# Yoram Lithwick - Northwestern

## Contact Details

NameYoram Lithwick |
||

AffiliationNorthwestern |
||

CountryZambia |
||

## Pubs By Year |
||

## External Links |
||

## Pub CategoriesEarth and Planetary Astrophysics (23) Astrophysics (16) Solar and Stellar Astrophysics (10) Physics - Fluid Dynamics (3) Cosmology and Nongalactic Astrophysics (2) Physics - Atmospheric and Oceanic Physics (1) Astrophysics of Galaxies (1) |

## Publications Authored By Yoram Lithwick

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. Read More

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. Read More

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. Read More

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. Read More

**Affiliations:**

^{1}Cambridge,

^{2}Toronto,

^{3}Northwestern

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. Read More

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. Read More

**Affiliations:**

^{1}Northwestern,

^{2}Toronto

**Category:**Earth and Planetary Astrophysics

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. Read More

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. Read More

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. Read More

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. Read More

**Affiliations:**

^{1}Toronto,

^{2}Toronto,

^{3}Northwestern

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. Read More

**Affiliations:**

^{1}Cambridge,

^{2}Toronto,

^{3}Northwestern

**Category:**Earth and Planetary Astrophysics

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. Read More

**Affiliations:**

^{1}Northwestern

**Category:**Earth and Planetary Astrophysics

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. Read More

**Affiliations:**

^{1}Toronto,

^{2}Northwestern

**Category:**Earth and Planetary Astrophysics

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. Read More

**Affiliations:**

^{1}Northwestern,

^{2}Toronto,

^{3}Toronto

**Category:**Earth and Planetary Astrophysics

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. Read More

**Affiliations:**

^{1}Northwestern,

^{2}Toronto

**Category:**Earth and Planetary Astrophysics

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. Read More

**Affiliations:**

^{1}Toronto,

^{2}Northwestern

**Category:**Earth and Planetary Astrophysics

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. Read More

**Affiliations:**

^{1}Lund University,

^{2}Harvard-Smithsonian Center for Astrophysics,

^{3}Northwestern University

**Category:**Earth and Planetary Astrophysics

Modelling the formation of super-km-sized planetesimals by gravitational collapse of regions overdense in small particles requires numerical algorithms capable of handling simultaneously hydrodynamics, particle dynamics and particle collisions. While the initial phases of radial contraction are dictated by drag forces and gravity, particle collisions become gradually more significant as filaments contract beyond Roche density. Here we present a new numerical algorithm for treating momentum and energy exchange in collisions between numerical superparticles representing a high number of physical particles. Read More

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. Read More

We study the dynamical evolution of a test particle that orbits a star in the presence of an exterior massive planet, considering octupole-order secular interactions. In the standard Kozai mechanism (SKM), the planet's orbit is circular, and so the particle conserves vertical angular momentum. As a result, the particle's orbit oscillates periodically, exchanging eccentricity for inclination. Read More

**Affiliations:**

^{1}Northwestern,

^{2}Toronto

We study the chaotic orbital evolution of planetary systems, focusing on secular (i.e., orbit-averaged) interactions, because these often dominate on long timescales. Read More

**Affiliations:**

^{1}Toronto,

^{2}Northwestern

In a planetary system with two or more well-spaced, eccentric, inclined planets, secular interactions may lead to chaos. The innermost planet may gradually become very eccentric and/or inclined, as a result of the secular degrees of freedom drifting towards equipartition of angular momentum deficit. Secular chaos is known to be responsible for the eventual destabilization of Mercury in our own Solar System. Read More

About 25 per cent of `hot Jupiters' (extrasolar Jovian-mass planets with close-in orbits) are actually orbiting counter to the spin direction of the star. Perturbations from a distant binary star companion can produce high inclinations, but cannot explain orbits that are retrograde with respect to the total angular momentum of the system. Such orbits in a stellar context can be produced through secular (that is, long term) perturbations in hierarchical triple-star systems. Read More

We investigate the collapse and internal structure of dark matter halos. We consider halo formation from initially scale-free perturbations, for which gravitational collapse is self-similar. Fillmore and Goldreich (1984) and Bertschinger (1985) solved the one dimensional (i. Read More

A longstanding puzzle of fundamental importance in modern cosmology has been the origin of the nearly universal density profiles of dark matter halos found in N-body simulations -- the so-called NFW profile. We show how this behavior may be understood, simply, by applying adiabatic contraction to peaks of Gaussian random fields. We argue that dynamical friction acts to reduce enormously the effect of random scatter in the properties of initial peaks, providing a key simplification. Read More

How did Pluto's recently discovered minor moons form? Ward and Canup propose an elegant solution in which Nix and Hydra formed in the collision that produced Charon, then were caught into corotation resonances with Charon, and finally were transported to their current location as Charon migrated outwards. We show with numerical integrations that, if Charon's eccentricity is judiciously chosen, this scenario works beautifully for either Nix or Hydra. However, it cannot work for both Nix and Hydra simultaneously. Read More

Pluto's recently discovered minor moons, Nix and Hydra, have almost circular orbits, and are nearly coplanar with Charon, Pluto's major moon. This is surprising because tidal interactions with Pluto are too weak to damp their eccentricities. We consider an alternative possibility: that Nix and Hydra circularize their orbits by exciting Charon's eccentricity via secular interactions, and Charon in turn damps its own eccentricity by tidal interaction with Pluto. Read More

Two dimensional hydrodynamical disks are nonlinearly unstable to the formation of vortices. Once formed, these vortices essentially survive forever. What happens in three dimensions? We show with pseudospectral simulations that in 3D a vortex in a short box forms and survives just as in 2D. Read More

**Affiliations:**

^{1}CITA,

^{2}CITA

**Category:**Astrophysics

We describe the diffusion and random velocities of solid particles due to stochastic forcing by turbulent gas. We include the orbital dynamics of Keplerian disks, both in-plane epicycles and vertical oscillations. We obtain a new result for the diffusion of solids. Read More

We examine how perturbed shear flows evolve in two-dimensional, incompressible, inviscid hydrodynamical fluids, with the ultimate goal of understanding the dynamics of accretion disks. To linear order, vorticity waves are swung around by the background shear, and their velocities are amplified transiently before decaying. It has been speculated that sufficiently amplified modes might couple nonlinearly, leading to turbulence. Read More

We present new high-resolution observations of Sagittarius A* at wavelengths of 17.4 to 23.8 cm with the Very Large Array in A configuration with the Pie Town Very Long Baseline Array antenna. Read More

We present a new, simple, fast algorithm to numerically evolve disks of inelastically colliding particles surrounding a central star. Our algorithm adds negligible computational cost to the fastest existing collisionless N-body codes, and can be used to simulate, for the first time, the interaction of planets with disks over many viscous times. Though the algorithm is implemented in two dimensions-i. Read More

**Category:**Astrophysics

We present a phenomenological model of imbalanced MHD turbulence in an incompressible magnetofluid. The steady-state cascades, of waves traveling in opposite directions along the mean magnetic field, carry unequal energy fluxes to small length scales, where they decay due to viscous and resistive dissipation. The inertial-range scalings are well-understood when both cascades are weak. Read More

We report the discovery of a transient radio source 2.7 arcsec (0.1 pc projected distance) South of the Galactic Center massive black hole, Sagittarius A*. Read More

Planets form in the circumstellar disks of young stars. We review the basic physical processes by which solid bodies accrete each other and alter each others' random velocities, and we provide order-of-magnitude derivations for the rates of these processes. We discuss and exercise the two-groups approximation, a simple yet powerful technique for solving the evolution equations for protoplanet growth. Read More

**Category:**Astrophysics

We address three questions regarding solar system planets. What determined their number? Why are their orbits nearly circular and coplanar? How long did they take to form? Runaway accretion in a disk of small bodies resulted in a tiny fraction of the bodies growing much larger than all the others. This was followed by oligarchic growth during which the big bodies maintained similar masses and uniformly spaced semi-major axes. Read More

**Affiliations:**

^{1}Caltech,

^{2}Caltech,

^{3}Caltech

**Category:**Astrophysics

It appears that at least several percent of large Kuiper belt objects are members of wide binaries. Physical collisions are too infrequent to account for their formation. Collisionless gravitational interactions are more promising. Read More

MHD turbulence consists of waves that propagate along magnetic fieldlines, in both directions. When two oppositely directed waves collide, they distort each other, without changing their respective energies. In weak MHD turbulence, a given wave suffers many collisions before cascading. Read More

Radio-wave scintillation observations reveal a nearly Kolmogorov spectrum of density fluctuations in the ionized interstellar medium. Although this density spectrum is suggestive of turbulence, no theory relevant to its interpretation exists. We calculate the density spectrum in turbulent magnetized plasmas by extending the theory of incompressible MHD turbulence given by Goldreich & Sridhar to include the effects of compressibility and particle transport. Read More

**Affiliations:**

^{1}Caltech,

^{2}Caltech

**Category:**Astrophysics

As is well-known, the requirement that gamma ray bursts (GRB's) be optically thin to high energy photons yields a lower limit on the Lorentz factor (\gamma) of the expansion. In this paper, we provide a simple derivation of the lower limit on \gamma due to the annihilation of photon pairs, and correct the errors in some of the previous calculations of this limit. We also derive a second limit on \gamma due to scattering of photons by pair-created electrons and positrons. Read More

Extremely strong magnetic fields change the vacuum index of refraction. This induces a lensing effect that is not unlike the lensing phenomenon in strong gravitational fields. The main difference between the two is the polarization dependency of the magnetic lensing, a behaviour that induces a handful of interesting effects. Read More