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

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

Thermal structure of a gas-permeable lava dome and timescale separation in its response to perturbation

The thermal boundary layer at the surface of a volcanic lava dome is investigated through a continuum model of the thermodynamic advection diffusion processes resulting from magmatic gas flow through the dome matrix. The magmatic gas mass flux, porosity and permeability of the rock are identified as key parameters. New, theoretical, nonlinear steady-state thermal profiles are reported which give a realistic surface temperature of 210 degC for a region of lava dome surface through which a gas flux of 3.5 x 10-3 kg s-1 m-2 passes. This contrasts favourably with earlier purely diffusive thermal models, which cool too quickly. Results are presented for time-dependent perturbations of the steady states as a response to: changes in surface pressure, a sudden rockfall from the lava dome surface, and a change in the magmatic gas mass flux at depth. Together with a generalized analysis using the method of multiple scales, this identifies two characteristic time scales associated with the thermal evolution of a dome carapace: a short time scale of several minutes, over which the magmatic gas mass flux, density, and pressure change to a new quasi-steady-state, and a longer time scale of several days, over which the thermal profile changes to a new equilibrium distribution. Over the longer time scale the dynamic properties of the dome continue to evolve, but only in slavish response to the ongoing temperature evolution. In the light of this time scale separation, the use of surface temperature measurements to infer changes in the magmatic gas flux for use in volcanic hazard prediction is discussed

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

Vlasov-Fokker-Planck equation: stochastic stability of resonances and unstable manifold expansion

We investigate the dynamics close to a homogeneous stationary state of Vlasov equation in one dimension, in presence of a small dissipation modeled by a Fokker-Planck operator. When the stationary state is stable, we show the stochastic stability of Landau poles. When the stationary state is unstable, depending on the relative size of the dissipation and the unstable eigenvalue, we find three distinct nonlinear regimes: for a very small dissipation, the system behaves as a pure Vlasov equation; for a strong enough dissipation, the dynamics presents similarities with a standard dissipative bifurcation; in addition, we identify an intermediate regime interpolating between the two previous ones. The non linear analysis relies on an unstable manifold expansion, performed using Bargmann representation for the functions and operators analyzed. The resulting series are estimated with Mellin transform techniques.Comment: 26 pages, 3 figure

Excitation of solar-like oscillations across the HR diagram

We extend semi-analytical computations of excitation rates for solar oscillation modes to those of other solar-like oscillating stars to compare them with recent observations. Numerical 3D simulations of surface convective zones of several solar-type oscillating stars are used to characterize the turbulent spectra as well as to constrain the convective velocities and turbulent entropy fluctuations in the uppermost part of the convective zone of such stars. These constraints, coupled with a theoretical model for stochastic excitation, provide the rate 'P' at which energy is injected into the p-modes by turbulent convection. These energy rates are compared with those derived directly from the 3D simulations. The excitation rates obtained from the 3D simulations are systematically lower than those computed from the semi-analytical excitation model. We find that Pmax, the excitation rate maximum, scales as (L/M)^s where s is the slope of the power law and L and M are the mass and luminosity of the 1D stellar model built consistently with the associated 3D simulation. The slope is found to depend significantly on the adopted form of the eddy time-correlation ; using a Lorentzian form results in s=2.6, whereas a Gaussian one gives s=3.1. Finally, values of Vmax, the maximum in the mode velocity, are estimated from the computed power laws for Pmax and we find that Vmax increases as (L/M)^sv. Comparisons with the currently available ground-based observations show that the computations assuming a Lorentzian eddy time-correlation yield a slope, sv, closer to the observed one than the slope obtained when assuming a Gaussian. We show that the spatial resolution of the 3D simulations must be high enough to obtain accurate computed energy rates.Comment: 14 pages ; 7 figures ; accepted for publication in Astrophysics & Astronom

Asteroseismic Theory of Rapidly Oscillating Ap Stars

This paper reviews some of the important advances made over the last decade concerning theory of roAp stars.Comment: 9 pages, 5 figure

Time resolved spectroscopy of the cool Ap star HD 213637

We present an analysis of high time resolution spectra of the chemically peculiar Ap star HD 213637. The star shows rapid radial velocity variations with a period close to the photometric pulsation period. Radial velocity pulsation amplitudes vary significantly for different rare earth elements. The highest pulsation amplitudes belong to lines of Tb III (∼360 m s−1), Pr II (∼250 m s−1) and Pr III (∼230 m s−1).We did not detect any pulsations from spectral lines of Eu II and in Hα, in contrast to many other roAp stars. We also did not find radial velocity pulsations using spectral lines of other chemical elements, including Mg, Si, Ca, Sc, Cr, Fe, Ni, Y and Ba. There are phase shifts between the maxima of pulsation amplitudes of different rare earth elements and ions, which is evidence of an outwardly running magneto-acoustic wave propagating through the upper stellar atmosphere