Surface layer independent model fitting by phase matching: theory and application to HD49933 an HD177153 (aka Perky)

Aims. To describe the theory of surface layer independent model fitting by phase matching and to apply this to the stars HD49933 observed by CoRoT, and HD177153 (aka Perky), observed by Kepler Methods. We use theoretical analysis, phase shifts, and model fitting. Results. We define the inner and outer phase shifts of a frequency set of a model star and show that the outer phase shifts are (almost) independent of degree $\ell$, and that a function of the inner phase shifts (the phase function) collapses to an $\ell$ independent function of frequency in the outer layers. We then show how to use this result in a model fitting technique to find a best fit model to an observed frequency set by calculating the inner phase shifts of a model using the observed frequencies and determining the extent to which the phase function collapses to a single function of frequency in the outer layers. We give two examples applying this technique to the frequency sets of HD49933 observed by CoRoT and HD177153 (aka Perky) observed by Kepler, and compare our results with those of previous studies and show that they are compatible with those obtained using different techniques. We show that there can be many different models that fit the data within the errors and that better precision on the frequencies is needed to discriminate between the models. We compare this technique to that using the ratios of small to large separations, showing that in principle it is more accurate and avoids the problem of correlated errors in separation ratio fitting.Comment: 9 pages 15 figure

On the use of the average large separation in surface layer independent model fitting

The physics of the outer layers of a star are not well understood but these layers make a major contribution to the large separation. We quantify this using stellar models and show that the contribution ranges from 6\% from the outer 0.1\% of the radius to 30\% from the outer 5\%. and therefore argue that the large separation should not be used as a constraint on surface layer independent model fitting. The mass and luminosity are independent of the outer layers and can be used as constraints, the mass being determined from binarity or from surface gravity and radius. The radius can be used as a constraint but with enhanced error estimates. We briefly consider the determination of the large separation for $\alpha$ Cen A and find that mass derived from surface gravity is closer to the binary mass than that derived from the large separation.Comment: 4 pages, 6 figure

Anomalies in the Kepler Asteroseismic Legacy Project Data. A re-analysis of 16 Cyg A&B, KIC8379927 and 6 solar-like stars

I compare values of the frequencies, separation ratios, errors and covariance matrices from a new analysis of 9 solar-like stars with the Legacy project values reported by Lund et al and, for 16Cyg A&B and KIC8379927, with values derived by Davies et al. There is good agreement between my results (using Davies power spectra) and Davies's for these 3 stars, but no such agreement with the Legacy project results. My frequencies differ from the Legacy values, there are inconsistencies in the Legacy frequency covariance matrices which are not positive definite, and the Legacy errors on separation ratios are up to 40 times larger than mine and the values and upper limits derived from the Legacy frequency covariances. There are similar anomalies for 6 other solar-like stars: frequencies and separation ratio errors disagree and 2 have non positive definite covariance matrices. There are inconsistencies in the covariance matrices of 27 the 66 stars in the full Legacy set and problems with the ratio errors for the vast majority of these stars}Comment: 10 pages, 11 figure

On the use of the ratio of small to large separations in asteroseismic model fitting

Context. The use of ratios of small to large separations as a diagnostic of stellar interiors. Aims. To demonstrate that model fitting by comparing observed and model separation ratios at the same n values is in error, and to present a correct procedure. Methods. Theoretical analysis using phase shifts and numerical models. Results. We show that the separation ratios of stellar models with the same interior structure, but different outer layers, are not the same when compared at the same n values, but are the same when evaluated at the same frequencies by interpolation. The separation ratios trace the phase shift differences as a function of frequency not of n. We give examples from model fitting where the ratios at the same n values agree within the error estimates, but do not agree when evaluated at the same frequencies and the models do not have the same interior structure. The correct procedure is to compare observed ratios with those of models interpolated to the observed frequencies.Comment: 7 pages, 14 figures, 3 table

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