Dipolar modes in luminous red giants

Lots of information on solar-like oscillations in red giants has been obtained thanks to observations with CoRoT and Kepler space telescopes. Data on dipolar modes appear most interesting. We study properties of dipolar oscillations in luminous red giants to explain mechanism of mode trapping in the convective envelope and to assess what may be learned from the new data. Equations for adiabatic oscillations are solved by numerical integration down to the bottom of convective envelope, where the boundary condition is applied. The condition is based on asymptotic decomposition of the fourth order system into components describing a running wave and a uniform shift of radiative core. If the luminosity of a red giant is sufficiently high, for instance at M = 2 Msun greater than about 100 Lsun, the dipolar modes become effectively trapped in the acoustic cavity, which covers the outer part of convective envelope. Energy loss caused by gravity wave emission at the envelope base is a secondary or negligible source of damping. Frequencies are insensitive to structure of the deep interior.Comment: 10 pages, 7 figures, accepted for publication in Astronomy and Astrophysic

Solar Magnetic Field Signatures in Helioseismic Splitting Coefficients

Normal modes of oscillation of the Sun are useful probes of the solar interior. In this work, we use the even-order splitting coefficients to study the evolution of magnetic fields in the convection zone over solar cycle 23, assuming that the frequency splitting is only due to rotation and a large scale magnetic field. We find that the data are best fit by a combination of a poloidal field and a double-peaked near-surface toroidal field. The toroidal fields are centered at r=0.999R_solar and r=0.996R_solar and are confined to the near-surface layers. The poloidal field is a dipole field. The peak strength of the poloidal field is 124 +/- 17G. The toroidal field peaks at 380 +/- 30G and 1.4 +/- 0.2kG for the shallower and deeper fields respectively. The field strengths are highly correlated with surface activity. The toroidal field strength shows a hysteresis-like effect when compared to the global 10.7 cm radio flux. The poloidal field strength shows evidence of saturation at high activity.Comment: 10 pages, accepted for publication in Ap

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

Has a star enough energy to excite the thousand of modes observed with CoRoT?

The recent analyses of the light curves provided by CoRoT have revealed pulsation spectra of unprecedented richness and precision, in particular, thousands of pulsating modes, and a clear distribution of amplitudes with frequency. In the community, some scientists have started doubting about the validity of the classical tools to analyze these very accurate light curves. This work provides the asteroseismic community with answers to this question showing that (1) it is physically possible for a star to excite at a time and with the observed amplitudes such a large number of modes; and (2) that the kinetic energy accumulated in all those modes does not destroy the equilibrium of the star. Consequently, mathematical tools presently applied in the analyses of light curves can a priori be trusted. This conclusion is even more important now, when a large amount of space data coming from Kepler are currently being analyzed. The power spectrum of different stellar cases, and the non-adiabatic code GraCo have been used to estimate the upper limit of the energy per second required to excite all the observed modes, and their total kinetic energy. A necessary previous step for this study is to infer the relative radial pulsational amplitude from the observed photometric amplitude, scaling our linear pulsational solutions to absolute values. The derived upper limits for the required pulsational energy were compared with 1) the luminosity of the star; and 2) the gravitational energy. We obtained that both upper energy limits are orders of magnitude smaller.Comment: 18 pages, 2 figures, accepted by ApJ Letters Dec 15, 200