intense gravitational perturbations the dual stars impart on the disk. The gas component of circumbinary protoplanetary disks is perturbed in a similar manner to the solid, planetesimal dominated counterpart, although the mechanism by which disk eccentricity originates differs. This is the first work of a series that aims to investigate the conditions for planet formation in circumbinary protoplanetary disks.…
We continue to investigate the binary system Kepler-16, consisting of a K-type main-sequence star, a red dwarf, and a circumbinary Saturnian planet. As part of our study, we describe the system's habitable zone based on different climate models. We also report on stability investigations for possible Earth-mass Trojans while expanding a previous study by B. L. Quarles and collaborators given in 2012. For the climate models we carefully consider the relevance of the system's parameters. Furthermore, we pursue new stability simulations for the Earth-mass objects starting along the orbit of Keple…
Three transiting circumbinary planets (Kepler-16 b, Kepler-34 b, and Kepler-35 b) have recently been discovered from photometric data taken by the Kepler spacecraft. Their orbits are significantly non-Keplerian because of the large secondary-to-primary mass ratio and orbital eccentricity of the binaries, as well as the proximity of the planets to the binaries. We present an analytic theory, with the planet treated as a test particle, which shows that the planetary motion can be represented by the superposition of the circular motion of a guiding center, the forced oscillations due to the non-a…
We establish the three-dimensional architecture of the Kepler-419 (previously KOI-1474) system to be eccentric yet with a low mutual inclination. Kepler-419b is a warm Jupiter at semi-major axis a = 0.370 +0.007/-0.006 AU with a large eccentricity e=0.85 +0.08/-0.07 measured via the "photoeccentric effect." It exhibits transit timing variations induced by the non-transiting Kepler-419c, which we uniquely constrain to be a moderately eccentric (e=0.184 +/- 0.002), hierarchically-separated (a=1.68 +/- 0.03 AU) giant planet (7.3 +/- 0.4 MJup). We combine sixteen quarters of Kepler photometry, rad…
Approximately half of the planets discovered by NASA's Kepler mission are in systems where just a single planet transits its host star, and the remaining planets are observed to be in multi-planet systems. Recent analyses have reported a dichotomy in the eccentricity distribution displayed by systems where a single planet transits compared with that displayed by the multi-planet systems. Using $N$-body simulations, we examine the hypothesis that this dichotomy has arisen because inner systems of super-Earths are frequently accompanied by outer systems of giant planets that can become dynamical…
Recent studies suggest that ultra-short period planets (USPs), Earth-sized planets with sub-day periods, constitute a statistically distinct sub-sample of {\it Kepler} planets: USPs have smaller radii ($1-1.4R_\oplus$) and larger mutual inclinations with neighboring planets than nominal {\it Kepler} planets, and their period distribution is steeper than longer-period planets. We study a "low-eccentricity" migration scenario for the formation of USPs, in which a low-mass planet with initial period of a few days maintains a small but finite eccentricity due to secular forcings from exterior comp…
In the outer regions of the habitable zone, the risk of transitioning into a globally frozen "snowball" state poses a threat to the habitability of planets with the capacity to host water-based life. We use a one-dimensional energy balance climate model (EBM) to examine how obliquity, spin rate, orbital eccentricity, and ocean coverage might influence the onset of such a snowball state. For an exoplanet, these parameters may be strikingly different from the values observed for Earth. Since, for constant semimajor axis, the annual mean stellar irradiation scales with (1-e^2)^(-1/2), one might e…
In order to understand the climate on terrestrial planets orbiting nearby Sun-like stars, one would like to know their thermal inertia. We use a global climate model to simulate the thermal phase variations of Earth-analogs and test whether these data could distinguish between planets with different heat storage and heat transport characteristics. In particular, we consider a temperate climate with polar ice caps (like modern Earth), and a snowball state where the oceans are globally covered in ice. We first quantitatively study the periodic radiative forcing from, and climatic response to, ro…
The exquisite photometry of Kepler has revealed reflected light from exoplanets, tidal distortion of host stars and Doppler beaming of a star's light due to its motion (Borucki 2016; Demory et al. 2012; Welsh et al. 2010; Bloemen et al. 2012). Esteves et al. (2013, 2015) and Shporer et al. (2014) reported additional odd harmonics in the light curves of two hot Jupiters: HAT-P-7b and Kepler-13Ab. They measured non-zero power at three times the orbital frequency that persisted while the planet was eclipsed and hence must originate in the star (Esteves et al. 2015). Penoyre & Sandford (2018) show…
From Stability to Instability: Characterizing the Eccentricities of Multi-planet Systems in the California Kepler Survey as a Means of Studying Stability
Second-order mean-motion resonances lead to an interesting phenomenon in the sculpting of the period ratio distribution due to their shape and width in period-ratio/eccentricity space. As the osculating periods librate in resonance, the time-averaged period ratio approaches the exact commensurability. The width of second-order resonances increases with increasing eccentricity, and thus more eccentric systems have a stronger peak at commensurability when averaged over sufficient time. The libration period is short enough that this time-averaging behavior is expected to appear on the timescale o…
The planets with a radius $<$ 4 $R$$_\oplus$ observed by the Kepler mission exhibit a unique feature, and propose a challenge for current planetary formation models. The tidal effect between a planet and its host star plays an essential role in reconfiguring the final orbits of the short-period planets. In this work, based on various initial Rayleigh distributions of the orbital elements, the final semi-major axis distributions of the planets with a radius $<$ 4 $R_\oplus$ after suffering tidal evolutions are investigated. Our simulations have qualitatively revealed some statistical properties…
The nearly circular (mean eccentricity <e>~0.06) and coplanar (mean mutual inclination <i>~3 deg) orbits of the Solar System planets motivated Kant and Laplace to put forth the hypothesis that planets are formed in disks, which has developed into the widely accepted theory of planet formation. Surprisingly, the first several hundred extrasolar planets (mostly Jovian) discovered using the Radial Velocity (RV) technique are commonly on eccentric orbits (<e> ~ 0.3). This raises a fundamental question: Are the Solar System and its formation special? The Kepler mission has found thousands of transi…
The insolation a planet receives from its parent star is the main driver of the climate and depends on the planet's orbital configuration. Planets with non-zero obliquity and eccentricity experience seasonal insolation variations. As a result, the climate exhibits a seasonal cycle, with its strength depending on the orbital configuration and atmospheric characteristics. In this study, using an idealized general circulation model, we examine the climate response to changes in eccentricity for both zero and non-zero obliquity planets. In the zero obliquity case, a comparison between the seasonal…
We extract densities and eccentricities of 139 sub-Jovian planets by analyzing transit time variations (TTVs) obtained by the Kepler mission through Quarter 12. We partially circumvent the degeneracies that plague TTV inversion with the help of an analytical formula for the TTV. From the observed TTV phases, we find that most of these planets have eccentricities of order a few percent. More precisely, the r.m.s. eccentricity is 0.018^{+0.005}_{-0.004}, and planets smaller than 2.5R_\earth are around twice as eccentric as those bigger than 2.5R_\earth. We also find a best-fit density-radius rel…
In this work, we investigate configuration formation of two inner terrestrial planets near mean motion resonance (MMRs) induced by the perturbation of a distant gas-giant for the Kepler-68 system, by conducting thousands of numerical simulations. The results show that the formation of terrestrial planets is relevant to the speed of Type I migration, the mass of planets, and the existence of giant planet. The mass and eccentricity of the giant planet may play a crucial role in shaping the final configuration of the system. The inner planet pair can be trapped in 5:3 or 7:4 MMRs if the giant pla…
A significant fraction of Kepler systems are closely-packed, largely coplanar and circular. We study the stability of a 6-planet system, Kepler-11, to gain insights on the dynamics and formation history of such systems. Using a technique called `frequency maps' as fast indicators for long-term stability, we explore the stability of Kepler-11 system by analyzing the neighbourhood space around its orbital parameters. Frequency maps provide a visual representation of chaos and stability, and their dependence on orbital parameters. We find that the current system is stable, but lies within a few p…
Previous attempts to describe circumbinary habitable zones have been concerned with the spatial extent of the zone, calculated analytically according to the combined radiation field of both stars. By contrast to these "spatial HZs", we present a numerical analysis of the "orbital HZ", a habitable zone defined as a function of planet orbital elements. This orbital HZ is better equipped to handle (for example) eccentric planet orbits, and is more directly connected to the data returned by exoplanet observations. Producing an orbital HZ requires a large number of climate simulations to be run to …
A large number of observed exoplanets are part of multiple planet systems. Most of these systems are sufficiently close-in to be tidally evolving. In such systems, there is a competition between the excitation caused by planet-planet interactions and tidal damping. Using as an example two multiple planet systems, which host planets in the surface liquid water habitable zone (HZ): Kepler-62 and Kepler-186, we show the importance and effect of both planetary and stellar tides on the dynamical evolution of planets and on the climate of the HZ planets.
With the detection of extrasolar moons (exomoons) on the horizon, it is important to consider their potential for habitability. If we consider the circumstellar Habitable Zone (HZ, often described in terms of planet semi-major axis and orbital eccentricity), we can ask, "How does the HZ for an Earth-like exomoon differ from the HZ for an Earth-like exoplanet?" For the first time, we use 1D latitudinal energy balance modelling to address this question. The model places an Earth-like exomoon in orbit around a Jupiter mass planet, which in turn orbits a Sun-like star. The exomoon's surface temper…
Most of super-Earths detected by the radial velocity (RV) method have significantly smaller eccentricities than the eccentricities corresponding to velocity dispersion equal to their surface escape velocity ("escape eccentricities"). If orbital instability followed by giant impacts among protoplanets that have migrated from outer region is considered, it is usually considered that eccentricities of the merged bodies become comparable to those of orbital crossing bodies, which are excited up to their escape eccentricities by close scattering. However, the eccentricity evolution in the {\it in s…
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 Kepler mission has discovered about a dozen circumbinary planetary systems, all containing planets on ~ 1 AU orbits. We place bounds on the locations in the circumbinary protoplanetary disk, where these planets could have formed through collisional agglomeration starting from small (km-sized or less) planetesimals. We first present a model of secular planetesimal dynamics that accounts for the (1) perturbation due to the eccentric precessing binary, as well as the (2) gravity and (3) gas drag from a precessing eccentric disk. Their simultaneous action leads to rich dynamics, with (multiple…
Due to fortuitous circumstances, the two giant planets around Kepler-419 have well characterized 3-D orbits. They are nearly coplanar to each other; the inner one has a large eccentricity (~0.82); and the apses of the two orbits librate around anti-alignment. Such a state defies available proposals for large eccentricities. We argue that it is instead uniquely produced by a decaying protoplanetary disk. When the disk was massive, its precessional effect on the planets forced the two apses to center around an anti-aligned state. And as the disk is gradually eroded, the pair of planets are adiab…
The existence of planets orbiting a central binary star system immediately raises questions regarding their formation and dynamical evolution. Recent discoveries of circumbinary planets by the Kepler space telescope has shown that some of these planets reside close to the dynamical stability limit where it is very difficult to form planets in situ. For binary systems with nearly circular orbits, such as Kepler-38, the observed proximity of planetary orbits to the stability limit can be understood by an evolutionary process in which planets form farther out in the disk and migrate inward to the…
We consider the so-called Keplerian periodogram, in which the putative detectable signal is modelled by a highly non-linear Keplerian radial velocity function, appearing in Doppler exoplanetary surveys. We demonstrate that for planets on high-eccentricity orbits the Keplerian periodogram is far more efficient than the classic Lomb-Scargle periodogram and even the multiharmonic periodograms, in which the periodic signal is approximated by a truncated Fourier series. We provide new numerical algorithm for computation of the Keplerian periodogram. This algorithm adaptively increases the parameter…
Exoplanet systems with multiple planets in mean motion resonances have often been hailed as a signpost of disk driven migration. Resonant chains like Kepler-223 and Kepler-80 consist of a trio of planets with the three-body resonant angle librating and/or with a two-body resonant angle librating for each pair. Here we investigate whether close-in super-Earths and mini-Neptunes forming in situ can lock into resonant chains due to dissipation from a depleted gas disk. We simulate the giant impact phase of planet formation, including eccentricity damping from a gaseous disk, followed by subsequen…
We present results of simulations of the climate of the newly discovered planet Proxima Centauri B, performed using the Met Office Unified Model (UM). We examine the responses of both an `Earth-like' atmosphere and simplified nitrogen and trace carbon dioxide atmosphere to the radiation likely received by Proxima Centauri B. Additionally, we explore the effects of orbital eccentricity on the planetary conditions using a range of eccentricities guided by the observational constraints. Overall, our results are in agreement with previous studies in suggesting Proxima Centauri B may well have surf…
We examine the formation of planets around binary stars in light of the recently discovered systems Kepler 16, 34 and 35. We conduct hydrodynamical simulations of self gravitating disks around binary systems. The selected binary and disk parameters are chosen consistent with observed systems. The disks are evolved until they settle in a quasi-equilibrium and the resulting systems are compared with the parameters of Kepler 16, 34 and 35. We find a close correspondence of the peak density at the inner disk gap and the orbit of the observed planets. We conclude, based on our simulations, that the…
The vast majority of well studied giant-planet systems, including the Solar System, are nearly coplanar which implies dissipation within a primordial gas disk. however, intrinsic instability may lead to planet-planet scattering, which often produces non-coplanar, eccentric orbits. Planet scattering theories have been developed to explain observed high eccentricity systems and also hot Jupiters; thus far their predictions for mutual inclination (I) have barely been tested. Here we characterize a highly mutually-inclined (I ~ 15-60 degrees), moderately eccentric (e >~ 0.1) giant planet system: K…
There exists a positive correlation between orbital eccentricity and the average stellar flux that planets receive from their parent star. Often, though, it is assumed that the average equilibrium temperature would correspondingly increase with eccentricity. Here we test this assumption by calculating and comparing analytic solutions for both the spatial and temporal averages of orbital distance, stellar flux, and equilibrium temperature. Our solutions show that the average equilibrium temperature of a planet, with a constant albedo, slowly decreases with eccentricity until converging to a val…
A Bayesian analysis of 47 Ursae Majoris (47 UMa) radial velocity data confirms and refines the properties of two previously reported planets with periods of 1079 and 2325 days and finds evidence for an additional long period planet with a period of approximately 10000 days. The three planet model is found to be 10^5 times more probable than the next most probable model which is a two planet model. The nonlinear model fitting is accomplished with a new hybrid Markov chain Monte Carlo (HMCMC) algorithm which incorporates parallel tempering, simulated annealing and genetic crossover operations. E…
