A more realistic representation of overshoot at the base of the solar convective envelope as seen by helioseismology

The stratification near the base of the Sun's convective envelope is governed by processes of convective overshooting and element diffusion, and the region is widely believed to play a key role in the solar dynamo. The stratification in that region gives rise to a characteristic signal in the frequencies of solar p modes, which has been used to determine the depth of the solar convection zone and to investigate the extent of convective overshoot. Previous helioseismic investigations have shown that the Sun's spherically symmetric stratification in this region is smoother than that in a standard solar model without overshooting, and have ruled out simple models incorporating overshooting, which extend the region of adiabatic stratification and have a more-or-less abrupt transition to subadiabatic stratification at the edge of the overshoot region. In this paper we consider physically motivated models which have a smooth transition in stratification bridging the region from the lower convection zone to the radiative interior beneath. We find that such a model is in better agreement with the helioseismic data than a standard solar model.Comment: 18 pages, 4 tables, 24 figures - to appear in MNRAS (version a: equation 9 corrected

Stellar Oscillations Network Group

Stellar Oscillations Network Group (SONG) is an initiative aimed at designing and building a network of 1m-class telescopes dedicated to asteroseismology and planet hunting. SONG will have 8 identical telescope nodes each equipped with a high-resolution spectrograph and an iodine cell for obtaining precision radial velocities and a CCD camera for guiding and imaging purposes. The main asteroseismology targets for the network are the brightest (V<6) stars. In order to improve performance and reduce maintenance costs the instrumentation will only have very few modes of operation. In this contribution we describe the motivations for establishing a network, the basic outline of SONG and the expected performance.Comment: Proc. Vienna Workshop on the Future of Asteroseismology, 20 - 22 September 2006. Comm. in Asteroseismology, Vol. 150, in the pres

A theoretical approach for the interpretation of pulsating PMS intermediate-mass stars

The investigation of the pulsation properties of pre-main-sequence intermediate-mass stars is a promising tool to evaluate the intrinsic properties of these stars and to constrain current evolutionary models. Many new candidates of this class have been discovered during the last decade and very accurate data are expected from space observations obtained for example with the CoRoT satellite. In this context we aim at developing a theoretical approach for the interpretation of observed frequencies, both from the already available ground-based observations and from the future more accurate and extensive CoRoT results. To this purpose we have started a project devoted to the computations of fine and extensive grids of asteroseismic models of intermediate mass pre-main-sequence stars. The obtained frequencies are used to derive an analytical relation between the large frequency separation and the stellar luminosity and effective temperature and to develop a tool to compare theory and observations in the echelle diagram. The predictive capabilities of the proposed method are verified through the application to two test stars. As a second step, we apply the procedure to two true observations from multisite campaigns and we are able to constrain their stellar parameters, in particular the mass, in spite of the small number of frequencies. We expect that with a significantly higher number of frequencies both the stellar mass and age could be constrained and, at the same time, the physics of the models could be tested.Comment: Accepted for publication on A&

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

Local models of stellar convection II: Rotation dependence of the mixing length relations

We study the mixing length concept in comparison to three-dimensional numerical calculations of convection with rotation. In a limited range, the velocity and temperature fluctuations are linearly proportional to the superadiabaticity, as predicted by the mixing length concept and in accordance with published results. The effects of rotation are investigated by varying the Coriolis number, Co = 2 Omega tau, from zero to roughly ten, and by calculating models at different latitudes. We find that \alpha decreases monotonically as a function of the Coriolis number. This can be explained by the decreased spatial scale of convection and the diminished efficiency of the convective energy transport, the latter of which leads to a large increase of the superadibaticity, \delta = \nabla - \nabla_ad as function of Co. Applying a decreased mixing length parameter in a solar model yields very small differences in comparison to the standard model within the convection zone. The main difference is the reduction of the overshooting depth, and thus the depth of the convection zone, when a non-local version of the mixing length concept is used. Reduction of \alpha by a factor of roughly 2.5 is sufficient to reconcile the difference between the model and helioseismic results. The numerical results indicate reduction of \alpha by this order of magnitude.Comment: Final published version, 8 pages, 9 figure

What Fraction of Boron-8 Solar Neutrinos arrive at the Earth as a nu_2 mass eigenstate?

We calculate the fraction of B^8 solar neutrinos that arrive at the Earth as a nu_2 mass eigenstate as a function of the neutrino energy. Weighting this fraction with the B^8 neutrino energy spectrum and the energy dependence of the cross section for the charged current interaction on deuteron with a threshold on the kinetic energy of the recoil electrons of 5.5 MeV, we find that the integrated weighted fraction of nu_2's to be 91 \pm 2 % at the 95% CL. This energy weighting procedure corresponds to the charged current response of the Sudbury Neutrino Observatory (SNO). We have used SNO's current best fit values for the solar mass squared difference and the mixing angle, obtained by combining the data from all solar neutrino experiments and the reactor data from KamLAND. The uncertainty on the nu_2 fraction comes primarily from the uncertainty on the solar delta m^2 rather than from the uncertainty on the solar mixing angle or the Standard Solar Model. Similar results for the Super-Kamiokande experiment are also given. We extend this analysis to three neutrinos and discuss how to extract the modulus of the Maki-Nakagawa-Sakata mixing matrix element U_{e2} as well as place a lower bound on the electron number density in the solar B^8 neutrino production region.Comment: 23 pages, 8 postscript figures, latex. Dedicated to the memory of John Bahcall who championed solar neutrinos for many lonely year

Probing the internal magnetic field of slowly pulsating B-stars through g modes

We suggest that high-order g modes can be used as a probe of the internal magnetic field of SPB (slowly pulsating B) stars. The idea is based on earlier work by the authors which analytically investigated the effect of a vertical magnetic field on p and g modes in a plane-parallel isothermal stratified atmosphere. It was found that even a weak field can significantly shift the g-mode frequencies -- the effect increases with mode order. In the present study we adopt the classical perturbative approach to estimate the internal field of a 4 solar mass SPB star by looking at its effect on a low-degree ($l=1$) and high-order ($n=20$) g mode with a period of about 1.5 d. We find that a polar field strength of about 110 kG on the edge of the convective core is required to produce a frequency shift of 1%. Frequency splittings of that order have been observed in several SPB variables, in some cases clearly too small to be ascribed to rotation. We suggest that they may be due to a poloidal field with a strength of order 100 kG, buried in the deep interior of the star.Comment: 4 pages, 2 figures (to appear in Astronomy & Astrophysics

Solar-like oscillations in the G8 V star tau Ceti

We used HARPS to measure oscillations in the low-mass star tau Cet. Although the data were compromised by instrumental noise, we have been able to extract the main features of the oscillations. We found tau Cet to oscillate with an amplitude that is about half that of the Sun, and with a mode lifetime that is slightly shorter than solar. The large frequency separation is 169 muHz, and we have identified modes with degrees 0, 1, 2, and 3. We used the frequencies to estimate the mean density of the star to an accuracy of 0.45% which, combined with the interferometric radius, gives a mass of 0.783 +/- 0.012 M_sun (1.6%).Comment: accepted for publication in A&