Demographic studies of extrasolar planets

Uncovering the demographics of extrasolar planets is crucial to understanding the processes of their formation and evolution. In this thesis, we present four studies that contribute to this end, three of which relate to NASA's Kepler mission, which has revolutionized the field of exoplanets in the last few years.

In the pre-Kepler study, we investigate a sample of exoplanet spin-orbit measurements---measurements of the inclination of a planet's orbit relative to the spin axis of its host star---to determine whether a dominant planet migration channel can be identified, and at what confidence. Applying methods of Bayesian model comparison to distinguish between the predictions of several different migration models, we find that the data strongly favor a two-mode migration scenario combining planet-planet scattering and disk migration over a single-mode Kozai migration scenario. While we test only the predictions of particular Kozai and scattering migration models in this work, these methods may be used to test the predictions of any other spin-orbit misaligning mechanism.

We then present two studies addressing astrophysical false positives in Kepler data. The Kepler mission has identified thousands of transiting planet candidates, and only relatively few have yet been dynamically confirmed as bona fide planets, with only a handful more even conceivably amenable to future dynamical confirmation. As a result, the ability to draw detailed conclusions about the diversity of exoplanet systems from Kepler detections relies critically on understanding the probability that any individual candidate might be a false positive. We show that a typical a priori false positive probability for a well-vetted Kepler candidate is only about 5-10%, enabling confidence in demographic studies that treat candidates as true planets. We also present a detailed procedure that can be used to securely and efficiently validate any individual transit candidate using detailed information of the signal's shape as well as follow-up observations, if available.

Finally, we calculate an empirical, non-parametric estimate of the shape of the radius distribution of small planets with periods less than 90 days orbiting cool (less than 4000K) dwarf stars in the Kepler catalog. This effort reveals several notable features of the distribution, in particular a maximum in the radius function around 1-1.25 Earth radii and a steep drop-off in the distribution larger than 2 Earth radii. Even more importantly, the methods presented in this work can be applied to a broader subsample of Kepler targets to understand how the radius function of planets changes across different types of host stars.

SuperWASP-North extrasolar planet candidates: candidates from fields 17h

We have performed photometric observations of nearly seven million stars with 8 <V <15 with the SuperWASP-North instrument from La Palma between 2004 May to September. Fields in the right ascension range 17-18h, yielding over 185000 stars with sufficient quality data, have been searched for transits using a modified box least-squares (BLS) algorithm. We find a total of 58 initial transiting candidates which have high signal-to-noise ratio in the BLS, show multiple transit-like dips and have passed visual inspection. Analysis of the blending and the inferred planetary radii for these candidates leave, a total of seven transiting planet candidates which pass all the tests plus four which pass the majority. We discuss the derived parameters for these candidates and their properties and comment on the implications for future transit searches.

SuperWASP-N extrasolar planet candidates between 18 <RA <21h

The SuperWASP-I (Wide Angle Search for Planets-I) instrument observed 6.7 million stars between 8 and 15mag from La Palma during the 2004 May-September season. Our transit-hunting algorithm selected 11626 objects from the 184442 stars within the RA (right ascension) range 18-21h. We describe our thorough selection procedure whereby catalogue information is exploited along with careful study of the SuperWASP data to filter out, as far as possible, transit mimics. We have identified 35 candidates which we recommend for follow-up observations.

SuperWASP-North extrasolar planet candidates between 3h <RA <6h

The Wide Angle Search for Planets (WASP) photometrically surveys a large number of nearby stars to uncover candidate extrasolar planet systems by virtue of small-amplitude light curve dips on a

SuperWASP-N extrasolar planet candidates from fields 06h

TheWide Angle Search for Planets (WASP) survey currently operates two installations, designated SuperWASP-N and SuperWASP-S, located in the Northern and Southern hemispheres, respectively. These installations are designed to provide high time-resolution photometry for the purpose of detecting transiting extrasolar planets, asteroids, and transient events. Here, we present results from a transit-hunting observing campaign using SuperWASP-N covering a right ascension (RA) range of 06h < RA < 16h. This paper represents the fifth and final in the series of transit candidates released from the 2004 observing season. In total, 729 335 stars from 33 fields were monitored with 130 566 having sufficient precision to be scanned for transit signatures. Using a robust transit detection algorithm and selection criteria, six stars were found to have events consistent with the signature of a transiting extrasolar planet based on the photometry, including the known transiting planet XO-1b. These transit candidates are presented here along with discussion of follow-up observations and the expected number of candidates in relation to the overall observing strategy.

A Correlation Between Host Star Activity and Planet Mass for Close-in Extrasolar Planets?

The activity levels of stars are influenced by several stellar properties, such as stellar rotation, spectral type, and the presence of stellar companions. Analogous to binaries, planetary companions are also thought to be able to cause higher activity levels in their host stars, although at lower levels. Especially in X-rays, such influences are hard to detect because coronae of cool stars exhibit a considerable amount of intrinsic variability. Recently, a correlation between the mass of close-in exoplanets and their host star's X-ray luminosity has been detected, based on archival X-ray data from the ROSAT All-Sky Survey. This finding has been interpreted as evidence for star-planet interactions. We show in our analysis that this correlation is caused by selection effects due to the flux limit of the X-ray data used and due to the intrinsic planet detectability of the radial velocity method, and thus does not trace possible planet-induced effects. We also show that the correlation is not present in a corresponding complete sample derived from combined XMM-Newton and ROSAT data.

Intercomparison of general circulation models for hot extrasolar planets

We compare five general circulation models (GCMs) which have been recently used to study hot extrasolar planet atmospheres (BOB, CAM, IGCM, MITgcm, and PEQMOD), under three test cases useful for assessing model convergence and accuracy. Such a broad, detailed intercomparison has not been performed thus far for extrasolar planets study. The models considered all solve the traditional primitive equations, but employ di↵erent numerical algorithms or grids (e.g., pseudospectral and finite volume, with the latter separately in longitude-latitude and ‘cubed-sphere’ grids). The test cases are chosen to cleanly address specific aspects of the behaviors typically reported in hot extrasolar planet simulations: 1) steady-state, 2) nonlinearly evolving baroclinic wave, and 3) response to fast timescale thermal relaxation. When initialized with a steady jet, all models maintain the steadiness, as they should—except MITgcm in cubed-sphere grid. A very good agreement is obtained for a baroclinic wave evolving from an initial instability in pseudospectral models (only). However, exact numerical convergence is still not achieved across the pseudospectral models: amplitudes and phases are observably di↵erent. When subject to a typical ‘hot-Jupiter’-like forcing, all five models show quantitatively di↵erent behavior—although qualitatively similar, time-variable, quadrupole-dominated flows are produced. Hence, as have been advocated in several past studies, specific quantitative predictions (such as the location of large vortices and hot regions) by GCMs should be viewed with caution. Overall, in the tests considered here, pseudospectral models in pressure coordinate (PEBOB and PEQMOD) perform the best and MITgcm in cubed-sphere grid performs the worst.

Baroclinic instability on hot extrasolar planets

We investigate baroclinic instability in flow conditions relevant to hot extrasolar planets. The instability is important for transporting and mixing heat, as well as for influencing large-scale variability on the planets. Both linear normal mode analysis and non-linear initial value cal- culations are carried out – focusing on the freely-evolving, adiabatic situation. Using a high- resolution general circulation model (GCM) which solves the traditional primitive equations, we show that large-scale jets similar to those observed in current GCM simulations of hot ex- trasolar giant planets are likely to be baroclinically unstable on a timescale of few to few tens of planetary rotations, generating cyclones and anticyclones that drive weather systems. The growth rate and scale of the most unstable mode obtained in the linear analysis are in qual- itative, good agreement with the full non-linear calculations. In general, unstable jets evolve differently depending on their signs (eastward or westward), due to the change in sign of the jet curvature. For jets located at or near the equator, instability is strong at the flanks – but not at the core. Crucially, the instability is either poorly or not at all captured in simulations with low resolution and/or high artificial viscosity. Hence, the instability has not been observed or emphasized in past circulation studies of hot extrasolar planets.

Reliability of orbital fits for resonant extrasolar planetary systems: the case of HD82943

We perform a statistical study of the process of orbital determination of the HD82943 extrasolar planetary system, using the current observational data set of N = 165 radial velocity (RV) measurements. Our aim is to analyse the dispersion of possible orbital fits leading to residuals compatible with the best solution, and to discuss the sensitivity of the results with respect to both the data set and the error distribution around the best fit. Although some orbital parameters (e.g. semimajor axis) appear well constrained, we show that the best fits for the HD82943 system are not robust, and at present it is not possible to estimate reliable solutions for these bodies. Finally, we discuss the possibility of a third planet, with a mass of 0.35M(Jup) and an orbital period of 900 d. Stability analysis and simulations of planetary migration indicate that such a hypothetical three-planet system could be locked in a double 2/1 mean-motion resonance, similar to the so-called Laplace resonance of the three inner Galilean satellites of Jupiter.

DETECTABILITY AND ERROR ESTIMATION IN ORBITAL FITS OF RESONANT EXTRASOLAR PLANETS

We estimate the conditions for detectability of two planets in a 2/1 mean-motion resonance from radial velocity data, as a function of their masses, number of observations and the signal-to-noise ratio. Even for a data set of the order of 100 observations and standard deviations of the order of a few meters per second, we find that Jovian-size resonant planets are difficult to detect if the masses of the planets differ by a factor larger than similar to 4. This is consistent with the present population of real exosystems in the 2/1 commensurability, most of which have resonant pairs with similar minimum masses, and could indicate that many other resonant systems exist, but are currently beyond the detectability limit. Furthermore, we analyze the error distribution in masses and orbital elements of orbital fits from synthetic data sets for resonant planets in the 2/1 commensurability. For various mass ratios and number of data points we find that the eccentricity of the outer planet is systematically overestimated, although the inner planet`s eccentricity suffers a much smaller effect. If the initial conditions correspond to small-amplitude oscillations around stable apsidal corotation resonances, the amplitudes estimated from the orbital fits are biased toward larger amplitudes, in accordance to results found in real resonant extrasolar systems.

Stable satellites around extrasolar giant planets

In this work, we study the stability of hypothetical satellites of extrasolar planets. Through numerical simulations of the restricted elliptic three-body problem we found the borders of the stable regions around the secondary body. From the empirical results, we derived analytical expressions of the critical semimajor axis beyond which the satellites would not remain stable. The expressions are given as a function of the eccentricities of the planet, e(P), and of the satellite, e(sat). In the case of prograde, satellites, the critical semimajor axis, in the units of Hill's radius, is given by a(E) approximate to 0.4895 (1.0000 - 1.0305e(P) - 0.2738e(sat)). In the case of retrograde satellites, it is given by a(E) approximate to 0.9309 (1.0000 - 1.0764e(P) - 0.9812e(sat)). We also computed the satellite stability region (a(E)) for a set of extrasolar planets. The results indicate that extrasolar planets in the habitable zone could harbour the Earth-like satellites.

A new analysis of the GJ581 extrasolar planetary system

We have done a new analysis of the available observations of the GJ581 exoplanetary system. Today this system is controversial due to choices that can be done in the orbital determination. The main ones are the occurrence of aliases and the additional bodies-the planets f and g-announced in Vogt et al. (Astrophys J 723:954-965, 2010). Any dynamical study of exoplanets requires the good knowledge of the orbital elements and the investigations involving the planet g are particularly interesting, since this body would lie in the habitable zone (HZ) of the star GJ581. This region, for this system, is very attractive of the dynamical point of view due to several resonances of two and three bodies present there. In this work, we investigate the conditions under which the planet g may exist. We stress the fact that the planet g is intimately related with the orbital elements of the planet d; more precisely, we conclude that it is not possible to disconnect its existence from the determination of the eccentricity of the planet d. Concerning the planet f, we have found one solution with period a parts per thousand 450 days, but we are judicious about any affirmation concerning this body because its signal is in the threshold of detection and the high period is in a spectral region where the occurrence of aliases is very common. Besides, we outline some dynamical features of the HZ with the dynamical map and point out the role played by some resonances laying there.

Multi-planet extrasolar systems - detection and dynamics

20 years after the discovery of the first planets outside our solar system, the current exoplanetary population includes more than 700 confirmed planets around main sequence stars. Approximately 50% belong to multiple-planet systems in very diverse dynamical configurations, from two-planet hierarchical systems to multiple resonances that could only have been attained as the consequence of a smooth large-scale orbital migration. The first part of this paper reviews the main detection techniques employed for the detection and orbital characterization of multiple-planet systems, from the (now) classical radial velocity (RV) method to the use of transit time variations (TTV) for the identification of additional planetary bodies orbiting the same star. In the second part we discuss the dynamical evolution of multi-planet systems due to their mutual gravitational interactions. We analyze possible modes of motion for hierarchical, secular or resonant configurations, and what stability criteria can be defined in each case. In some cases, the dynamics can be well approximated by simple analytical expressions for the Hamiltonian function, while other configurations can only be studied with semi-analytical or numerical tools. In particular, we show how mean-motion resonances can generate complex structures in the phase space where different libration islands and circulation domains are separated by chaotic layers. In all cases we use real exoplanetary systems as working examples.