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Eccentricity Evolution of Resonant Migrating Planets  [PDF]
N. Murray,M. Paskowitz,M. Holman
Physics , 2001, DOI: 10.1086/324536
Abstract: We examine the eccentricity evolution of a system of two planets locked in a mean motion resonance, in which the outer planet loses energy and angular momentum. The sink of energy and angular momentum could be either a gas or planetesimal disk. We show that the eccentricity of both planetary bodies can grow to large values, particularly if the inner body does not directly exchange energy or angular momentum with the disk. We analytically calculate the eccentricity damping rate in the case of a single planet migrating through a planetesimal disk. We present the results of numerical integrations of two resonant planets showing rapid growth of eccentricity. We also present integrations in which a Jupiter-mass planet is forced to migrate inward through a system of 5-10 roughly Earth mass planets. The migrating planet can eject or accrete the smaller bodies; roughly 5% of the mass (averaged over all the integrations) accretes onto the central star. The results are discussed in the context of the currently known extrasolar planetary systems.
Resonant capture by inward migrating planets  [PDF]
Qingjuan Yu,Scott Tremaine
Physics , 2000, DOI: 10.1086/319401
Abstract: We investigate resonant capture of small bodies by planets that migrate inwards, using analytic arguments and three-body integrations. If the orbits of the planet and the small body are initially circular and coplanar, the small body is captured when it crosses the 2:1 resonance with the planet. As the orbit shrinks it becomes more eccentric, until by the time its semimajor axis has shrunk by a factor of four, its eccentricity reaches nearly unity (1-e<<10^{-4}). In typical planetary systems, bodies in this high-eccentricity phase are likely to be consumed by the central star. If they can avoid this fate, as migration continues the inclination flips from 0 to i=180 degrees; thereafter the eccentricity declines until the semimajor axis is a factor of nine smaller than at capture, at which point the small body is released from the 2:1 resonance on a nearly circular retrograde orbit. Small bodies captured into resonance from initially inclined or eccentric orbits can also be ejected from the system, or released from the resonance on highly eccentric polar orbits (i\simeq 90 degrees) that are stabilized by a secular resonance. We conclude that migration can drive much of the inner planetesimal disk into the star, and that post-migration multi-planet systems may not be coplanar.
Resonant inclination excitation of migrating giant planets  [PDF]
Edward W. Thommes,Jack J. Lissauer
Physics , 2003, DOI: 10.1086/378317
Abstract: The observed orbits of extrasolar planets suggest that many giant planets migrate a considerable distance towards their parent star as a result of interactions with the protoplanetary disk, and that some of these planets become trapped in eccentricity-exciting mean motion resonances with one another during this migration. Using three-dimensional numerical simulations, we find that as long as the timescale for damping of the planets' eccentricities by the disk is close to or longer than the disk-induced migration timescale, and the outer planet is more than half the mass of the inner, resonant inclination excitation will also occur. Neither the addition of a (simple, fixed) disk potential, nor the introduction of a massive inner planetary system, inhibit entry into the inclination resonance. Therefore, such a mechanism may not be uncommon in the early evolution of a planetary system, and a significant fraction of exoplanetary systems may turn out to be non-coplanar.
Collision probabilities of migrating small bodies and dust particles with planets  [PDF]
S. I. Ipatov
Physics , 2009, DOI: 10.1017/S174392131000147X
Abstract: Probabilities of collisions of migrating small bodies and dust particles produced by these bodies with planets were studied. Various Jupiter-family comets, Halley-type comets, long-period comets, trans-Neptunian objects, and asteroids were considered. The total probability of collisions of any considered body or particle with all planets did not exceed 0.2. The amount of water delivered from outside of Jupiter's orbit to the Earth during the formation of the giant planets could exceed the amount of water in Earth's oceans. The ratio of the mass of water delivered to a planet by Jupiter-family comets or Halley-type comets to the mass of the planet can be greater for Mars, Venus, and Mercury, than that for Earth.
Hot Big Planets Kepler Survey: Measuring the Repopulation Rate of the Shortest-Period Planets  [PDF]
Stuart F. Taylor
Physics , 2013,
Abstract: By surveying new fields for the shortest-period "big" planets, the Kepler spacecraft could provide the statistics to more clearly measure the occurrence distributions of giant and medium planets. This would allow separate determinations for giant and medium planets of the relationship between the inward rate of tidal migration of planets and the strength of the stellar tidal dissipation (as expressed by the tidal quality factor Q). We propose a "Hot Big Planets Survey" to find new big planets to better determine the planet occurrence distribution at the shortest period. We call planets that Kepler will be able to find as "big", for the purpose of comparing the distribution of giant and medium planets (above and below 8 earth radii). The distribution of planets from one field has been interpreted to show that the shortest period giant planets are at the end of an ongoing flow of high eccentricity migration, likely from scattering from further out. The numbers of planets at these short periods is still small, leaving uncertainty over the result that the distribution shows the expected power index for inward tidal migration. The current statistics make it hard to say whether the presence of more giant planets at the shortest periods despite there being more medium planets at most periods indicates a greater migration of giant than medium planets. We propose a repurposed Kepler mission to make enough 45-day observations to survey 10 times as many stars as in the survey of the original field, to survey for planets with periods of up to fifteen days with at least three transits. The current statistics make it hard to say whether the presence of more giant planets at the shortest periods despite there being more medium planets at most periods indicates a greater migration of giant than medium planets.
On the gap-opening criterion of migrating planets in protoplanetary disks  [PDF]
Matej Malik,Farzana Meru,Lucio Mayer,Michael R. Meyer
Physics , 2015, DOI: 10.1088/0004-637X/802/1/56
Abstract: We perform two-dimensional hydrodynamical simulations to quantitatively explore the torque balance criterion for gap-opening (as formulated by Crida et al. 2006) in a variety of disks when considering a migrating planet. We find that even when the criterion is satisfied, there are instances when planets still do not open gaps. We stress that gap-opening is not only dependent on whether a planet has the ability to open a gap, but whether it can do so quickly enough. This can be expressed as an additional condition on the gap-opening timescale versus the crossing time, i.e. the time it takes the planet to cross the region which it is carving out. While this point has been briefly made in the previous literature, our results quantify it for a range of protoplanetary disk properties and planetary masses, demonstrating how crucial it is for gap-opening. This additional condition has important implications for the survival of planets formed by core accretion in low mass disks as well as giant planets or brown dwarfs formed by gravitational instability in massive disks. It is particularly important for planets with intermediate masses susceptible to Type III-like migration. For some observed transition disks or disks with gaps, we expect that estimates on the potential planet masses based on the torque balance gap-opening criterion alone may not be sufficient. With consideration of this additional timescale criterion theoretical studies may find a reduced planet survivability or that planets may migrate further inwards before opening a gap.
Migrating Planets  [PDF]
Norm Murray,Brad Hansen,Matt Holman,Scott Tremaine
Physics , 1998, DOI: 10.1126/science.279.5347.69
Abstract: A planet orbiting in a disk of planetesimals can experience an instability in which it migrates to smaller orbital radii. Resonant interactions between the planet and planetesimals remove angular momentum from the planetesimals, increasing their eccentricities. Subsequently, the planetesimals either collide with or are ejected by the planet, reducing the semimajor axis of the planet. If the surface density of planetesimals exceeds a critical value, corresponding to 0.03 solar masses of gas inside the orbit of Jupiter, the planet will migrate inward a large distance. This instability may explain the presence of Jupiter-mass objects in small orbits around nearby stars.
Evolution of eccentricity and orbital inclination of migrating planets in 2:1 mean motion resonance  [PDF]
Jean Teyssandier,Caroline Terquem
Physics , 2014, DOI: 10.1093/mnras/stu1137
Abstract: We determine, analytically and numerically, the conditions needed for a system of two migrating planets trapped in a 2:1 mean motion resonance to enter an inclination-type resonance. We provide an expression for the asymptotic equilibrium value that the eccentricity $e_{\rm i}$ of the inner planet reaches under the combined effects of migration and eccentricity damping. We also show that, for a ratio $q$ of inner to outer masses below unity, $e_{\rm i}$ has to pass through a value $e_{\rm i,res}$ of order 0.3 for the system to enter an inclination-type resonance. Numerically, we confirm that such a resonance may also be excited at another, larger, value $e_{\rm i, res} \simeq 0.6$, as found by previous authors. A necessary condition for onset of an inclination-type resonance is that the asymptotic equilibrium value of $e_{\rm i}$ is larger than $e_{\rm i,res}$. We find that, for $q \le 1$, the system cannot enter an inclination-type resonance if the ratio of eccentricity to semimajor axis damping timescales $t_e/t_a$ is smaller than 0.2. This result still holds if only the eccentricity of the outer planet is damped and $q \lesssim 1$. As the disc/planet interaction is characterized by $t_e/t_a \sim 10^{-2}$, we conclude that excitation of inclination through the type of resonance described here is very unlikely to happen in a system of two planets migrating in a disc.
A Study of the Shortest-Period Planets Found With Kepler  [PDF]
Roberto Sanchis-Ojeda,Saul Rappaport,Joshua N. Winn,Michael C. Kotson,Alan M. Levine,Ileyk El Mellah
Physics , 2014, DOI: 10.1088/0004-637X/787/1/47
Abstract: We present the results of a survey aimed at discovering and studying transiting planets with orbital periods shorter than one day (ultra--short-period, or USP, planets), using data from the {\em Kepler} spacecraft. We computed Fourier transforms of the photometric time series for all 200,000 target stars, and detected transit signals based on the presence of regularly spaced sharp peaks in the Fourier spectrum. We present a list of 106 USP candidates, of which 18 have not previously been described in the literature. In addition, among the objects we studied, there are 26 USP candidates that had been previously reported in the literature which do not pass our various tests. All 106 of our candidates have passed several standard tests to rule out false positives due to eclipsing stellar systems. A low false positive rate is also implied by the relatively high fraction of candidates for which more than one transiting planet signal was detected. By assuming these multi-transit candidates represent coplanar multi-planet systems, we are able to infer that the USP planets are typically accompanied by other planets with periods in the range 1-50 days, in contrast with hot Jupiters which very rarely have companions in that same period range. Another clear pattern is that almost all USP planets are smaller than 2 $R_\oplus$, possibly because gas giants in very tight orbits would lose their atmospheres by photoevaporation when subject to extremely strong stellar irradiation. Based on our survey statistics, USP planets exist around approximately $(0.51\pm 0.07)\%$ of G-dwarf stars, and $(0.83\pm 0.18)\%$ of K-dwarf stars.
Does the innermost occurrence distribution measure tidal dissipation, reveal a flow of giant planets, or both?  [PDF]
S. F. Taylor
Physics , 2012,
Abstract: The occurrence distribution of the shortest period giant exoplanets as found by Kepler show a drop-off that is a remarkable match to the drop-off expected by taking migration due to tides in the star. We present a comparison that can show the level of tidal dissipation (friction) as a function of the distribution of the ages of the star and planet system, with known dependencies on basic star and planet parameters. Use of this relation enables constraints to be put on the value of the tidal dissipation, constraints that will be improved as the distribution of the ages are determined. For the giant planets, this leads to an unexpectedly low value of tidal dissipation. This over-abundance of short period giant planets may be due to a continuing resupply of longer period giant planets migrating into a shorter period pileup, disrupting the presence of smaller planets along the way. Perhaps the occurrence distribution of close Neptune sized planets will better measure the tidal friction, while the distribution of Jupiter sized planets reveals that giant planets are more likely to complete a gradual migration into the star.
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