On the seismic age and heavy-element abundance of the Sun

We estimate the main-sequence age and heavy-element abundance of the Sun by means of an asteroseismic calibration of theoretical solar models using only low-degree acoustic modes from the BiSON. The method can therefore be applied also to other solar-type stars, such as those observed by the NASA satellite Kepler and the planned ground-based Danish-led SONG network. The age, 4.60+/-0.04 Gy, obtained with this new seismic method, is similar to, although somewhat greater than, today's commonly adopted values, and the surface heavy-element abundance by mass, Zs=0.0142+/-0.0005, lies between the values quoted recently by Asplund et al. (2009) and by Caffau et al. (2009). We stress that our best-fitting model is not a seismic model, but a theoretically evolved model of the Sun constructed with `standard' physics and calibrated against helioseismic data.Comment: 16 pages, 11 figures, 5 tables, accepted for publication in MNRA

Progress report on solar age calibration

We report on an ongoing investigation into a seismic calibration of solar models designed for estimating the main-sequence age and a measure of the chemical abundances of the Sun. Only modes of low degree are employed, so that with appropriate modification the procedure could be applied to other stars. We have found that, as has been anticipated, a separation of the contributions to the seismic frequencies arising from the relatively smooth, glitch-free, background structure of the star and from glitches produced by helium ionization and the abrupt gradient change at the base of the convection zone renders the procedure more robust than earlier calibrations that fitted only raw frequencies to glitch-free asymptotics. As in the past, we use asymptotic analysis to design seismic signatures that are, to the best of our ability, contaminated as little as possible by those uncertain properties of the star that are not directly associated with age and chemical composition. The calibration itself, however, employs only numerically computed eigenfrequencies. It is based on a linear perturbation from a reference model. Two reference models have been used, one somewhat younger, the other somewhat older than the Sun. The two calibrations, which use BiSON data, are more-or-less consistent, and yield a main-sequence age $t_\odot=4.68\pm0.02$Gy, coupled with a formal initial heavy-element abundance $Z=0.0169\pm0.0005$. The error analysis has not yet been completed, so the estimated precision must be taken with a pinch of salt.Comment: 8 pages, 3 figures, in L. Deng, K.L. Chan, C. Chiosi, eds, The Art of Modelling Stars in the 21st Century, Proc. IAU Symp. No. 252, invited contributed pape

An asteroseismic signature of helium ionization

We investigate the influence of the ionization of helium on the low-degree acoustic oscillation frequencies in model solar-type stars. The signature in the oscillation frequencies characterizing the ionization-induced depression of the first adiabatic exponent $\gamma$ is a superposition of two decaying periodic functions of frequency $\nu$, with `frequencies' that are approximately twice the acoustic depths of the centres of the Helium I and Helium II ionization regions. That variation is probably best exhibited in the second frequency difference $\Delta_2\nu_{n,l}\equiv\nu_{n-1,l}-2\nu{n,l}+\nu_{n+1,l}$. We show how an analytic approximation to the variation of $\gamma$ leads to a simple representation of this oscillatory contribution to $\Delta_2\nu$ which can be used to characterize the $\gamma$ variation, our intention being to use it as a seismic diagnostic of the helium abundance of the star. We emphasize that the objective is to characterize $\gamma$, not merely to find a formula for $\Delta_2\nu$ that reproduces the data.Comment: 22 pages, 16 figures, accepted by MNRAS on 21 November 200

Oscillations of alpha UMa and other red giants

There is growing observational evidence that the variability of red giants could be caused by excitation of global modes of oscillation. The most recent evidence of such oscillations was reported for alpha UMa by Buzasi et al.(2000). We address the problem of radial and nonradial mode excitation in red giants from the theoretical point of view. In particular, we present the results of numerical computations of oscillation properties of a model of alpha UMa and of several models of a 2M_sun star in the red-giant phase. In the red giant stars by far most of the nonradial modes are confined to to the deep interior, where they have the g-mode character. Only modes at resonant frequencies of the p-mode cavity have substantial amplitudes in the outer layers. We have shown that such modes can be unstable with the linear growth rates similar to those of corresponding to radial modes. We have been unable to explain the observed oscillation properties of alpha UMa, either in terms of mode instability or in terms of stochastic excitation by turbulent convection. Modes at the lowest frequencies, which exhibit the largest amplitudes and may correspond to the first three radial modes, are found stable if all effects of convection are taken into account. The observed frequency dependence of amplitudes does not agree with what one expects from stochastic excitation. The predicted fundamental mode amplitude is by about two orders of magnitude smaller than those of high frequency modes, which is in stark disagreement with the observations.Comment: MNRAS in pres

Critically rotating stars in binaries - an unsolved problem -

In close binaries mass and angular momentum can be transferred from one star to the other during Roche-lobe overflow. The efficiency of this process is not well understood and constitutes one of the largest uncertainties in binary evolution. One of the problems lies in the transfer of angular momentum, which will spin up the accreting star. In very tight systems tidal friction can prevent reaching critical rotation, by locking the spin period to the orbital period. Accreting stars in systems with orbital periods larger than a few days reach critical rotation after accreting only a fraction of their mass, unless there is an effective mechanism to get rid of angular momentum. In low mass stars magnetic field might help. In more massive stars angular momentum loss will be accompanied by strong mass loss. This would imply that most interacting binaries with initial orbital periods larger than a few days evolve very non-conservatively. In this contribution we wish to draw attention to the unsolved problems related to mass and angular momentum transfer in binary systems. We do this by presenting the first results of an implementation of spin up by accretion into the TWIN version of the Eggleton stellar evolution code.Comment: 5 pages, 1 figure, to appear in the proceedings of the conference "Unsolved Problems in Stellar Physics", Cambridge, 2-6 July 200