Vortex lattice stability and phase coherence in three-dimensional rapidly rotating Bose condensates

We establish the general equations of motion for the modes of a vortex lattice in a rapidly rotating Bose-Einstein condensate in three dimensions, taking into account the elastic energy of the lattice and the vortex line bending energy. As in two dimensions, the vortex lattice supports Tkachenko and gapped sound modes. In contrast, in three dimensions the Tkachenko mode frequency at long wavelengths becomes linear in the wavevector for any propagation direction out of the transverse plane. We compute the correlation functions of the vortex displacements and the superfluid order parameter for a homogeneous Bose gas of bounded extent in the axial direction. At zero temperature the vortex displacement correlations are convergent at large separation, but at finite temperatures, they grow with separation. The growth of the vortex displacements should lead to observable melting of vortex lattices at higher temperatures and somewhat lower particle number and faster rotation than in current experiments. At zero temperature a system of large extent in the axial direction maintains long range order-parameter correlations for large separation, but at finite temperatures the correlations decay with separation.Comment: 10 pages, 2 figures, Changes include the addition of the particle density - vortex density coupling and the correct value of the shear modulu

Tkachenko modes of vortex lattices in rapidly rotating Bose-Einstein condensates

We calculate the in-plane modes of the vortex lattice in a rotating Bose condensate from the Thomas-Fermi to the mean-field quantum Hall regimes. The Tkachenko mode frequency goes from linear in the wavevector, $k$, for lattice rotational velocities, $\Omega$, much smaller than the lowest sound wave frequency in a finite system, to quadratic in $k$ in the opposite limit. The system also supports an inertial mode of frequency $\ge 2\Omega$. The calculated frequencies are in good agreement with recent observations of Tkachenko modes at JILA, and provide evidence for the decrease in the shear modulus of the vortex lattice at rapid rotation.Comment: 4 pages, 2 figure

Grid Search in Stellar Parameters: a software for spectrum analysis of single stars and binary systems

The currently operating space missions, as well as those that will be launched in the near future, (will) deliver high-quality data for millions of stellar objects. Since the majority of stellar astrophysical applications still (at least partly) rely on spectroscopic data, an efficient tool for the analysis of medium- to high-resolution spectroscopy is needed. We aim at developing an efficient software package for the analysis of medium- to high-resolution spectroscopy of single stars and those in binary systems. The major requirements are that the code has a high performance, represents the state-of-the-art analysis tool, and provides accurate determinations of atmospheric parameters and chemical compositions for different types of stars. We use the method of atmosphere models and spectrum synthesis, which is one of the most commonly used approaches for the analysis of stellar spectra. Our Grid Search in Stellar Parameters (GSSP) code makes use of the OpenMPI implementation, which makes it possible to run in parallel mode. The method is first tested on the simulated data and is then applied to the spectra of real stellar objects. The majority of test runs on the simulated data were successful in the sense that we could recover the initially assumed sets of atmospheric parameters. We experimentally find the limits in signal-to-noise ratios of the input spectra, below which the final set of parameters gets significantly affected by the noise. Application of the GSSP package to the spectra of three Kepler stars, KIC11285625, KIC6352430, and KIC4931738, was also largely successful. We found an overall agreement of the final sets of the fundamental parameters with the original studies. For KIC6352430, we found that dependence of the light dilution factor on wavelength cannot be ignored, as it has significant impact on the determination of the atmospheric parameters of this binary system.Comment: 19 pages, 6 figures, 4 tables, 2 appendices one of which includes detailed description of input and output files. Accepted for publication in Astronomy & Astrophysi

Probing high-mass stellar evolutionary models with binary stars

Mass discrepancy is one of the problems that is pending a solution in (massive) binary star research field. The problem is often solved by introducing an additional near core mixing into evolutionary models, which brings theoretical masses of individual stellar components into an agreement with the dynamical ones. In the present study, we perform a detailed analysis of two massive binary systems, V380 Cyg and Sigma Sco, to provide an independent, asteroseismic measurement of the overshoot parameter, and to test state-of-the-art stellar evolution models.Comment: 5 pages, 1 figure, 3 tables; proceedings of the IAU Symposium 307 held in Geneva in June 201

Vortex lattices in rapidly rotating Bose-Einstein condensates: modes and correlation functions

After delineating the physical regimes which vortex lattices encounter in rotating Bose-Einstein condensates as the rotation rate, $\Omega$, increases, we derive the normal modes of the vortex lattice in two dimensions at zero temperature. Taking into account effects of the finite compressibility, we find an inertial mode of frequency $\ge 2\Omega$, and a primarily transverse Tkachenko mode, whose frequency goes from being linear in the wave vector in the slowly rotating regime, where $\Omega$ is small compared with the lowest compressional mode frequency, to quadratic in the wave vector in the opposite limit. We calculate the correlation functions of vortex displacements and phase, density and superfluid velocities, and find that the zero-point excitations of the soft quadratic Tkachenko modes lead in a large system to a loss of long range phase correlations, growing logarithmically with distance, and hence lead to a fragmented state at zero temperature. The vortex positional ordering is preserved at zero temperature, but the thermally excited Tkachenko modes cause the relative positional fluctuations to grow logarithmically with separation at finite temperature. The superfluid density, defined in terms of the transverse velocity autocorrelation function, vanishes at all temperatures. Finally we construct the long wavelength single particle Green's function in the rotating system and calculate the condensate depletion as a function of temperature.Comment: 11 pages Latex, no figure

Tkachenko modes as sources of quasiperiodic pulsar spin variations

We study the long wavelength shear modes (Tkachenko waves) of triangular lattices of singly quantized vortices in neutron star interiors taking into account the mutual friction between the superfluid and the normal fluid and the shear viscosity of the normal fluid. The set of Tkachenko modes that propagate in the plane orthogonal to the spin vector are weakly damped if the coupling between the superfluid and normal fluid is small. In strong coupling, their oscillation frequencies are lower and are undamped for small and moderate shear viscosities. The periods of these modes are consistent with the observed ~100-1000 day variations in spin of PSR 1828-11.Comment: 7 pages, 3 figures, uses RevTex, v2: added discussion/references, matches published versio