Simulations of core convection in rotating A-type stars: Differential rotation and overshooting

We present the results of 3--D simulations of core convection within A-type stars of 2 solar masses, at a range of rotation rates. We consider the inner 30% by radius of such stars, thereby encompassing the convective core and some of the surrounding radiative envelope. We utilize our anelastic spherical harmonic (ASH) code, which solves the compressible Navier-Stokes equations in the anelastic approximation, to examine highly nonlinear flows that can span multiple scale heights. The cores of these stars are found to rotate differentially, with central cylindrical regions of strikingly slow rotation achieved in our simulations of stars whose convective Rossby number (R_{oc}) is less than unity. Such differential rotation results from the redistribution of angular momentum by the nonlinear convection that strongly senses the overall rotation of the star. Penetrative convective motions extend into the overlying radiative zone, yielding a prolate shape (aligned with the rotation axis) to the central region in which nearly adiabatic stratification is achieved. This is further surrounded by a region of overshooting motions, the extent of which is greater at the equator than at the poles, yielding an overall spherical shape to the domain experiencing at least some convective mixing. We assess the overshooting achieved as the stability of the radiative exterior is varied, and the weak circulations that result in that exterior. The convective plumes serve to excite gravity waves in the radiative envelope, ranging from localized ripples of many scales to some remarkable global resonances.Comment: 48 pages, 16 figures, some color. Accepted to Astrophys. J. Color figures compressed with appreciable loss of quality; a PDF of the paper with better figures is available at http://lcd-www.colorado.edu/~brownim/core_convectsep24.pd

Line asymmetry of solar p-modes: Reversal of asymmetry in intensity power spectra

The sense of line asymmetry of solar p-modes in the intensity power spectra is observed to be opposite of that seen in the velocity power spectra. Theoretical calculations provide a good understanding and fit to the observed velocity power spectra whereas the reverse sense of asymmetry in the intensity power spectrum has been poorly understood. We show that when turbulent eddies arrive at the top of the convection zone they give rise to an observable intensity fluctuation which is correlated with the oscillation they generate, thereby affecting the shape of the line in the p-mode power spectra and reversing the sense of asymmetry (this point was recognized by Nigam et al. and Roxburgh & Vorontsov). The addition of the correlated noise displaces the frequencies of peaks in the power spectrum. Depending on the amplitude of the noise source the shift in the position of the peak can be substantially larger than the frequency shift in the velocity power spectra. In neither case are the peak frequencies precisely equal to the eigenfrequencies of p-modes. We suggest two observations which can provide a test of the model discussed here.Comment: Revised version. To appear in Ap

Response of a spaceborne gravitational wave antenna to solar oscillations

We investigate the possibility of observing very small amplitude low frequency solar oscillations with the proposed laser interferometer space antenna (LISA). For frequencies $\nu$ below $3\times 10^{-4} {\rm Hz}$ the dominant contribution is from the near zone time dependent gravitational quadrupole moments associated with the normal modes of oscillation. For frequencies $\nu$ above $3\times 10^{-4} {\rm Hz}$ the dominant contribution is from gravitational radiation generated by the quadrupole oscillations which is larger than the Newtonian signal by a factor of the order $(2 \pi r \nu/ c)^4$, where $r$ is the distance to the Sun, and $c$ is the velocity of light. The low order solar quadrupole pressure and gravity oscillation modes have not yet been detected above the solar background by helioseismic velocity and intensity measurements. We show that for frequencies $\nu \lesssim 2\times 10^{-4} {\rm Hz}$, the signal due to solar oscillations will have a higher signal to noise ratio in a LISA type space interferometer than in helioseismology measurements. Our estimates of the amplitudes needed to give a detectable signal on a LISA type space laser interferometer imply surface velocity amplitudes on the sun of the order of 1-10 mm/sec in the frequency range $1\times 10^{-4} -5\times 10^{-4} {\rm Hz}$. If such modes exist with frequencies and amplitudes in this range they could be detected with a LISA type laser interferometer.Comment: 16 pages, 6 figures, 1 table. A reworked and considerably improved version of ArXiv:astro-ph/0103472, Published in PR

Open issues in probing interiors of solar-like oscillating main sequence stars: 2. Diversity in the HR diagram

We review some major open issues in the current modelling of low and intermediate mass, main sequence stars based on seismological studies. The solar case was discussed in a companion paper, here several issues specific to other stars than the Sun are illustrated with a few stars observed with CoRoT and expectations from Kepler data.Comment: GONG 2010 - SoHO 24, A new era of seismology of the Sun and solar-like stars, To be published in the Journal of Physics: Conference Series (JPCS

Peaks and Troughs in Helioseismology: The Power Spectrum of Solar Oscillations

I present a matched-wave asymptotic analysis of the driving of solar oscillations by a general localised source. The analysis provides a simple mathematical description of the asymmetric peaks in the power spectrum in terms of the relative locations of eigenmodes and troughs in the spectral response. It is suggested that the difference in measured phase function between the modes and the troughs in the spectrum will provide a key diagnostic of the source of the oscillations. I also suggest a form for the asymmetric line profiles to be used in the fitting of solar power spectra. Finally I present a comparison between the numerical and asymptotic descriptions of the oscillations. The numerical results bear out the qualitative features suggested by the asymptotic analysis but suggest that numerical calculations of the locations of the troughs will be necessary for a quantitative comparison with the observations.Comment: 18 pages + 8 separate figures. To appear in Ap

What Causes P-mode Asymmetry Reversal?

The solar acoustic p-mode line profiles are asymmetric. Velocity spectra have more power on the low-frequency sides, whereas intensity profiles show the opposite sense of asymmetry. Numerical simulations of the upper convection zone have resonant p-modes with the same asymmetries and asymmetry reversal as the observed modes. The temperature and velocity power spectra at optical depth $\tau_{\rm cont} = 1$ have the opposite asymmetry as is observed for the intensity and velocity spectra. At a fixed geometrical depth, corresponding to $=1$, however, the temperature and velocity spectra have the same asymmetry. This indicates that the asymmetry reversal is produced by radiative transfer effects and not by correlated noise.Comment: 16 pages, 10 figures, submitted to Astrophysical Journa

Simulations of Oscillation Modes of the Solar Convection Zone

We use the three-dimensional hydrodynamic code of Stein and Nordlund to realistically simulate the upper layers of the solar convection zone in order to study physical characteristics of solar oscillations. Our first result is that the properties of oscillation modes in the simulation closely match the observed properties. Recent observations from SOHO/MDI and GONG have confirmed the asymmetry of solar oscillation line profiles, initially discovered by Duvall et al. In this paper we compare the line profiles in the power spectra of the Doppler velocity and continuum intensity oscillations from the SOHO/MDI observations with the simulation. We also compare the phase differences between the velocity and intensity data. We have found that the simulated line profiles are asymmetric and have the same asymmetry reversal between velocity and intensity as observed. The phase difference between the velocity and intensity signals is negative at low frequencies and jumps in the vicinity of modes as is also observed. Thus, our numerical model reproduces the basic observed properties of solar oscillations, and allows us to study the physical properties which are not observed.Comment: Accepted for publication in ApJ Letter

The Relation between Physical and Gravitational Geometry

The appearance of two geometries in one and the same gravitational theory is familiar. Usually, as in the Brans-Dicke theory or in string theory, these are conformally related Riemannian geometries. Is this the most general relation between the two geometries allowed by physics ? We study this question by supposing that the physical geometry on which matter dynamics take place could be Finslerian rather than just Riemannian. An appeal to the weak equivalence principle and causality then leads us the conclusion that the Finsler geometry has to reduce to a Riemann geometry whose metric - the physical metric - is related to the gravitational metric by a generalization of the conformal transformation.Comment: 15 pages, Te