HKU Scholars Hubhttp://hub.hku.hkThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Tue, 24 Nov 2020 10:35:03 GMT2020-11-24T10:35:03Z50881- The formation environment of the Galilean Moonshttp://hdl.handle.net/10722/190776Title: The formation environment of the Galilean Moons
Authors: Turner, NJ; Lee, MH; Sano, T
Abstract: We show that the disks of gas and dust orbiting gas giant protoplanets are subject to turbulence driven by the magneto-rotational instability, provided (1) sufficient X-rays reach them from the vicinity of the host star, and ...
Description: Poster Session 415 - Solar System Origin, Planet and Satellite Formation: abstract no. 415.03
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10722/1907762012-01-01T00:00:00Z
- On the in situ formation of Pluto's small satelliteshttp://hdl.handle.net/10722/218247Title: On the in situ formation of Pluto's small satellites
Authors: Woo, MY; Lee, MH
Abstract: The formation of Pluto's small satellites - Styx, Nix, Keberos and Hydra remains a mystery. Their orbits are nearly circular (eccentricity e = 0.0055 or less) and near resonances and coplanar with respect to Charon. One scenario suggests that they all formed close to their current locations from a disk of debris, which was ejected from the Charon-forming impact. We test the validity of this scenario by performing N-body simulations with Pluto-Charon evolving tidally from an initial orbit at a few Pluto radii. The small satellites are modeled as test particles with initial orbital distances within the range of the current small satellites and damped to their coldest orbits by collisional damping. It is found that if Charon is formed from a debris disk and has low initial eccentricity, all test particles survive to the end of the tidal evolution, but there is no preference for resonances and the test particles' final e is typically > 0.01. If Charon is formed in the preferred intact capture scenario and has initial orbital eccentricity ~ 0.2, the outcome depends on the relative rate of tidal dissipation in Charon and Pluto, A. If A is large and Charon's orbit circularizes quickly, a significant fraction of the test particles survives outside resonances with e >~ 0.01. Others are ejected by resonance or survive in resonance with very large e (> 0.1). If A is small and Charon's orbit remains eccentric throughout most of the tidal evolution, most of the test particles are ejected. The test particles that survive have e >~ 0.01, including some with e > 0.1. None of the above cases results in test particles with sufficiently low final e.This work is supported in part by Hong Kong RGC grant HKU 7030/11P. (c) 2015: American Astronomical Society
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2182472015-01-01T00:00:00Z
- On the Origin of Pluto's Small Satellites by Resonant Transporthttp://hdl.handle.net/10722/202780Title: On the Origin of Pluto's Small Satellites by Resonant Transport
Authors: CHENG, WH; Peale, SJ; Lee, MH
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10722/2027802014-01-01T00:00:00Z
- Two Massive Planets Orbiting the Giant Star eta Cethttp://hdl.handle.net/10722/205160Title: Two Massive Planets Orbiting the Giant Star eta Cet; Alternative Title: Discovery of a planetary system around the K giant star eta Cet
Authors: Trifonov, T; Reffert, S; Tan, X; Lee, MH; Quirrenbach, A
Description: Poster Presentation; Topic 58: Exoplanets: Detection: Radial Velocity
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/2051602013-01-01T00:00:00Z
- On the Migration of the Galilean Satelliteshttp://hdl.handle.net/10722/205159Title: On the Migration of the Galilean Satellites
Authors: Li, WY; Lee, MH
Abstract: The migration of the Galilean satellites during formation due to interactions with the circumjovian disk
is studied. In the gas-starved disk model proposed by Canup & Ward (2002, 2006), the Galilean
satellites are the last generation of satellites formed in the circumjovian disk, and their migration
and accretion depend on disk viscosity, opacity and material inflow rate. Relaxing the migration to
non-isothermal type I regime (e.g. Paardekooper et al. 2010) allows the satellites to migrate outwards
in optically-thick disk regions, and there is a position where the disk torque is zero. This contrasts with
278the results in the isothermal type I regime in which the satellites always migrate inwards. Including
the effect of temperature dependence of disk opacity can produce multiple zero-torque positions in
the circumjovian disk. As the disk depletes, these zero-torque positions shift towards Jupiter. Under
this setting, a satellite at a range of initial locations will eventually converge to near one of these
zero-torque positions, but stays at a fixed distance away (with the distance depending on satellite
mass), so that it is moving inwards with the zero-torque position. However, if the satellite starts at
a large-enough distance from Jupiter, it may move in a trajectory that does not converge to any of
these zero-torque positions and survives to the end. The effect of satellite growth and variation of disk
parameters on satellite migration will be discussed. The migration in multiple satellite system, and how
these settings can possibly result in the Laplace resonance among the Galilean satellites, will be also
investigated.
This work is supported in part by Hong Kong RGC grant HKU 7030/11P
Description: Poster Presentation; Topic 67: Solar System: General
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/2051592013-01-01T00:00:00Z
- Formation environment of the Galilean Moonshttp://hdl.handle.net/10722/64178Title: Formation environment of the Galilean Moons
Authors: Lee, MH; Turner, NJ; Sano, T
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/641782009-01-01T00:00:00Z
- Magnetic Coupling in the Disks around Young Gas Giant Planetshttp://hdl.handle.net/10722/202777Title: Magnetic Coupling in the Disks around Young Gas Giant Planets
Authors: Turner, NJ; Lee, MH; Sano, T
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10722/2027772014-01-01T00:00:00Z
- On the Early In Situ Formation of Pluto’s Small Satelliteshttp://hdl.handle.net/10722/252731Title: On the Early In Situ Formation of Pluto’s Small Satellites
Authors: WOO, MY; Lee, MH
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10722/2527312018-01-01T00:00:00Z
- A multiple time step symplectic algorithm for integrating close encountershttp://hdl.handle.net/10722/150930Title: A multiple time step symplectic algorithm for integrating close encounters
Authors: Duncan, MJ; Levison, HF; Lee, MH
Abstract: We present a new symplectic algorithm that has the desirable properties of the sophisticated but highly efficient numerical algorithms known as mixed variable symplectic (MVS) methods and that, in addition, can handle close encounters between objects. This technique is based on a variant of the standard MVS methods, but it handles close encounters by employing a multiple time step technique. When the bodies are well separated, the algorithm has the speed of MVS methods, and whenever two bodies suffer a mutual encounter, the time step for the relevant bodies is recursively subdivided to whatever level is required. We demonstrate the power of this method using several tests of the technique. We believe that this algorithm will be a valuable tool for the study of planetesimal dynamics and planet formation.
Thu, 01 Jan 1998 00:00:00 GMThttp://hdl.handle.net/10722/1509301998-01-01T00:00:00Z
- Gravitational lensing by a smoothly variable three-dimensional mass distributionhttp://hdl.handle.net/10722/150939Title: Gravitational lensing by a smoothly variable three-dimensional mass distribution
Authors: Lee, MH; Paczyński, B
Abstract: A smooth three-dimensional mass distribution is approximated by a model with multiple thin screens, with surface mass density varying smoothly on each screen. We find that 16 screens are sufficient for a good approximation of the three-dimensional distribution of matter. We also find that in this multiscreen model the distribution of amplifications of single images is dominated by the convergence due to matter within the beam. The shear caused by matter outside the beam has no significant effect. This finding considerably simplifies the modeling of lensing by a smooth three-dimensional mass distribution by effectively reducing the problem to one dimension, as it is sufficient to know the mass distribution along a straight light ray.
Mon, 01 Jan 1990 00:00:00 GMThttp://hdl.handle.net/10722/1509391990-01-01T00:00:00Z
- Dynamics and origin of the 2:1 orbital resonances of the GJ 876 planetshttp://hdl.handle.net/10722/150929Title: Dynamics and origin of the 2:1 orbital resonances of the GJ 876 planets
Authors: Lee, MH; Peale, SJ
Abstract: The discovery by Marcy and coworkers of two planets in 2:1 orbital resonance about the star GJ 876 has been supplemented by a dynamical fit to the data by Laughlin & Chambers, which places the planets in coplanar orbits deep in three resonances at the 2:1 mean-motion commensurability. The selection of this almost singular state by the dynamical fit means that the resonances are almost certainly real, and with the small amplitudes of libration of the resonance variables, indefinitely stable. Several unusual properties of the 2:1 resonances are revealed by the GJ 876 system. The libration of both lowest order mean-motion resonance variables and the secular resonance variable,θ1 = λ1 - 2λ2 + ω̄1, θ2 = λ1 - 2λ2 + ω̄2, and θ3 = ω̄1- ω̄2 about 0° (where λ1,2 are the mean longitudes of the inner and outer planet and ω̄1,2 are the longitudes of periapse) differs from the familiar geometry of the Io-Europa pair, where θ2 and θ3 librate about 180°. By considering the condition that ω̄1 = ω̄2 for stable simultaneous librations of θ1 and θ2, we show that the GJ 876 geometry results from the large orbital eccentricities ei, whereas the very small eccentricities in the Io-Europa system lead to the latter's geometry. Surprisingly, the GJ 876 configuration, with θ 1, θ2, and θ3 all librating, remains stable for e1 up to 0.86 and for amplitude of libration of θ1 approaching 45° with the current eccentricities - further supporting the indefinite stability of the existing system. Any process that drives originally widely separated orbits toward each other could result in capture into the observed resonances at the 2:1 commensurability. We find that forced inward migration of the outer planet of the GJ 876 system results in certain capture into the observed resonances if initially e1 ≲ 0.06 and e2 ≲ 0.03 and the migration rate | ȧ 2/a2 ≲ 3 × 10-2(a 2/AU)-3/2 yr-1. Larger eccentricities lead to likely capture into higher order resonances before the 2:1 commensurability is reached. The planets are sufficiently massive to open gaps in the nebular disk surrounding the young GJ 876 and to clear the disk material between them, and the resulting planet-nebular interaction typically forces the outer planet to migrate inward on the disk viscous timescale, whose inverse is about 3 orders of magnitude less than the above upper bound on | ȧ2/a 2 | for certain capture. If there is no eccentricity damping, eccentricity growth is rapid with continued migration within the resonance, with ei exceeding the observed values after a further reduction in the semimajor axes ai of only 7%. With eccentricity damping ėi/ei= - K | ȧi/ai, the eccentricities reach equilibrium values that remain constant for arbitrarily long migration within the resonances. The equilibrium eccentricities are close to the observed eccentricities for K ≈ 100 if there is migration and damping of the outer planet only, but for K ≈ 10 if there is also migration and damping of the inner planet. This result is independent of the magnitude or functional form of the migration rate ȧi, as long as ė i/ei = - K | ȧi/ai . Although existing analytic estimates of the effects of planet-nebula interaction are consistent with this form of eccentricity damping for certain disk parameter values, it is as yet unclear that such interaction can produce the large value of K required to obtain the observed eccentricities. The alternative eccentricity damping by tidal dissipation within the star or the planets is completely negligible, so the observed dynamical properties of the GJ 876 system may require an unlikely fine-tuning of the time of resonance capture to be near the end of the nebula lifetime.
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/10722/1509292002-01-01T00:00:00Z
- Probability of capture for the 3:1 mean-motion resonancehttp://hdl.handle.net/10722/160477Title: Probability of capture for the 3:1 mean-motion resonance
Authors: Chan, KH; Lee, MH
Abstract: Mean-motion resonances are frequently observed in extrasolar planetary systems. It is generally believed that the resonances result from the convergent migration of planets. The much larger number of systems near the 2:1 resonance compared to 3:1 in both the radial velocity and Kepler data may be due to a difference in the capture behaviors of 2:1 and 3:1 resonances. To study the capture probability of 3:1 resonance, we use numerical three-body integrations with forced migration to examine how the probability depends on migration rate, planetary masses, and initial orbital eccentricities. We first confirm our numerical results with analytic theory in the adiabatic limit (Borderies & Golderich 1986) and numerical results of Hamiltonian model beyond this limit (Mustill & Wyatt 2010) for both the interior and exterior resonances in the circular restricted three-body problem. We then extend our numerical exploration of the restricted three-body problem to non-zero planet eccentricity in the adiabatic limit. The capture probability decreases with increasing planet eccentricity at small test particle eccentricity but does not depend strongly on the planet eccentricity at higher test particle eccentricity. Finally, we extend beyond the restricted problem to different planetary mass ratio m2/m1. In the cases where both planets are initially on circular orbits, we find that the critical migration rate for certain capture agrees with that of Quillen (2006) in the limit that one of the bodies is a test particle but that it does not change monotonically with m2/m1 and peaks at m2/m1 = 1. In the adiabatic regime, the capture probability for comparable masses (m2 m1) shows oscillatory behaviors as a function of eccentricities, which is significantly different from the test particle limits.
Description: Session 01 - Exoplanets: abstract no. 01.09
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10722/1604772012-01-01T00:00:00Z
- Collisions in the Solar Systemhttp://hdl.handle.net/10722/160923Title: Collisions in the Solar System
Authors: Lee, MH
Description: The Chinese-American Kavli Frontiers of Science symposia are sponsored by the U.S. National Academy of Sciences and the Chinese Academy of Sciences
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/1609232011-01-01T00:00:00Z
- On the dynamical state of the HD 82943 Planetary Systemhttp://hdl.handle.net/10722/160922Title: On the dynamical state of the HD 82943 Planetary System
Authors: Lee, MH; Tan, X; Ford, EB; Payne, MJ; Howard, AW; Marcy, GW; Johnson, JA; Wright, JT
Abstract: Previous analysis of radial velocity data of the star HD 82943 has shown that it hosts a pair of planets that are likely in 2:1 mean-motion resonance, with the orbital periods about 220 and 440 days (Lee et al. 2006). However, alternative fits that are qualitatively different have also been suggested, with the two planets in 1:1 resonance or the addition of a third planet possibly in a Laplace resonance with the other two (Gozdziewski & Konacki 2006; Beaugé et al. 2008). We present a new analysis of the HD 82943 system based on 10 years of radial velocity measurements obtained with the Keck telescope. An efficient and reliable method to explore the parameter space is needed because of the large number of model parameters and the cost of orbital integrations. We compare the results obtained using different approaches: multiple-Keplerian or N-body fitting, combined with the least-squares method on parameter grids or the Markov chain Monte Carlo method. A systematic exploration of the parameter space that combines statistical and dynamical analysis is performed to assess the viability of the different types of fits for the HD 82943 system.
Description: Session 28: Multiple-Planet Systems (Poster): no. 28.03; The Conference program's website is located at http://ciera.northwestern.edu/Jackson2011/
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/1609222011-01-01T00:00:00Z
- The evolution of the pluto systemhttp://hdl.handle.net/10722/160924Title: The evolution of the pluto system
Authors: Peale, SJ; Cheng, WH; Lee, MH
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/1609242011-01-01T00:00:00Z
- Tilting saturn without tilting jupiter: constraints on giant planet migrationhttp://hdl.handle.net/10722/221895Title: Tilting saturn without tilting jupiter: constraints on giant planet migration
Authors: Brasser, R; Lee, MH
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2218952015-01-01T00:00:00Z
- Did our Solar System lose a giant planet?http://hdl.handle.net/10722/218248Title: Did our Solar System lose a giant planet?
Authors: Lee, MH
Description: Conference Theme: Gravitational Dynamics
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10722/2182482014-01-01T00:00:00Z
- New evidence for planets on S-type orbits in close binary systemshttp://hdl.handle.net/10722/233286Title: New evidence for planets on S-type orbits in close binary systems
Authors: Trifonov, TH; Lee, MH; Reffert, S; Quirrenbach, A
Abstract: We present evidence for two Jovian planets orbiting the evolved giant stars 39 Cygni and HR 2877, based on more than 10 years of high-precision Doppler data taken at the Lick Observatory. Both stars are the primary components of compact binary systems, and thus these systems provide important clues on how planets could form and remain stable in S-type orbit around a star under the strong gravitational influence from a close stellar companion. We investigate large sets of orbital fits for both systems by applying systematic chi^2 grid-search techniques coupled with self-consistent dynamical fitting. We also perform long-term dynamical simulations to constrain the permitted orbital configurations. We find that 39 Cygni is accompaniedby a low-mass star having nearly circular orbit at a_B > 7.5 AU. The planet orbiting the primary is well separated (a_b ˜ 1.6 AU) from the secondary and thus the system is generally stable. HR 2877 has astellar companion of at least 0.6 M_&sun; on a highly eccentric orbit with e_b ˜ 0.7. The binary semimajor axis is a_B ˜ 13.6 AU, but the pericentre distance is only 3.7 AU leading to stronginteractions with the planet, which is at a_b ˜ 1.1 AU. If the binary and the planet in this system have prograde and aligned coplanar orbits, there are only narrow regions of stable orbital solutions. For this system we also test dynamical models with the planet having a retrograde orbit, and we find that in this case thesystem is fully stable in a large set of orbital solutions. Only a handful of S-type planetary candidates in compact binary systems are known in the literature, and the 39 Cygni and HR 2877 systems are significant additions to the sample.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2332862015-01-01T00:00:00Z
- On the 2:1 Orbital resonance in the HD 82943 planetary systemhttp://hdl.handle.net/10722/151189Title: On the 2:1 Orbital resonance in the HD 82943 planetary system
Authors: Lee, MH; Paul Butler, R; Fischer, DA; Marcy, GW; Vogt, SS
Abstract: We present an analysis of the HD 82943 planetary system based on a radial velocity data set that combines new measurements obtained with the Keck telescope and the CORALIE measurements published in graphical form. We examine simultaneously the goodness of fit and the dynamical properties of the best-fit double-Keplerian model as a function of the poorly constrained eccentricity and argument of periapse of the outer planet's orbit. The fit with the minimum χ v 2 is dynamically unstable if the orbits are assumed to be coplanar. However, the minimum is relatively shallow, and there is a wide range of fits outside the minimum with reasonable χ v 2, For an assumed coplanar inclination i = 30° (sin i = 0.5), only good fits with both of the lowest order, eccentricity-type mean-motion resonance variables at the 2:1 commensurability, θ 1 and θ 2, librating about 0° are stable. For sin i = 1, there are also some good fits with only θ 1 (involving the inner planet's periapse longitude) librating that are stable for at least 10 8 yr. The libration semiamplitudes are about 6° for θ 1 and 10° for θ 2 for the stable good fit with the smallest libration amplitudes of both θ 1 and θ 2. We do not find any good fits that are nonresonant and stable. Thus, the two planets in the HD 82943 system are almost certainly in 2:1 mean-motion resonance, with at least θ 1 librating, and the observations may even be consistent with small-amplitude librations of both θ 1 and θ 2. © 2006. The American Astronomical Society. All rights reserved.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10722/1511892006-01-01T00:00:00Z
- Constraints on giant planet migration: obliquities and stabilityhttp://hdl.handle.net/10722/128107Title: Constraints on giant planet migration: obliquities and stability
Authors: McNeil, DS; Lee, MH
Description: 石垣島国際会議「進化する惑星形成論」
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1281072010-01-01T00:00:00Z
- The formation environment of the Galilean Moonshttp://hdl.handle.net/10722/141321Title: The formation environment of the Galilean Moons
Authors: Turner, NJ; Lee, MH; Sano, T
Abstract: The regular satellites of the gas giant planets were formed in circumplanetary disks of gas and dust, whose evolution was governed by mass and angular momentum transport of uncertain origins. Turbulence driven by the magneto-rotational instability can provide the transport if the gas is sufficiently ionised to couple to the embedded magnetic fields. We compute the ionisation states of the minimum-mass and gas-starved models of the Jovian sub-nebula, including the key effects known from Solar nebula studies: ionisation by cosmic rays and stellar X-rays, charge transfer to metal atoms, and recombination on grains. The results show that magneto-rotational turbulence develops in a region whose size depends on the absorbing mass column, the grain surface area, the gas-phase metal abundance and the strength of the turbulent mixing. The turbulence is almost entirely absent from the minimum-mass sub-nebula model over a wide range in these parameters. In contrast, turbulence occurs in the gas-starved model in the surface layers and throughout the parts furthest from the planet, provided sub-micron grains are underabundant. This work was carried out in part at the Jet Propulsion Laboratory, California Institute of Technology with support from the NASA Outer Planets Research program, and at the University of Hong Kong under RGC grant HKU 7024/08P.
Description: Poster - Session 24. Solar System Origin, Planet and Satellite Formation: 24.08
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1413212010-01-01T00:00:00Z
- Tilting Saturn without tilting Jupiter or ejecting an ice giant: constraints on migrationhttp://hdl.handle.net/10722/141322Title: Tilting Saturn without tilting Jupiter or ejecting an ice giant: constraints on migration
Authors: McNeil, DS; Lee, MH
Abstract: The obliquities of the giant planets preserve information about their migration and encounter histories. Are the classic Nice models (Tsiganis et al. 2005) or the resonant Nice models (Morbidelli et al. 2007) compatible with Jupiter's 3 degree tilt and Saturn's 27? Here we consider the obliquity evolution of the giants during the planetesimal-driven migration phase using two methods: (1) a purely secular integration of the Laplace-Lagrange equations with spin, and (2) a hybrid N-body scheme with full interactions between the Sun and the giants but imposed prescriptions for migration and eccentricity and inclination damping. We find that it is difficult to reproduce today's obliquity values as migration timescales sufficient to tilt Saturn via the Hamilton & Ward (2004) secular spin-orbit resonance mechanism generally suffice to tilt Jupiter more than is observed. Moreover, long migration timescales which make tilting Saturn easier simultaneously reduce the survival fraction (to below 20% for timescales longer than 20 Myr.) We discuss the constraints these observations provide on the dynamical history of the giant planets, and the remaining possibility of tilting Saturn during a late very slow migration of Neptune to its present location after the main phase of migration is complete. [This work was supported by Hong Kong RGC grant HKU 7024/08P.]
Description: Oral - Session 04. Solar System Origin, Planet and Satellite Formation: 04.04
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1413222010-01-01T00:00:00Z
- Collisions in the Solar Systemhttp://hdl.handle.net/10722/141323Title: Collisions in the Solar System
Authors: Lee, MH
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/1413232011-01-01T00:00:00Z
- Planetary migration and eccentricity and inclination resonances in extrasolar planetary systemshttp://hdl.handle.net/10722/129163Title: Planetary migration and eccentricity and inclination resonances in extrasolar planetary systems
Authors: Lee, MH; Thommes, EW
Abstract: The differential migration of two planets due to planet-disk interaction can result in capture into the 2:1 eccentricity-type mean-motion resonances. Both the sequence of 2:1 eccentricity resonances that the system is driven through by continued migration and the possibility of a subsequent capture into the 4:2 inclination resonances are sensitive to the migration rate within the range expected for type II migration due to planet-disk interaction. If the migration rate is fast, the resonant pair can evolve into a family of 2:1 eccentricity resonances different from those found by Lee. This new family has outer orbital eccentricity e 2 ≳ 0.4-0.5, asymmetric librations of both eccentricity resonance variables, and orbits that intersect if they are exactly coplanar. Although this family exists for an inner-to-outer planet mass ratio m 1/m 2 ≳ 0.2, it is possible to evolve into this family by fast migration only for m 1/m 2 ≳ 2. Thommes and Lissauer have found that a capture into the 4:2 inclination resonances is possible only for m 1/m 2 ≲ 2. We show that this capture is also possible for m 1/m 2 ≳ 2 if the migration rate is slightly slower than that adopted by Thommes and Lissauer. There is significant theoretical uncertainty in both the sign and the magnitude of the net effect of planet-disk interaction on the orbital eccentricity of a planet. If the eccentricity is damped on a timescale comparable to or shorter than the migration timescale, e 2 may not be able to reach the values needed to enter either the new 2:1 eccentricity resonances or the 4:2 inclination resonances. Thus, if future observations of extrasolar planetary systems were to reveal certain combinations of mass ratio and resonant configuration, they would place a constraint on the strength of eccentricity damping during migration, as well as on the rate of the migration itself. © 2009 The American Astronomical Society. All rights reserved.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/1291632009-01-01T00:00:00Z
- Formation environment of the Galilean Moonshttp://hdl.handle.net/10722/130351Title: Formation environment of the Galilean Moons
Authors: Lee, MH; Turner, NJ; Sano, T
Description: DDPW01 - Poster Session A: No. 18
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/1303512009-01-01T00:00:00Z
- Breakthrough revisited: investigating the requirements for growth of dust beyond the bouncing barrierhttp://hdl.handle.net/10722/252317Title: Breakthrough revisited: investigating the requirements for growth of dust beyond the bouncing barrier
Authors: Booth, RA; Meru, F; Lee, MH; Clarke, CJ
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10722/2523172018-01-01T00:00:00Z
- New evidence for planets on S-type orbits in close binary systemshttp://hdl.handle.net/10722/213711Title: New evidence for planets on S-type orbits in close binary systems
Authors: Trifonov, TH; Lee, MH; Reffert, S; Quirrenbach, A
Abstract: We present evidence for two Jovian planets orbiting the evolved giant stars 39 Cygni and HR 2877, based on more than 10 years of high-precision Doppler data taken at the Lick Observatory. Both stars are the primary components of compact binary systems, and thus these systems provide important clues on how planets could form and remain stable in S-type orbit around a star under the strong gravitational influence from a close stellar companion. We investigate large sets of orbital fits for both systems by applying systematic $chi^2$ grid-search techniques coupled with self-consistent dynamical fitting. We also perform long-term dynamical simulations to constrain the permitted orbital configurations. We find that 39 Cygni is accompanied by a low-mass star having nearly circular orbit at $a_B$ > 7.5 AU. The planet orbiting the primary is well separated ($a_b sim$ 1.6 AU) from the secondary and thus the system is generally stable. HR 2877 has a stellar companion of at least $0.6 M_odot$ on a highly eccentric orbit with $e_b$ = 0.73. The binary semimajor axis is $a_B sim$ 13.6 AU, but the pericentre distance is only 3.7 AU leading to strong interactions with the planet, which is at $a_b sim$ 1.1 AU. If the binary and the planet in this system have prograde and aligned coplanar orbits, there are only narrow regions of stable orbital solutions. For this system we also test dynamical models with the planet having a retrograde orbit, and we find that in this case the system is fully stable in a large set of orbital solutions. Only a handful of S-type planetary candidates in compact binary systems are known in the literature, and the 39 Cygni and HR 2877 systems are significant additions to the sample.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2137112015-01-01T00:00:00Z
- Tilting saturn without tilting Jupiter: constraints on Giant Planet Migrationhttp://hdl.handle.net/10722/218249Title: Tilting saturn without tilting Jupiter: constraints on Giant Planet Migration
Authors: Brasser, R; Lee, MH
Abstract: The migration and encounter histories of the giant planets in our Solar System can be constrained by the obliquities of Jupiter and Saturn. We have performed secular simulations with imposed migration and N-body simulations with planetesimals to study the expected obliquity distribution of migrating planets with initial conditions resembling those of the smooth migration model, the resonant Nice model and two models with five giant planets initially in resonance (one compact and one loose configuration). For smooth migration, the secular spin-orbit resonance mechanism can tilt Saturn's spin axis to the current obliquity if the product of the migration time scale and the orbital inclinations is sufficiently large (exceeding 30 Myr deg). For the resonant Nice model with imposed migration, it is difficult to reproduce today's obliquity values, because the compactness of the initial system raises the frequency that tilts Saturn above the spin precession frequency of Jupiter, causing a Jupiter spin-orbit resonance crossing. Migration time scales sufficiently long to tilt Saturn generally suffice to tilt Jupiter more than is observed. The full N-body simulations tell a somewhat different story, with Jupiter generally being tilted as often as Saturn, but on average having a higher obliquity. The main obstacle is the final orbital spacing of the giant planets, coupled with the tail of Neptune's migration. The resonant Nice case is barely able to simultaneously reproduce the {orbital and spin} properties of the giant planets, with a probability ~0.15%. The loose five planet model is unable to match all our constraints (probability <0.08%). The compact five planet model has the highest chance of matching the orbital and obliquity constraints simultaneously (probability ~0.3%).
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10722/2182492014-01-01T00:00:00Z
- An analytical approach to gravitational lensing by an ensemble of axisymmetric lenseshttp://hdl.handle.net/10722/151138Title: An analytical approach to gravitational lensing by an ensemble of axisymmetric lenses
Authors: Lee, MH; Spergel, DN
Abstract: We consider the problem of gravitational lensing by an ensemble of identical axisymmetric lenses randomly distributed on a single lens plane and derive a formal expression for the joint probability density of finding shear (γ1, γ2) and convergence κ at a random point on the plane. The amplification probability for a source can be accurately estimated from the distribution in shear and convergence. We apply this method to two cases: lensing by an ensemble of point masses and by an ensemble of objects with Gaussian surface mass density. There is no convergence for point masses whereas shear is negligible for wide Gaussian lenses. We find excellent agreement with results from recent Monte Carlo simulations with σav = 0.2.
Mon, 01 Jan 1990 00:00:00 GMThttp://hdl.handle.net/10722/1511381990-01-01T00:00:00Z
- Statistics of gravitational microlensing magnification. I. Two-dimensional lens distributionhttp://hdl.handle.net/10722/151157Title: Statistics of gravitational microlensing magnification. I. Two-dimensional lens distribution
Authors: Kofman, L; Kaiser, N; Lee, MH; Babul, A
Abstract: The propagation of light from distant sources through a distribution of clumpy matter, acting as point-mass lenses, produces multiple images that contribute to the total brightness of the observed macroimages. In this paper, we refine the theory of gravitational microlensing for a planar distribution of point masses. In an accompanying paper, we extend the analysis to a three-dimensional lens distribution. In the two-dimensional case, we derive the probability distribution of macroimage magnification, P(A), at A -1 ≫ τ 2 for a low optical depth lens distribution by modeling the illumination pattern as a superposition of the patterns due to individual "point-mass plus weak-shear" lenses. A point-mass lens perturbed by weak shear S produces an astroid-shaped caustic. We show that the magnification cross section σ(A / S) of the point-mass plus weak-shear lens obeys a simple scaling property, and we provide a useful analytic approximation for the cross section. By convolving this cross section with the probability distribution of the shear due to the neighboring point masses, we obtain a caustic-induced feature in P(A) that also exhibits a simple scaling property. This feature results in a 20% enhancement in P(A) at A ≈ 2/τ. In the low-magnification (A - 1 ≪ 1) limit, the macroimage consists of a single bright primary image and a large number of faint secondary images formed close to each of the point masses. The magnifications of the primary and the secondary images can be strongly correlated. Taking into account the correlations, we derive P(A) for low magnification and find that P(A) has a peak of amplitude ≈0.16/τ 2 at A - 1 ≈ 0.84τ 2. The low-magnification distribution matches smoothly the distribution for A - 1 ≫ τ 2 in the overlapping regimes A - 1 ≫ τ 2 and A ≪ 1/τ. Finally, after a discussion of the correct normalization for P(A), we combine the results and obtain a practical semianalytic expression for the macroimage magnification distribution P(A). This semianalytic distribution is in qualitative agreement with the results of previous numerical simulations, but the latter show stronger caustic-induced features at moderate A (1.5 ≲ A ≲ 10) for τ as small as 0.1. We resolve this discrepancy by reexamining the criterion for low optical depth. A simple argument shows that the fraction of caustics of individual lenses that merge with those of their neighbors is approximately 1 - exp (-8τ). For τ = 0.1, the fraction is surprisingly high: ≈ 55%. A simple criterion for the low optical depth analysis to be valid is τ ≪1/8, though the comparison with numerical simulations indicates that the semianalytic distribution is a reasonable fit to P(A) for τ up to 0.05. © 1997. The American Astronomical Society. All rights reserved.
Wed, 01 Jan 1997 00:00:00 GMThttp://hdl.handle.net/10722/1511571997-01-01T00:00:00Z
- On the orbits and masses of the satellites of the Pluto-Charon systemhttp://hdl.handle.net/10722/151194Title: On the orbits and masses of the satellites of the Pluto-Charon system
Authors: Lee, MH; Peale, SJ
Abstract: Two small satellites of Pluto, S/2005 P1 (hereafter P1) and S/2005 P2 (hereafter P2), have recently been discovered outside the orbit of Charon, and their orbits are nearly circular and nearly coplanar with that of Charon. Because the mass ratio of Charon-Pluto is ∼0.1, the orbits of P2 and P1 are significantly non-Keplerian even if P2 and P1 have negligible masses. We present an analytic theory, with P2 and P1 treated as test particles, which shows that the motion can be represented by the superposition of the circular motion of a guiding center, the forced oscillations due to the non-axisymmetric components of the potential rotating at the mean motion of Pluto-Charon, the epicyclic motion, and the vertical motion. The analytic theory shows that the azimuthal periods of P2 and P1 are shorter than the Keplerian orbital periods, and this deviation from Kepler's third law is already detected in the unperturbed Keplerian fit of Buie and coworkers. In this analytic theory, the periapse and ascending node of each of the small satellites precess at nearly equal rates in opposite directions. From direct numerical orbit integrations, we show the increasing influence of the proximity of P2 and P1 to the 3:2 mean-motion commensurability on their orbital motion as their masses increase within the ranges allowed by the albedo uncertainties. If the geometric albedos of P2 and P1 are high and of order of that of Charon, the masses of P2 and P1 are sufficiently low that their orbits are well described by the analytic theory. The variation in the orbital radius of P2 due to the forced oscillations is comparable in magnitude to that due to the best-fit Keplerian eccentricity, and there is at present no evidence that P2 has any significant epicyclic eccentricity. However, the orbit of P1 has a significant epicyclic eccentricity, and the prograde precession of its longitude of periapse with a period of 5300 days should be easily detectable. If the albedos of P2 and P1 are as low as that of comets, the large inferred masses induce significant short-term variations in the epicyclic eccentricities and/or periapse longitudes on the 400-500-day timescales due to the proximity to the 3:2 commensurability. In fact, for the maximum inferred masses, P2 and P1 may be in the 3:2 mean-motion resonance, with the resonance variable involving the periapse longitude of P1 librating. Observations that sample the orbits of P2 and P1 well on the 400-500-day timescales should provide strong constraints on the masses of P2 and P1 in the near future. © 2006 Elsevier Inc. All rights reserved.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10722/1511942006-01-01T00:00:00Z
- The kozai mechanism and the evolution of binary supermassive black holeshttp://hdl.handle.net/10722/151106Title: The kozai mechanism and the evolution of binary supermassive black holes
Authors: Blaes, O; Lee, MH; Socrates, A
Abstract: We consider the dynamical evolution of bound, hierarchical triples of supermassive black holes that might be formed in the nuclei of galaxies undergoing sequential mergers. The tidal force of the outer black hole on the inner binary produces eccentricity oscillations through the Kozai mechanism, and this can substantially reduce the gravitational wave merger time of the inner binary. We numerically calculate the merger time for a wide range of initial conditions and black hole mass ratios, including the effects of octupole interactions in the triple as well as general relativistic periastron precession in the inner binary. The semimajor axes and the mutual inclination of the inner and outer binaries are the most important factors affecting the merger time. We find that for a random distribution of inclination angles and approximately equal mass black holes, it is possible to reduce the merger time of a near circular inner binary by more than a factor of 10 in over 50% of all cases. We estimate that a typical exterior quadrupole moment from surrounding matter in the galaxy may also be sufficient to excite eccentricity oscillations in supermassive black hole binaries and to accelerate black hole mergers.
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/10722/1511062002-01-01T00:00:00Z
- A survey of numerical solutions to the coagulation equationhttp://hdl.handle.net/10722/151078Title: A survey of numerical solutions to the coagulation equation
Authors: Lee, MH
Abstract: We present the results of a systematic survey of numerical solutions to the coagulation equation for a rate coefficient of the form Aij α (iμ jν + iν jμ) and monodisperse initial conditions. The results confirm that there are three classes of rate coefficients with qualitatively different solutions. For ν ≤ 1 and λ = μ + ν ≤ 1, the numerical solution evolves in an orderly fashion and tends towards a self-similar solution at large time t. The properties of the numerical solution in the scaling limit agree with the analytic predictions of van Dongen and Ernst. In particular, for the subset with μ > 0 and λ < 1, we disagree with Krivitsky and find that the scaling function approaches the analytically predicted power-law behaviour at small mass, but in a damped oscillatory fashion that was not known previously. For ν ≤ 1 and λ > 1, the numerical solution tends towards a self-similar solution as t approaches a finite time t0. The mass spectrum nk develops at t0 a power-law tail nk α k-τ at large masses that violates mass conservation, and runaway growth/gelation is expected to start at tcrit = t0 in the limit the initial number of particles n0 → ∞. The exponent τ is in general less than the analytic prediction (λ + 3)/2, and t0 = K/[(λ - 1)n0A11] with K = 1-2 if λ ≲ 1.1. For ν > 1, the behaviours of the numerical solution are similar to those found in a previous paper by us. They strongly suggest that there are no self-consistent solutions at any time and that runaway growth is instantaneous in the limit n0 → ∞. They also indicate that the time Tcrit for the onset of runaway growth decreases slowly towards zero with increasing n0. .
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/10722/1510782001-01-01T00:00:00Z
- N-body evolution of dense clusters of compact starshttp://hdl.handle.net/10722/151130Title: N-body evolution of dense clusters of compact stars
Authors: Lee, MH
Abstract: The dynamical evolution of dense clusters of compact stars is studied using direct N-body simulations. The formation of binaries and their subsequent merging by gravitational radiation emission is important to the evolution of such clusters. Aarseth's NBODY5 N-body simulation code is modified to include the lowest order gravitational radiation force during two-body encounters and to handle the decay and merger of radiating binaries. It is used to study the evolution of small-N (= 1000) clusters with different initial velocity dispersions. The initial evolution is similar to that obtained by Quinlan & Shapiro (1989) using a multimass Fokker-Planck code and shows orderly formation of heavy objects. However, the late evolution differs qualitatively from previous results. In particular, we find runaway growth for the most massive object in the cluster: it acquires a mass much larger than that of the other objects and is detached from the smooth mass spectrum of the rest of the objects. We discuss why the Fokker-Planck equation with a mean-rate approach to the merger process cannot model runaway growth, and we present arguments to show that merger by gravitational radiation is expected to be unstable to runaway growth. The results suggest that a seed massive black hole can be formed by runaway growth in a dense cluster of compact stars. The possibility of runaway growth in dense clusters of normal stars is also discussed.
Fri, 01 Jan 1993 00:00:00 GMThttp://hdl.handle.net/10722/1511301993-01-01T00:00:00Z
- Secular evolution of hierarchical planetary systemshttp://hdl.handle.net/10722/151107Title: Secular evolution of hierarchical planetary systems
Authors: Lee, MH; Peale, SJ
Abstract: We investigate the dynamical evolution of coplanar, hierarchical, two-planet systems where the ratio of the orbital semimajor axes α = a1/a2 is small. Hierarchical two-planet systems are likely to be ubiquitous among extrasolar planetary systems. We show that the orbital parameters obtained from a multiple-Kepler fit to the radial velocity variations of a host star are best interpreted as Jacobi coordinates and that Jacobi coordinates should be used in any analyses of hierarchical planetary systems. An approximate theory that can be applied to coplanar, hierarchical, two-planet systems with a wide range of masses and orbital eccentricities is the octopole-level secular perturbation theory, which is based on an expansion to order α3 and orbit averaging. It reduces the coplanar problem to 1 degree of freedom, with e1 (or e2) and ω̄1 - ω̄2 as the relevant phase-space variables (where e1,2 are the orbital eccentricities of the inner and outer orbits, respectively, and ω̄1,2 are the longitudes of periapse). The octopole equations show that if the ratio of the maximum orbital angular momenta, λ = L1/L2 ≈ (m1/m2)α1/2, for given semimajor axes is approximately equal to a critical value λcrit, then libration of ω̄1 - ω̄2 about either 0° or 180° is almost certain, with possibly large amplitude variations of both eccentricities. From a study of the HD 168443 and HD 12661 systems and their variants using both the octopole theory and direct numerical orbit integrations, we establish that the octopole theory is highly accurate for systems with α≲0.1 and reasonably accurate even for systems with α as large as 1/3, provided that α is not too close to a significant mean-motion commensurability or above the stability boundary. The HD 168443 system is not in a secular resonance, and its ω̄ 1 - ω̄2 circulates. The HD 12661 system is the first extrasolar planetary system found to have ω̄1 - ω̄2 librating about 180°. The secular resonance means that the lines of apsides of the two orbits are on average antialigned, although the amplitude of libration of ω̄1 - ω̄2 is large. The libration ω̄1 - ω̄2 and the large amplitude variations of both eccentricities in the HD 12661 system are consistent with the analytic results on systems with λ ≈ λcrit. The evolution of the HD 12661 system with the best-fit orbital parameters and sin i = 1 (i is the inclination of the orbital plane from the plane of the sky) is affected by the close proximity to the 11:2 mean-motion commensurability, but small changes in the orbital period of the outer planet within the uncertainty can result in configurations that are not affected by mean-motion commensurabilities. The stability of the HD 12661 system requires sin i > 0.3.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10722/1511072003-01-01T00:00:00Z
- A primordial origin of the laplace relation among the Galilean satelliteshttp://hdl.handle.net/10722/151089Title: A primordial origin of the laplace relation among the Galilean satellites
Authors: Peale, SJ; Lee, MH
Abstract: Understanding the origin of the orbital resonances of the Galilean satellites of Jupiter will constrain the longevity of the extensive voicanism on lo, may explain a liquid ocean on Europa, and may guide studies of the dissipative properties of stars and Jupiter-like planets. The differential migration of the newly formed Galilean satellites due to interactions with a circumjovian disk can lead to the primordial formation of the Laplace relation n1-3n2 + 2n3 = 0, where the ni are the mean orbital angular velocities of lo, Europa, and Ganymede, respectively. This contrasts with the formation of the resonances by differential expansion of the orbits from tidal torques from Jupiter.
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/10722/1510892002-01-01T00:00:00Z
- Are the kepler near-resonance planet pairs due to tidal dissipation?http://hdl.handle.net/10722/190777Title: Are the kepler near-resonance planet pairs due to tidal dissipation?
Authors: Lee, MH; Fabrycky, D; Lin, DNC
Description: Conference Theme: Exoplanets in Multi-body Systems in the Kepler Era
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/1907772013-01-01T00:00:00Z
- Are the kepler near-resonance planet pairs due to tidal dissipation?http://hdl.handle.net/10722/189005Title: Are the kepler near-resonance planet pairs due to tidal dissipation?
Authors: Lee, MH; Fabrycky, D; Lin, DNC
Abstract: The multiple-planet systems discovered by the Kepler mission show an excess of planet pairs with period ratios just wide of exact commensurability for first-order resonances like 2:1 and 3:2. In principle, these planet pairs could have both resonance angles associated with the resonance librating if the orbital eccentricities are sufficiently small, because the width of first-order resonances diverges in the limit of vanishingly small eccentricity. We consider a widely held scenario in which pairs of planets were captured into first-order resonances by migration due to planet–disk interactions, and subsequently became detached from the resonances, due to tidal dissipation in the planets. In the context of this scenario, we find a constraint on the ratio of the planet’s tidal dissipation function and Love number that implies that some of the Kepler planets are likely solid. However, tides are not strong enough to move many of the planet pairs to the observed separations, suggesting that additional dissipative processes are at play.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/1890052013-01-01T00:00:00Z
- On the dynamical state of the HD 82943 planetary systemhttp://hdl.handle.net/10722/160925Title: On the dynamical state of the HD 82943 planetary system
Authors: Tan, X; Lee, MH; Howard, AW; Marcy, GW; Johnson, JA; Wright, JT
Abstract: We present new results from an analysis of radial velocity data of the HD 82943 planetary system based on 10 years of measurements obtained with the Keck telescope. Previous study has shown that the HD 82943 system has two planets that are likely in 2:1 mean-motion resonance (MMR), with the orbital periods about 220 and 440 days (Lee et al. 2006). However, alternative fits that are qualitatively different have also been suggested, with the two planets in 1:1 resonance or the addition of a third planet possibly in a Laplace 4:2:1 resonance with the other two (Gozdziewski & Konacki 2006; Beague et al. 2008). Here we use the chi-square minimization method combined with parameter grid search to investigate the orbital parameters and dynamical states of the qualitatively different types of fits. Our results tend to support the 2:1 MMR configuration for this system. The fits of coplanar 2:1 MMR show a chi-square minimum at 20 degree inclination that is dynamically stable with both resonant angles librating around 0 degree. The fits of 1:1 resonance and 3-planet Laplace resonance are ruled out according to chi-square statistic and dynamical instability.
Description: Session 01 - Exoplanets: abstract no. 01.08
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10722/1609252012-01-01T00:00:00Z
- Constraints on giant planet migration: obliquities and stabilityhttp://hdl.handle.net/10722/130352Title: Constraints on giant planet migration: obliquities and stability
Authors: Lee, MH; McNeil, DS
Abstract: We have performed both secular and N-body simulations of the migration of the giants planets in our Solar System. The simulations ahow that the obliquities (the angle between the spin axis and the orbit normal) of Jupiter and Saturn and the survival of all four giant planets provide strong constraints on the migration. In the Nice model for the establishment of the orbital architecture of the giant planet, the outer Solar System was initially compact, and the scattering of planetesimals caused Jupiter to migrate inward and Saturn, Uranus, and Neptune outward (Tsiganis et al. 2005). The decrease in the orbital precession frequencies due to the migration of the planets could lead to the capture of Saturn into the spin-orbit resonance and an increase in Saturn's obliquity to the observed 27 degrees (Ward and Hamilton 2004; Hamilton and Ward 2004). The migration must be sufficiently slow for Saturn to stay in the spin-orbit resonance, and the critical migration timescale decreases with orbital inclinations (Boue et al. 2009). For the orbital inclinations generated during the encounter phase of the Nice model, it is possible to produce a Saturnian obiliquity comparable to the observed one, if the migration timescale is of the order of 20 Myr. Jupiter is usually also captured into spin-orbit resonance, and the resulting obliquity of Jupiter is comparable to or larger than that of Saturn, in contrast to the observed 3 degrees. In addition, if the migration timescale is of the order of 20 Myr or longer, the probability that all four planets survive is less than about 20%.
Description: 19th Kingston Meeting; Topic: The Theory of the Universe and Everything in It
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1303522010-01-01T00:00:00Z
- An Analytic Theory for the Orbits of Circumbinary Planetshttp://hdl.handle.net/10722/181665Title: An Analytic Theory for the Orbits of Circumbinary Planets
Authors: Leung, CK; Lee, MH
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/1816652013-01-01T00:00:00Z
- Dynamical Analysis of the Circumprimary Planet in the Eccentric Binary System HD 59686http://hdl.handle.net/10722/252732Title: Dynamical Analysis of the Circumprimary Planet in the Eccentric Binary System HD 59686
Authors: Trifonov, TH; Lee, MH; Reffert, S; Quirrenbach, A
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10722/2527322018-01-01T00:00:00Z
- Modeling the resonant planetary system GJ 876http://hdl.handle.net/10722/151155Title: Modeling the resonant planetary system GJ 876
Authors: Kley, W; Lee, MH; Murray, N; Peale, SJ
Abstract: The evolution of the GJ 876 system using two-dimensional hydrodynamical simulations including viscous heating and radiative cooling was discussed. It was found that the relaxed disk remained circular in all models for low planet-to-star mass ratio q2, but becomes eccentric for high mass ratios for those models with fixed temperature structure. A more comprehensive set of numerical calculations treating the evolution of two planets interacting with their protoplanetary disk was presented with special emphasis on the resonant system GJ 876. The results show that it was possible to reduce the final values of the eccentricities close to the observed values.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10722/1511552005-01-01T00:00:00Z
- Planets around Giant Starshttp://hdl.handle.net/10722/218250Title: Planets around Giant Stars
Authors: Lee, MH; Trifonov, TH; Quirrenbach, A; Reffert, S
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2182502015-01-01T00:00:00Z
- Statistics of gravitational microlensing magnification. II. Three-dimensional lens distributionhttp://hdl.handle.net/10722/151103Title: Statistics of gravitational microlensing magnification. II. Three-dimensional lens distribution
Authors: Lee, MH; Babul, A; Kofman, L; Kaiser, N
Abstract: In the first paper of this series, we studied the theory of gravitational microlensing for a planar distribution of point masses. In this second paper, we extend the analysis to a three-dimensional lens distribution. First we study the lensing properties of three-dimensional lens distributions by considering in detail the critical curves, the caustics, the illumination patterns, and the magnification cross sections σ(A) of multiplane configurations with two, three, and four point masses. For N* point masses that are widely separated in Lagrangian space (i.e., in projection), we find that there are ∼2 N* -1 critical curves in total, but that only ∼N* of these produce prominent caustic-induced features in σ(A) at moderate to high magnifications (A ≳ 2). In the case of a random distribution of point masses at low optical depth, we show that the multiplane lens equation near a point mass can be reduced to the single-plane equation of a point mass perturbed by weak shear. This allows us to calculate the caustic-induced feature in the macroimage magnification distribution P(A) as a weighted sum of the semianalytic feature derived in Paper I for a planar lens distribution. The resulting semianalytic caustic-induced feature is similar to the feature in the planar case, but it does not have any simple scaling properties, and it is shifted to higher magnification. The semianalytic distribution is compared with the results of previous numerical simulations for optical depth τ ≈0.1, and they are in better agreement than a similar comparison in the planar case. We explain this by estimating the fraction of caustics of individual lenses that merge with those of their neighbors. For τ = 0.1, the fraction is ≈20%, much less than the ≈55% for the planar case. In the three-dimensional case, a simple criterion for the low optical depth analysis to be valid is τ ≪ 0.4, though the comparison with numerical simulations indicates that the semianalytic distribution is a reasonable fit to P(A) for τ up to 0.2. © 1997. The American Astronomical Society. All rights reserved.
Wed, 01 Jan 1997 00:00:00 GMThttp://hdl.handle.net/10722/1511031997-01-01T00:00:00Z
- Erratum: Secular evolution of hierarchical planetary systems (The Astrophysical Journal (2003) 592 (1201))http://hdl.handle.net/10722/151117Title: Erratum: Secular evolution of hierarchical planetary systems (The Astrophysical Journal (2003) 592 (1201))
Authors: Lee, MH; Peale, SJ
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10722/1511172003-01-01T00:00:00Z
- Evolution of the obliquities of the giant planets in encounters during migrationhttp://hdl.handle.net/10722/151211Title: Evolution of the obliquities of the giant planets in encounters during migration
Authors: Lee, MH; Peale, SJ; Pfahl, E; Ward, WR
Abstract: Tsiganis et al. [Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459-461] have proposed that the current orbital architecture of the outer Solar System could have been established if it was initially compact and Jupiter and Saturn crossed the 2:1 orbital resonance by divergent migration. The crossing led to close encounters among the giant planets, but the orbital eccentricities and inclinations were damped to their current values by interactions with planetesimals. Brunini [Brunini, A., 2006. Nature 440, 1163-1165] has presented widely publicized numerical results showing that the close encounters led to the current obliquities of the giant planets. We present a simple analytic argument which shows that the change in the spin direction of a planet relative to an inertial frame during an encounter between the planets is very small and that the change in the obliquity (which is measured from the orbit normal) is due to the change in the orbital inclination. Since the inclinations are damped by planetesimal interactions on timescales much shorter than the timescales on which the spins precess due to the torques from the Sun, especially for Uranus and Neptune, the obliquities should return to small values if they are small before the encounters. We have performed simulations using the symplectic integrator SyMBA, modified to include spin evolution due to the torques from the Sun and mutual planetary interactions. Our numerical results are consistent with the analytic argument for no significant remnant obliquities. © 2007 Elsevier Inc. All rights reserved.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10722/1512112007-01-01T00:00:00Z
- 26Al decay: Heat production and a revised age for Iapetushttp://hdl.handle.net/10722/64145Title: 26Al decay: Heat production and a revised age for Iapetus
Authors: CastilloRogez, J; Johnson, TV; Lee, MH; Turner, NJ; Matson, DL; Lunine, J
Abstract: We revisit the appropriate energies to be used for computing heat production from 26Al decay. Due to the complexity of the decay scheme of this radioisotope, previous geophysical studies have used values ranging from 1.2 to 4 MeV per decay. The upper bound corresponds to the difference in mass energy between the 26Al and 26Mg ground states. This includes energy carried away by neutrinos, which does not contribute to heating planetary material. The lower bound does not account for the heating caused by the absorption of the γ rays from the excited 26Mg, or for the annihilation energy deposited in the material if the decay occurs inside even small planetesimals. Based on the calculations described by Schramm et al. [Schramm, D., Tera, F., Wasserburg, G.J., 1970. The isotopic abundance of 26Mg and limits on 26Al in the early Solar System. Earth Planet. Sci. Lett. 10, 44-59] updated with the most recent nuclear constants, we recommend using a heat production value of 3.12 MeV per decay, which is the total energy of disintegration minus the energy carried off by the neutrinos. This heat production value is higher than the value used in the modeling of Iapetus by Castillo-Rogez et al. [Castillo-Rogez, J., Matson, D.L., Sotin, C., Johnson, T.V., Lunine, J.I., Thomas, P.C., 2007. Iapetus' geophysics: Rotation rate, shape, and equatorial ridge. Icarus 190, 179-202] by about a factor 2.5. The resulting estimate of the time of formation of Iapetus is shifted by about 1 Myr, to between ∼3.4 and 5.4 Myr after the production of the calcium-aluminum inclusions (CAIs). © 2009 Elsevier Inc.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/641452009-01-01T00:00:00Z
- Precise Radial Velocities of Giant Stars: VI. A possible 2:1 resonant planet pair around the K giant star η Cethttp://hdl.handle.net/10722/202779Title: Precise Radial Velocities of Giant Stars: VI. A possible 2:1 resonant planet pair around the K giant star η Cet
Authors: Trifonov, T; Reffert, S; TAN, X; Lee, MH; Quirrenbach, A
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10722/2027792014-01-01T00:00:00Z
- On the Validity of the Coagulation Equation and the Nature of Runaway Growthhttp://hdl.handle.net/10722/150932Title: On the Validity of the Coagulation Equation and the Nature of Runaway Growth
Authors: Lee, MH
Abstract: The coagulation equation, which is widely used for modeling growth in planet formation and other astrophysical problems, is the mean-rate equation that describes the evolution of the mass spectrum of a collection of particles due to successive mergers. A numerical code that can yield accurate solutions to the coagulation equation with a reasonable number of mass bins is developed, and it is used to study the properties of solutions to the coagulation equation. We consider limiting cases of the merger rate coefficient Aij for gravitational interaction, with the power-law index of the mass-radius relation β=1/3 (for planetesimals) and 2/3 (for stars). We classify the mass dependence of Aij using the exponent λ for the merger between two particles of comparable mass, and the exponents μ and ν for the merger between a heavy particle and a light particle. For the two cases with λ≤1 and ν≤1, the mass spectrum evolves in an orderly fashion. For the remaining cases, which have ν>1, we find strong numerical and analytical evidence that there are no self-consistent solutions to the coagulation equation at any time. The results for the ν>1 cases are qualitatively different from the well-known example with Aij∝ij. For the latter case, which is in the range ν≤1 and λ>1, there is an analytic solution to the coagulation equation that is valid for a finite amount of time t0. We discuss a simplified merger problem that illustrates the qualitative differences in the solutions to the coagulation equation for the three classes of Aij. Our results strongly suggest that there are two types of runaway growth. For Aij with ν≤1 and λ>1, runaway growth starts at tcrit≈t0, the time at which the coagulation equation solution becomes invalid. For Aij with ν>1, which include all gravitational interaction cases expected to show runaway growth, the dependence of the time tcrit for the onset of runaway growth on the parameters of the problem is not yet well understood, but there are indications that tcrit (in units of 1/(n0A11)) may decrease slowly toward zero with increasing initial total number of particles n0. © 2000 Academic Press.
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/10722/1509322000-01-01T00:00:00Z