88,140 research outputs found
Interaction of Close-in Planets with the Magnetosphere of their Host Stars I: Diffusion, Ohmic Dissipation of Time Dependent Field, Planetary Inflation, and Mass Loss
The unanticipated discovery of the first close-in planet around 51 Peg has
rekindled the notion that shortly after their formation outside the snow line,
some planets may have migrated to the proximity of their host stars because of
their tidal interaction with their nascent disks. If these planets indeed
migrated to their present-day location, their survival would require a halting
mechanism in the proximity of their host stars. Most T Tauri stars have strong
magnetic fields which can clear out a cavity in the innermost regions of their
circumstellar disks and impose magnetic induction on the nearby young planets.
Here we consider the possibility that a magnetic coupling between young stars
and planets could quench the planet's orbital evolution. After a brief
discussion of the complexity of the full problem, we focus our discussion on
evaluating the permeation and ohmic dissipation of the time dependent component
of the stellar magnetic field in the planet's interior. Adopting a model first
introduced by C. G. Campbell for interacting binary stars, we determine the
modulation of the planetary response to the tilted magnetic field of a
non-synchronously spinning star. We first compute the conductivity in the young
planets, which indicates that the stellar field can penetrate well into the
planet's envelope in a synodic period. For various orbital configurations, we
show that the energy dissipation rate inside the planet is sufficient to induce
short-period planets to inflate. This process results in mass loss via Roche
lobe overflow and in the halting of the planet's orbital migration.Comment: 47 pages, 12 figure
Toward a Deterministic Model of Planetary Formation VII: Eccentricity Distribution of Gas Giants
The ubiquity of planets and diversity of planetary systems reveal planet
formation encompass many complex and competing processes. In this series of
papers, we develop and upgrade a population synthesis model as a tool to
identify the dominant physical effects and to calibrate the range of physical
conditions. Recent planet searches leads to the discovery of many
multiple-planet systems. Any theoretical models of their origins must take into
account dynamical interaction between emerging protoplanets. Here, we introduce
a prescription to approximate the close encounters between multiple planets. We
apply this method to simulate the growth, migration, and dynamical interaction
of planetary systems. Our models show that in relatively massive disks, several
gas giants and rocky/icy planets emerge, migrate, and undergo dynamical
instability. Secular perturbation between planets leads to orbital crossings,
eccentricity excitation, and planetary ejection. In disks with modest masses,
two or less gas giants form with multiple super-Earths. Orbital stability in
these systems is generally maintained and they retain the kinematic structure
after gas in their natal disks is depleted. These results reproduce the
observed planetary mass-eccentricity and semimajor axis-eccentricity
correlations. They also suggest that emerging gas giants can scatter residual
cores to the outer disk regions. Subsequent in situ gas accretion onto these
cores can lead to the formation of distant (> 30AU) gas giants with nearly
circular orbits.Comment: 54 pages, 14 Figures; accepted for publication in Astrophysical
Journa
Thermal instabilities in protogalactic clouds
The means by which a protogalaxy can fragment to form the first generation of stars and globular clusters remains an important problem in astrophysics. Gravitational instabilities grow on timescales too long to drive fragmentation before the background density grows by many orders of magnitude (see Murray and Lin 1989a, and references therein). Thermal instability provides a much more likely mechanism. After its initial collapse, a protogalactic cloud is expected to be shock heated to its virial temperature approx. 10(exp 6) K. Cooling by H and He+ below 10(exp 6) K has a negative slope, so that the cloud is subject to strong thermal instabilities. Density enhancements may then grow rapidly, fragmenting the protogalaxy as it cools to lower temperatures. The role of dynamical effects upon the growth of perturbations is considered here. The method used is similar to that used in Murray and Lin (1989a; see also the Erratum to appear September 15), which examined the growth of thermal instabilities with a one-dimensional Lagrangian hydrodynamics code, written for spherical symmetry. Perturbed regions therefore take the form of shells. The dynamical variables are integrated explicitly, while the temperature, ionization fraction, and molecular fraction are integrated implicitly, and account is taken for non-equilibrium values of these quantities
Toward a Deterministic Model of Planetary Formation IV: Effects of Type-I Migration
In a further development of a deterministic planet-formation model (Ida & Lin
2004), we consider the effect of type-I migration of protoplanetary embryos due
to their tidal interaction with their nascent disks. During the early embedded
phase of protostellar disks, although embryos rapidly emerge in regions
interior to the ice line, uninhibited type-I migration leads to their efficient
self-clearing. But, embryos continue to form from residual planetesimals at
increasingly large radii, repeatedly migrate inward, and provide a main channel
of heavy element accretion onto their host stars. During the advanced stages of
disk evolution (a few Myr), the gas surface density declines to values
comparable to or smaller than that of the minimum mass nebula model and type-I
migration is no longer an effective disruption mechanism for mars-mass embryos.
Over wide ranges of initial disk surface densities and type-I migration
efficiency, the surviving population of embryos interior to the ice line has a
total mass several times that of the Earth. With this reservoir, there is an
adequate inventory of residual embryos to subsequently assemble into rocky
planets similar to those around the Sun. But, the onset of efficient gas
accretion requires the emergence and retention of cores, more massive than a
few M_earth, prior to the severe depletion of the disk gas. The formation
probability of gas giant planets and hence the predicted mass and semimajor
axis distributions of extrasolar gas giants are sensitively determined by the
strength of type-I migration. We suggest that the observed fraction of
solar-type stars with gas giant planets can be reproduced only if the actual
type-I migration time scale is an order of magnitude longer than that deduced
from linear theories.Comment: 32 pages, 8 figures, 1 table, accepted for publication in Ap
Eccentricity Evolution of Extrasolar Multiple Planetary Systems due to the Depletion of Nascent Protostellar Disks
Most extrasolar planets are observed to have eccentricities much larger than
those in the solar system. Some of these planets have sibling planets, with
comparable masses, orbiting around the same host stars. In these multiple
planetary systems, eccentricity is modulated by the planets' mutual secular
interaction as a consequence of angular momentum exchange between them. For
mature planets, the eigenfrequencies of this modulation are determined by their
mass and semi-major axis ratios. But, prior to the disk depletion, self gravity
of the planets' nascent disks dominates the precession eigenfrequencies. We
examine here the initial evolution of young planets' eccentricity due to the
apsidal libration or circulation induced by both the secular interaction
between them and the self gravity of their nascent disks. We show that as the
latter effect declines adiabatically with disk depletion, the modulation
amplitude of the planets' relative phase of periapse is approximately invariant
despite the time-asymmetrical exchange of angular momentum between planets.
However, as the young planets' orbits pass through a state of secular
resonance, their mean eccentricities undergo systematic quantitative changes.
For applications, we analyze the eccentricity evolution of planets around
Upsilon Andromedae and HD168443 during the epoch of protostellar disk
depletion. We find that the disk depletion can change the planets' eccentricity
ratio. However, the relatively large amplitude of the planets' eccentricity
cannot be excited if all the planets had small initial eccentricities.Comment: 50 pages including 11 figures, submitted to Ap
Three-region inequalities for the second order elliptic equation with discontinuous coefficients and size estimate
In this paper, we would like to derive a quantitative uniqueness estimate,
the three-region inequality, for the second order elliptic equation with jump
discontinuous coefficients. The derivation of the inequality relies on the
Carleman estimate proved in our previous work. We then apply the three-region
inequality to study the size estimate problem with one boundary measurement.Comment: 16 pages, 1 figur
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