2,345 research outputs found
On the tilting of protostellar disks by resonant tidal effects
We consider the dynamics of a protostellar disk surrounding a star in a
circular-orbit binary system. Our aim is to determine whether, if the disk is
initially tilted with respect to the plane of the binary orbit, the inclination
of the system will increase or decrease with time. The problem is formulated in
the binary frame in which the tidal potential of the companion star is static.
We consider a steady, flat disk that is aligned with the binary plane and
investigate its linear stability with respect to tilting or warping
perturbations. The dynamics is controlled by the competing effects of the m=0
and m=2 azimuthal Fourier components of the tidal potential. In the presence of
dissipation, the m=0 component causes alignment of the system, while the m=2
component has the opposite tendency. We find that disks that are sufficiently
large, in particular those that extend to their tidal truncation radii, are
generally stable and will therefore tend to alignment with the binary plane on
a time-scale comparable to that found in previous studies. However, the effect
of the m=2 component is enhanced in the vicinity of resonances where the outer
radius of the disk is such that the natural frequency of a global bending mode
of the disk is equal to twice the binary orbital frequency. Under such
circumstances, the disk can be unstable to tilting and acquire a warped shape,
even in the absence of dissipation. The outer radius corresponding to the
primary resonance is always smaller than the tidal truncation radius. For disks
smaller than the primary resonance, the m=2 component may be able to cause a
very slow growth of inclination through the effect of a near resonance that
occurs close to the disk center. We discuss these results in the light of
recent observations of protostellar disks in binary systems.Comment: 21 pages, 7 figures, to be published in the Astrophysical Journa
An alpha theory of time-dependent warped accretion discs
The non-linear fluid dynamics of a warped accretion disc was investigated in
an earlier paper by developing a theory of fully non-linear bending waves in a
thin, viscous disc. That analysis is here extended to take proper account of
thermal and radiative effects by solving an energy equation that includes
viscous dissipation and radiative transport. The problem is reduced to simple
one-dimensional evolutionary equations for mass and angular momentum, expressed
in physical units and suitable for direct application. This result constitutes
a logical generalization of the alpha theory of Shakura & Sunyaev to the case
of a time-dependent warped accretion disc. The local thermal-viscous stability
of such a disc is also investigated.Comment: 16 pages, 3 figures, to be published in MNRA
Global m=1 modes and migration of protoplanetary cores in eccentric protoplanetary discs
We calculate global modes with low pattern speed corresponding to
introducing a finite eccentricity into a protoplanetary disc. We consider disc
models which are either isolated or contain one or two protoplanets orbiting in
an inner cavity. Global modes that are strongly coupled to inner protoplanets
are found to have disc orbits which tend to have apsidal lines antialigned with
respect to those of the inner protoplanets. Other modes corresponding to free
disc modes may be global over a large range of length scales and accordingly be
long lived. We consider the motion of a protoplanet in the earth mass range
embedded in an eccentric disc and determine the equilibrium orbits which
maintain fixed apsidal alignment with respect to the disc gas orbits.
Equilibrium eccentricities are found to be comparable or possibly exceed the
disc eccentricity. We then approximately calculate the tidal interaction with
the disc in order to estimate the orbital migration rate. Results are found to
deviate from the case of axisymmetric disc with near circular protoplanet orbit
once eccentricities of protoplanet and disc orbits become comparable to the
disc aspect ratio in magnitude. Aligned protoplanet orbits with very similar
eccentricity to that of the gas disc are found to undergo litle eccentricity
change while undergoing inward migration in general. However, for significantly
larger orbital eccentricities, migration may be significantly reduced or even
reverse from inwards to outwards. Thus the existence of global non circular
motions in discs with radial excursions comparable to the semi-thickness may
have important consequences for the migration and survival of protoplanetary
cores in the earth mass range.Comment: Accepted for publication by A &
Hydrodynamic Simulations of Propagating Warps and Bending Waves In Accretion Discs
We present the results of a study of propagating warp or bending waves in
accretion discs. Three dimensional hydrodynamic simulations were performed
using SPH, and the results of these are compared with calculations based on the
linear theory of warped discs. We consider primarily the physical regime in
which the dimensionless viscosity parameter `alpha' < H/r, the disc aspect
ratio, so that bending waves are expected to propagate. We also present
calculations in which `alpha' > H/r, where the warps are expected to behave
diffusively. Small amplitude perturbations are studied in both Keplerian and
slightly non Keplerian discs, and we find that the SPH results can be
reasonably well fitted by those of the linear theory. The main results of these
calculations are: (1) the warp in Keplerian discs when `alpha' < H/r propagates
with little dispersion and damps at a rate expected from estimates of the code
viscosity, (2) warps evolve diffusively when `alpha' > H/r, (3) the non
Keplerian discs exhibit a substantially more dispersive behaviour of the warps.
Initially imposed higher amplitude nonlinear warping disturbances were studied
in Keplerian discs. The results indicate that nonlinear warps can lead to the
formation of shocks, and that the evolution of the warp becomes less wave-like
and more diffusive in character. This work is relevant to the study of the
warped accretion discs that may occur around Kerr black holes or in misaligned
binary systems. The results indicate that SPH can accurately model the
hydrodynamics of warped discs, even when using rather modest numbers of
particles.Comment: 14 pages, 9 figures, to appear in MNRA
Theory of Abelian Projection
Analytic methods for Abelian projection are developed. A number of results
are obtained related to string tension measurements. It is proven that even
without gauge fixing, abelian projection yields string tensions of the
underlying non-Abelian theory. Strong arguments are given for similar results
in the case where gauge fixing is employed. The methods used emphasize that the
projected theory is derived from the underlying non-Abelian theory rather than
vice versa. In general, the choice of subgroup used for projection is not very
important, and need not be Abelian. While gauge fixing is shown to be in
principle unnecessary for the success of Abelian projection, it is
computationally advantageous for the same reasons that improved operators,
e.g., the use of fat links, are advantageous in Wilson loop measurements. Two
other issues, Casimir scaling and the conflict between projection and critical
universality, are also discussed.Comment: Minor corrections, new section added, 14 pages, 3 figures, RevTe
A First Principles Estimate of Finite Size Effects in Quark-Gluon Plasma Formation
Using lattice simulations of quenched QCD we estimate the finite size effects
present when a gluon plasma equilibrates in a slab geometry, i.e., finite width
but large transverse dimensions. Significant differences are observed in the
free energy density for the slab when compared with bulk behavior. A small
shift in the critical temperature is also seen. The free energy required to
liberate heavy quarks relative to bulk is measured using Polyakov loops; the
additional free energy required is on the order of 30-40 MeV at 2-3 T_c.Comment: 10 pages, 5 figures, RevTeX; revised version includes comparison with
the Bjorken model and various small improvement
Center clusters in the Yang-Mills vacuum
Properties of local Polyakov loops for SU(2) and SU(3) lattice gauge theory
at finite temperature are analyzed. We show that spatial clusters can be
identified where the local Polyakov loops have values close to the same center
element. For a suitable definition of these clusters the deconfinement
transition can be characterized by the onset of percolation in one of the
center sectors. The analysis is repeated for different resolution scales of the
lattice and we argue that the center clusters have a continuum limit.Comment: Table added. Final version to appear in JHE
On equilibrium tides in fully convective planets and stars
We consider the tidal interaction of a fully convective primary star and a
point mass. Using a normal mode decomposition we calculate the evolution of the
primary angular velocity and orbit for arbitrary eccentricity e. The
dissipation acting on the tidal perturbation is associated with convective
turbulence. A novel feature of the Paper is that, to take into account of the
fact that there is a relaxation time t_{c}, being the turn-over time of
convective eddies, associated with the process, this is allowed to act non
locally in time, producing a dependence of the dissipation on tidal forcing
frequency. Results are expressed in terms of the Fourier coefficients of the
tidal potential. We find analytical approximations for these valid for .
When the tidal response is frequency independent, our results are equivalent to
those obtained in the standard constant time lag approximation. When there is
the frequency dependence of the dissipative response, the evolution can differ
drastically. In that case the system can evolve through a sequence of
spin-orbit corotation resonances with Omega_{r}/Omega_{orb}=n/2, where
Omega_{r} and Omega_{orb} are the rotation and orbital frequencies and n is an
integer. We study this case analytically and numerically.Comment: The size of the shown abstract is reduced. Submitted to MNRA
Nonperturbative Gauge Fixing and Perturbation Theory
We compare the gauge-fixing approach proposed by Jona-Lasinio and Parrinello,
and by Zwanziger (JPLZ) with the standard Fadeev-Popov procedure, and
demonstrate perturbative equality of gauge-invariant quantities, up to
irrelevant terms induced by the cutoff. We also show how a set of local,
renormalizable Feynman rules can be constructed for the JPLZ procedure.Comment: 9 pages, latex, version to appear in Phys. Rev.
On the width and shape of the corotation region for low-mass planets
We study the coorbital flow for embedded, low mass planets. We provide a
simple semi-analytic model for the corotation region, which is subsequently
compared to high resolution numerical simulations. The model is used to derive
an expression for the half-width of the horseshoe region, x_s, which in the
limit of zero softening is given by x_s/r_p = 1.68(q/h)^(1/2), where q is the
planet to central star mass ratio, h is the disc aspect ratio and r_p the
orbital radius. This is in very good agreement with the same quantity measured
from simulations. This result is used to show that horseshoe drag is about an
order of magnitude larger than the linear corotation torque in the zero
softening limit. Thus the horseshoe drag, the sign of which depends on the
gradient of specific vorticity, is important for estimates of the total torque
acting on the planet. We further show that phenomena, such as the Lindblad
wakes, with a radial separation from corotation of ~ a pressure scale height H
can affect x_s, even though for low-mass planets x_s << H. The effect is to
distort streamlines and to reduce x_s through the action of a back pressure.
This effect is reduced for smaller gravitational softening parameters and
planets of higher mass, for which x_s becomes comparable to H.Comment: 15 pages, 11 figures, accepted for publication in MNRA
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