Seismic modelling of the β \beta\,Cep star HD\,180642 (V1449\,Aql)

We present modelling of the $\beta\,$Cep star HD\,180642 based on its observational properties deduced from CoRoT and ground-based photometry as well as from time-resolved spectroscopy. We investigate whether present-day state-of-the-art models are able to explain the full seismic behaviour of this star, which has extended observational constraints for this type of pulsator. We constructed a dedicated database of stellar models and their oscillation modes tuned to fit the dominant radial mode frequency of HD\,180642, by means of varying the hydrogen content, metallicity, mass, age, and core overshooting parameter. We compared the seismic properties of these models with those observed. We find models that are able to explain the numerous observed oscillation properties of the star, for a narrow range in mass of 11.4--11.8\,M$_\odot$ and no or very mild overshooting (with up to 0.05 local pressure scale heights), except for an excitation problem of the $\ell=3$, p$_1$ mode. We deduce a rotation period of about 13\,d, which is fully compatible with recent magnetic field measurements. The seismic models do not support the earlier claim of solar-like oscillations in the star. We instead ascribe the power excess at high frequency to non-linear resonant mode coupling between the high-amplitude radial fundamental mode and several of the low-order pressure modes. We report a discrepancy between the seismic and spectroscopic gravity at the $2.5\sigma$ level.Comment: 10 pages, 2 Tables, 6 Figures. Accepted for publication in Astronomy and Astrophysic

Bulk viscosity in the nonlinear and anharmonic regime of strange quark matter

The bulk viscosity of cold, dense three-flavor quark matter is studied as a function of temperature and the amplitude of density oscillations. The study is also extended to the case of two different types of anharmonic oscillations of density. We point several qualitative effects due to the anharmonicity, although quantitatively they appear to be relatively small. We also find that, in most regions of the parameter space, with the exception of the case of a very large amplitude of density oscillations (i.e. 10% and above), nonlinear effects and anharmonicity have a small effect on the interplay of the nonleptonic and semileptonic processes in the bulk viscosity.Comment: 14 pages, 6 figures; v2: Appendix B is omitted, a few new discussions added and some new references adde

Variable turbulent convection as the cause of the Blazhko effect - testing the Stothers model

The amplitude and phase modulation observed in a significant fraction of the RR Lyrae variables - the Blazhko effect - represents a long-standing enigma in stellar pulsation theory. No satisfactory explanation for the Blazhko effect has been proposed so far. In this paper we focus on the Stothers (2006) idea, in which modulation is caused by changes in the structure of the outer convective zone, caused by a quasi-periodically changing magnetic field. However, up to this date no quantitative estimates were made to investigate whether such a mechanism can be operational and whether it is capable of reproducing the light variation we observe in Blazhko variables. We address the latter problem. We use a simplified model, in which the variation of turbulent convection is introduced into the non-linear hydrodynamic models in an ad hoc way, neglecting interaction with the magnetic field. We study the light curve variation through the modulation cycle and properties of the resulting frequency spectra. Our results are compared with Kepler observations of RR Lyr. We find that reproducing the light curve variation, as is observed in RR Lyr, requires a huge modulation of the mixing length, of the order of +/-50 per cent, on a relatively short time-scale of less than 40 days. Even then, we are not able to reproduce neither all the observed relations between modulation components present in the frequency spectrum, nor the relations between Fourier parameters describing the shape of the instantaneous light curves.Comment: 17 pages, 13 figures, accepted for publication in MNRAS; for associated animation, see http://homepage.univie.ac.at/radek.smolec/publications/KASC11a

Nonlinear Couplings Between r-modes of Rotating Neutron Stars

The r-modes of neutron stars can be driven unstable by gravitational radiation. While linear perturbation theory predicts the existence of this instability, linear theory can't provide any information about the nonlinear development of the instability. The subject of this paper is the weakly nonlinear regime of fluid dynamics. In the weakly nonlinear regime, the nonlinear fluid equations are approximated by an infinite set of oscillators which are coupled together so that terms quadratic in the mode amplitudes are kept in the equations of motion. In this paper, the coupling coefficients between the r-modes are computed. The stellar model assumed is a polytropic model where a source of buoyancy is included so that the Schwarzschild discriminant is nonzero. The properties of these coupling coefficients and the types of resonances possible are discussed in this paper. It is shown that no exact resonance involving the unstable $l=m=2$ r-mode occur and that only a small number of modes have a dimensionless coupling constant larger than unity. However, an infinite number of resonant mode triplets exist which couple indirectly to the unstable r-mode. All couplings in this paper involve the l>|m| r-modes which only exist if the star is slowly rotating. This work is complementary to that of Schenk et al (2002) who consider rapidly rotating stars which are neutral to convection.Comment: 21 pages, 1 figure, to appear in Ap

Nonlinear mode coupling in rotating stars and the r-mode instability in neutron stars

We develop the formalism required to study the nonlinear interaction of modes in rotating Newtonian stars in the weakly nonlinear regime. The formalism simplifies and extends previous treatments. At linear order, we elucidate and extend slightly a formalism due to Schutz, show how to decompose a general motion of a rotating star into a sum over modes, and obtain uncoupled equations of motion for the mode amplitudes under the influence of an external force. Nonlinear effects are added perturbatively via three-mode couplings. We describe a new, efficient way to compute the coupling coefficients, to zeroth order in the stellar rotation rate, using spin-weighted spherical harmonics. We apply this formalism to derive some properties of the coupling coefficients relevant to the nonlinear interactions of unstable r-modes in neutron stars, postponing numerical integrations of the coupled equations of motion to a later paper. From an astrophysical viewpoint, the most interesting result of this paper is that many couplings of r-modes to other rotational modes (modes with zero frequencies in the non-rotating limit) are small: either they vanish altogether because of various selection rules, or they vanish to lowest order in the angular velocity. In zero-buoyancy stars, the coupling of three r-modes is forbidden entirely and the coupling of two r-modes to one hybrid rotational mode vanishes to zeroth order in rotation frequency. In incompressible stars, the coupling of any three rotational modes vanishes to zeroth order in rotation frequency.Comment: 62 pages, no figures. Corrected error in computation of coupling coefficients, added new selection rule and an appendix on energy and angular momentum of mode

Mercury's Crustal Thickness Correlates With Lateral Variations in Mantle Melt Production

peer reviewe

Interior structure of terrestrial planets: Modeling Mars’ mantle andits electromagnetic, geodetic, and seismic properties

International audienceWe present a new procedure to describe the one-dimensional thermodynamical stateand mineralogy of any Earth-like planetary mantle, with Mars as an example. The modelparameters are directly related to expected results from a geophysical network mission, inthis case electromagnetic, geodetic, and seismological processed observationssupplemented with laboratory measurements. We describe the internal structure of theplanet in terms of a one-dimensional model depending on a set of eight parameters: for thecrust, the thickness and the mean density, for the mantle, the bulk volume fraction of iron,the olivine volume fraction, the pressure gradient, and the temperature profile, and for thecore, its mass and radius. Currently, available geophysical and geochemical knowledgeconstrains the range of the parameter values. In the present paper, we develop the forwardproblem and present the governing equations from which synthetic data are computedusing a set of parameter values. Among all Martian models fitting the currently availableknowledge, we select eight candidate models for which we compute synthetic networkscience data sets. The synergy between the three geophysical experiments ofelectromagnetic sounding, geodesy, and seismology is emphasized. The stochasticinversion of the synthetic data sets will be presented in a companion paper