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

Vortex states of rapidly rotating dilute Bose-Einstein condensates

We show that, in the Thomas-Fermi regime, the cores of vortices in rotating dilute Bose-Einstein condensates adjust in radius as the rotation velocity, $\Omega$, grows, thus precluding a phase transition associated with core overlap at high vortex density. In both a harmonic trap and a rotating hard-walled bucket, the core size approaches a limiting fraction of the intervortex spacing. At large rotation speeds, a system confined in a bucket develops, within Thomas-Fermi, a hole along the rotation axis, and eventually makes a transition to a giant vortex state with all the vorticity contained in the hole.Comment: 4 pages, 2 figures, RevTex4. Version as published; discussion extended, some references added and update

Modelling of the B-type binaries CW Cep and U Oph: A critical view on dynamical masses, core boundary mixing, and core mass

Context: Intermediate-Mass stars are often overlooked as they are not supernova progenitors but still host convective cores and complex atmospheres which require computationally expensive treatment. Due to this, there is a general lack of such stars modelled by state of the art stellar structure and evolution codes. Aims: This paper aims to use high-quality spectroscopy to update the dynamically obtained stellar parameters and produce a new evolutionary assessment of the bright B0.5+B0.5 and B5V+B5V binary systems CW Cep and U Oph. Methods: We use new spectroscopy obtained with the Hermes spectrograph to revisit the photometric binary solution of the two systems. The updated mass ratio and effective temperatures are incorporated to obtain new dynamical masses for the primary and secondary. With these, we perform isochrone-cloud based evolutionary modelling to investigate the core properties of these stars. Results: We report the first abundances for CW Cep and U Oph as well as report an updated dynamical solution for both systems. We find that we cannot uniquely constrain the amount of core boundary mixing in any of the stars we consider. Instead, we report their core masses and compare our results to previous studies. Conclusions: We find that the per-cent level precision on fundamental stellar quantities are accompanied with core mass estimates to between ~ 5-15%. We find that differences in analysis techniques can lead to substantially different evolutionary modeComment: 15 pages, 7 figures, two appendices with 4 figures each. Accepted for publication in Astronomy & Astrophysic

Pinning and collective modes of a vortex lattice in a Bose-Einstein condensate

We consider the ground state of vortices in a rotating Bose-Einstein condensate that is loaded in a corotating two-dimensional optical lattice. Due to the competition between vortex interactions and their potential energy, the vortices arrange themselves in various patterns, depending on the strength of the optical potential and the vortex density. We outline a method to determine the phase diagram for arbitrary vortex filling factor. Using this method, we discuss several filling factors explicitly. For increasing strength of the optical lattice, the system exhibits a transition from the unpinned hexagonal lattice to a lattice structure where all the vortices are pinned by the optical lattice. The geometry of this fully pinned vortex lattice depends on the filling factor and is either square or triangular. For some filling factors there is an intermediate half-pinned phase where only half of the vortices is pinned. We also consider the case of a two-component Bose-Einstein condensate, where the possible coexistence of the above-mentioned phases further enriches the phase diagram. In addition, we calculate the dispersion of the low-lying collective modes of the vortex lattice and find that, depending on the structure of the ground state, they can be gapped or gapless. Moreover, in the half-pinned and fully pinned phases, the collective mode dispersion is anisotropic. Possible experiments to probe the collective mode spectrum, and in particular the gap, are suggested.Comment: 29 pages, 4 figures, changes in section

Giant Vortex Lattice Deformations in Rapidly Rotating Bose-Einstein Condensates

We have performed numerical simulations of giant vortex structures in rapidly rotating Bose-Einstein condensates within the Gross-Pitaevskii formalism. We reproduce the qualitative features, such as oscillation of the giant vortex core area, formation of toroidal density hole, and the precession of giant vortices, observed in the recent experiment [Engels \emph{et.al.}, Phys. Rev. Lett. {\bf 90}, 170405 (2003)]. We provide a mechanism which quantitatively explains the observed core oscillation phenomenon. We demonstrate the clear distinction between the mechanism of atom removal and a repulsive pinning potential in creating giant vortices. In addition, we have been able to simulate the transverse Tkachenko vortex lattice vibrations.Comment: 5 pages, 6 figures; revised description of core oscillation, new subfigur

Spectrum Analysis of Bright Kepler late B- to early F- Stars

The Kepler satellite mission delivers single band-pass light curves of a huge number of stars observed in the Cygnus-Lyra region opening a new window for asteroseismology. In order to accomplish one of the preconditions for the asteroseismic modelling of the stars, we aim to derive fundamental parameters and individual abundances for a sample of 18 Gamma Dor (GD)/Delta Sct (DSct) and 8 SPB/beta Cep candidate stars in the Kepler satellite field of view. We use the spectral synthesis method to model newly obtained, high-resolution spectra of 26 stars in order to derive their fundamental parameters and individual abundances. The stars are then placed into the log(Teff)-log(g) diagram and the obtained spectroscopic classification is compared to the existing photometric one. For hot stars, the KIC temperatures appear to be systematically underestimated, in agreement with previous findings. We also find that the temperatures derived from our spectra agree reasonably well with those derived from the SED fitting. According to their position in the log(Teff)-log(g) diagram, two stars are expected GD stars, four stars are expected DSct stars, and four stars are possibly DSct stars at the blue edge of the instability strip. Two stars are confirmed SPB variables, and one star falls into the SPB instability region but its parameters might be biased by binarity. Two of the four stars that fall into the DSct instability region show GD-type oscillation in their light curves implying that GD-like oscillations are much more common among the DSct stars than is theoretically expected. Moreover, one of the stars located at the hot border of the DSct instability strip is classified as DSct-GD hybrid pulsator from its light curve analysis. Given that these findings are fully consistent with recent investigations, we conclude that a revision of the GD and DSct instability strips is essential.Comment: 14 pages, 14 figures, 6 tables; accepted for publication in MNRA

Vortex distribution in the Lowest Landau Level

We study the vortex distribution of the wave functions minimizing the Gross Pitaevskii energy for a fast rotating condensate in the Lowest Landau Level (LLL): we prove that the minimizer cannot have a finite number of zeroes thus the lattice is infinite, but not uniform. This uses the explicit expression of the projector onto the LLL. We also show that any slow varying envelope function can be approximated in the LLL by distorting the lattice. This is used in particular to approximate the inverted parabola and understand the role of ``invisible'' vortices: the distortion of the lattice is very small in the Thomas Fermi region but quite large outside, where the "invisible" vortices lie.Comment: 4 pages, 1 figur

Two-component Bose-Einstein Condensates with Large Number of Vortices

We consider the condensate wavefunction of a rapidly rotating two-component Bose gas with an equal number of particles in each component. If the interactions between like and unlike species are very similar (as occurs for two hyperfine states of $^{87}$Rb or $^{23}$Na) we find that the two components contain identical rectangular vortex lattices, where the unit cell has an aspect ratio of $\sqrt{3}$, and one lattice is displaced to the center of the unit cell of the other. Our results are based on an exact evaluation of the vortex lattice energy in the large angular momentum (or quantum Hall) regime.Comment: 4 pages, 2 figures, RevTe