53 research outputs found
The effect of an isothermal atmosphere on the propagation of three-dimensional waves in a thermally stratified accretion disk
We extend our analysis of the three-dimensional response of a vertically
polytropic disk to tidal forcing at Lindblad resonances by including the
effects of a disk atmosphere. The atmosphere is modeled as an isothermal layer
that joins smoothly on to an underlying polytropic layer. The launched wave
progressively enters the atmosphere as it propagates away from the resonance.
The wave never propagates vertically, however, and the wave energy rises to a
(finite) characteristic height in the atmosphere. The increase of wave
amplitude associated with this process of wave channeling is reduced by the
effect of the atmosphere. For waves of large azimuthal mode number m generated
by giant planets embedded in a disk, the increase in wave amplitude is still
substantial enough to be likely to dissipate the wave energy by shocks for even
modest optical depths (tau greater than about 10) over a radial distance of a
few times the disk thickness. For low-m waves generated in circumstellar disks
in binary stars, the effects of wave channeling are less important and the
level of wave nonlinearity increases by less than a factor of 10 in going from
the disk edge to the disk center. For circumbinary disks, the effects of wave
channeling remain important, even for modest values of optical depth.Comment: 11 pages, 4 figures, submitted to the Astrophysical Journa
Three-dimensional waves generated at Lindblad resonances in thermally stratified disks
We analyze the linear, 3D response to tidal forcing of a disk that is thin
and thermally stratified in the direction normal to the disk plane. We model
the vertical disk structure locally as a polytrope which represents a disk of
high optical depth. We solve the 3D gas-dynamic equations semi-analytically in
the neighborhood of a Lindblad resonance. These solutions match asymptotically
on to those valid away from resonances and provide solutions valid at all
radii. We obtain the following results. 1) A variety of waves are launched at
resonance. However, the f mode carries more than 95% of the torque exerted at
the resonance. 2) These 3D waves collectively transport exactly the amount of
angular momentum predicted by the 2D torque formula. 3) Near resonance, the f
mode occupies the full vertical extent of the disk. Away from resonance, the f
mode becomes confined near the surface of the disk, and, in the absence of
other dissipation mechanisms, damps via shocks. The radial length scale for
this process is roughly r_L/m (for resonant radius r_L and azimuthal wavenumber
m), independent of the disk thickness H. This wave channeling process is due to
the variations of physical quantities in r and is not due to wave refraction.
4) However, the inwardly propagating f mode launched from an m=2 inner Lindblad
resonance experiences relatively minor channeling.
We conclude that for binary stars, tidally generated waves in highly
optically thick circumbinary disks are subject to strong nonlinear damping by
the channeling mechanism, while those in circumstellar accretion disks are
subject to weaker nonlinear effects. We also apply our results to waves excited
by young planets for which m is approximately r/H and conclude that the waves
are damped on the scale of a few H.Comment: 15 pages, 3 figures, 2 colour plates, to be published in the
Astrophysical Journa
Astronomical engineering: a strategy for modifying planetary orbits
The Sun's gradual brightening will seriously compromise the Earth's biosphere
within ~ 1E9 years. If Earth's orbit migrates outward, however, the biosphere
could remain intact over the entire main-sequence lifetime of the Sun. In this
paper, we explore the feasibility of engineering such a migration over a long
time period. The basic mechanism uses gravitational assists to (in effect)
transfer orbital energy from Jupiter to the Earth, and thereby enlarges the
orbital radius of Earth. This transfer is accomplished by a suitable
intermediate body, either a Kuiper Belt object or a main belt asteroid. The
object first encounters Earth during an inward pass on its initial highly
elliptical orbit of large (~ 300 AU) semimajor axis. The encounter transfers
energy from the object to the Earth in standard gravity-assist fashion by
passing close to the leading limb of the planet. The resulting outbound
trajectory of the object must cross the orbit of Jupiter; with proper timing,
the outbound object encounters Jupiter and picks up the energy it lost to
Earth. With small corrections to the trajectory, or additional planetary
encounters (e.g., with Saturn), the object can repeat this process over many
encounters. To maintain its present flux of solar energy, the Earth must
experience roughly one encounter every 6000 years (for an object mass of 1E22
g). We develop the details of this scheme and discuss its ramifications.Comment: 21 pgs, 7 figs. Paper to appear in Astrophysics and Space Scienc
Big Impacts and Transient Oceans on Titan
We have studied the thermal consequences of very big impacts on Titan [1]. Titan's thick atmosphere and volatile-rich surface cause it to respond to big impacts in a somewhat Earth-like manner. Here we construct a simple globally-averaged model that tracks the flow of energy through the environment in the weeks, years, and millenia after a big comet strikes Titan. The model Titan is endowed with 1.4 bars of N2 and 0.07 bars of CH4, methane lakes, a water ice crust, and enough methane underground to saturate the regolith to the surface. We assume that half of the impact energy is immediately available to the atmosphere and surface while the other half is buried at the site of the crater and is unavailable on time scales of interest. The atmosphere and surface are treated as isothermal. We make the simplifying assumptions that the crust is everywhere as methane saturated as it was at the Huygens landing site, that the concentration of methane in the regolith is the same as it is at the surface, and that the crust is made of water ice. Heat flow into and out of the crust is approximated by step-functions. If the impact is great enough, ice melts. The meltwater oceans cool to the atmosphere conductively through an ice lid while at the base melting their way into the interior, driven down in part through Rayleigh-Taylor instabilities between the dense water and the warm ice. Topography, CO2, and hydrocarbons other than methane are ignored. Methane and ethane clathrate hydrates are discussed quantitatively but not fully incorporated into the model
Dust Distribution in Gas Disks. A Model for the Ring Around HR 4796A
There have been several model analyses of the near and mid IR flux from the
circumstellar ring around HR4796A. In the vicinity of a young star, the
possibility that the dust ring is embedded within a residual protostellar gas
disk cannot be ruled out. In a gas-rich environment, larger sizes () are needed for the particles to survive the radiative blow out. The total
dust mass required to account for the IR flux is . The
combined influence of gas and stellar radiation may also account for the
observed sharp inner boundary and rapidly fading outer boundary of the ring.
The pressure gradient induced by a small (10%) amplitude variation in the
surface density distribution of a low-mass gaseous disk would be sufficient to
modify the rotation speed of the gas.Comment: proof read version, 26 pages, LaTex, 11 figures. To appear in The
Astronomical Journal June 200
Type I planet migration in nearly laminar disks - long term behavior
We carry out 2-D high resolution numerical simulations of type I planet
migration with different disk viscosities. We find that the planet migration is
strongly dependent on disk viscosities. Two kinds of density wave damping
mechanisms are discussed. Accordingly, the angular momentum transport can be
either viscosity dominated or shock dominated, depending on the disk
viscosities. The long term migration behavior is different as well. Influences
of the Rossby vortex instability on planet migration are also discussed. In
addition, we investigate very weak shock generation in inviscid disks by small
mass planets and compare the results with prior analytic results.Comment: Accepted for publication in Ap
Hydraulic/Shock-Jumps in Protoplanetary Disks
In this paper, we describe the nonlinear outcome of spiral shocks in
protoplanetary disks. Spiral shocks, for most protoplanetary disk conditions,
create a loss of vertical force balance in the post-shock region and result in
rapid expansion of the gas perpendicular to the disk midplane. This expansion
has characteristics similar to hydraulic jumps, which occur in incompressible
fluids. We present a theory to describe the behavior of these hybrids between
shocks and hydraulic jumps (shock bores) and then compare the theory to
three-dimensional hydrodynamics simulations. We discuss the fully
three-dimensional shock structures that shock bores produce and discuss
possible consequences for disk mixing, turbulence, and evolution of solids.Comment: 39 pages, 18 figures, 1 table. Edited to match as closely as possible
the ApJ proofs, which resulted in the correction of several typos. In
addition, section 5.3 was slightly altered because an error in an analysis
tool was discovered; the differences between the entropy gradient method and
the Schwarzschild criterion method are minor. Figure 18 now only includes
what was Figure18
Hydrodynamic modeling of tsunamis from the Currituck landslide
This paper is not subject to U.S. copyright. The definitive version was published in Marine Geology 264 (2009): 41-52, doi:10.1016/j.margeo.2008.09.005.Tsunami generation from the Currituck landslide offshore North Carolina and propagation of waves toward the U.S. coastline are modeled based on recent geotechnical analysis of slide movement. A long and intermediate wave modeling package (COULWAVE) based on the non-linear Boussinesq equations are used to simulate the tsunami. This model includes procedures to incorporate bottom friction, wave breaking, and overland flow during runup. Potential tsunamis generated from the Currituck landslide are analyzed using four approaches: (1) tsunami wave history is calculated from several different scenarios indicated by geotechnical stability and mobility analyses; (2) a sensitivity analysis is conducted to determine the effects of both landslide failure duration during generation and bottom friction along the continental shelf during propagation; (3) wave history is calculated over a regional area to determine the propagation of energy oblique to the slide axis; and (4) a high-resolution 1D model is developed to accurately model wave breaking and the combined influence of nonlinearity and dispersion during nearshore propagation and runup. The primary source parameter that affects tsunami severity for this case study is landslide volume, with failure duration having a secondary influence. Bottom friction during propagation across the continental shelf has a strong influence on the attenuation of the tsunami during propagation. The high-resolution 1D model also indicates that the tsunami undergoes nonlinear fission prior to wave breaking, generating independent, short-period waves. Wave breaking occurs approximately 40–50 km offshore where a tsunami bore is formed that persists during runup. These analyses illustrate the complex nature of landslide tsunamis, necessitating the use of detailed landslide stability/mobility models and higher-order hydrodynamic models to determine their hazard.Research conducted by Lynett for this paper was partially
supported by grants from the National Science Foundation (CBET-
0427014, CMMI-0619083)
- …