arXiv subjects

Man Hoi Lee

Publications and source records attributed to Man Hoi Lee.

At least 37 records · Page 2Linked to original sources

arXiv2018

New HARPS and FEROS observations of GJ1046

In this paper we present new precise Doppler data of GJ1046 taken between November 2005 and July 2018 with the HARPS and the FEROS high-resolution spectographs. In addition, we provide a new stellar mass estimate of GJ1046 and we update the orbital parameters of the GJ1046 system. These new data and analysis could be used together with the GAIA epoch astrometry, when available, for braking the $\sin i$ degeneracy and revealing the true mass of the GJ1046 system.

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arXiv2018

On the Early In Situ Formation of Pluto's Small Satellites

The formation of Pluto's small satellites - Styx, Nix, Keberos and Hydra - remains a mystery. Their orbits are nearly circular and are near mean-motion resonances and nearly coplanar with Charon's orbit. One scenario suggests that they all formed close to their current locations from a disk of debris that was ejected from the Charon-forming impact before the tidal evolution of Charon. The validity of this scenario is tested by performing $N$-body simulations with the small satellites treated as test particles and Pluto-Charon evolving tidally from an initial orbit at a few Pluto radii with initial eccentricity $e_{\rm C} = 0$ or 0.2. After tidal evolution, the free eccentricities $e_{\rm free}$ of the test particles are extracted by applying fast Fourier transformation to the distance between the test particles and the center of mass of the system and compared with the current eccentricities of the four small satellites. The only surviving test particles with $e_{\rm free}$ matching the eccentricities of the current satellites are those not affected by mean-motion resonances during the tidal evolution in a model with Pluto's effective tidal dissipation function $Q = 100$ and an initial $e_{\rm C}$ = 0.2 that is damped down rapidly. However, these test particles do not have any preference to be in or near 4:1, 5:1 and 6:1 resonances with Charon. An alternative scenario may be needed to explain the formation of Pluto's small satellites.

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arXiv2018

Dynamical analysis of the circumprimary planet in the eccentric binary system HD59686

We present a detailed orbital and stability analysis of the HD~59686 binary-star planet system. HD~59686 is a single-lined moderately close ($a_{B} = 13.6\,$AU) eccentric ($e_{B} = 0.73$) binary, where the primary is an evolved K giant with mass $M = 1.9 M_{\odot}$ and the secondary is a star with a minimum mass of $m_{B} = 0.53 M_{\odot}$. Additionally, on the basis of precise radial velocity (RV) data a Jovian planet with a minimum mass of $m_p = 7 M_{\mathrm{Jup}}$, orbiting the primary on a nearly circular S-type orbit with $e_p = 0.05$ and $a_p = 1.09\,$AU, has recently been announced. We investigate large sets of orbital fits consistent with HD 59686's radial velocity data by applying bootstrap and systematic grid-search techniques coupled with self-consistent dynamical fitting. We perform long-term dynamical integrations of these fits to constrain the permitted orbital configurations. We find that if the binary and the planet in this system have prograde and aligned coplanar orbits, there are narrow regions of stable orbital solutions locked in a secular apsidal alignment with the angle between the periapses, $Δω$, librating about $0^\circ$. We also test a large number of mutually inclined dynamical models in an attempt to constrain the three-dimensional orbital architecture. We find that for nearly coplanar and retrograde orbits with mutual inclination $145^\circ \lesssim Δi \leq 180^\circ$, the system is fully stable for a large range of orbital solutions.

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arXiv2017

Breakthrough revisited: investigating the requirements for growth of dust beyond the bouncing barrier

For grain growth to proceed effectively and lead to planet formation a number of barriers to growth must be overcome. One such barrier, relevant for compact grains in the inner regions of the disc, is the `bouncing barrier' in which large grains ($\sim$ mm size) tend to bounce off each other rather than sticking. However, by maintaining a population of small grains it has been suggested that cm-size particles may grow rapidly by sweeping up these small grains. We present the first numerically resolved investigation into the conditions under which grains may be lucky enough to grow beyond the bouncing barrier by a series of rare collisions leading to growth (so-called `breakthrough'). Our models support previous results, and show that in simple models breakthrough requires the mass ratio at which high velocity collisions transition to growth instead of causing fragmentation to be low, $ϕ\lesssim 50$. However, in models that take into account the dependence of the fragmentation threshold on mass-ratio, we find breakthrough occurs more readily, even if mass transfer is relatively inefficient. This suggests that bouncing may only slow down growth, rather than preventing growth beyond a threshold barrier. However, even when growth beyond the bouncing barrier is possible, radial drift will usually prevent growth to arbitrarily large sizes.

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arXiv2016

Precise radial velocities of giant stars IX. HD 59686 Ab: a massive circumstellar planet orbiting a giant star in a ~13.6 au eccentric binary system

Context: For over 12 yr, we have carried out a precise radial velocity survey of a sample of 373 G and K giant stars using the Hamilton Échelle Spectrograph at Lick Observatory. There are, among others, a number of multiple planetary systems in our sample as well as several planetary candidates in stellar binaries. Aims: We aim at detecting and characterizing substellar+stellar companions to the giant star HD 59686 A (HR 2877, HIP 36616). Methods: We obtained high precision radial velocity (RV) measurements of the star HD 59686 A. By fitting a Keplerian model to the periodic changes in the RVs, we can assess the nature of companions in the system. In order to discriminate between RV variations due to non-radial pulsation or stellar spots we used infrared RVs taken with the CRIRES spectrograph at the Very Large Telescope. Additionally, to further characterize the system, we obtain high-resolution images with LMIRCam at the Large Binocular Telescope. Results: We report the likely discovery of a giant planet with a mass of $m_{p}~\sin i=6.92_{-0.24}^{+0.18}~M_{Jup}$ orbiting at $a_{p}=1.0860_{-0.0007}^{+0.0006}$ au from the giant star HD 59686 A. Besides the planetary signal, we discover an eccentric ($e_{B}=0.729_{-0.003}^{+0.004}$) binary companion with a mass of $m_{B}~\sin i=0.5296_{-0.0008}^{+0.0011}~M_{Sun}$ orbiting at a semi-major axis of just $a_{B}=13.56_{-0.14}^{+0.18}$ au. Conclusions: The existence of the planet HD 59686 Ab in a tight eccentric binary system severely challenges standard giant planet formation theories and requires substantial improvements to such theories in tight binaries. Otherwise, alternative planet formation scenarios such as second generation planets or dynamical interactions in an early phase of the system's lifetime should be seriously considered in order to better understand the origin of this enigmatic planet.

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arXiv2015

Tilting Saturn without tilting Jupiter: Constraints on giant planet migration

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%).

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arXiv2014

On the Origin of Pluto's Small Satellites by Resonant Transport

The orbits of Pluto's four small satellites (Styx, Nix, Kerberos, and Hydra) are nearly circular and coplanar with the orbit of the large satellite Charon, with orbital periods nearly in the ratios 3:1, 4:1, 5:1, and 6:1 with Charon's orbital period. These properties suggest that the small satellites were created during the same impact event that placed Charon in orbit and had been pushed to their current positions by being locked in mean-motion resonances with Charon as Charon's orbit was expanded by tidal interactions with Pluto. Using the Pluto-Charon tidal evolution models developed by Cheng et al. (2014), we show that stable capture and transport of a test particle in multiple resonances at the same mean-motion commensurability is possible at the 5:1, 6:1, and 7:1 commensurabilities, if Pluto's zonal harmonic $J_{2P} = 0$. However, the test particle has significant orbital eccentricity at the end of the tidal evolution of Pluto-Charon in almost all cases, and there are no stable captures and transports at the 3:1 and 4:1 commensurabilities. Furthermore, a non-zero hydrostatic value of $J_{2P}$ destroys the conditions necessary for multiple resonance migration. Simulations with finite but minimal masses of Nix and Hydra also fail to yield any survivors. We conclude that the placing of the small satellites at their current orbital positions by resonant transport is extremely unlikely.

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arXiv2014

Precise radial velocities of giant stars VI. A possible 2:1 resonant planet pair around the K giant star $η$ Cet

We report the discovery of a new planetary system around the K giant $η$ Cet (HIP 5364, HD 6805) based on 118 high-precision optical radial velocities taken at Lick Observatory since July 2000. Since October 2011 an additional nine near-infrared Doppler measurements have been taken using the ESO CRIRES spectrograph (VLT, UT1). The visible data set shows two clear periodicities. Although we cannot completely rule out that the shorter period is due to rotational modulation of stellar features, the infrared data show the same variations as in the optical, which strongly supports that the variations are caused by two planets. Assuming the mass of $η$ Cet to be 1.7 $M_\odot$, the best edge-on coplanar dynamical fit to the data is consistent with two massive planets ($m_b\sin i$ = 2.6 $\pm$ 0.2 $M_{\mathrm{Jup}}$, $m_c\sin i$ = 3.3 $\pm$ 0.2 $M_{\mathrm{Jup}}$), with periods of $P_b$ = 407 $\pm$ 3 days and $P_c$ = 740 $\pm$ 5 days and eccentricities of $e_b$ = 0.12 $\pm$ 0.05 and $e_c$ = 0.08 $\pm$ 0.03. We tested a wide variety of edge-on coplanar and inclined planetary configurations for stability, which agree with the derived radial velocities. We find that in certain coplanar orbital configurations with moderate $e_b$ eccentricity, the planets can be effectively trapped in an anti-aligned 2:1 mean motion resonance. A much larger non-resonant stable region exists in low-eccentricity parameter space, although it appears to be much farther from the best fit than the 2:1 resonant region. In all other cases, the system is categorized as unstable or chaotic. Another conclusion from the coplanar inclined dynamical test is that the planets can be at most a factor of $\sim$ 1.4 more massive than their suggested minimum masses. This stability constraint on the inclination excludes the possibility of two brown dwarfs, and strongly favors a planetary system.

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arXiv2014

Complete Tidal Evolution of Pluto-Charon

Both Pluto and its satellite Charon have rotation rates synchronous with their orbital mean motion. This is the theoretical end point of tidal evolution where transfer of angular momentum has ceased. Here we follow Pluto's tidal evolution from an initial state having the current total angular momentum of the system but with Charon in an eccentric orbit with semimajor axis $a \approx 4R_P$ (where $R_P$ is the radius of Pluto), consistent with its impact origin. Two tidal models are used, where the tidal dissipation function $Q \propto$ 1/frequency and $Q=$ constant, where details of the evolution are strongly model dependent. The inclusion of the gravitational harmonic coefficient $C_{22}$ of both bodies in the analysis allows smooth, self consistent evolution to the dual synchronous state, whereas its omission frustrates successful evolution in some cases. The zonal harmonic $J_2$ can also be included, but does not cause a significant effect on the overall evolution. The ratio of dissipation in Charon to that in Pluto controls the behavior of the orbital eccentricity, where a judicious choice leads to a nearly constant eccentricity until the final approach to dual synchronous rotation. The tidal models are complete in the sense that every nuance of tidal evolution is realized while conserving total angular momentum - including temporary capture into spin-orbit resonances as Charon's spin decreases and damped librations about the same.

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arXiv2013

A Detailed Analysis of the HD 73526 2:1 Resonant Planetary System

We present six years of new radial-velocity data from the Anglo-Australian and Magellan Telescopes on the HD 73526 2:1 resonant planetary system. We investigate both Keplerian and dynamical (interacting) fits to these data, yielding four possible configurations for the system. The new data now show that both resonance angles are librating, with amplitudes of 40 degrees and 60 degrees, respectively. We then perform long-term dynamical stability tests to differentiate these solutions, which only differ significantly in the masses of the planets. We show that while there is no clearly preferred system inclination, the dynamical fit with i=90 degrees provides the best combination of goodness-of-fit and long-term dynamical stability.

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arXiv2013

Characterizing the Orbital and Dynamical State of the HD 82943 Planetary System With Keck Radial Velocity Data

We present an updated analysis of radial velocity data of the HD 82943 planetary system based on 10 years of measurements obtained with the Keck telescope. Previous studies have 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 two planets in a 1:1 resonance (Gozdziewski & Konacki 2006) or three planets in a Laplace 4:2:1 resonance (Beauge et al. 2008). Here we use \c{hi}2 minimization combined with parameter grid search to investigate the orbital parameters and dynamical states of the qualitatively different types of fits, and we compare the results to those obtained with the differential evolution Markov chain Monte Carlo method. Our results support the coplanar 2:1 MMR configuration for the HD 82943 system, and show no evidence for either the 1:1 or 3-planet Laplace resonance fits. The inclination of the system with respect to the sky plane is well constrained at about 20(+4.9 -5.5) degree, and the system contains two planets with masses of about 4.78 MJ and 4.80 MJ (where MJ is the mass of Jupiter) and orbital periods of about 219 and 442 days for the inner and outer planet, respectively. The best fit is dynamically stable with both eccentricity-type resonant angles θ1 and θ2 librating around 0 degree.

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arXiv2013

Are the Kepler Near-Resonance Planet Pairs due to Tidal Dissipation?

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.

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arXiv2012

An Analytic Theory for the Orbits of Circumbinary Planets

Three transiting circumbinary planets (Kepler-16 b, Kepler-34 b, and Kepler-35 b) have recently been discovered from photometric data taken by the Kepler spacecraft. Their orbits are significantly non-Keplerian because of the large secondary-to-primary mass ratio and orbital eccentricity of the binaries, as well as the proximity of the planets to the binaries. We present an analytic theory, with the planet treated as a test particle, which shows that the planetary 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 binary's potential, the epicyclic motion, and the vertical motion. In this analytic theory, the periapse and ascending node of the planet precess at nearly equal rates in opposite directions. The largest forced oscillation term corresponds to a forced eccentricity (which is an explicit function of the parameters of the binary and of the guiding center radius of the planet), and the amplitude of the epicyclic motion (which is a free parameter of the theory) is the free eccentricity. Comparisons with direct numerical orbit integrations show that this analytic theory gives an accurate description of the planetary motion for all three Kepler systems. We find that all three Kepler circumbinary planets have nonzero free eccentricities.

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arXiv2009

Planetary Migration and Eccentricity and Inclination Resonances in Extrasolar Planetary Systems

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. 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 (2004). 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 (2003) 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 migration rate itself.

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arXiv2007

Evolution of the Obliquities of the Giant Planets in Encounters during Migration

Tsiganis et al. (2005) 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 (2006) 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.

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arXiv2006

On the Orbits and Masses of the Satellites of the Pluto-Charon System

(Abridged) The orbits of the recently discovered satellites of Pluto, S/2005 P2 and S/2005 P1, are significantly non-Keplerian, even if P2 and P1 have negligible masses, because the mass ratio of Charon-Pluto is ~0.1. We present an analytic theory with P2 and P1 treated as test particles. This analytic theory shows that the azimuthal periods of P2 and P1 are shorter than the Keplerian orbital periods and that the periapse and ascending node of each of the satellites precess at nearly equal rates in opposite directions. The deviation from Kepler's third law is already detected in the unperturbed Keplerian fit of Buie and coworkers. We also present direct numerical orbit integrations with different assumed masses for P2 and P1 within the ranges allowed by the albedo uncertainties. If the albedos are as high as that of Charon, the masses of P2 and P1 are sufficiently low that their orbits are well described by the analytic theory. There is at present no evidence that P2 has any significant epicyclic eccentricity. However, the orbit of P1 has a significant epicyclic eccentricity, and its prograde periapse precession with a period of 5300 days should be easily detectable. If the albedos are as low as that of comets, the large inferred masses induce significant variations in the epicyclic eccentricities and/or periapse longitudes on the 400-500-day timescales, due to the proximity of P2 and P1 to the 3:2 mean-motion 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.

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arXiv2005

On the 2:1 Orbital Resonance in the HD 82943 Planetary System

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 chi_{nu}^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 chi_{nu}^2. For an assumed coplanar inclination i = 30 deg. (sin i = 0.5), only good fits with both of the lowest order, eccentricity-type mean-motion resonance variables at the 2:1 commensurability, theta_1 and theta_2, librating about 0 deg. are stable. For sin i = 1, there are also some good fits with only theta_1 (involving the inner planet's periapse longitude) librating that are stable for at least 10^8 years. The libration semiamplitudes are about 6 deg. for theta_1 and 10 deg. for theta_2 for the stable good fit with the smallest libration amplitudes of both theta_1 and theta_2. We do not find any good fits that are non-resonant and stable. Thus the two planets in the HD 82943 system are almost certainly in 2:1 mean-motion resonance, with at least theta_1 librating, and the observations may even be consistent with small-amplitude librations of both theta_1 and theta_2.

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arXiv2004

Diversity and Origin of 2:1 Orbital Resonances in Extrasolar Planetary Systems

(Abridged) A diversity of 2:1 resonance configurations can be expected in extrasolar planetary systems, and their geometry can provide information about the origin of the resonances. Assembly during planet formation by the differential migration of planets due to planet-disk interaction is one scenario for the origin of mean-motion resonances in extrasolar planetary systems. The stable 2:1 resonance configurations that can be reached by differential migration of planets with constant masses and initially coplanar and nearly circular orbits are (1) anti-symmetric configurations with the mean-motion resonance variables theta_1 and theta_2 (in deg.) librating about 0 and 180, respectively (as in the Io-Europa pair), (2) symmetric configurations with both theta_1 and theta_2 librating about 0 (as in the GJ 876 system), and (3) asymmetric configurations with theta_1 and theta_2 librating about angles far from either 0 or 180. There are, however, stable 2:1 resonance configurations with symmetric (theta_1 = theta_2 = 0), asymmetric, and anti-symmetric (theta_1 = 180 and theta_2 = 0) librations that cannot be reached by differential migration of planets with constant masses and initially coplanar and nearly circular orbits. If real systems with these configurations are ever found, their origin would require (1) a change in the planetary mass ratio m_1/m_2 during migration, (2) a migration scenario involving inclination resonances, or (3) multiple-planet scattering in crowded planetary systems. We find that the asymmetric configurations with large e_2 and the theta_1 = 180 and theta_2 = 0 configurations have intersecting orbits and that the theta_1 = theta_2 = 0 configurations with e_1 > 0.714 have prograde periapse precessions.

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