1,249 research outputs found
Compressible MHD Turbulence in Interstellar Plasmas
Radio-wave scintillation observations reveal a nearly Kolmogorov spectrum of
density fluctuations in the ionized interstellar medium. Although this density
spectrum is suggestive of turbulence, no theory relevant to its interpretation
exists. We calculate the density spectrum in turbulent magnetized plasmas by
extending the theory of incompressible MHD turbulence given by Goldreich &
Sridhar to include the effects of compressibility and particle transport. Our
most important results are as follows. (1) Density fluctuations are due to the
slow mode and the entropy mode. Both modes are passively mixed by the cascade
of shear Alfven waves. Since the shear Alfven waves have a Kolmogorov spectrum,
so do the density fluctuations. (2) Observed density fluctuation amplitudes
imply either that the magnetic and gas pressures are comparable, or that the
outer scale of the turbulence is very small. (3) A high degree of ionization is
required for the cascade to survive damping by neutrals and thereby to extend
to small lengthscales. Regions that are insufficiently ionized produce density
fluctuations only on lengthscales larger than the neutral damping scale. These
regions may account for the excess of power that is found on large scales. (4)
Both the entropy mode and the slow mode are damped on lengthscales below that
at which protons can diffuse across an eddy during the eddy's turnover time.
Consequently, eddies whose extents along the magnetic field are smaller than
the proton collisional mean free path do not contribute to the density
spectrum. However, in MHD turbulence eddies are highly elongated along the
magnetic field. From an observational perspective, the relevant lengthscale is
that transverse to the magnetic field. Thus the cut-off lengthscale for density
fluctuations is significantly smaller than the proton mean free path.Comment: 19 pages, 2 figures, submitted to Ap
Resonant capture by inward migrating planets
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.Comment: 12 pages, 5 figures, submitted to Astronomical Journa
Toward a theory of interstellar turbulence. II. Strong Alfvénic turbulence
We continue to investigate the possibility that interstellar turbulence is caused by nonlinear interactions
among shear Alfvén waves. Here, as in Paper I, we restrict attention to the symmetric case where the oppositely directed waves carry equal energy fluxes. This precludes application to the solar wind in which the outward flux significantly exceeds the ingoing one. All our detailed calculations are carried out for an incompressible
magnetized fluid. In incompressible magnetohydrodynamics (MHD), nonlinear interactions only occur between oppositely direct waves. Paper I contains a detailed derivation of the inertial range spectrum for the weak turbulence of shear Alfvén waves. As energy cascades to high perpendicular wavenumbers, interactions become so strong that the assumption of weakness is no longer valid. Here, we present a theory for the strong turbulence of shear Alfvén waves. It has the following main characteristics. (1) The inertial-range energy spectrum exhibits a critical balance beween linear wave periods and nonlinear turnover timescales. (2) The "eddies" are elongated in the direction of the field on small spatial scales; the parallel and perpendicular components of the wave vector, k_z and k_⊥, are related by k_z ≈ k^(2/3) _⊥L^(-1/3), where L is the outer scale of the turbulence. (3) The "one-dimensional" energy spectrum is proportional to k^(-5/3) _⊥-an anisotropic Kolmogorov energy spectrum. Shear Alfvénic turbulence mixes specific entropy as a passive contaminant. This gives rise to an electron density power spectrum whose form mimics the energy spectrum of the turbulence. Radio, wave scattering by these electron density fluctuations produces anisotropic scatter-broadened images. Damping by ion-neutral collisions restricts Alfvénic turbulence to highly ionized regions of the interstellar medium. We expect negligible generation of compressive MHD waves by shear Alfvén waves belonging to the critically balanced cascade. Viscous and collisionless damping are also unimportant in the interstellar medium (ISM). Our calculations support the general picture of interstellar turbulence advanced by Higdon
Toward a theory of interstellar turbulence. I: Weak Alfvénic turbulence
We study weak Alfvénic turbulence of an incompressible, magnetized fluid in some detail, with a view to developing a firm theoretical basis for the dynamics of small-scale turbulence in the interstellar medium. We prove that resonant 3-wave interactions are absent. We also show that the Iroshnikov-Kraichnan theory of incompressible, magnetohydrodynamic turbulence-which is widely accepted-describes weak 3-wave turbulence; consequently, it is incorrect. Physical arguments, as well as detailed calculations of the coupling coefficients are used to demonstrate that these interactions are empty. We then examine resonant 4-wave interactions, and show that the resonance relations forbid energy transport to small spatial scales along the direction of the mean magnetic field, for both the shear Alfvén wave and the pseudo Alfvén wave. The threedimensional inertial-range energy spectrum of 4-wave shear Alfvén turbulence guessed from physical arguments reads E(k_z,k_⊥) ~ V_Av_LL^(-1/3) k^(-10/3) _⊥, where V_A is the Alfvén speed, and v_L is the velocity difference across the outer scale L. Given this spectrum, the velocity difference across λ_⊥ ~ k^(-1) _⊥ is V_(λ⊥) ~ v_L(λ_⊥/L)^(2/3). We derive a kinetic equation, and prove that this energy spectrum is a stationary solution and that it implies a positive flux of energy in k-space, along directions perpendicular to the mean magnetic field. Using this energy spectrum, we deduce that 4-wave interactions strengthen as the energy cascades to small, perpendicular spatial scales; beyond an upper bound in perpendicular wavenumber, k_⊥L ~ (V_A/v_L)^(3/2), weak turbulence theory ceases to be valid. Energy excitation amplitudes must be very small for the 4-wave inertial-range to be substantial.
When the excitation is strong, the width of the 4-wave inertial-range shrinks to zero. This seems likely to be
the case in the interstellar medium. The physics of strong turbulence is explored in Paper II
MHD Turbulence Revisited
Kraichnan (1965) proposed that MHD turbulence occurs as a result of
collisions between oppositely directed Alfv\'en wave packets. Recent work has
generated some controversy over the nature of non linear couplings between
colliding Alfv\'en waves. We find that the resolution to much of the confusion
lies in the existence of a new type of turbulence, intermediate turbulence, in
which the cascade of energy in the inertial range exhibits properties
intermediate between those of weak and strong turbulent cascades. Some
properties of intermediate MHD turbulence are: (i) in common with weak
turbulent cascades, wave packets belonging to the inertial range are long
lived; (ii) however, components of the strain tensor are so large that, similar
to the situation in strong turbulence, perturbation theory is not applicable;
(iii) the breakdown of perturbation theory results from the divergence of
neighboring field lines due to wave packets whose perturbations in velocity and
magnetic fields are localized, but whose perturbations in displacement are not;
(iv) 3--wave interactions dominate individual collisions between wave packets,
but interactions of all orders make comparable contributions to the
intermediate turbulent energy cascade; (v) successive collisions are correlated
since wave packets are distorted as they follow diverging field lines; (vi) in
common with the weak MHD cascade, there is no parallel cascade of energy, and
the cascade to small perpendicular scales strengthens as it reaches higher wave
numbers; (vii) For an appropriate weak excitation, there is a natural
progression from a weak, through an intermediate, to a strong cascade.Comment: 25 pages, to appear in The Astrophysical Journa
The Extent and Cause of the Pre-White Dwarf Instability Strip
One of the least understood aspects of white dwarf evolution is the process
by which they are formed. We are aided, however, by the fact that many H- and
He-deficient pre-white dwarfs (PWDs) are multiperiodic g-mode pulsators.
Pulsations in PWDs provide a unique opportunity to probe their interiors, which
are otherwise inaccesible to direct observation. Until now, however, the nature
of the pulsation mechanism, the precise boundaries of the instability strip,
and the mass distribution of the PWDs were complete mysteries. These problems
must be addressed before we can apply knowledge of pulsating PWDs to improve
understanding of white dwarf formation. This paper lays the groundwork for
future theoretical investigations of these stars. In recent years, Whole Earth
Telescope observations led to determination of mass and luminosity for the
majority of the (non-central star) PWD pulsators. With these observations, we
identify the common properties and trends PWDs exhibit as a class. We find that
pulsators of low mass have higher luminosity, suggesting the range of
instability is highly mass-dependent. The observed trend of decreasing periods
with decreasing luminosity matches a decrease in the maximum (standing-wave)
g-mode period across the instability strip. We show that the red edge can be
caused by the lengthening of the driving timescale beyond the maximum
sustainable period. This result is general for ionization-based driving
mechanisms, and it explains the mass-dependence of the red edge. The observed
form of the mass-dependence provides a vital starting point for future
theoretical investigations of the driving mechanism. We also show that the blue
edge probably remains undetected because of selection effects arising from
rapid evolution.Comment: 40 pages, 6 figures, accepted by ApJ Oct 27, 199
On the Decelerating Shock Instability of Plane-Parallel Slab with Finite Thickness
Dynamical stability of the shock compressed layer with finite thickness is
investigated. It is characterized by self-gravity, structure, and shock
condition at the surfaces of the compressed layer. At one side of the shocked
layer, its surface condition is determined via the ram pressure, while at the
other side the thermal pressure supports its structure. When the ram pressure
dominates the thermal pressure, we expect deceleration of the shocked layer.
Especially, in this paper, we examine how the stratification of the
decelerating layer has an effect on its dynamical stability. Performing the
linear perturbation analysis, a {\it more general} dispersion relation than the
previous one obtained by one of the authors is derived. It gives us an
interesting information about the stability of the decelerating layer.
Importantly, the DSI (Decelerating Shock Instability) and the gravitational
instability are always incompatible. We also consider the evolution effect of
the shocked layer. In the early stages of its evolution, only DSI occurs. On
the contrary, in the late stages, it is possible for the shocked layer to be
unstable for the DSI (in smaller scale) and the gravitational instability (in
larger scale). Furthermore, we find there is a stable range of wavenumbers
against both the DSI and the gravitational instability between respective
unstable wavenumber ranges. These stable modes suggest the ineffectiveness of
DSI for the fragmentation of the decelerating slab.Comment: 17 pages, 6 figures. The Astrophysical Journal Vol.532 in pres
Quasi-Periodic Oscillations from Magnetorotational Turbulence
Quasi-periodic oscillations (QPOs) in the X-ray lightcurves of accreting
neutron star and black hole binaries have been widely interpreted as being due
to standing wave modes in accretion disks. These disks are thought to be highly
turbulent due to the magnetorotational instability (MRI). We study wave
excitation by MRI turbulence in the shearing box geometry. We demonstrate that
axisymmetric sound waves and radial epicyclic motions driven by MRI turbulence
give rise to narrow, distinct peaks in the temporal power spectrum. Inertial
waves, on the other hand, do not give rise to distinct peaks which rise
significantly above the continuum noise spectrum set by MRI turbulence, even
when the fluid motions are projected onto the eigenfunctions of the modes. This
is a serious problem for QPO models based on inertial waves.Comment: 4 pages, 2 figures. submitted to ap
Super-Reflection in Fluid Discs: Corotation Amplifier, Corotation Resonance, Rossby Waves, and Overstable Modes
In differentially rotating discs with no self-gravity, density waves cannot
propagate around the corotation, where the wave pattern rotation speed equals
the fluid rotation rate. Waves incident upon the corotation barrier may be
super-reflected (commonly referred to as corotation amplifier), but the
reflection can be strongly affected by wave absorptions at the corotation
resonance/singularity. The sign of the absorption is related to the Rossby wave
zone very near the corotation radius. We derive the explicit expressions for
the complex reflection and transmission coefficients, taking into account wave
absorption at the corotation resonance. We show that for generic discs, this
absorption plays a much more important role than wave transmission across the
corotation barrier. Depending on the sign of the gradient of the specific
vorticity of the disc the corotation resonance can either enhance or diminish
the super-reflectivity, and this can be understood in terms of the location of
the Rossby wave zone relative to the corotation radius. Our results provide the
explicit conditions (in terms of disc thickness, rotation profile and specific
vorticity gradient) for which super-reflection can be achieved. Global
overstable disc modes may be possible for discs with super-reflection at the
corotation barrier.Comment: 16 pages, 5 figures, MNRAS in pres
On over-reflection and generation of Gravito-Alfven waves in solar-type stars
The dynamics of linear perturbations is studied in magnetized plasma shear
flows with a constant shearing rate and with gravity-induced stratification.
The general set of linearized equations is derived and the two-dimensional case
is considered in detail. The Boussinesq approximation is used in order to
examine relatively small-scale perturbations of low-frequency modes:
Gravito-Alfven waves (GAW) and Entropy Mode (EM) perturbations. It is shown
that for flows with arbitrary shearing rate there exists a finite time interval
of non-adiabatic evolution of the perturbations. The non-adiabatic behavior
manifests itself in a twofold way, viz. by the over-reflection of the GAWs and
by the generation of GAWs from EM perturbations. It is shown that these
phenomena act as efficient transformers of the equilibrium flow energy into the
energy of the perturbations for moderate and high shearing rate solar plasma
flows. Efficient generation of GAW by EM takes place for shearing rates about
an order of magnitude smaller than necessary for development of a shear
instability. The latter fact could have important consequences for the problem
of angular momentum redistribution within the Sun and solar-type stars.Comment: 20 pages (preprint format), 4 figures; to appear in The Astrophysical
Journal (August 1, 2007, v664, N2 issue
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