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

Nonadiabatic resonant dynamic tides and orbital evolution in close binaries

This investigation is devoted to the effects of nonadiabatic resonant dynamic tides generated in a uniformly rotating stellar component of a close binary. The companion is considered to move in a fixed Keplerian orbit, and the effects of the centrifugal force and the Coriolis force are neglected. Semi-analytical solutions for the linear, nonadiabatic resonant dynamic tides are derived by means of a two-time variable expansion procedure. The solution at the lowest order of approximation consists of the resonantly excited oscillation mode and displays a phase shift with respect to the tide-generating potential. Expressions are established for the secular variations of the semi-major axis, the orbital eccentricity, and the star's angular velocity of rotation caused by the phase shift. The orders of magnitude of these secular variations are considerably larger than those derived earlier by Zahn (1977) for the limiting case of dynamic tides with small frequencies. For a 5 solar mass ZAMS star, an orbital eccentricity e = 0.5, and orbital periods in the range from 2 to 5 days, numerous resonances of dynamic tides with second-degree lower-order gravity modes are seen to induce secular variations of the semi-major axis, the orbital eccentricity, and the star's angular velocity of rotation with time scales shorter than the star's nuclear life time.Comment: accepted for publication in A&A, 13 page

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

Simulated recovery of Europa's global shape and tidal Love numbers from altimetry and radio tracking during a dedicated flyby tour

The fundamental scientific objectives for future spacecraft exploration of Jupiter's moon Europa include confirmation of the existence of subsurface ocean beneath the surface ice shell and constraints on the physical properties of the ocean. Here we conduct a comprehensive simulation of a multiple-flyby mission. We demonstrate that radio tracking data can provide an estimate of the gravitational tidal Love number k2 with sufficient precision to confirm the presence of a liquid layer. We further show that a capable long-range laser altimeter can improve determination of the spacecraft position, improve the k2 determination (2 (3-4% error), which is directly related to the amplitude of the surface tidal deformation. These measurements, in addition to the global shape accurately constrained by the long altimetric profiles, can yield further constraints on the interior structure of Europa. Key Points A multiple-flyby mission to Europa can recover key geophysical parameters Laser altimetry can uniquely and accurately recover the global shape of Europa Laser altimetry enables the recovery of h2 to constrain the ice shell thicknes

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