arXiv subjects

Yoram Lithwick

Publications and source records attributed to Yoram Lithwick.

At least 37 records · Page 2Linked to original sources

arXiv2016

Secular dynamics of multiplanet systems: implications for the formation of hot and warm Jupiters via high-eccentricity migration

Hot Jupiters (HJs) are Jupiter-like planets that reside very closely to their host star, within $\sim 0.1\,\mathrm{AU}$. Their formation is not well understood. It is generally believed that they cannot have formed in situ, implying that some form of migration must have occurred after their initial formation. We study the production of HJs through secular evolution in multiplanet systems with three to five planets. In this variant of high-$e$ migration, the eccentricity of the orbit of the innermost planet is excited on secular time-scales, triggering orbital migration due to tidal dissipation. We use a secular dynamics code and carry out a population synthesis study. We find that HJs are only produced if the viscous time-scale is short ($\approx 0.014$ yr). In contrast, in up to $\approx 0.3$ of systems, the innermost planet is tidally disrupted. The orbital period distribution is peaked around 5 d, consistent with observations. The median HJ mass is $1\,M_\mathrm{J}$ with a maximum of $\approx 2 \, M_\mathrm{J}$, similar to observed HJs. Approximately 0.1 of the HJs have retrograde orbits with respect to the stellar spin. We do not find any warm Jupiters in our simulations, i.e. planets with semimajor axes between 0.1 and 1 AU.

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arXiv2016

Kepler Planet Masses and Eccentricities from TTV Analysis

We conduct a uniform analysis of the transit timing variations (TTVs) of 145 planets from 55 Kepler multiplanet systems to infer planet masses and eccentricities. Eighty of these planets do not have previously reported mass and eccentricity measurements. We employ two complementary methods to fit TTVs: Markov chain Monte Carlo simulations based on N-body integration and an analytic fitting approach. Mass measurements of 49 planets, including 12 without previously reported masses, meet our criterion for classification as robust. Using mass and radius measurements, we infer the masses of planets' gaseous envelopes for both our TTV sample as well as transiting planets with radial velocity observations. Insight from analytic TTV formulae allows us to partially circumvent degeneracies inherent to inferring eccentricities from TTV observations. We find that planet eccentricities are generally small, typically a few percent, but in many instances are non-zero.

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arXiv2016

Dynamical constraints on the origin of hot and warm Jupiters with close friends

Gas giants orbiting their host star within the ice line are thought to have migrated to their current locations from farther out. Here we consider the origin and dynamical evolution of observed Jupiters, focusing on hot and warm Jupiters with outer friends. We show that the majority of the observed Jupiter pairs (twenty out of twenty-four) will be dynamically unstable if the inner planet was placed at >~1AU distance from the stellar host. This finding is at odds with formation theories that invoke the migration of such planets from semi-major axes >~1AU due to secular dynamical processes (e.g., secular chaos, Lidov-Kozai oscillations) coupled with tidal dissipation. In fact, the results of N-body integrations show that the evolution of dynamically unstable systems does not lead to tidal migration but rather to planet ejections and collisions with the host star. This and other arguments lead us to suggest that most of the observed planets with a companion could not have been transported from further out through secular migration processes. More generally, by using a combination of numerical and analytic techniques we show that the high-e Lidov-Kozai migration scenario can only account for less than 10% of all gas giants observed between 0.1-1 AU. Simulations of multi-planet systems support this result. Our study indicates that rather than starting on highly eccentric orbits with orbital periods above one year, these "warm" Jupiters are more likely to have reached the region where they are observed today without having experienced significant tidal dissipation.

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arXiv2016

Forming the Cold Classical Kuiper Belt in a light Disk

Large Kuiper Belt Objects are conventionally thought to have formed out of a massive planetesimal belt that is a few thousand times its current mass. Such a picture, however, is incompatible with multiple lines of evidence. Here, we present a new model for the conglomeration of Cold Classical Kuiper belt objects, out of a solid belt only a few times its current mass, or a few percent of the solid density in a Minimum Mass Solar Nebula. This is made possible by depositing most of the primordial mass in grains of size centimetre or smaller. These grains collide frequently and maintain a dynamically cold belt out of which large bodies grow efficiently: an order-unity fraction of the solid mass can be converted into large bodies, in contrast to the ~0.1% efficiency in conventional models. Such a light belt may represent the true outer edge of the Solar system, and it may have effectively halted the outward migration of Neptune. In addition to the high efficiency, our model can also produce a mass spectrum that peaks at an intermediate size, similar to the observed Cold Classicals, if one includes the effect of cratering collisions. In particular, the observed power-law break observed at ~30 km for Cold Classicals, one that has been interpreted as a result of collisional erosion, may be primordial in origin.

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arXiv2015

Numerical and Analytical Modelling of Transit Time Variations

We develop and apply methods to extract planet masses and eccentricities from observed transit time variations (TTVs). First, we derive simple analytic expressions for the TTV that include the effects of both first- and second-order resonances. Second, we use N-body Markov chain Monte Carlo (MCMC) simulations, as well as the analytic formulae, to measure the masses and eccentricities of ten planets discovered by Kepler that have not previously been analyzed. Most of the ten planets have low densities. Using the analytic expressions to partially circumvent degeneracies, we measure small eccentricities of a few percent or less.

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arXiv2015

Conglomeration of kilometre-sized planetesimals

We study the efficiency of forming large bodies, starting from a sea of equal-sized planetesimals. This is likely one of the earlier steps of planet formation and relevant for the formation of the asteroid belt, the Kuiper belt and extra-solar debris disks. Here we consider the case that the seed planetesimals do not collide frequently enough for dynamical collisional to be important (the collisionless limit), using a newly constructed conglomeration code, and by carefully comparing numerical results with analytical scalings. In the absence of collisional cooling, as large bodies grow by accreting small bodies, the velocity dispersion of the small bodies ($u$) is increasingly excited. Growth passes from the well-known run-away stage (when $u$ is higher than the big bodies' hill velocity) to the newly discovered trans-hill stage (when $u$ and big bodies both grow, but $u$ remains at the big bodies' hill velocity). We find, concurring with the analytical understandings developed in Lithwick (2014), as well as previous numerical studies, that a size spectrum $dn/dR \propto R^{-4}$ results, and that the formation efficiency, defined as mass fraction in bodies much larger than the initial size, is $\sim {\mathrm{ a \,\, few}}\times R_\odot/a$, or $\sim 10^{-3}$ at the distance of the Kuiper belt. We argue that this extreme inefficiency invalidates the conventional conglomeration model for the formation of both our Kuiper belt and extra-solar debris disks. New theories, possibly involving direct gravitational collapse, or strong collisional cooling of small planetesimals, are required.

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arXiv2014

Theory and simulations of rotating convection

We study thermal convection in a rotating fluid in order to better understand the properties of convection zones in rotating stars and planets. We first derive mixing-length theory for rapidly-rotating convection, arriving at the results of Stevenson (1979) via simple physical arguments. The theory predicts the properties of convection as a function of the imposed heat flux and rotation rate, independent of microscopic diffusivities. In particular, it predicts the mean temperature gradient; the rms velocity and temperature fluctuations; and the size of the eddies that dominate heat transport. We test all of these predictions with high resolution three-dimensional hydrodynamical simulations of Boussinesq convection in a Cartesian box. The results agree remarkably well with the theory across more than two orders of magnitude in rotation rate. For example, the temperature gradient is predicted to scale as the rotation rate to the 4/5th power at fixed flux, and the simulations yield $0.75\pm 0.06$. We conclude that the mixing length theory is a solid foundation for understanding the properties of convection zones in rotating stars and planets.

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arXiv2014

Frequency of Close Companions among Kepler Planets - a TTV study

A transiting planet exhibits sinusoidal transit-time-variations (TTVs) if perturbed by a companion near a mean-motion-resonance (MMR). We search for sinusoidal TTVs in more than 2600 Kepler candidates, using the publicly available Kepler light-curves (Q0-Q12). We find that the TTV fractions rise strikingly with the transit multiplicity. Systems where four or more planets transit enjoy roughly five times higher TTV fraction than those where a single planet transits, and about twice higher than those for doubles and triples. In contrast, models in which all transiting planets arise from similar dynamical configurations predict comparable TTV fractions among these different systems. One simple explanation for our results is that there are at least two different classes of Kepler systems, one closely packed and one more sparsely populated.

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arXiv2014

Densities and Eccentricities of 139 Kepler Planets from Transit Time Variations

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 relationship ρ~3 g/cm^3 \times (R/3R_\earth)^{-2.3} for the 56 planets that likely have small eccentricity and hence small statistical correction to their masses. Many planets larger than 2.5R_\earth are less dense than water, implying that their radii are largely set by a massive hydrogen atmosphere.

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arXiv2013

Secular chaos and its application to Mercury, hot Jupiters, and the organization of planetary systems

In the inner solar system, the planets' orbits evolve chaotically, driven primarily by secular chaos. Mercury has a particularly chaotic orbit, and is in danger of being lost within a few billion years. Just as secular chaos is reorganizing the solar system today, so it has likely helped organize it in the past. We suggest that extrasolar planetary systems are also organized to a large extent by secular chaos. A hot Jupiter could be the end state of a secularly chaotic planetary system reminiscent of the solar system. But in the case of the hot Jupiter, the innermost planet was Jupiter- (rather than Mercury-) sized, and its chaotic evolution was terminated when it was tidally captured by its star. In this contribution, we review our recent work elucidating the physics of secular chaos and applying it to Mercury and to hot Jupiters. We also present new results comparing the inclinations of hot Jupiters thus produced with observations.

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arXiv2013

Nonlinear evolution of the tidal elliptical instability in gaseous planets and stars

Tidally distorted rotating stars and gaseous planets are subject to a well-known linear fluid instability -- the elliptical instability. It has been proposed that this instability might drive enough energy dissipation to solve the long-standing problem of the origin of tidal dissipation in stars and planets. But the nonlinear outcome of the elliptical instability has yet to be investigated in the parameter regime of interest, and the resulting turbulent energy dissipation has not yet been quantified. We do so by performing three dimensional hydrodynamical simulations of a small patch of a tidally deformed fluid planet or star subject to the elliptical instability. We show that when the tidal deformation is weak, the nonlinear outcome of the instability leads to the formation of long-lived columnar vortices aligned with the axis of rotation. These vortices shut off the elliptical instability, and the net result is insufficient energy dissipation to account for tidal dissipation. However, further work is required to account for effects neglected here, including magnetic fields, turbulent convection, and realistic boundary conditions.

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arXiv2013

Nonlinear evolution of the elliptical instability in the presence of weak magnetic fields

We investigate whether the elliptical instability is important for tidal dissipation in gaseous planets and stars. In a companion paper, we found that the conventional elliptical instability results in insufficient dissipation because it produces long-lived vortices that then quench further instability. Here, we study whether the addition of a magnetic field prevents those vortices from forming, and hence leads to enhanced dissipation. We present results from magnetohydrodynamical simulations that evolve the elliptical instability in a local patch of a rotating planet or star, in the presence of a weak magnetic field. We find that magnetic fields do indeed prevent vortices from forming, and hence greatly enhance the steady state dissipation rate. In addition, the resulting turbulence acts as a small-scale dynamo, amplifying the initially weak field. The inferred tidal dissipation is potentially important at short orbital periods. For example, it can circularise hot Jupiters with orbital periods shorter than 2.5 days, and synchronise their spins with their orbits out to 6 days. However, it appears unable to account for the hot Jupiters that appear to have been circularised out to six to ten day orbital periods. It also cannot account for the inferred circularisation of many close binary stars.

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arXiv2013

Density and Eccentricity of Kepler Planets

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 velocity, yield a best fit mass-radius relation M~3 M_E (R/R_E). This corresponds to a constant surface escape velocity of 20km/s. We separate the planets into two distinct groups, "mid-sized" (those greater than 3 R_E), and "compact" (those smaller). All mid-sized planets are found to be less dense than water and therefore contain extensive H/He envelopes, likely comparable in mass to that of their cores. We argue that these planets have been significantly sculpted by photoevaporation. Surprisingly, mid-sized planets are discovered exclusively around stars more massive than 0.8 M_sun. The compact planets, on the other hand, are often denser than water. Combining our density measurements with those from radial velocity studies, we find that hotter compact planets tend to be denser, with the hottest ones reaching rock density. Moreover, hotter planets tend to be smaller in sizes. These results can be explained if the compact planets are made of rocky cores overlaid with a small amount of hydrogen, < 1% in mass, with water contributing little to their masses or sizes. Photoevaporation has exposed bare rocky cores in cases of the hottest planets. Our conclusion that these planets are likely not water-worlds contrasts with some previous studies.

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arXiv2013

After Runaway: The Trans-Hill Stage of Planetesimal Growth

When planetesimals begin to grow by coagulation, they enter an epoch of runaway, during which the biggest bodies grow faster than all the others. The questions of how runaway ends and what comes next have not been answered satisfactorily. Here we show that runaway is followed by a `trans-hill stage' that commences once the bodies become trans-hill, i.e. once the Hill velocity of the bodies that dominate viscous stirring matches the random speed of the small bodies they accrete. Subsequently, the small bodies' speed grows in lockstep with the big bodies' sizes, such that the bodies remain in the trans-hill state. Trans-hill growth is crucial for determining the efficiency of growing big bodies, as well as their growth timescale and size spectrum. We work out the properties of trans-hill growth analytically and confirm these numerically. Trans-hill growth has two sub-stages. In the earlier one, collisional cooling is irrelevant, in which case the efficiency of forming big bodies remains very low (0.1% in the Kuiper belt) and their mass spectrum is flat. This explains results from previous coagulation simulations for both the Kuiper belt and the asteroid belt. The second sub-stage commences when small bodies begin to collide with one another. Collisional cooling then controls the evolution, in which case the efficiency of forming big bodies rises, and their size spectrum becomes more top-heavy. Trans-hill growth terminates in one of two ways, depending on parameters. First, mutual accretion of big bodies can become significant and conglomeration proceeds until half the total mass is converted into big bodies. This mode of growth may explain the size distributions of minor bodies in the Solar System, and is explored in forthcoming work. Second, if big bodies become separated by their Hill radius, oligarchy commences. This mode likely precedes the formation of fully-fledged planets.

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arXiv2013

Secular Dynamics in Hierarchical Three-Body Systems

The secular approximation for the evolution of hierarchical triple configurations has proven to be very useful in many astrophysical contexts, from planetary to triple-star systems. In this approximation the orbits may change shape and orientation, on time scales longer than the orbital time scales, but the semi major axes are constant. For example, for highly inclined triple systems, the Kozai-Lidov mechanism can produce large-amplitude oscillations of the eccentricities and inclinations. Here we revisit the secular dynamics of hierarchical triple systems. We derive the secular evolution equations to octupole order in Hamiltonian perturbation theory. Our derivation corrects an error in some previous treatments of the problem that implicitly assumed a conservation of the z-component of the angular momentum of the inner orbit (i.e., parallel to the total angular momentum of the system). Already to quadrupole order, our results show new behaviors including the possibility for a system to oscillate from prograde to retrograde orbits. At the octupole order, for an eccentric outer orbit, the inner orbit can reach extremely high eccentricities and undergo chaotic flips in its orientation. We discuss applications to a variety of astrophysical systems, from stellar triples to merging compact binaries and planetary systems. Our results agree with those of previous studies done to quadrupole order only in the limit in which one of the inner two bodies is a massless test particle and the outer orbit is circular;our results agree with previous studies at octupole order for the eccentricity evolution, but not for the inclination evolution.

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arXiv2012

Ohmic Heating Suspends, not Reverses, the Cooling Contraction of Hot Jupiters

We study the radius evolution of close-in extra-solar jupiters under Ohmic heating, a mechanism that was recently proposed to explain the large observed sizes of many of these planets. Planets are born with high entropy and they subsequently cool and contract. We focus on two cases: first, that ohmic heating commences when the planet is hot (high entropy); and second, that it commences after the planet has cooled. In the former case, we use analytical scalings and numerical experiments to confirm that Ohmic heating is capable of suspending the cooling as long as a few percent of the stellar irradiation is converted into Ohmic heating, and the planet has a surface wind that extends to pressures of ~10 bar or deeper. For these parameters, the radii at which cooling is stalled are consistent with (or larger than) the observed radii of most planets. The only two exceptions are WASP-17b and HAT-P-32b. In contrast to the high entropy case, we show that Ohmic heating cannot significantly re-inflate planets after they have already cooled. This leads us to suggest that the diversity of radii observed in hot jupiters may be partially explained by the different epochs at which they are migrated to their current locations.

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arXiv2012

Extracting Planet Mass and Eccentricity From TTV data

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 amplitude of the TTV depends on planet mass and free eccentricity, and it determines planet mass uniquely only when the free eccentricity is sufficiently small. We proceed to analyze the TTV signals of six short period Kepler pairs. We find that three of these pairs (Kepler-18,24,25) have TTV phase consistent with zero. The other three (Kepler-23,28,32) have small TTV phases, but ones that are distinctly non-zero. We deduce that the free eccentricities of the planets are small, < 0.01, but not always vanishing. Furthermore, as a consequence of this, we deduce that the true masses of the planets are fairly accurately determined by the TTV amplitudes, within a factor < 2. The smallness of the free eccentricities suggests that the planets have experienced substantial dissipation. This is consistent with the hypothesis that the observed pile-up of Kepler pairs near mean-motion resonances is caused by resonant repulsion. But the fact that some of the planets have non-vanishing free eccentricity suggests that after resonant repulsion occurred there was a subsequent phase in the planets' evolution when their eccentricities were modestly excited, perhaps by interplanetary interactions.

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arXiv2012

Resonant Repulsion of Kepler Planet Pairs

Planetary systems discovered by the Kepler space telescope exhibit an intriguing feature. While the period ratios of adjacent low-mass planets appear largely random, there is a significant excess of pairs that lie just wide of resonances and a deficit on the near side. We demonstrate that this feature naturally arises when two near-resonant planets interact in the presence of weak dissipation that damps eccentricities. The two planets repel each other as orbital energy is lost to heat. This moves near-resonant pairs just beyond resonance, by a distance that reflects the integrated dissipation they experienced over their lifetimes. We find that the observed distances may be explained by tides if tidal dissipation is unexpectedly efficient (tidal quality factor ~10). Once the effect of resonant repulsion is accounted for, the initial orbits of these low mass planets show little preference for resonances. This could constrain their origin.

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