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

Modelling the Autocovariance of the Power Spectrum of a Solar-Type Oscillator

Asteroseismology is able to conduct studies on the interiors of solar-type stars from the analysis of stellar acoustic spectra. However, such an analysis process often has to rely upon subjective choices made throughout. A recurring problem is to determine whether a signal in the acoustic spectrum originates from a radial or a dipolar oscillation mode. In order to overcome this problem, we present a procedure for modelling and fitting the autocovariance of the power spectrum which can be used to obtain global seismic parameters of solar-type stars, doing so in an automated fashion without the need to make subjective choices. From the set of retrievable global seismic parameters we emphasize the mean small frequency separation and, depending on the intrinsic characteristics of the power spectrum, the mean rotational frequency splitting. Since this procedure is automated, it can serve as a useful tool in the analysis of the more than one thousand solar-type stars expected to be observed as part of the Kepler Asteroseismic Investigation (KAI). We apply the aforementioned procedure to simulations of the Sun. Assuming different apparent magnitudes, we address the issues of how accurately and how precisely we can retrieve the several global seismic parameters were the Sun to be observed as part of the KAI.Comment: 10 pages, 8 figures, accepted for publication in MNRA

Gross solids from combined sewers in dry weather and storms, elucidating production, storage and social factors

Variation in rates of sanitary hygiene products, toilet tissue and faeces occurring in sewers are presented for dry and wet weather from three steep upstream urban catchments with different economic, age and ethnic profiles. Results show, for example, that total daily solids per capita from the low income and ageing populations are almost twice that from high income or ethnic populations. Relative differences are verified through independent questionnaires. The relationship between solids stored in sewers prior to storms, antecedent dry weather period and the proportion of roof to total catchment area is quantified. A full solids' flush occurs when storm flows exceed three times the peak dry weather flow. The data presented will assist urban drainage designers in managing pollution caused by the discharge of sewage solids

Angular momentum transport by internal gravity waves III - Wave excitation by core convection and the Coriolis effect

This is the third in a series of papers that deal with angular momentum transport by internal gravity waves. We concentrate on the waves excited by core convection in a 3Msun, Pop I main sequence star. Here, we want to examine the role of the Coriolis acceleration in the equations of motion that describe the behavior of waves and to evaluate its impact on angular momentum transport. We use the so-called traditional approximation of geophysics, which allows variable separation in radial and horizontal components. In the presence of rotation, the horizontal structure is described by Hough functions instead of spherical harmonics. The Coriolis acceleration has two main effects on waves. It transforms pure gravity waves into gravito-inertial waves that have a larger amplitude closer to the equator, and it introduces new waves whose restoring force is mainly the conservation of vorticity. Taking the Coriolis acceleration into account changes the subtle balance between prograde and retrograde waves in non-rotating stars. It also introduces new types of waves that are either purely prograde or retrograde. We show in this paper where the local deposition of angular momentum by such waves is important.Comment: 9 pages, 10 figures, accepted for publication by A&

Eccentricity evolution of giant planet orbits due to circumstellar disk torques

The extrasolar planets discovered to date possess unexpected orbital elements. Most orbit their host stars with larger eccentricities and smaller semi-major axes than similarly sized planets in our own solar system do. It is generally agreed that the interaction between giant planets and circumstellar disks (Type II migration) drives these planets inward to small radii, but the effect of these same disks on orbital eccentricity, e, is controversial. Several recent analytic calculations suggest that disk-planet interactions can excite eccentricity, while numerical studies generally produce eccentricity damping. This paper addresses this controversy using a quasi-analytic approach, drawing on several preceding analytic studies. This work refines the current treatment of eccentricity evolution by removing several approximations from the calculation of disk torques. We encounter neither uniform damping nor uniform excitation of orbital eccentricity, but rather a function de/dt that varies in both sign and magnitude depending on eccentricity and other solar system properties. Most significantly, we find that for every combination of disk and planet properties investigated herein, corotation torques produce negative values of de/dt for some range in e within the interval [0.1, 0.5]. If corotation torques are saturated, this region of eccentricity damping disappears, and excitation occurs on a short timescale of less than 0.08 Myr. Thus, our study does not produce eccentricity excitation on a timescale of a few Myr -- we obtain either eccentricity excitation on a short time scale, or eccentricity damping on a longer time scale. Finally, we discuss the implications of this result for producing the observed range in extrasolar planet eccentricity.Comment: 24 pages including 13 figures; accepted to ICARU

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