arXiv subjects

Konstantin Batygin

Publications and source records attributed to Konstantin Batygin.

At least 91 records · Page 5Linked to original sources

arXiv2020

Tidal Inflation Reconciles Low-Density Sub-Saturns with Core Accretion

While the Solar System contains no planets between the sizes of Uranus and Saturn, our current exoplanet census includes several dozen such planets with well-measured masses and radii. These sub-Saturns exhibit a diversity of bulk densities, ranging from ~$0.1-3\ \rm{g\ cm}^{-3}$. When modeled simply as hydrogen/helium envelopes atop rocky cores, this diversity in densities translates to a diversity in planetary envelope fractions, $f_\rm{env}=M_\rm{env}/M_p$ ranging from ~$10\%$ to ~$50\%$. Planets with $f_\rm{env}\sim50\%$ pose a challenge to traditional models of giant planet formation by core-nucleated accretion, which predict the onset of runaway gas accretion when $M_\rm{env}\sim M_\rm{core}$. Here we show that many of these apparent $f_\rm{env}\sim50\%$ planets are less envelope rich than they seem, after accounting for tidal heating. We present a new framework for modeling sub-Saturn interiors that incorporates envelope inflation due to tides, which are driven by the observed non-zero eccentricities, as well as potential obliquities. Consequently, when we apply our models to known sub-Saturns, we infer lower $f_\rm{env}$ than tides-free estimates. We present a case study of K2-19 b, a moderately eccentric sub-Saturn. Neglecting tides, K2-19 b appears to have $f_\rm{env}\sim50\%$, poised precariously near the runaway threshold; by including tides, we find $f_\rm{env}\sim10\%$, resolving the tension. Through a systematic analysis of $4-8\ R_{\oplus}$ planets, we find that most (but not all) of the similarly envelope-rich planets have more modest envelopes of $f_\rm{env}\sim10\%-20\%$. Thus, many sub-Saturns may be understood as sub-Neptunes that have undergone significant radius inflation, rather than a separate class of objects. Tidal radius inflation likely plays an important role in other size classes of planets including ultra-low-density Jupiter-size planets like WASP-107 b.

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arXiv2020

Formation of Giant Planet Satellites

Recent analyses have shown that the concluding stages of giant planet formation are accompanied by the development of large-scale meridional flow of gas inside the planetary Hill sphere. This circulation feeds a circumplanetary disk that viscously expels gaseous material back into the parent nebula, maintaining the system in a quasi-steady state. Here we investigate the formation of natural satellites of Jupiter and Saturn within the framework of this newly outlined picture. We begin by considering the long-term evolution of solid material, and demonstrate that the circumplanetary disk can act as a global dust trap, where $s_{\bullet}\sim0.1-10\,$mm grains achieve a hydrodynamical equilibrium, facilitated by a balance between radial updraft and aerodynamic drag. This process leads to a gradual increase in the system's metallicity, and eventually culminates in the gravitational fragmentation of the outer regions of the solid sub-disk into $\mathcal{R}\sim100\,$km satellitesimals. Subsequently, satellite conglomeration ensues via pairwise collisions, but is terminated when disk-driven orbital migration removes the growing objects from the satellitesimal feeding zone. The resulting satellite formation cycle can repeat multiple times, until it is brought to an end by photo-evaporation of the parent nebula. Numerical simulations of the envisioned formation scenario yield satisfactory agreement between our model and the known properties of the Jovian and Saturnian moons.

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arXiv2020

Strong Near-Infrared Spectral Variability of the Young Cloudy L Dwarf Companion VHS J1256-1257 b

Rotationally-modulated variability of brown dwarfs and giant planets provides unique information about their surface brightness inhomogeneities, atmospheric circulation, cloud evolution, vertical atmospheric structure, and rotational angular momentum. We report results from Hubble Space Telescope/Wide Field Camera 3 near-infrared time-series spectroscopic observations of three companions with masses in or near the planetary regime: VHS J125601.92-125723.9 b, GSC 6214-210 B, and ROXs 42 B b. VHS J1256-1257 b exhibits strong total intensity and spectral variability with a brightness difference of 19.3% between 1.1-1.7 $μ$m over 8.5 hours and even higher variability at the 24.7% level at 1.27 $μ$m. The light curve of VHS J1256-1257 b continues to rise at the end of the observing sequence so these values represent lower limits on the full variability amplitude at this epoch. This observed variability rivals (and may surpass) the most variable brown dwarf currently known, 2MASS J21392676+0220226. The implied rotation period of VHS J1256-1257 b is $\approx$21-24 hr assuming sinusoidal modulations, which is unusually long for substellar objects. No significant variability is evident in the light curves of GSC 6214-210 B ($<$1.2%) and ROXs 42 B b ($<$15.6%). With a spectral type of L7, an especially red spectrum, and a young age, VHS J1256-1257 b reinforces emerging patterns between high variability amplitude, low surface gravity, and evolutionary phase near the L/T transition.

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arXiv2020

Energy Optimization in Binary Star Systems: Explanation for Equal Mass Members in Close Orbits

Observations indicate that members of close stellar binaries often have mass ratios close to unity, while longer-period systems exhibit a more uniform mass-ratio distribution. This paper provides a theoretical explanation for this finding by determining the tidal equilibrium states for binary star systems --- subject to the constraints of conservation of angular momentum and constant total mass. This work generalizes previous treatments by including the mass fraction as a variable in the optimization problem. The results show that the lowest energy state accessible to the system corresponds to equal mass stars on a circular orbit, where the stellar spin angular velocities are both synchronized and aligned with the orbit. These features are roughly consistent with observed properties of close binary systems. We also find the conditions required for this minimum energy state to exist: [1] The total angular momentum must exceed a critical value, [2] the orbital angular momentum must be three times greater than the total spin angular momentum, and [3] the semimajor axis is bounded from above. The last condition implies that sufficiently wide binaries are not optimized with equal mass stars, where the limiting binary separation occurs near $a_0\approx16R_\ast$.

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arXiv2020

Energy Optimization in Extrasolar Planetary Systems: The Transition from Peas-in-a-Pod to Runaway Growth

Motivated by the trends found in the observed sample of extrasolar planets, this paper determines tidal equilibrium states for forming planetary systems --- subject to conservation of angular momentum, constant total mass, and fixed orbital spacing. In the low-mass limit, valid for superearth-class planets with masses of order $m_{\rm p}\sim10M_\oplus$, previous work showed that energy optimization leads to nearly equal mass planets, with circular orbits confined to a plane. The present treatment generalizes previous results by including the self-gravity of the planetary bodies. For systems with sufficiently large total mass $m_{\scriptstyle T}$ in planets, the optimized energy state switches over from the case of nearly equal mass planets to a configuration where one planet contains most of the material. This transition occurs for a critical mass threshold of approximately $m_{\scriptstyle T} \ge m_{\scriptstyle C}\sim40M_\oplus$ (where the value depends on the semimajor axes of the planetary orbits, the stellar mass, and other system properties). These considerations of energy optimization apply over a wide range of mass scales, from binary stars to planetary systems to the collection of moons orbiting the giant planets in our solar system.

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arXiv2020

Dynamics of Planetary Systems Within Star Clusters: Aspects of the Solar System's Early Evolution

Most planetary systems -- including our own -- are born within stellar clusters, where interactions with neighboring stars can help shape the system architecture. This paper develops an orbit-averaged formalism to characterize the cluster's mean-field effects as well as the physics of long-period stellar encounters. Our secular approach allows for an analytic description of the dynamical consequences of the cluster environment on its constituent planetary systems. We analyze special cases of the resulting Hamiltonian, corresponding to eccentricity evolution driven by planar encounters, as well as hyperbolic perturbations upon dissipative disks. We subsequently apply our results to the early evolution of our solar system, where the cluster's collective potential perturbs the solar system's plane, and stellar encounters act to increase the velocity dispersion of the Kuiper belt. Our results are two-fold: first, we find that cluster effects can alter the mean plane of the solar system by $\lesssim1°$, and are thus insufficient to explain the $ψ\approx6°$ obliquity of the sun. Second, we delineate the extent to which stellar flybys excite the orbital dispersion of the cold classical Kuiper belt, and show that while stellar flybys may grow the cold belt's inclination by the observed amount, the resulting distribution is incompatible with the data. Correspondingly, our calculations place an upper limit on the product of the stellar number density and residence time of the sun in its birth cluster, $η\,τ\lesssim2\times10^4\,$Myr/pc$^3$.

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arXiv2019

K2-19b and c are in a 3:2 Commensurability but out of Resonance: A Challenge to Planet Assembly by Convergent Migration

K2-19b and c were among the first planets discovered by NASA's K2 mission and together stand in stark contrast with the physical and orbital properties of the solar system planets. The planets are between the size of Uranus and Saturn at 7.0$\pm$0.2 R_E and 4.1$\pm$0.2 R_E, respectively, and reside a mere 0.1% outside the nominal 3:2 mean-motion resonance. They represent a different outcome of the planet formation process than the solar system, as well as the vast majority of known exoplanets. We measured the physical and orbital properties of these planets using photometry from K2, Spitzer, and ground-based telescopes, along with radial velocities from Keck/HIRES. Through a joint photodynamical model, we found that the planets have moderate eccentricities of $e \approx0.20$ and well-aligned apsides $Δ\varpi \approx 0$ deg. The planets occupy a strictly non-resonant configuration: the resonant angles circulate rather than librate. This defies the predictions of standard formation pathways that invoke convergent or divergent migration, both of which predict $Δ\varpi \approx 180$ deg and eccentricities of a few percent or less. We measured masses of $M_{p,b}$ = 32.4$\pm$1.7 M_E and $M_{p,c}$ = 10.8$\pm$0.6 M_E. Our measurements, with 5% fractional uncertainties, are among the most precise of any sub-Jovian exoplanet. Mass and size reflect a planet's core/envelope structure. Despite having a relatively massive core of $M_{core} \approx15$ $M_E$, K2-19b is envelope-rich, with an envelope mass fraction of roughly 50%. This planet poses a challenge to standard models core-nucleated accretion, which predict that cores $\gtrsim 10$ $M_E$ will quickly accrete gas and trigger runaway accretion when the envelope mass exceeds that of the core.

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arXiv2019

Aero-Resonant Migration

The process of planet conglomeration, which primarily unfolds in a geometrically thin disk of gas and dust, is often accompanied by dynamical excitation of the forming planets and planetesimals. The ensuing orbital crossing can lead to large-scale collisional fragmentation, populating the system with icy and rocky debris. In a gaseous nebula, such leftover solid matter tends to spiral down towards the host star due to aerodynamic drag. Along the way, the inward drifting debris can encounter planets and gravitationally couple to them via mean-motion resonances, sapping them of their orbital energy and causing them to migrate. Here, we develop a simple theory for this migration mechanism, which we call "Aero-Resonant Migration" (ARM), in which small planetesimals ($10\,$m $\lesssim s \lesssim 10\,$km) undergo orbital decay due to aerodynamic drag and resonantly shepherd planets ahead of them. Using a combination of analytical calculations and numerical experiments, we show that ARM is a robust migration mechanism, able to significantly transport planets on timescales $\lesssim1$ Myr, and present simple formulae for the ARM rate.

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arXiv2019

Excitation of Planetary Obliquities Through Planet-Disk Interactions

The tilt of a planet's spin axis off its orbital axis ("obliquity") is a basic physical characteristic that plays a central role in determining the planet's global circulation and energy redistribution. Moreover, recent studies have also highlighted the importance of obliquities in sculpting not only the physical features of exoplanets but also their orbital architectures. It is therefore of key importance to identify and characterize the dominant processes of excitation of non-zero axial tilts. Here we highlight a simple mechanism that operates early on and is likely fundamental for many extrasolar planets and perhaps even Solar System planets. While planets are still forming in the protoplanetary disk, the gravitational potential of the disk induces nodal recession of the orbits. The frequency of this recession decreases as the disk dissipates, and when it crosses the frequency of a planet's spin axis precession, large planetary obliquities may be excited through capture into a secular spin-orbit resonance. We study the conditions for encountering this resonance and calculate the resulting obliquity excitation over a wide range of parameter space. Planets with semi-major axes in the range $0.3 \ \mathrm{AU} \lesssim a \lesssim 2 \ \mathrm{AU}$ are the most readily affected, but large-$a$ planets can also be impacted. We present a case study of Uranus and Neptune and show that this mechanism likely cannot help explain their high obliquities. While it could have played a role if finely tuned and envisioned to operate in isolation, large-scale obliquity excitation was likely inhibited by gravitational planet-planet perturbations.

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arXiv2019

The role of dissipative evolution for three-planet, near-resonant extrasolar systems

Early dynamical evolution of close-in planetary systems is shaped by an intricate combination of planetary gravitational interactions, orbital migration, and dissipative effects. While the process of convergent orbital migration is expected to routinely yield resonant planetary systems, previous analyses have shown that the semi-major axes of initially resonant pairs of planets will gradually diverge under the influence of long-term energy damping, producing an overabundance of planetary period ratios in slight excess of exact commensurability. While this feature is clearly evident in the orbital distribution of close-in extrasolar planets, the existing theoretical picture is limited to the specific case of the planetary three-body problem. In this study, we generalise the framework of dissipative divergence of resonant orbits to multi-resonant chains, and apply our results to the current observational census of well-characterised three-planet systems. Focusing on the 2:1 and 3:2 commensurabilities, we identify three 3-planet systems, whose current orbital architecture is consistent with an evolutionary history wherein convergent migration first locks the planets into a multi-resonant configuration and subsequent dissipation repels the orbits away from exact commensurability. Nevertheless, we find that the architecture of the overall sample of multi planetary systems is incompatible with this simple scenario, suggesting that additional physical mechanisms must play a dominant role during the early stages of planetary systems' dynamical evolution.

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arXiv2019

On the Anomalous Acceleration of 1I/2017 U1 `Oumuamua

We show that the $P\sim8\,{\rm h}$ photometric period and the astrometrically measured $A_{\rm ng}\sim2.5\times10^{-4}\,{\rm cm\,s^{-2}}$ non-gravitational acceleration (at $r\sim1.4\,{\rm AU}$) of the interstellar object 1I/2017 (`Oumuamua) can be explained by a nozzle-like venting of volatiles whose activity migrated to track the sub-solar location on the object's surface. Adopting the assumption that `Oumuamua was an elongated $a\times b \times c$ ellipsoid, this model produces a pendulum-like rotation of the body and implies a long semi-axis $a\sim 5A_{\rm ng}P^2/4π^2 \sim 260\,{\rm m}$. This scale agrees with the independent estimates of `Oumuamua's size that stem from its measured brightness, assuming an albedo of $p\sim0.1$, appropriate to ices that have undergone long-duration exposure to the interstellar cosmic ray flux. Using ray-tracing, we generate light curves for ellipsoidal bodies that are subject to both physically consistent sub-solar torques and to the time-varying geometry of the Sun-Earth-`Oumuamua configuration. Our synthetic light curves display variations from chaotic tumbling and changing cross-sectional illumination that are consistent with the observations, while avoiding significant secular changes in the photometric periodicity. If our model is correct, `Oumuamua experienced mass loss that wasted $\sim 10\%$ of its total mass during the $\sim 100\,{\rm d}$ span of its encounter with the inner Solar System and had an icy composition with a very low $[{\rm C}/{\rm O}]\lesssim 0.003$. Our interpretation of `Oumuamua's behavior is consistent with the hypothesis that it was ejected from either the outer regions of a planetesimal disk after an encounter with an embedded $M_{\rm p} \sim M_{\rm Nep}$ planet or from an exo-Oort cloud.

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arXiv2019

The Planet Nine Hypothesis

Over the course of the past two decades, observational surveys have unveiled the intricate orbital structure of the Kuiper Belt, a field of icy bodies orbiting the Sun beyond Neptune. In addition to a host of readily-predictable orbital behavior, the emerging census of trans-Neptunian objects displays dynamical phenomena that cannot be accounted for by interactions with the known eight-planet solar system alone. Specifically, explanations for the observed physical clustering of orbits with semi-major axes in excess of $\sim250\,$AU, the detachment of perihelia of select Kuiper belt objects from Neptune, as well as the dynamical origin of highly inclined/retrograde long-period orbits remain elusive within the context of the classical view of the solar system. This newly outlined dynamical architecture of the distant solar system points to the existence of a new planet with mass of $m_9\sim 5-10\,M_{\oplus}$, residing on a moderately inclined orbit ($i_9\sim15-25°$) with semi-major axis $a_9\sim 400 - 800\,$AU and eccentricity between $e_9 \sim 0.2 - 0.5$. This paper reviews the observational motivation, dynamical constraints, and prospects for detection of this proposed object known as Planet Nine.

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arXiv2019

An Excess of Jupiter Analogs in Super-Earth Systems

We use radial velocity observations to search for long-period gas giant companions in systems hosting inner super-Earth (1-4 R_Earth, 1-10 M_Earth) planets to constrain formation and migration scenarios for this population. We consistently re-fit published RV datasets for 65 stars and find 9 systems with statistically significant trends indicating the presence of an outer companion. We combine these RV data with AO images to constrain the masses and semi-major axes of these companions. We quantify our sensitivity to the presence of long-period companions by fitting the sample with a power law distribution and find an occurrence rate of 39+/-7% for companions 0.5-20 M_Jup and 1-20 AU. Half of our systems were discovered by the transit method and half were discovered by the RV method. While differences in RV baselines and number of data points between the two samples lead to different sensitivities to distant companions, we find that occurrence rates of gas giant companions in each sample are consistent at the 0.5$σ$ level. We compare the frequency of Jupiter analogs in these systems to the equivalent rate from field star surveys and find that Jupiter analogs are more common around stars hosting super-Earths. We conclude that the presence of outer gas giants does not suppress the formation of inner super-Earths, and that these two populations of planets instead appear to be correlated. We also find that the stellar metallicities of systems with gas giant companions are higher than those without companions, in agreement with the well-established metallicity correlation from RV surveys of field stars.

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arXiv2019

Orbital clustering in the distant solar system

The most distant Kuiper belt objects appear to be clustered in longitude of perihelion and in orbital pole position. To date, the only two suggestions for the cause of these apparent clusterings have been either the effects of observational bias or the existence of the distant giant planet in an eccentric inclined orbit known as Planet Nine. To determine if observational bias can be the cause of these apparent clusterings, we develop a rigorous method of quantifying the observational biases in the observations of longitude of perihelion and orbital pole position. From this now more complete understanding of the biases we calculate that the probability that these distant Kuiper belt objects would be clustered as strongly as observed in both longitude of perihelion and in orbital pole position is only 0.2%. While explanations other than Planet Nine may someday be found, the statistical significance of this clustering is now difficult to discount.

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arXiv2018

The hot Jupiter period-mass distribution as a signature of in situ formation

More than two decades after the widespread detection of Jovian-class planets on short-period orbits around other stars, their dynamical origins remain imperfectly understood. In the traditional narrative, these highly irradiated giant planets, like Jupiter and Saturn, are envisioned to have formed at large stello-centric distances and to have subsequently undergone large-scale orbital decay. Conversely, more recent models propose that a large fraction of hot Jupiters could have formed via rapid gas accretion in their current orbital neighborhood. In this study, we examine the period-mass distribution of close-in giant planets, and demonstrate that the inner boundary of this population conforms to the expectations of the in-situ formation scenario. Specifically, we show that if conglomeration unfolds close to the disk's inner edge, the semi-major axis - mass relation of the emergent planets should follow a power law $a \propto M^{-2/7}$ - a trend clearly reflected in the data. We further discuss corrections to this relationship due to tidal decay of planetary orbits. Although our findings do not discount orbital migration as an active physical process, they suggest that the characteristic range of orbital migration experienced by giant planets is limited.

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arXiv2018

Feasibility of a resonance-based Planet Nine search

It has been proposed that mean motion resonances (MMRs) between Planet Nine and distant objects of the scattered disk might inform the semimajor axis and instantaneous position of Planet Nine. Within the context of this hypothesis, the specific distribution of occupied MMRs largely determines the available constraints. Here we characterize the behavior of scattered Kuiper Belt objects arising in the presence of an eccentric Planet Nine ($e_9 \in 0.1$, $0.7$), focusing on relative sizes of populations occupying particular commensurabilities. Highlighting the challenge of predicting the exact MMR of a given object, we find that the majority of resonant test particles have period ratios with Planet Nine other than those of the form $P_9/P=N/1$, $N/2$ $(N \in \mathbb{Z}^+)$. Taking into account the updated prior distribution of MMRs outlined in this work, we find that the close spacing of high-order resonances, as well as chaotic transport, preclude resonance-based Planet Nine constraints from current observational data.

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arXiv2018

Characterizing K2 Candidate Planetary Systems Orbiting Low-Mass Stars III: A High Mass & Low Envelope Fraction for the Warm Neptune K2-55b

K2-55b is a Neptune-sized planet orbiting a K7 dwarf with a radius of $0.715^{+0.043}_{-0.040}R_\odot$, a mass of $0.688\pm0.069 M_\odot$, and an effective temperature of $4300^{+107}_{-100}$K. Having characterized the host star using near-infrared spectra obtained at IRTF/SpeX, we observed a transit of K2-55b with Spitzer/IRAC and confirmed the accuracy of the original K2 ephemeris for future follow-up transit observations. Performing a joint fit to the Spitzer/IRAC and K2 photometry, we found a planet radius of $4.41^{+0.32}_{-0.28} R_\oplus$, an orbital period of $2.84927265_{-6.42\times10^{-6}}^{+6.87\times10^{-6}}$ days, and an equilibrium temperature of roughly 900K. We then measured the planet mass by acquiring twelve radial velocity (RV) measurements of the system using HIRES on the 10m Keck I Telescope. Our RV data set precisely constrains the mass of K2-55b to $43.13^{+5.98}_{-5.80} M_\oplus$, indicating that K2-55b has a bulk density of $2.8_{-0.6}^{+0.8}$ g cm$^{-3}$ and can be modeled as a rocky planet capped by a modest H/He envelope ($M_{\rm envelope} = 12\pm3\% M_p$). K2-55b is denser than most similarly sized planets, raising the question of whether the high planetary bulk density of K2-55b could be attributed to the high metallicity of K2-55. The absence of a substantial volatile envelope despite the large mass of K2-55b poses a challenge to current theories of gas giant formation. We posit that K2-55b may have escaped runaway accretion by migration, late formation, or inefficient core accretion or that K2-55b was stripped of its envelope by a late giant impact.

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arXiv2018

Dynamics and Formation of the Near-Resonant K2-24 System: Insights from Transit-Timing Variations and Radial Velocities

While planets between the size of Uranus and Saturn are absent within the Solar System, the star K2-24 hosts two such planets, K2-24b and c, with radii equal to $5.4~R_E$ and $7.5~R_E$, respectively. The two planets have orbital periods of 20.9 days and 42.4 days, residing only 1% outside the nominal 2:1 mean-motion resonance. In this work, we present results from a coordinated observing campaign to measure planet masses and eccentricities that combines radial velocity (RV) measurements from Keck/HIRES and transit-timing measurements from K2 and Spitzer. K2-24b and c have low, but non-zero, eccentricities of $e_1 \sim e_2 \sim 0.08$. The low observed eccentricities provide clues regarding the formation and dynamical evolution of K2-24b and K2-24c, suggesting that they could be the result of stochastic gravitational interactions with a turbulent protoplanetary disk, among other mechanisms. K2-24b and c are $19\pm2~M_E$ and $15\pm2~M_E$, respectively; K2-24c is 20% less massive than K2-24b, despite being 40% larger. Their large sizes and low masses imply large envelope fractions, which we estimate at $26^{+3}_{-3}\%$ and $52^{+5}_{-3}\%$. In particular, K2-24c's large envelope presents an intriguing challenge to the standard model of core nucleated accretion that predicts the onset of runaway accretion when $f_{env} \approx 50\%$.

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