Oscillations of rapidly rotating stratified neutron stars

We use time evolutions of the linear perturbation equations to study the oscillations of rapidly rotating neutrons stars. Our models account for the buoyancy due to composition gradients and we study, for the first time, the nature of the resultant g modes in a fast spinning star. We provide detailed comparisons of non-stratified and stratified models. This leads to an improved understanding of the relationship between the inertial modes of a non-stratified star and the g modes of a stratified system. In particular, we demonstrate that each g mode becomes rotation dominated, i.e. approaches a particular inertial mode, as the rotation rate of the star is increased. We also discuss issues relating to the gravitational wave driven instability of the various classes of oscillation modes.     

The Detection of Multimodal Oscillations on alpha Ursae Majoris

We have used the star camera on the Wide-Field Infrared Explorer satellite to observe the K0 III star alpha UMa, and we report the apparent detection of 10 oscillation modes. The lowest frequency mode is at 1.82 μHz, and it appears to be the fundamental mode. The mean spacing between the mode frequencies is 2.94 μHz, which implies that all detected modes are radial. The mode frequencies are consistent with the physical parameters of a K0 III star, if we assume that only radial modes are excited. Mode amplitudes are 100-400 μmag, which is consistent with the scaling relation of Kjeldsen & Bedding.     

Long-term variations in the β Cephei stars 16 (EN) Lac and ν Eri

We present results of an investigation of the long-term variations of the amplitudes of the three strongest modes of 16 (EN) Lac and of the period of the strongest mode of ν Eri. We show that in the case of the first star there are feasible explanations of the observed variations. The explanations involve non-linear interaction between pulsation modes (the first two observed modes) and beating between two non-interacting modes of constant amplitudes (the third observed mode). In the case of the second star, however, we can only indicate the difficulty of accounting for the long-term period variation.     

Pulsations of the B[e]-type component in the CI camelopardalis system

CI Cam is a well-known B[e]-type star and an X-ray transient, which underwent a powerful outburst in all parts of electromagnetic spectrum in 1998. An extensive V-band photometric monitoring revealed that rapid variability of CI Cam on the time scale of several hours is due to the pulsations of the B4 III–V type component. High-precision CCD photometry of the star was performed with the 50-cm Maksutov (meniscus) telescope of the Crimean station of the Sternberg Astronomical Institute of Moscow State University in December 2006 during the quiescent state of the star. The data are analyzed using the methods of discrete Fourier transform and by modeling of the light curve. The amplitude spectrum of the star is dominated by two peaks corresponding to the periods of 0.41521 and 0.26647 days with the period ratio close to 3:2. At least two pulsation modes are excited and the star exhibits signs of the resonance between modes.     

The magnetohydrodynamics model of twin kilohertz quasi-periodic oscillations in low-mass X-ray binaries

We suggest an explanation for the twin kilohertz quasi-periodic oscillations (kHz QPOs) in low-mass X-ray binaries (LMXBs) based on magnetohydrodynamics (MHD) oscillation modes in neutron star magnetospheres. Including the effect of the neutron star spin, we derive several MHD wave modes by solving the dispersion equations, and propose that the coupling of the two resonant MHD modes may lead to the twin kHz QPOs. This model naturally relates the upper, lower kHz QPO frequencies with the spin frequencies of the neutron stars, and can well account for the measured data of six LMXBs.     

The pulsating DA white dwarf star EC 14012−1446: results from four epochs of time-resolved photometry

The pulsating DA white dwarfs are the coolest degenerate stars that undergo self-driven oscillations. Understanding their interior structure will help us to understand the previous evolution of the star. To this end, we report the analysis of more than 200 h of time-resolved CCD photometry of the pulsating DA white dwarf star EC 14012−1446 acquired during four observing epochs in three different years, including a coordinated three-site campaign. A total of 19 independent frequencies in the star's light variations together with 148 combination signals up to fifth order could be detected. We are unable to obtain the period spacing of the normal modes and therefore a mass estimate of the star, but we infer a fairly short rotation period of  0.61 ±0.03 d  , assuming the rotationally split modes are  ℓ= 1  . The pulsation modes of the star undergo amplitude and frequency variations, in the sense that modes with higher radial overtone show more pronounced variability and that amplitude changes are always accompanied by frequency variations. Most of the second-order combination frequencies detected have amplitudes that are a function of their parent mode amplitudes, but we found a few cases of possible resonantly excited modes. We point out the complications in the analysis and interpretation of data sets of pulsating white dwarfs that are affected by combination frequencies of the form   f _A + f _B − f _C   intruding into the frequency range of the independent modes.     

Radial velocity variations of the pulsating subdwarf B star PG 1605+072

We present an analysis of high-speed spectroscopy of the pulsating subdwarf B star PG 1605+072. Periodic radial motions are detected at frequencies similar to those reported for photometric variations in the star, with amplitudes of up to 6 km s⁻¹. Differences between relative strengths for given frequency peaks for our velocity data and previously measured photometry are probably a result of shifting of power between modes over time. Small differences in the detected frequencies may also indicate mode-shifting. We report the detection of line-shape variations using the moments of the cross-correlation function profiles. It may be possible to use the moments to identify the pulsation modes of the star.     

The inverse problem for pulsating neutron stars: a 'fingerprint analysis' for the supranuclear equation of state

We study the problem of detecting, and inferring astrophysical information from, gravitational waves from a pulsating neutron star. We show that the fluid f and p modes, as well as the gravitational-wave w modes, may be detectable from sources in our own Galaxy, and investigate how accurately the frequencies and damping rates of these modes can be inferred from a noisy gravitational-wave data stream. Based on the conclusions of this discussion we propose a strategy for revealing the supranuclear equation of state using the neutron star fingerprints: the observed frequencies of an f and a p mode. We also discuss how well the source can be located in the sky using observations with several detectors.     

Surface trapping and leakage of low-frequency g modes in rotating early-type stars – II. Global analysis

A global analysis of the surface trapping of low-frequency non-radial g modes in rotating early-type stars is undertaken within the Cowling, adiabatic and traditional approximations. The dimensionless pulsation equations governing these modes are reviewed, and the boundary conditions necessary for solution of the equations are considered; in particular, an outer mechanical boundary condition, which does not enforce complete wave trapping at the stellar surface, is derived and discussed in detail. The pulsation equations are solved for a 7-M_⊙ model star over a range of rotation rates, using a numerical approach.
The results of the calculations confirm the findings of the preceding paper in the series: modes with eigenfrequencies below a cut-off cannot be fully trapped within the star, and exhibit leakage in the form of outwardly propagating waves at the surface. The damping rates resulting from leakage are calculated for such 'virtual' modes, and found to be appreciably larger than typical growth rates associated with opacity-driven pulsation. Furthermore, it is demonstrated that the surface perturbations generated by virtual modes are significantly changed from those caused by fully trapped modes; the latter result suggests differences in the line-profile variations exhibited by these two types of mode.
The findings are discussed in the context of the 53 Per, SPB and pulsating Be classes of variable star. Whilst wave leakage will probably not occur for overstable g modes in the 53 Per and slowly rotating SPB stars, the adoption of the new outer mechanical boundary condition may still affect the pulsational stability of these systems. Wave leakage for overstable modes remains a possibility in Be stars and the more rapidly rotating SPB stars.     

The magnetosphere of oscillating neutron stars in general relativity

Just as a rotating magnetized neutron star has material pulled away from its surface to populate a magnetosphere, a similar process can occur as a result of neutron-star pulsations rather than rotation. This is of interest in connection with the overall study of neutron star oscillation modes but with a particular focus on the situation for magnetars. Following a previous Newtonian analysis of the production of a force-free magnetosphere in this way Timokhin et al., we present here a corresponding general-relativistic analysis. We give a derivation of the general relativistic Maxwell equations for small-amplitude arbitrary oscillations of a non-rotating neutron star with a generic magnetic field and show that these can be solved analytically under the assumption of low current density in the magnetosphere. We apply our formalism to toroidal oscillations of a neutron star with a dipole magnetic field and find that the low current density approximation is valid for at least half of the oscillation modes, similarly to the Newtonian case. Using an improved formula for the determination of the last closed field line, we calculate the energy losses resulting from toroidal stellar oscillations for all of the modes for which the size of the polar cap is small. We find that general relativistic effects lead to shrinking of the size of the polar cap and an increase in the energy density of the outflowing plasma. These effects act in opposite directions but the net result is that the energy loss from the neutron star is significantly smaller than suggested by the Newtonian treatment.     

The imprint of the equation of state on the axial w-modes of oscillating neutron stars

We discuss the dependence of the pulsation frequencies of the axial quasi-normal modes of a non-rotating neutron star upon the equation of state describing the star interior. The continued fraction method has been used to compute the complex frequencies for a set of equations of state based on different physical assumptions and spanning a wide range of stiffness. The numerical results show that axial gravitational waves carry relevant information on both the structure of neutron star matter and the nature of the hadronic interactions.     

A toy model for global magnetar oscillation

The presence of a magnetic field in a neutron star interior results in a dynamical coupling between the fluid core and the elastic crust. We consider a simple toy-model where this coupling is taken into account and compute the system’s mode oscillations. Our results suggest that the notion of pure torsional crust modes is not useful for the coupled system, instead all modes excite Alfvén waves in the core. However, we also show that among a rich spectrum of global MHD modes the ones most likely to be excited by a fractured crust are those for which the crust and the core oscillate in concert. For our simple model, the frequencies of these modes are similar to the “pure crustal” frequencies. We advocate the significant implications of these results for the attempted theoretical interpretation of QPOs during magnetar flares in terms of neutron star oscillations.      

Another look at theR-modes

Possible oscillation modes for a rotating star are listed. The only assumption made is that oscillations are adiabatic and that rotation is uniform. It is found that two modes not present for non-rotating stars are possible. Oscillation frequencies of these modes are rather different from those given in the literature for so-calledr-modes.     

Alfvén node-free vibrations of white dwarf in the model of solid star with toroidal magnetic field

In the context of white dwarf asteroseismology, we investigate the vibrational properties of a non-convective solid star with an axisymmetric purely toroidal intrinsic magnetic field of two different shapes. Focus is laid on the regime of node-free global Lorentz-force-driven vibrations about the symmetry axis at which material displacements have one and the same form as those for nodeless spheroidal and torsional vibrations restored by Hooke’s force of elastic shear stresses. Particular attention is given to the even-parity poloidal Alfvén modes whose frequency spectra are computed in analytic form, showing how the purely toroidal magnetic fields completely buried beneath the star surface can manifest itself in seismic vibrations of non-magnetic white dwarfs. The spectral formulae obtained are discussed in juxtaposition with those for Alfvén modes in the solid star model with the poloidal, homogeneous internal and dipolar external, magnetic field whose inferences are relevant to Alfvén vibrations in magnetic white dwarfs.     

Towards gravitational wave asteroseismology

We present new results for pulsating neutron stars. We have calculated the eigenfrequencies of the modes that one would expect to be the most important gravitational wave sources: the fundamental fluid f mode, the first pressure p mode and the first gravitational wave w mode, for twelve realistic equations of state. From these numerical data we have inferred a set of 'empirical relations' between the mode frequencies and the parameters of the star (the radius R and the mass M ). Some of these relations prove to be surprisingly robust, and we show how they can be used to extract the details of the star from observed modes. The results indicate that, should the various pulsation modes be detected by the new generation of gravitational wave detectors that come online in a few years, the mass and the radius of neutron stars can be deduced with errors no larger than a few per cent.     

Photometry and the determination of oscillation modes for high amplitude Delta Scuti (HADS) variable GSC 1566-2802

CCD photometry observation of a newly discovered, high amplitude Delta Scuti star GSC 1566-2802, with a visible filter, is presented. The observations were carried out at Alborz Observatory located in Mahdasht, Karaj, Iran.The main goal of this project was to update our knowledge of the periodic variations of the target star. This paper covers three analyses, first calculating a new ephemeris and plotting a new light curve based on 19 times of maxima; then a Fourier analysis of the observed data points which results in determining probable oscillation modes, as well as computing its physical parameters which guide us to its harmonics and pulsation modes.     

Star formation regions as galactic dissipative structures

The theory of dissipative structures, applied to star formation systems, provides a conceptual framework for the study of the behaviour and evolution of these systems. As shown by an analysis of a model star formation process system, prolonged stationary star formation in localized areas and repetitive bursting star formation events can be understood as different behavioural modes of galactic dissipative structures. Young stellar associations with theirHII regions and molecular clouds are manifestations of the ordered distribution of matter participating in the star formation processes. A self-organization with the appearance of ordered structures is, in general, to be expected in nonequilibrium systems in which nonlinear processes occur. However, lacking a thermodynamic theory that can be applied to self-gravitating systems, the behaviour of star-forming regions can only be studied by model calculations simulating the process system within the region.     

Crustal oscillations of slowly rotating relativistic stars

We study low-amplitude crustal oscillations of slowly rotating relativistic stars consisting of a central fluid core and an outer thin solid crust. We estimate the effect of rotation on the torsional toroidal modes and on the interfacial and shear spheroidal modes. The results compared against the Newtonian ones for wide range of neutron star models and equations of state.     

Eight new δ Scuti stars

HD 23194, a member of the Pleiades, was found to pulsate with a period of about 30 min. The literature on the star is reviewed, and it is concluded that it may be a marginal Am star in a binary system. HD 95321 is an evolved Am ( ρ Puppis) star with a 5.1-h periodicity. Mode identification of its pulsation, based on multicolour photometry, suggests that the oscillation is probably non-radial with ℓ=2. We also report on the discovery of six other new δ Scuti stars, some of which may be pulsating in gravity modes.     

Comparison of the large-scale clustering in the APM and the EDSGC galaxy surveys

We present the results of a numerical study of the fluid f, p and the gravitational w modes for increasingly relativistic non-rotating polytropes. The results for f and w modes are in good agreement with previous data for uniform density stars, which supports an understanding of the nature of the gravitational wave modes based on the uniform density data. We show that the p modes can become extremely long-lived for some relativistic stars. This effect is attributed to the change in the perturbed density distribution as the star becomes more compact.