arXiv subjects

Konstantin Batygin

Publications and source records attributed to Konstantin Batygin.

At least 145 records · Page 8Linked to original sources

arXiv2014

Pre-LHB Evolution of the Earth's Obliquity

The Earth's obliquity is stabilized by the Moon, which facilitates a rapid precession of the Earth's spin-axis, de-tuning the system away from resonance with orbital modulation. It is however, likely that the architecture of the Solar System underwent a dynamical instability-driven transformation, where the primordial configuration was more compact. Hence, the characteristic frequencies associated with orbital perturbations were likely faster in the past, potentially allowing for secular resonant encounters. In this work we examine if at any point in the Earth's evolutionary history, the obliquity varied significantly. Our calculations suggest that even though the orbital perturbations were different, the system nevertheless avoided resonant encounters throughout its evolution. This indicates that the Earth obtained its current obliquity during the formation of the Moon.

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arXiv2014

Non-Axisymmetric Flows on Hot Jupiters with Oblique Magnetic Fields

Giant planets that reside in close proximity to their host stars are subject to extreme irradiation, which gives rise to thermal ionization of trace Alkali metals in their atmospheres. On objects where the atmospheric electrical conductivity is substantial, the global circulation couples to the background magnetic field, inducing supplementary fields and altering the nature of the flow. To date, a number of authors have considered the influence of a spin-pole aligned dipole magnetic field on the dynamical state of a weakly-ionized atmosphere and found that magnetic breaking may lead to significantly slower winds than predicted within a purely hydrodynamical framework. Here, we consider the effect of a tilted dipole magnetic field on the circulation and demonstrate that in addition to regulating wind velocities, an oblique field generates stationary non-axisymmetric structures that adhere to the geometry of the magnetic pole. Using a kinematic perturbative approach, we derive a closed-form solution for the perturbed circulation and show that the fractional distortion of zonal jets scales as the product of the field obliquity and the Elsasser number. The results obtained herein suggest that on planets with oblique magnetic fields, advective shifts of dayside hotspots may have substantial latitudinal components. This prediction may be tested observationally using the eclipse mapping technique.

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arXiv2014

Early Excitation of Spin-Orbit Misalignments in Close-in Planetary Systems

Continued observational characterization of transiting planets that reside in close proximity to their host stars has shown that a substantial fraction of such objects posses orbits that are inclined with respect to the spin axes of their stars. Mounting evidence for the wide-spread nature of this phenomenon has challenged the conventional notion that large-scale orbital transport occurs during the early epochs of planet formation and is accomplished via planet-disk interactions. However, recent work has shown that the excitation of spin-orbit misalignment between protoplanetary nebulae and their host stars can naturally arise from gravitational perturbations in multi-stellar systems as well as magnetic disk-star coupling. In this work, we examine these processes in tandem. We begin with a thorough exploration of the gravitationally-facilitated acquisition of spin-orbit misalignment and analytically show that the entire possible range of misalignments can be trivially reproduced. Moreover, we demonstrate that the observable spin-orbit misalignment only depends on the primordial disk-binary orbit inclination. Subsequently, we augment our treatment by accounting for magnetic torques and show that more exotic dynamical evolution is possible, provided favorable conditions for magnetic tilting. Cumulatively, our results suggest that observed spin-orbit misalignments are fully consistent with disk-driven migration as a dominant mechanism for the origin of close-in planets.

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arXiv2014

Spin-Orbit angle distribution and the origin of (mis)aligned hot Jupiters

For 61 transiting hot Jupiters, the projection of the angle between the orbital plane and the stellar equator (called the spin-orbit angle) has been measured. For about half of them, a significant misalignment is detected, and retrograde planets have been observed. This challenges scenarios of the formation of hot Jupiters. In order to better constrain formation models, we relate the distribution of the real spin-orbit angle $Ψ$ to the projected one $β$. Then, a comparison with the observations is relevant. We analyse the geometry of the problem to link analytically the projected angle $β$ to the real spin-orbit angle $Ψ$. The distribution of $Ψ$ expected in various models is taken from the literature, or derived with a simplified model and Monte-Carlo simulations in the case of the disk-torquing mechanism. An easy formula to compute the probability density function (PDF) of $β$ knowing the PDF of $Ψ$ is provided. All models tested here look compatible with the observed distribution beyond 40 degrees, which is so far poorly constrained by only 18 observations. But only the disk-torquing mechanism can account for the excess of aligned hot Jupiters, provided that the torquing is not always efficient. This is the case if the exciting binaries have semi-major axes as large as 10000 AU. Based on comparison with the set of observations available today, scattering models and the Kozai cycle with tidal friction models can not be solely responsible for the production of all hot Jupiters. Conversely, the presently observed distribution of the spin-orbit angles is compatible with most hot Jupiters having been transported by smooth migration inside a proto-planetary disk, itself possibly torqued by a companion.

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arXiv2014

On the Spin-axis Dynamics of a Moonless Earth

The variation of a planet's obliquity is influenced by the existence of satellites with a high mass ratio. For instance, the Earth's obliquity is stabilized by the Moon, and would undergo chaotic variations in the Moon's absence. In turn, such variations can lead to large-scale changes in the atmospheric circulation, rendering spin-axis dynamics a central issue for understanding climate. The relevant quantity for dynamically-forced climate change is the rate of chaotic diffusion. Accordingly, here we reexamine the spin-axis evolution of a Moonless Earth within the context of a simplified perturbative framework. We present analytical estimates of the characteristic Lyapunov coefficient as well as the chaotic diffusion rate and demonstrate that even in absence of the Moon, the stochastic change in the Earth's obliquity is sufficiently slow to not preclude long-term habitability. Our calculations are consistent with published numerical experiments and illustrate the putative system's underlying dynamical structure in a simple and intuitive manner.

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arXiv2014

WASP-12b and HAT-P-8b are Members of Triple Star Systems

We present high spatial resolution images that demonstrate the hot Jupiters WASP-12b and HAT-P-8b orbit the primary star of hierarchical triple star systems. In each case, two distant companions with colors and brightness consistent with M dwarfs co-orbit the planet host as well as one another. Our adaptive optics images spatially resolve the secondary around WASP-12, previously identified by Bergfors et al. 2011 and Crossfield et al. 2012, into two distinct sources separated by 84.3+/-0.6 mas (21 +/- 3 AU). We find that the secondary to HAT-P-8, also identified by Bergfors et al. 2011, is in fact composed of two stars separated by 65.3+/-0.5 mas (15+/-1 AU). Our follow-up observations demonstrate physical association through common proper-motion. HAT-P-8 C has a particularly low mass, which we estimate to be 0.18+/-0.02Msun using photometry. Due to their hierarchy, WASP-12 BC and HAT-P-8 BC will enable the first dynamical mass determination for hot Jupiter stellar companions. These previously well-studied planet hosts now represent higher-order multi-star systems with potentially complex dynamics, underscoring the importance of diffraction-limited imaging and providing additional context for understanding the migrant population of transiting hot Jupiters.

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arXiv2014

Friends of Hot Jupiters I: A Radial Velocity Search for Massive, Long-Period Companions to Close-In Gas Giant Planets

In this paper we search for distant massive companions to known transiting gas giant planets that may have influenced the dynamical evolution of these systems. We present new radial velocity observations for a sample of 51 planets obtained using the Keck HIRES instrument, and find statistically significant accelerations in fifteen systems. Six of these systems have no previously reported accelerations in the published literature: HAT-P-10, HAT-P-22, HAT-P-29, HAT-P-32, WASP-10, and XO-2. We combine our radial velocity fits with Keck NIRC2 adaptive optics (AO) imaging data to place constraints on the allowed masses and orbital periods of the companions responsible for the detected accelerations. The estimated masses of the companions range between 1-500 M_Jup, with orbital semi-major axes typically between 1-75 AU. A significant majority of the companions detected by our survey are constrained to have minimum masses comparable to or larger than those of the transiting planets in these systems, making them candidates for influencing the orbital evolution of the inner gas giant. We estimate a total occurrence rate of 51 +/- 10% for companions with masses between 1-13 M_Jup and orbital semi-major axes between 1-20 AU in our sample. We find no statistically significant difference between the frequency of companions to transiting planets with misaligned or eccentric orbits and those with well-aligned, circular orbits. We combine our expanded sample of radial velocity measurements with constraints from transit and secondary eclipse observations to provide improved measurements of the physical and orbital characteristics of all of the planets included in our survey.

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arXiv2014

The Absolute Magnitude Distribution of Kuiper Belt Objects

Here we measure the absolute magnitude distributions (H-distribution) of the dynamically excited and quiescent (hot and cold) Kuiper Belt objects (KBOs), and test if they share the same H-distribution as the Jupiter Trojans. From a compilation of all useable ecliptic surveys, we find that the KBO H-distributions are well described by broken power-laws. The cold population has a bright-end slope, $α_{\textrm{1}}=1.5_{-0.2}^{+0.4}$, and break magnitude, $H_{\textrm{B}}=6.9_{-0.2}^{+0.1}$ (r'-band). The hot population has a shallower bright-end slope of, $α_{\textrm{1}}=0.87_{-0.2}^{+0.07}$, and break magnitude $H_{\textrm{B}}=7.7_{-0.5}^{+1.0}$. Both populations share similar faint end slopes of $α_2\sim0.2$. We estimate the masses of the hot and cold populations are $\sim0.01$ and $\sim3\times10^{-4} \mbox{ M$_{\bigoplus}$}$. The broken power-law fit to the Trojan H-distribution has $α_\textrm{1}=1.0\pm0.2$, $α_\textrm{2}=0.36\pm0.01$, and $H_{\textrm{B}}=8.3$. The KS test reveals that the probability that the Trojans and cold KBOs share the same parent H-distribution is less than 1 in 1000. When the bimodal albedo distribution of the hot objects is accounted for, there is no evidence that the H-distributions of the Trojans and hot KBOs differ. Our findings are in agreement with the predictions of the Nice model in terms of both mass and H-distribution of the hot and Trojan populations. Wide field survey data suggest that the brightest few hot objects, with $H_{\textrm{r'}}\lesssim3$, do not fall on the steep power-law slope of fainter hot objects. Under the standard hierarchical model of planetesimal formation, it is difficult to account for the similar break diameters of the hot and cold populations given the low mass of the cold belt.

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arXiv2013

Magnetic and Gravitational Disk-Star Interactions: An Interdependence of PMS Stellar Rotation Rates and Spin-Orbit Misalignments

The presence of giant gaseous planets that reside in close proximity to their host stars may be a consequence of large-scale radial migration through the proto-planetary nebulae. Within the context of this picture, significant orbital obliquities characteristic of a substantial fraction of such planets can be attributed to external torques that perturb the disks out of alignment with the spin axes of their host stars. Therefore, the acquisition of orbital obliquity exhibits sensitive dependence on the physics of disk-star interactions. Here, we analyze the primordial excitation of spin-orbit misalignment of Sun-like stars, in light of disk-star angular momentum transfer. We begin by calculating the stellar pre-main sequence rotational evolution, accounting for spin-up due to gravitational contraction and accretion as well as spin-down due to magnetic star-disk coupling. We devote particular attention to angular momentum transfer by accretion, and show that while generally subdominant to gravitational contraction, this process is largely controlled by the morphology of the stellar magnetic field (i.e. specific angular momentum accreted by stars with octupole-dominated surface fields is smaller than that accreted by dipole-dominated stars by an order of magnitude). Subsequently, we examine the secular spin-axis dynamics of disk-bearing stars, accounting for the time-evolution of stellar and disk properties and demonstrate that misalignments are preferentially excited in systems where stellar rotation is not overwhelmingly rapid. Moreover, we show that the excitation of spin-orbit misalignment occurs impulsively, through an encounter with a resonance between the stellar precession frequency and the disk-torquing frequency. Cumulatively, the model developed herein opens up a previously unexplored avenue towards understanding star-disk evolution and its consequences in a unified manner.

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arXiv2013

Dynamical Measurements of the Interior Structure of Exoplanets

Giant gaseous planets often reside on orbits in sufficient proximity to their host stars for the planetary quadrupole gravitational field to become non-negligible. In presence of an additional planetary companion, a precise characterization of the system's orbital state can yield meaningful constraints on the transiting planet's interior structure. However, such methods can require a very specific type of system. This paper explores the dynamic range of applicability of these methods and shows that interior structure calculations are possible for a wide array of orbital architectures. The HAT-P-13 system is used as a case study, and the implications of perturbations arising from a third distant companion on the feasibility of an interior calculation are discussed. We find that the method discussed here is likely to be useful in studying other planetary systems, allowing the possibility of an expanded survey of the interiors of exoplanets.

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arXiv2013

Magnetically Controlled Circulation on Hot Extrasolar Planets

Through the process of thermal ionization, intense stellar irradiation renders Hot Jupiter atmospheres electrically conductive. Simultaneously, lateral variability in the irradiation drives the global circulation with peak wind speeds of order ~ km/s. In turn, the interactions between the atmospheric flows and the background magnetic field give rise to Lorentz forces that can act to perturb the flow away from its purely hydrodynamical counterpart. Using analytical theory and numerical simulations, here we show that significant deviations away from axisymmetric circulation are unstable in presence of a non-negligible axisymmetric magnetic field. Specifically, our results suggest that dayside-to-nightside flows, often obtained within the context of three-dimensional circulation models, only exist on objects with anomalously low magnetic fields, while the majority of highly irradiated exoplanetary atmospheres are entirely dominated by zonal jets.

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arXiv2013

Analytical Treatment of Planetary Resonances

An ever-growing observational aggregate of extrasolar planets has revealed that systems of planets that reside in or near mean-motion resonances are relatively common. While the origin of such systems is attributed to protoplanetary disk-driven migration, a qualitative description of the dynamical evolution of resonant planets remains largely elusive. Aided by the pioneering works of the last century, we formulate an approximate, integrable theory for first-order resonant motion. We utilize the developed theory to construct an intuitive, geometrical representation of resonances within the context of the unrestricted three-body problem. Moreover, we derive a simple analytical criterion for the appearance of secondary resonances between resonant and secular motion. Subsequently, we demonstrate the onset of rapid chaotic motion as a result of overlap among neighboring first-order mean-motion resonances, as well as the appearance of slow chaos as a result of secular modulation of the planetary orbits. Finally, we take advantage of the integrable theory to analytically show that, in the adiabatic regime, divergent encounters with first-order mean-motion resonances always lead to persistent apsidal anti-alignment.

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arXiv2013

A Primordial Origin for Misalignments Between Stellar Spin Axes and Planetary Orbits

The presence of gaseous giant planets whose orbits lie in extreme proximity to their host stars ("hot Jupiters"), can largely be accounted for by planetary migration, associated with viscous evolution of proto-planetary nebulae. Recently, observations of the Rossiter-McLaughlin effect during planetary transits have revealed that a considerable fraction of detected hot Jupiters reside on orbits that are misaligned with respect to the spin-axes of their host stars. This observational fact has cast significant doubts on the importance of disk-driven migration as a mechanism for production of hot Jupiters, thereby reestablishing the origins of close-in planetary orbits as an open question. Here we show that misaligned orbits can be a natural consequence of disk migration. Our argument rests on an enhanced abundance of binary stellar companions in star formation environments, whose orbital plane is uncorrelated with the spin axes of the individual stars. We analyze the dynamical evolution of idealized proto-planetary disks under perturbations from massive distant bodies and demonstrate that the resulting gravitational torques act to misalign the orbital planes of the disks relative to the spin poles of their host stars. As a result, we predict that in the absence of strong disk-host star angular momentum coupling or sufficient dissipation that acts to realign the stellar spin axis and the planetary orbits, the fraction of planetary systems (including systems of hot Neptunes and Super-Earths), whose angular momentum vectors are misaligned with respect to their host-stars should be commensurate with the rate of primordial stellar multiplicity.

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arXiv2013

Mass-Radius Relationships for Very Low Mass Gaseous Planets

Recently, the Kepler spacecraft has detected a sizable aggregate of objects, characterized by giant-planet-like radii and modest levels of stellar irradiation. With the exception of a handful of objects, the physical nature, and specifically the average densities, of these bodies remain unknown. Here, we propose that the detected giant planet radii may partially belong to planets somewhat less massive than Uranus and Neptune. Accordingly, in this work, we seek to identify a physically sound upper limit to planetary radii at low masses and moderate equilibrium temperatures. As a guiding example, we analyze the interior structure of the Neptune-mass planet Kepler-30d and show that it is acutely deficient in heavy elements, especially compared with its solar system counterparts. Subsequently, we perform numerical simulations of planetary thermal evolution and in agreement with previous studies, show that generally, 10 - 20 Earth mass, multi-billion year old planets, composed of high density cores and extended H/He envelopes can have radii that firmly reside in the giant planet range. We subject our results to stability criteria based on extreme ultraviolet radiation, as well as Roche-lobe overflow driven mass-loss and construct mass-radius relationships for the considered objects. We conclude by discussing observational avenues that may be used to confirm or repudiate the existence of putative low mass, gas-dominated planets.

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arXiv2012

NOTE: Explaining why the Uranian satellites have equatorial prograde orbits despite the large planetary obliquity

We show that the existence of prograde equatorial satellites is consistent with a collisional tilting scenario for Uranus. In fact, if the planet was surrounded by a proto-satellite disk at the time of the tilting and a massive ring of material was temporarily placed inside the Roche radius of the planet by the collision, the proto-satellite disk would have started to precess incoherently around the equator of the planet, up to a distance greater than that of Oberon. Collisional damping would then have collapsed it into a thin equatorial disk, from which the satellites eventually formed. The fact that the orbits of the satellites are prograde requires Uranus to have had a non-negligible initial obliquity (comparable to that of Neptune) before it was finally tilted to 98 degrees.

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arXiv2012

Dissipative Divergence of Resonant Orbits

A considerable fraction of multi-planet systems discovered by the observational surveys of extrasolar planets reside in mild proximity to first-order mean motion resonances. However, the relative remoteness of such systems from nominal resonant period ratios (e.g. 2:1, 3:2, 4:3) has been interpreted as evidence for lack of resonant interactions. Here we show that a slow divergence away from exact commensurability is a natural outcome of dissipative evolution and demonstrate that libration of critical angles can be maintained tens of percent away from nominal resonance. We construct an analytical theory for the long-term dynamical evolution of dissipated resonant planetary pairs and confirm our calculations numerically. Collectively, our results suggest that a significant fraction of the near-commensurate extrasolar planets are in fact resonant and have undergone significant dissipative evolution.

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arXiv2012

Evolution of Ohmically Heated Hot Jupiters

We present calculations of thermal evolution of Hot Jupiters with various masses and effective temperatures under Ohmic dissipation. The resulting evolutionary sequences show a clear tendency towards inflated radii for effective temperatures that give rise to significant ionization of alkali metals in the atmosphere, compatible with the trend of the data. The degree of inflation shows that Ohmic dissipation, along with the likely variability in heavy element content can account for all of the currently detected radius anomalies. Furthermore, we find that in absence of a massive core, low-mass hot Jupiters can over-flow their Roche-lobes and evaporate on Gyr time-scales, possibly leaving behind small rocky cores.

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arXiv2011

Instability-Driven Dynamical Evolution Model of a Primordially 5 Planet Outer Solar System

Over the last decade, evidence has mounted that the solar system's observed state can be favorably reproduced in the context of an instability-driven dynamical evolution model, such as the "Nice" model. To date, all successful realizations of instability models have concentrated on evolving the four giant planets onto their current orbits from a more compact configuration. Simultaneously, the possibility of forming and ejecting additional planets has been discussed, but never successfully implemented. Here we show that a large array of 5-planet (2 gas giants + 3 ice giants) multi-resonant initial states can lead to an adequate formation of the outer solar system, featuring an ejection of an ice giant during a phase of instability. Particularly, our simulations demonstrate that the eigenmodes which characterize the outer solar system's secular dynamics can be closely matched with a 5-planet model. Furthermore, provided that the ejection timescale of the extra planet is short, orbital excitation of a primordial cold classical Kuiper belt can also be avoided in this scenario. Thus the solar system is one of many possible outcomes of dynamical relaxation and can originate from a wide variety of initial states. This deems the construction of a unique model of solar system's early dynamical evolution impossible.

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