347 research outputs found
Inclusion of turbulence in solar modeling
The general consensus is that in order to reproduce the observed solar p-mode
oscillation frequencies, turbulence should be included in solar models.
However, until now there has not been any well-tested efficient method to
incorporate turbulence into solar modeling. We present here two methods to
include turbulence in solar modeling within the framework of the mixing length
theory, using the turbulent velocity obtained from numerical simulations of the
highly superadiabatic layer of the sun at three stages of its evolution. The
first approach is to include the turbulent pressure alone, and the second is to
include both the turbulent pressure and the turbulent kinetic energy. The
latter is achieved by introducing two variables: the turbulent kinetic energy
per unit mass, and the effective ratio of specific heats due to the turbulent
perturbation. These are treated as additions to the standard thermodynamic
coordinates (e.g. pressure and temperature). We investigate the effects of both
treatments of turbulence on the structure variables, the adiabatic sound speed,
the structure of the highly superadiabatic layer, and the p-mode frequencies.
We find that the second method reproduces the SAL structure obtained in 3D
simulations, and produces a p-mode frequency correction an order of magnitude
better than the first method.Comment: 10 pages, 12 figure
Solar-like oscillations of semiregular variables
Oscillations of the Sun and solar-like stars are believed to be excited
stochastically by convection near the stellar surface. Theoretical modeling
predicts that the resulting amplitude increases rapidly with the luminosity of
the star. Thus one might expect oscillations of substantial amplitudes in red
giants with high luminosities and vigorous convection. Here we present evidence
that such oscillations may in fact have been detected in the so-called
semiregular variables, extensive observations of which have been made by
amateur astronomers in the American Association for Variable Star Observers
(AAVSO). This may offer a new opportunity for studying the physical processes
that give rise to the oscillations, possibly leading to further information
about the properties of convection in these stars.Comment: Astrophys. J. Lett., in the press. Processed with aastex and
emulateap
Space and Ground Based Pulsation Data of Eta Bootis Explained with Stellar Models Including Turbulence
The space telescope MOST is now providing us with extremely accurate low
frequency p-mode oscillation data for the star Eta Boo. We demonstrate in this
paper that these data, when combined with ground based measurements of the high
frequency p-mode spectrum, can be reproduced with stellar models that include
the effects of turbulence in their outer layers. Without turbulence, the l=0
modes of our models deviate from either the ground based or the space data by
about 1.5-4.0 micro Hz. This discrepancy can be completely removed by including
turbulence in the models and we can exactly match 12 out of 13 MOST frequencies
that we identified as l=0 modes in addition to 13 out of 21 ground based
frequencies within their observational 2 sigma tolerances. The better agreement
between model frequencies and observed ones depends for the most part on the
turbulent kinetic energy which was taken from a 3D convection simulation for
the Sun.Comment: 13 pages, 7 figures, ApJ in pres
Solar Oscillations and Convection: II. Excitation of Radial Oscillations
Solar p-mode oscillations are excited by the work of stochastic,
non-adiabatic, pressure fluctuations on the compressive modes. We evaluate the
expression for the radial mode excitation rate derived by Nordlund and Stein
(Paper I) using numerical simulations of near surface solar convection. We
first apply this expression to the three radial modes of the simulation and
obtain good agreement between the predicted excitation rate and the actual mode
damping rates as determined from their energies and the widths of their
resolved spectral profiles. We then apply this expression for the mode
excitation rate to the solar modes and obtain excellent agreement with the low
l damping rates determined from GOLF data. Excitation occurs close to the
surface, mainly in the intergranular lanes and near the boundaries of granules
(where turbulence and radiative cooling are large). The non-adiabatic pressure
fluctuations near the surface are produced by small instantaneous local
imbalances between the divergence of the radiative and convective fluxes near
the solar surface. Below the surface, the non-adiabatic pressure fluctuations
are produced primarily by turbulent pressure fluctuations (Reynolds stresses).
The frequency dependence of the mode excitation is due to effects of the mode
structure and the pressure fluctuation spectrum. Excitation is small at low
frequencies due to mode properties -- the mode compression decreases and the
mode mass increases at low frequency. Excitation is small at high frequencies
due to the pressure fluctuation spectrum -- pressure fluctuations become small
at high frequencies because they are due to convection which is a long time
scale phenomena compared to the dominant p-mode periods.Comment: Accepted for publication in ApJ (scheduled for Dec 10, 2000 issue).
17 pages, 27 figures, some with reduced resolution -- high resolution
versions available at http://www.astro.ku.dk/~aake/astro-ph/0008048
Stellar Model Analysis of the Oscillation Spectrum of eta Bootis Obtained from MOST
Eight consecutive low-frequency radial p-modes are identified in the G0 IV
star eta Bootis based on 27 days of ultraprecise rapid photometry obtained by
the MOST (Microvariability & Oscillations of Stars) satellite. The MOST data
extend smoothly to lower overtones the sequence of radial p-modes reported in
earlier groundbased spectroscopy by other groups. The lower-overtone modes from
the MOST data constrain the interior structure of the model of eta Boo. With
the interior fit anchored by the lower-overtone modes seen by MOST, standard
models are not able to fit the higher-overtone modes with the same level of
accuracy. The discrepancy is similar to the discrepancy that exists between the
Sun's observed p-mode frequencies and the p-mode frequencies of the standard
solar model. This discrepancy promises to be a powerful constraint on models of
3D convection.Comment: 30 pages with 14 figures. Accepted for publication in Ap
Helioseismological Implications of Recent Solar Abundance Determinations
We show that standard solar models are in good agreement with the
helioseismologically determined sound speed and density as a function of solar
radius, the depth of the convective zone, and the surface helium abundance, as
long as those models do not incorporate the most recent heavy element abundance
determinations. However, sophisticated new analyses of the solar atmosphere
infer lower abundances of the lighter metals (like C, N, O, Ne, and Ar) than
the previously widely used surface abundances. We show that solar models that
include the lower heavy element abundances disagree with the solar profiles of
sound speed and density as well as the depth of the convective zone and the
helium abundance. The disagreements for models with the new abundances range
from factors of several to many times the quoted uncertainties in the
helioseismological measurements. The disagreements are at temperatures below
what is required for solar interior fusion reactions and therefore do not
significantly affect solar neutrino emission. If errors in thecalculated OPAL
opacities are solely responsible for the disagreements, then the corrections in
the opacity must extend from 2 times 10^6 K (R = 0.7R_Sun)to 5 times 10^6 K (R
= 0.4 R_Sun), with opacity increases of order 10%.Comment: ApJ in press; clarified Figure
Frozen spatial chaos induced by boundaries
We show that rather simple but non-trivial boundary conditions could induce
the appearance of spatial chaos (that is stationary, stable, but spatially
disordered configurations) in extended dynamical systems with very simple
dynamics. We exemplify the phenomenon with a nonlinear reaction-diffusion
equation in a two-dimensional undulated domain. Concepts from the theory of
dynamical systems, and a transverse-single-mode approximation are used to
describe the spatially chaotic structures.Comment: 9 pages, 6 figures, submitted for publication; for related work visit
http://www.imedea.uib.es/~victo
A stochastic flow rule for granular materials
There have been many attempts to derive continuum models for dense granular
flow, but a general theory is still lacking. Here, we start with Mohr-Coulomb
plasticity for quasi-2D granular materials to calculate (average) stresses and
slip planes, but we propose a "stochastic flow rule" (SFR) to replace the
principle of coaxiality in classical plasticity. The SFR takes into account two
crucial features of granular materials - discreteness and randomness - via
diffusing "spots" of local fluidization, which act as carriers of plasticity.
We postulate that spots perform random walks biased along slip-lines with a
drift direction determined by the stress imbalance upon a local switch from
static to dynamic friction. In the continuum limit (based on a Fokker-Planck
equation for the spot concentration), this simple model is able to predict a
variety of granular flow profiles in flat-bottom silos, annular Couette cells,
flowing heaps, and plate-dragging experiments -- with essentially no fitting
parameters -- although it is only expected to function where material is at
incipient failure and slip-lines are inadmissible. For special cases of
admissible slip-lines, such as plate dragging under a heavy load or flow down
an inclined plane, we postulate a transition to rate-dependent Bagnold
rheology, where flow occurs by sliding shear planes. With different yield
criteria, the SFR provides a general framework for multiscale modeling of
plasticity in amorphous materials, cycling between continuum limit-state stress
calculations, meso-scale spot random walks, and microscopic particle
relaxation
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