Brown dwarfs and giant exoplanets: bridging observations and theory with statistical methods

Stellar physics has been widely studied over the last century, with theoretical models for stars robustly tested by decades of observations. In contrast, studies of brown dwarfs and extra-solar giant planets were only possible for the last two decades due to the intrinsically faint luminosity of these objects. As a result, the fundamental properties of substellar objects are still poorly constrained. Formation mechanisms for brown dwarfs and planetary-mass objects remain heavily debated, and atmospheric models widely lack empirical validation at the lowest masses and temperatures. Theoretical models are currently the only available way to infer physical parameters (e.g. mass, temperature) for isolated objects and directly-imaged companions on wide orbits, and are thus widely used by the community in spite of the extremely high uncertainties they carry. More stringent observational constraints, or new alternative methods, are essential to allow for a further and deeper understanding of brown dwarfs and giant planets. Robust population studies provide invaluable insights into formation processes and empirical trends. Statistical methodologies may thus be used to refine theoretical models and obtain a more complete overview of the properties and statistics of the substellar populations. This dissertation addresses three problems in the framework of brown dwarfs and giant exoplanets, namely, substellar binary properties, the formation of massive planets and brown dwarfs around stars, and the detection and model-independent masses of direct imaging systems. Chapter 2 presents results from a multiplicity survey investigating the binary statistics of the lowest-mass brown dwarfs. As binarity is a direct outcome of formation, observed trends as a function of mass provide valuable insights into formation processes. In Chapter 3, I conduct a search for stellar companions to stars with close-in, massive planets, as a test of formation theory for giant planets and brown dwarfs on small orbital separations. Chapter 4 introduces a dedicated tool designed to identify new wide-orbit companions and constrain the orbits of astrometric systems. The method allows for the determination of dynamical masses for directly-imaged companions, a powerful way to circumvent the large uncertainties introduced by models. The common goal to these projects is to infer new, crucial observational constraints for formation theories or atmospheric models in the substellar regime. This will in turn provide a more comprehensive view of the characteristics and demographics of brown dwarfs and exoplanets

Population-level Eccentricity Distributions of Imaged Exoplanets and Brown Dwarf Companions: Dynamical Evidence for Distinct Formation Channels

The orbital eccentricities of directly imaged exoplanets and brown dwarf companions provide clues about their formation and dynamical histories. We combine new high-contrast imaging observations of substellar companions obtained primarily with Keck/NIRC2 together with astrometry from the literature to test for differences in the population-level eccentricity distributions of 27 long-period giant planets and brown dwarf companions between 5 and 100 au using hierarchical Bayesian modeling. Orbit fits are performed in a uniform manner for companions with short orbital arcs; this typically results in broad constraints for individual eccentricity distributions, but together as an ensemble, these systems provide valuable insight into their collective underlying orbital patterns. The shape of the eccentricity distribution function for our full sample of substellar companions is approximately flat from e = 0–1. When subdivided by companion mass and mass ratio, the underlying distributions for giant planets and brown dwarfs show significant differences. Low mass ratio companions preferentially have low eccentricities, similar to the orbital properties of warm Jupiters found with radial velocities and transits. We interpret this as evidence for in situ formation on largely undisturbed orbits within massive extended disks. Brown dwarf companions exhibit a broad peak at e ≈ 0.6–0.9 with evidence for a dependence on orbital period. This closely resembles the orbital properties and period-eccentricity trends of wide (1–200 au) stellar binaries, suggesting that brown dwarfs in this separation range predominantly form in a similar fashion. We also report evidence that the "eccentricity dichotomy" observed at small separations extends to planets on wide orbits: the mean eccentricity for the multi-planet system HR 8799 is lower than for systems with single planets. In the future, larger samples and continued astrometric orbit monitoring will help establish whether these eccentricity distributions correlate with other parameters such as stellar host mass, multiplicity, and age

Population-level Eccentricity Distributions of Imaged Exoplanets and Brown Dwarf Companions: Dynamical Evidence for Distinct Formation Channels

The orbital eccentricities of directly imaged exoplanets and brown dwarf companions provide clues about their formation and dynamical histories. We combine new high-contrast imaging observations of substellar companions obtained primarily with Keck/NIRC2 together with astrometry from the literature to test for differences in the population-level eccentricity distributions of 27 long-period giant planets and brown dwarf companions between 5 and 100 au using hierarchical Bayesian modeling. Orbit fits are performed in a uniform manner for companions with short orbital arcs; this typically results in broad constraints for individual eccentricity distributions, but together as an ensemble, these systems provide valuable insight into their collective underlying orbital patterns. The shape of the eccentricity distribution function for our full sample of substellar companions is approximately flat from e = 0–1. When subdivided by companion mass and mass ratio, the underlying distributions for giant planets and brown dwarfs show significant differences. Low mass ratio companions preferentially have low eccentricities, similar to the orbital properties of warm Jupiters found with radial velocities and transits. We interpret this as evidence for in situ formation on largely undisturbed orbits within massive extended disks. Brown dwarf companions exhibit a broad peak at e ≈ 0.6–0.9 with evidence for a dependence on orbital period. This closely resembles the orbital properties and period-eccentricity trends of wide (1–200 au) stellar binaries, suggesting that brown dwarfs in this separation range predominantly form in a similar fashion. We also report evidence that the "eccentricity dichotomy" observed at small separations extends to planets on wide orbits: the mean eccentricity for the multi-planet system HR 8799 is lower than for systems with single planets. In the future, larger samples and continued astrometric orbit monitoring will help establish whether these eccentricity distributions correlate with other parameters such as stellar host mass, multiplicity, and age

Planetesimals to brown dwarfs: What is a planet?

The past 15 years have brought about a revolution in our understanding of our Solar System and other planetary systems. During this time, discoveries include the first Kuiper belt objects (KBOs), the first brown dwarfs, and the first extrasolar planets. Although discoveries continue apace, they have called into question our previous perspectives on planets, both here and elsewhere. The result has been a debate about the meaning of the word "planet" itself. It is clear that scientists do not have a widely accepted or clear definition of what a planet is, and both scientists and the public are confused (and sometimes annoyed) by its use in various contexts. Because "planet" is a very widely used term, it seems worth the attempt to resolve this problem. In this essay, we try to cover all the issues that have come to the fore and bring clarity (if not resolution) to the debate

Hipparcos preliminary astrometric masses for the two close-in companions to HD 131664 and HD 43848. A brown dwarf and a low mass star

[abridged] We attempt to improve on the characterization of the properties (orbital elements, masses) of two Doppler-detected sub-stellar companions to the nearby G dwarfs HD 131664 and HD 43848. We carry out orbital fits to the Hipparcos IAD for the two stars, taking advantage of the knowledge of the spectroscopic orbits, and solving for the two orbital elements that can be determined in principle solely by astrometry, the inclination angle $i$ and the longitude of the ascending node $\Omega$. A number of checks are carried out in order to assess the reliability of the orbital solutions thus obtained. The best-fit solution for HD 131664 yields $i=55\pm33$ deg and $\Omega=22\pm28$ deg. The resulting inferred true companion mass is then $M_c = 23_{-5}^{+26}$ $M_J$. For \object{HD 43848}, we find $i=12\pm7$ deg and $\Omega=288\pm22$ deg, and $M_c = 120_{-43}^{+167}$ $M_J$. Based on the statistical evidence from an $F$-test, the study of the joint confidence intervals of variation of $i$ and $\Omega$, and the comparison of the derived orbital semi-major axes with a distribution of false astrometric orbits obtained for single stars observed by Hipparcos, the astrometric signal of the two companions to HD 131664 and HD 43848 is then considered detected in the Hipparcos IAD, with a level of statistical confidence not exceeding 95%. We constrain the true mass of HD 131664b to that of a brown dwarf to within a somewhat statistically significant degree of confidence ($\sim2-\sigma$). For HD 43848b, a true mass in the brown dwarf regime is ruled out at the $1-\sigma$ confidence level. [abridged]Comment: 13 pages, 6 figures, 4 tables. Accepted for publication in Astronomy & Astrophysic

High Orbital Eccentricities of Extrasolar Planets Induced by the Kozai Mechanism

One of the most remarkable properties of extrasolar planets is their high orbital eccentricities. Observations have shown that at least 20% of these planets, including some with particularly high eccentricities, are orbiting a component of a wide binary star system. The presence of a distant binary companion can cause significant secular perturbations to the orbit of a planet. In particular, at high relative inclinations, a planet can undergo a large-amplitude eccentricity oscillation. This so-called "Kozai mechanism" is effective at a very long range, and its amplitude is purely dependent on the relative orbital inclination. In this paper, we address the following simple question: assuming that every host star with a detected giant planet also has a (possibly unseen, e.g., substellar) distant companion, with reasonable distributions of orbital parameters and masses, how well could secular perturbations reproduce the observed eccentricity distribution of planets? Our calculations show that the Kozai mechanism consistently produces an excess of planets with very high (e >0.6) and very low (e < 0.1) eccentricities. The paucity of near-circular orbits in the observed sample cannot be explained solely by the Kozai mechanism, because, even with high enough inclinations, the Kozai mechanism often fails to produce significant eccentricity perturbations when there are other competing sources of orbital perturbations on secular timescales, such as general relativity. On the other hand, the Kozai mechanism can produce many highly eccentric orbits. Indeed the overproduction of high eccentricities observed in our models could be combined with plausible circularizing mechanisms (e.g., friction from residual gas) to create more intermediate eccentricities (e=0.1-0.6).Comment: 24 pages, 6 figures, ApJ, in press, minor changes to reflect the accepted versio

On the Possibility of Tidal Formation of Binary Planets Around Ordinary Stars

The planet formation process and subsequent planet migration may lead to configurations resulting in strong dynamical interactions among the various planets. Well-studied possible outcomes include collisions between planets, scattering events that eject one or more of the planets, and a collision of one or more of the planets with the parent star. In this work we consider one other possibility that has seemingly been overlooked in the various scattering calculations presented in the literature: the tidal capture of two planets which leads to the formation of a binary planet (or binary brown dwarf) in orbit about the parent star. We carry out extensive numerical simulations of such dynamical and tidal interactions to explore the parameter space for the formation of such binary planets. We show that tidal formation of binary planets is possible for typical planet masses and distances from the host star. The detection (or lack thereof) of planet-planet binaries can thus be used to constrain the properties of planetary systems, including their mutual spacing during formation, and the fraction of close planets in very eccentric orbits which are believed to form by a closely related process.Comment: 11 pages, 10 Figures, submitted to Ap

On the Mass Function, Multiplicity, and Origins of Wide-Orbit Giant Planets

A major outstanding question regarding the formation of planetary systems is whether wide-orbit giant planets form differently than close-in giant planets. We aim to establish constraints on two key parameters that are relevant for understanding the formation of wide-orbit planets: 1) the relative mass function and 2) the fraction of systems hosting multiple companions. In this study, we focus on systems with directly imaged substellar companions, and the detection limits on lower-mass bodies within these systems. First, we uniformly derive the mass probability distributions of known companions. We then combine the information contained within the detections and detection limits into a survival analysis statistical framework to estimate the underlying mass function of the parent distribution. Finally, we calculate the probability that each system may host multiple substellar companions. We find that 1) the companion mass distribution is rising steeply toward smaller masses, with a functional form of $N\propto M^{-1.3\pm0.3}$, and consequently, 2) many of these systems likely host additional undetected sub-stellar companions. Combined, these results strongly support the notion that wide-orbit giant planets are formed predominantly via core accretion, similar to the better studied close-in giant planets. Finally, given the steep rise in the relative mass function with decreasing mass, these results suggest that future deep observations should unveil a greater number of directly imaged planets.Comment: 19 pages, 10 figures, accepted to Ap