Gravity modes and mixed modes as probes of stellar cores in main‐sequence stars: From solar‐like to β Cep stars

We investigate how the frequencies of gravity modes depend on the detailed properties of the chemical composition gradient that develops near the core of main‐sequence stars and, therefore, on the transport processes that are able to modify the μ profile in the central regions. We show that in main‐sequence models, similarly to the case of white dwarfs, the periods of high‐order gravity modes are accurately described by a uniform period spacing superposed to an oscillatory component. The periodicity and amplitude of such a component are related, respectively, to the location and sharpness of the μ gradient. We briefly discuss and interpret, by means of this simple approximation, the effect of turbulent mixing near the core on the periods of both high‐order and low‐order g modes, as well as of modes of mixed pressure‐gravity character. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A procedure for modelling asymptotic g‐mode pulsators: The case of γ Doradus stars

Mode identification is one of the first and main problems we encounter in trying to develop the complete potential of asteroseismology. In the particular case of g‐mode pulsators, this is still an unsolved problem, from both the observational and theoretical points of view. Nevertheless, in recent years, some observational and theoretical efforts have been made to find a solution. In this work we use the latest theoretical and computational tools to understand asymptotic g‐mode pulsators: 1) the Frequency Ratio Method, and 2) Time Dependent Convection. With these tools, a self‐consistent procedure for mode identification and modelling of these g‐mode pulsators can be constructed. This procedure is illustrated using observational information available for the γ Doradus star 9Aurigae. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The limits of validity of the Frequency Ratio Method: The particular case of γ Doradus stars

This work provides a general vision of the limits of validity of the Frequency Ratio Method applied to the g‐mode pulsators in asymptotic regime, the γ Doradus stars. In particular, the work is mainly focused on the role of rotation which is found one of the most important source of uncertainty of the method. The particular case of the moderately rotating γ Doradus star HD48501 is discussed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the r-mode spectrum of relativistic stars

We present a mathematically rigorous proof that the r-mode spectrum of relativistic stars to the rotational lowest order has a continuous part. A rigorous definition of this spectrum is given in terms of the spectrum of a continuous linear operator. This study verifies earlier results by Kojima concerning the nature of the r-mode spectrum.     

Modelling the differential rotation of F stars

We model stellar differential rotation based on the mean-field theory of fluid dynamics. DR is mainly driven by Reynolds stress, which is anisotropic and has a non-diffusive component because the Coriolis force affects the convection pattern. Likewise, the convective heat transport is not strictly radial but slightly tilted towards the rotation axis, causing the polar caps to be slightly warmer than the equator. This drives a flow opposite to that caused by differential rotation and so allows the system to avoid the Taylor-Proudman state. Our model reproduces the rotation pattern in the solar convection zone and allows predictions for other stars with outer convection zones. The surface shear turns out to depend mainly on the spectral type and only weakly on the rotation rate. We present results for stars of spectral type F which show signs of very strong differential rotation in some cases. Stars just below the mass limit for outer convection zones have shallow convection zones with short convective turnover times. We find solar-type rotation and meridional flow patterns at much shorter rotation periods and horizontal shear much larger than on the solar surface, in agreement with recent observations. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Seismic study of stellar convective regions: the base of the convective envelope in low-mass stars

The possibility of observing solar-type oscillations on other stars is of great relevance to investigating the uncertain aspects of the internal structure of stars. One of these aspects is the convective overshoot that takes place at the borders of the envelopes of stars of mass similar to, or lower than, the Sun. It affects the temperature stratification, mixing, rotation and magnetic-field generation. Asteroseismology can provide an observational test for the studies of the structure of such overshoot regions.
The seismic study of the transition in the Sun, located at the base of the convection zone, has been successful in determining the characteristics of this layer in the Sun. In this work we consider the extension of the analysis to other solar-type stars (of mass between 0.85 and 1.2 M_⊙) in order to establish a method for determining the characteristics of their convective envelopes. In particular, we hope to be able to establish seismologically that a star does indeed possess a convective envelope, to measure the size of the convective region and also to constrain the properties of an overshoot layer at the bottom of the envelope. The limitations in terms of observational uncertainties and stellar characteristics, and the detectability of an overshoot layer, are discussed.     

Matching the frequency spectrum of pre-main sequence stars by means of standard and rotating models

We applied the aton evolutionary code to the computation of detailed grids of standard (non-rotating) and rotating pre-main sequence (PMS) models and computed their adiabatic oscillation spectra, with the aim of exploring the seismic properties of young stars. As, until now, only a few frequencies have been determined for ∼40 PMS stars, the way of approaching the interpretation of the oscillations is not unique. We adopt a method similar to the matching mode method by Guenther and Brown making use, when necessary, also of our rotating evolutionary code to compute the models for PMS stars. The method is described by a preliminary application to the frequency spectrum of two PMS stars (85 and 278) in the young open cluster NGC 6530. For the Star 85, we confirm with self-consistent rotating models, previous interpretation of the data, attributing three close frequencies to the mode   n = 4, l = 1  and   m = 0  , +1 and −1. For the Star 278, we find a different fit for the frequencies, corresponding to a model within the original error box of the star, and dispute the possibility that this star has a T _eff much cooler that the red boundary of the radial instability strip.     

The effect of r-mode instability on the evolution of isolated strange stars

We studied the evolution of isolated strange stars (SSs) synthetically, considering the influence of r -mode instability. Our results show that the cooling of SSs with non-ultrastrong magnetic fields is delayed by heating due to r -mode damping for millions of years, while the spin-down of the stars is dominated by gravitational radiation (GR). Especially for the SSs in a possible existing colour–flavour locked (CFL) phase, the effect of r -mode instability on the evolution of stars becomes extremely important because the viscosity, neutrino emissivity and specific heat involving pairing quarks are blocked. It leads to the cooling of these colour superconducting stars being very slow and the stars can remain at high temperature for millions of years, which differs completely from previous understanding. In this case, an SS in CFL phase can be located at the bottom of its r -mode instability window for a long time, but does not spin-down to a very low frequency for hours.     

Time-dependent convection seismic study of five γ Doradus stars

We apply for the first time the time-dependent convection (TDC) treatment of Gabriel and Grigahcène et al. to the photometric mode identification in γ Doradus (γ Dor) stars. We consider the influence of this treatment on the theoretical amplitude ratios and phase differences. Comparison with the observed amplitudes and phases of the stars γ Dor, 9 Aurigae, HD 207223 = HR 8330, HD 12901 and 48501 is presented and enables us to identify the degree ℓ of the pulsation modes for four of them. We also determine the mode stability for different models of these stars. We show that our TDC models agree better with observations than with frozen convection models. Finally, we compare the results obtained with different values of the mixing-length parameter α.     

On the r-mode spectrum of relativistic stars in the low-frequency approximation

The axial modes for non-barotropic relativistic rotating neutron stars with uniform angular velocity are studied, using the slow-rotation formalism together with the low-frequency approximation, first investigated by Kojima. The time-independent form of the equations leads to a singular eigenvalue problem, which admits a continuous spectrum. We show that for     , it is nevertheless also possible to find discrete mode solutions (the r modes). However, under certain conditions related to the equation of state and the compactness of the stellar model, the eigenfrequency lies inside the continuous band and the associated velocity perturbation is divergent; hence these solutions have to be discarded as being unphysical. We corroborate our results by explicitly integrating the time-dependent equations. For stellar models admitting a physical r-mode solution, it can indeed be excited by arbitrary initial data. For models admitting only an unphysical mode solution, the evolutions do not show any tendency to oscillate with the respective frequency. For higher values of l it seems that in certain cases there are no mode solutions at all.     

Pulsations and planets: The asteroseismology‐extrasolar‐planet connection

The disciplines of asteroseismology and extrasolar planet science overlap methodically in the branch of high‐precision photometric time series observations. Light curves are, amongst others, useful to measure intrinsic stellar variability due to oscillations, as well as to discover and characterize those extrasolar planets that transit in front of their host stars, periodically causing shallow dips in the observed brightness. Both fields ultimately derive fundamental parameters of stellar and planetary objects, allowing to study for example the physics of various classes of pulsating stars, or the variety of planetary systems, in the overall context of stellar and planetary system formation and evolution. Both methods typically also require extensive spectroscopic follow‐up to fully explore the dynamic characteristics of the processes under investigation. In particularly interesting cases, a combination of observed pulsations and signatures of a planet allows to characterize a system's components to a very high degree of completeness by combining complementary information. The planning of the relevant space missions has consequently converged with respect to science cases, where at the outset there was primarily a coincidence in instrumentation and techniques. Whether space‐ or ground‐based, a specific type of stellar pulsations can themselves be used in an innovative way to search for extrasolar planets. Results from this additional method at the interface of stellar pulsation studies and exoplanet hunts in a beyond‐mainstream area are presented (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the r-mode spectrum of relativistic stars: the inclusion of the radiation reaction

We consider both mode calculations and time-evolutions of axial r modes for relativistic uniformly rotating non-barotropic neutron stars, using the slow-rotation formalism, in which rotational corrections are considered up to linear order in the angular velocity Ω. We study various stellar models, such as uniform density models, polytropic models with different polytropic indices n , and some models based on realistic equations of state. For weakly relativistic uniform density models and polytropes with small values of n , we can recover the growth times predicted from Newtonian theory when standard multipole formulae for the gravitational radiation are used. However, for more compact models, we find that relativistic linear perturbation theory predicts a weakening of the instability compared to the Newtonian results. When turning to polytropic equations of state, we find that for certain ranges of the polytropic index n , the r mode disappears, and instead of a growth, the time-evolutions show a rapid decay of the amplitude. This is clearly at variance with the Newtonian predictions. It is, however, fully consistent with our previous results obtained in the low-frequency approximation.