462 research outputs found
Dynamical evolution of thin dispersion-dominated planetesimal disks
We study the dynamics of a vertically thin, dispersion-dominated disk of
planetesimals with eccentricities and inclinations (normalized in Hill
units) satisfying , . This situation may be typical
for e.g. a population of protoplanetary cores in the end of the oligarchic
phase of planet formation. In this regime of orbital parameters planetesimal
scattering has an anisotropic character and strongly differs from scattering in
thick () disks. We derive analytical expressions for the planetesimal
scattering coefficients and compare them with numerical calculations. We find
significant discrepancies in the inclination scattering coefficients obtained
by the two approaches and ascribe this difference to the effects not accounted
for in the analytical calculation: multiple scattering events (temporary
captures, which may be relevant for the production of distant planetary
satellites outside the Hill sphere) and distant interaction of planetesimals
prior to their close encounter. Our calculations show that the inclination of a
thin, dispersion-dominated planetesimal disk grows exponentially on a very
short time scale implying that (1) such disks must be very short-lived and (2)
planetesimal accretion in this dynamical phase is insignificant. Our results
are also applicable to the dynamics of shear-dominated disks switching to the
dispersion-dominated regime.Comment: 16 pages, 12 figures, submitted to A
Fast accretion of small planetesimals by protoplanetary cores
We explore the dynamics of small planetesimals coexisting with massive
protoplanetary cores in a gaseous nebula. Gas drag strongly affects the motion
of small bodies leading to the decay of their eccentricities and inclinations,
which are excited by the gravity of protoplanetary cores. Drag acting on larger
( km), high velocity planetesimals causes a mere reduction of their
average random velocity. By contrast, drag qualitatively changes the dynamics
of smaller ( km), low velocity objects: (1) small planetesimals
sediment towards the midplane of the nebula forming vertically thin subdisk;
(2) their random velocities rapidly decay between successive passages of the
cores and, as a result, encounters with cores typically occur at the minimum
relative velocity allowed by the shear in the disk. This leads to a drastic
increase in the accretion rate of small planetesimals by the protoplanetary
cores, allowing cores to grow faster than expected in the simple oligarchic
picture, provided that the population of small planetesimals contains more than
roughly 1% of the solid mass in the nebula. Fragmentation of larger
planetesimals ( km) in energetic collisions triggered by the
gravitational scattering by cores can easily channel this amount of material
into small bodies on reasonable timescales ( Myr in the outer Solar
System), providing a means for the rapid growth (within several Myr at 30 AU)
of rather massive protoplanetary cores. Effects of inelastic collisions between
planetesimals and presence of multiple protoplanetary cores are discussed.Comment: 17 pages, 8 figures, additional clarifications, 1 more figure and
table adde
Dynamical evolution of planetesimals in protoplanetary disks
The current picture of terrestrial planet formation relies heavily on our
understanding of the dynamical evolution of planetesimals -- asteroid-like
bodies thought to be planetary building blocks. In this study we investigate
the growth of eccentricities and inclinations of planetesimals in spatially
homogeneous protoplanetary disks using methods of kinetic theory. We explore
disks with a realistic mass spectrum of planetesimals evolving in time, similar
to that obtained in self-consistent simulations of planetesimal coagulation. We
calculate the behavior of planetesimal random velocities as a function of the
planetesimal mass spectrum both analytically and numerically; results obtained
by the two approaches agree quite well. Scaling of random velocity with mass
can always be represented as a combination of power laws corresponding to
different velocity regimes (shear- or dispersion-dominated) of planetesimal
gravitational interactions. For different mass spectra we calculate
analytically the exponents and time dependent normalizations of these power
laws, as well as the positions of the transition regions between different
regimes. It is shown that random energy equipartition between different
planetesimals can only be achieved in disks with very steep mass distributions
(differential surface number density of planetesimals falling off steeper than
m^{-4}), or in the runaway tails. In systems with shallow mass spectra
(shallower than m^{-3}) random velocities of small planetesimals turn out to be
independent of their masses. We also discuss the damping effects of inelastic
collisions between planetesimals and of gas drag, and their importance in
modifying planetesimal random velocities.Comment: 20 pages, 17 figures, 1 table, submitted to A
The growth of planetary embryos: orderly, runaway, or oligarchic?
We consider the growth of a protoplanetary embryo embedded in a planetesimal
disk. We take into account the dynamical evolution of the disk caused by (1)
planetesimal-planetesimal interactions, which increase random motions and
smooth gradients in the disk, and (2) gravitational scattering of planetesimals
by the embryo, which tends to heat up the disk locally and repels planetesimals
away. The embryo's growth is self-consistently coupled to the planetesimal disk
dynamics. We demonstrate that details of the evolution depend on only two
dimensionless parameters incorporating all the physical characteristics of the
problem: the ratio of the physical radius to the Hill radius of any solid body
in the disk and the number of planetesimals inside the annulus of the disk with
width equal to the planetesimal Hill radius. The results of exploration in the
framework of our model of several situations typical for protosolar nebula can
be summarized as follows: initially, the planetesimal disk dynamics is not
affected by the presence of the embryo and the growth of the embryo's mass
proceeds very rapidly in the runaway regime. Later on, when the embryo starts
being dynamically important, its accretion slows down similar to the
``oligarchic'' growth picture. The scenario of orderly growth suggested by
Safronov (1972) is never realized in our calculations; scenario of runaway
growth suggested by Wetherill & Stewart (1989) is only realized for a limited
range in mass. Slow character of the planetesimal accretion on the oligarchic
stage of the embryo's accumulation leads to a considerable increase of the
protoplanetary formation timescale compared to that following from a simple
runaway accretion picture valid in the homogeneous planetesimal disks.Comment: 42 pages, 13 figures, submitted to A
Planetesimal disk evolution driven by embryo-planetesimal gravitational scattering
The process of gravitational scattering of planetesimals by a massive
protoplanetary embryo is explored theoretically. We propose a method to
describe the evolution of the disk surface density, eccentricity, and
inclination caused by the embryo-planetesimal interaction. It relies on the
analytical treatment of the scattering in two extreme regimes of the
planetesimal epicyclic velocities: shear-dominated (dynamically ``cold'') and
dispersion-dominated (dynamically ``hot''). In the former, planetesimal
scattering can be treated as a deterministic process. In the latter, scattering
is mostly weak because of the large relative velocities of interacting bodies.
This allows one to use the Fokker-Planck approximation and the two-body
approximation to explore the disk evolution. We compare the results obtained by
this method with the outcomes of the direct numerical integrations of
planetesimal orbits and they agree quite well. In the intermediate velocity
regime an approximate treatment of the disk evolution is proposed based on
interpolation between the two extreme regimes. We also calculate the rate of
embryo's mass growth in an inhomogeneous planetesimal disk and demonstrate that
it is in agreement with both the simulations and earlier calculations. Finally
we discuss the question of the direction of the embryo-planetesimal interaction
in the dispersion-dominated regime and demonstrate that it is repulsive. This
means that the embryo always forms a gap in the disk around it, which is in
contrast with the results of other authors. The machinery developed here will
be applied to realistic protoplanetary systems in future papers.Comment: 40 pages, 9 figures, submitted to A
Boundary Layers of Accretion Disks: Wave-Driven Transport and Disk Evolution
Astrophysical objects possessing a material surface (white dwarfs, young
stars, etc.) may accrete gas from the disc through the so-called surface
boundary layer (BL), in which the angular velocity of the accreting gas
experiences a sharp drop. Acoustic waves excited by the supersonic shear in the
BL play an important role in mediating the angular momentum and mass transport
through that region. Here we examine the characteristics of the angular
momentum transport produced by the different types of wave modes emerging in
the inner disc, using the results of a large suite of hydrodynamic simulations
of the BLs. We provide a comparative analysis of the transport properties of
different modes across the range of relevant disc parameters. In particular, we
identify the types of modes which are responsible for the mass accretion onto
the central object. We find the correlated perturbations of surface density and
radial velocity to provide an important contribution to the mass accretion
rate. Although the wave-driven transport is intrinsically non-local, we do
observe a clear correlation between the angular momentum flux injected into the
disc by the waves and the mass accretion rate through the BL. We find the
efficiency of angular momentum transport (normalized by thermal pressure) to be
a weak function of the flow Mach number. We also quantify the wave-driven
evolution of the inner disc, in particular the modification of the angular
frequency profile in the disc. Our results pave the way for understanding
wave-mediated transport in future three-dimensional, magnetohydrodynamic
studies of the BLs.Comment: 16 pages, 9 figures, submitted to MNRA
Atmospheres of protoplanetary cores: critical mass for nucleated instability
We study quasi-static atmospheres of accreting protoplanetary cores for
different opacity behaviors and realistic planetesimal accretion rates in
various parts of protoplanetary nebula. Atmospheres segregate into those having
outer convective zone which smoothly merges with the nebular gas, and those
having almost isothermal outer radiative region decoupling atmospheric interior
from the nebula. Specific type of atmosphere depends only on the relations
between the Bondi radius of the core, photon mean free path in the nebular gas,
and the luminosity radius (roughly the size of the sphere which can radiate
luminosity of the core at effective temperature equal to the nebular
temperature). Cores in the inner parts of protoplanetary disk (within roughly
0.3 AU from the Sun) have large luminosity radii resulting in the atmospheres
of the first type, while cores in the giant planet region (beyond several AU)
have small luminosity radii and always accumulate massive atmospheres of the
second type. Critical core mass for nucleated instability is found to vary as a
function of distance from the Sun. It is 5-20 M_Earth at 0.1-1 AU which is too
large to permit the formation of ``hot Jupiters'' by nucleated instability near
the cores that have grown in situ. In the region of giant planets critical mass
is 20-60 M_Earth (for opacity 0.1 cm^2/g) if planetesimal accretion was fast
enough for protoplanetary cores to form prior to the nebular gas dissipation.
This might indicate that giant planets in the Solar System have gained their
atmospheres by nucleated instability only after their cores have accumulated
most of the mass in solids during the epoch of oligarchic growth, subsequent to
which planetesimal accretion slowed down and cores became supercritical.Comment: 19 pages, 7 figures, submitted to Ap
The Double Pulsar Eclipses I: Phenomenology and Multi-frequency Analysis
The double pulsar PSR J0737-3039A/B displays short, 30 s eclipses that arise
around conjunction when the radio waves emitted by pulsar A are absorbed as
they propagate through the magnetosphere of its companion pulsar B. These
eclipses offer a unique opportunity to probe directly the magnetospheric
structure and the plasma properties of pulsar B. We have performed a
comprehensive analysis of the eclipse phenomenology using multi-frequency radio
observations obtained with the Green Bank Telescope. We have characterized the
periodic flux modulations previously discovered at 820 MHz by McLaughlin et
al., and investigated the radio frequency dependence of the duration and depth
of the eclipses. Based on their weak radio frequency evolution, we conclude
that the plasma in pulsar B's magnetosphere requires a large multiplicity
factor (~ 10^5). We also found that, as expected, flux modulations are present
at all radio frequencies in which eclipses can be detected. Their complex
behavior is consistent with the confinement of the absorbing plasma in the
dipolar magnetic field of pulsar B as suggested by Lyutikov & Thompson and such
a geometric connection explains that the observed periodicity is harmonically
related to pulsar B's spin frequency. We observe that the eclipses require a
sharp transition region beyond which the plasma density drops off abruptly.
Such a region defines a plasmasphere which would be well inside the
magnetospheric boundary of an undisturbed pulsar. It is also two times smaller
than the expected standoff radius calculated using the balance of the wind
pressure from pulsar A and the nominally estimated magnetic pressure of pulsar
B.Comment: 9 pages, 7 figures, 3 tables, ApJ in pres
- …