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R. H. D. Townsend 《Monthly notices of the Royal Astronomical Society》2000,319(1):289-304
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. 相似文献
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. 相似文献
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Hideyuki Saio Norman H. Baker & Alfred Gautschy 《Monthly notices of the Royal Astronomical Society》1998,294(4):622-634
Properties of the so-called strange modes occurring in linear stability calculations of stellar models are discussed. The behaviour of these modes is compared for two different sets of stellar models, for very massive zero-age main-sequence stars and for luminous hydrogen-deficient stars, both with high luminosity-to-mass ratios. We have found that the peculiar behaviour of the frequencies of the strange modes with the change of a control parameter is caused by the pulsation amplitude of a particular eigenmode being strongly confined to the outer part of the envelope, around the density inversion zone. The frequency of a strange mode changes because the depth of the confinement zone changes with the control parameter. Weakly non-adiabatic strange modes tend to be overstable because the amplitude confinement quenches the effect of radiative damping. On the other hand, extremely non-adiabatic strange modes become overstable because the perturbation of radiation force (gradient of radiation pressure) provides a restoring force that can be out of phase with the density perturbation. We discuss this mechanism by using a plane-parallel two-zone model. 相似文献
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Margarida S. Cunha Douglas Gough 《Monthly notices of the Royal Astronomical Society》2000,319(4):1020-1038
We study the effect of a large-scale surface magnetic field on the non-radial acoustic modes of roAp stars. Special attention is given to the use of a variational principle which is used for determining the shifts in the frequencies with relative ease, enabling us to avoid having to calculate the perturbed eigenfunctions. With knowledge of the frequency shifts we then estimate the eigenfunctions in a simpler, albeit approximate way. The results indicate frequency shifts of the order of few μHz, which depend on the order, degree and azimuthal order of the mode. The loss of energy through Alfvén waves is also estimated from the imaginary parts of the frequency shifts. The results indicate that the loss is particularly high near specific frequencies. This might indicate the presence of a selection effect, which could make some modes more likely to be excited than others. However, our results do not explain why the modes observed appear always to be aligned with the axis of the magnetic field. Finally, the estimated perturbed eigenfunctions contain strong components of spherical harmonics that differ from those of the original unperturbed modes. 相似文献
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We summarize all the reported detections of, and upper limits to, the radio emission from persistent (i.e. non-transient) X-ray binaries. A striking result is a common mean observed radio luminosity from the black hole candidates (BHCs) in the low/hard X-ray state and the neutron star Z sources on the horizontal X-ray branch. This implies a common mean intrinsic radio luminosity to within a factor of 25 (or less, if there is significant Doppler boosting of the radio emission). Unless coincidental, these results imply a physical mechanism for jet formation that requires neither a black hole event horizon nor a neutron star surface. As a whole the populations of Atoll and X-ray pulsar systems are less luminous by factors of ≳5 and ≳10 at radio wavelengths than the BHCs and Z sources (while some Atoll sources have been detected, no high-field X-ray pulsar has ever been reliably detected as a radio source). We suggest that all of the persistent BHCs and the Z sources generate, at least sporadically, an outflow with physical dimensions 1012 cm; that is, significantly larger than the binary separations of most of the systems. We compare the physical conditions of accretion in each of the types of persistent X-ray binary and conclude that a relatively low (1010 G) magnetic field associated with the accreting object, and a high (0.1 Eddington) accretion rate and/or dramatic physical change in the accretion flow, are required for formation of a radio-emitting outflow or jet. 相似文献
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We investigate how the frequencies of gravity modes depend on the detailed properties of the chemical composition gradient that develops near the core of main‐sequence stars and, therefore, on the transport processes that are able to modify the μ profile in the central regions. We show that in main‐sequence models, similarly to the case of white dwarfs, the periods of high‐order gravity modes are accurately described by a uniform period spacing superposed to an oscillatory component. The periodicity and amplitude of such a component are related, respectively, to the location and sharpness of the μ gradient. We briefly discuss and interpret, by means of this simple approximation, the effect of turbulent mixing near the core on the periods of both high‐order and low‐order g modes, as well as of modes of mixed pressure‐gravity character. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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W. A. Dziembowski J. Daszy&#;ska-Daszkiewicz A. A. Pamyatnykh 《Monthly notices of the Royal Astronomical Society》2007,374(1):248-255
We use the traditional approximation to describe oscillations with frequencies comparable to the angular rotation rate. Validity of this approximation in application to main-sequence B stars is discussed. Numerical results regarding mode stability and visibility are presented for a model of the Be star HD 163868. For this object, Walker et al. detected a record number of mode frequencies using data from the small space telescope MOST . Our interpretation of these data differs from that of Walker et al. In particular, we interpret peaks in the lowest frequency range as retrograde g modes. We find instability in a large number of modes that remain undetectable because of unfavourable aspect and/or effect of cancellation. There is no clear preference to excitation of prograde modes. 相似文献
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T. Van Hoolst W. A. Dziembowski & S. D. Kawaler 《Monthly notices of the Royal Astronomical Society》1998,297(2):536-544
We study the possibility of the excitation of non-radial oscillations in classical pulsating stars. The stability of an RR Lyrae model is examined through non-adiabatic non-radial calculations. We also explore stability in the presence of non-linear coupling between radial and non-radial modes of nearly identical frequency. In our model, a large number of unstable low-degree (ℓ = 1,2) modes have frequencies in the vicinity of unstable radial mode frequencies. The growth rates of such modes, however, are considerably smaller than those of the radial modes. We also recover an earlier result that at higher degrees (ℓ = 6–12) there are modes trapped in the envelope with growth rates similar to those of radial modes. Subsequently, monomode radial pulsation of this model is considered. The destabilizing effect of the 1:1 resonance between the radial mode and nearby non-radial modes of low degrees is studied, with the assumption that the excited radial mode saturates the linear instability of all other modes. The instability depends on the radial mode amplitude, the frequency difference, the damping rate of the non-radial mode, and the strength of the non-linear coupling between the modes considered. At the pulsation amplitudes typical for RR Lyrae stars, the instability of the monomode radial pulsation and the concomitant resonant excitation of some non-radial oscillation modes is found to be very likely. 相似文献
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C. Karoff 《Monthly notices of the Royal Astronomical Society》2007,381(3):1001-1008
p-mode oscillations in solar-like stars are excited by the outer convection zone in these stars and reflected close to the surface. The p modes are trapped inside an acoustic cavity, but the modes only stay trapped up to a given frequency [known as the acoustic cut-off frequency (νac ) ] as modes with larger frequencies are generally not reflected at the surface. This means that modes with frequency larger than the acoustic cut-off frequency must be travelling waves. The high-frequency modes may provide information about the physics in the outer layers of the stars and the excitation source and are therefore highly interesting as it is the estimation of these two phenomena that cause some of the largest uncertainties when calculating stellar oscillations.
High-frequency modes have been detected in the Sun, in β Hydri and in α Cen A and α Cen B by smoothing the so-called echelle diagram and the large frequency separation as a function of frequency has been estimated. The large frequency separation has been compared with a simple model of the acoustic cavity which suggests that the reflectivity of the photosphere is larger at high frequency than predicted by standard models of the solar atmosphere and that the depth of the excitation source is larger than what has been estimated by other models and might depend on the order n and degree l of the modes. 相似文献
High-frequency modes have been detected in the Sun, in β Hydri and in α Cen A and α Cen B by smoothing the so-called echelle diagram and the large frequency separation as a function of frequency has been estimated. The large frequency separation has been compared with a simple model of the acoustic cavity which suggests that the reflectivity of the photosphere is larger at high frequency than predicted by standard models of the solar atmosphere and that the depth of the excitation source is larger than what has been estimated by other models and might depend on the order n and degree l of the modes. 相似文献
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Shin'ichirou Yoshida Yoshiharu Eriguchi 《Monthly notices of the Royal Astronomical Society》2001,322(2):389-396
By using the Cowling approximation, quasi-radial modes of rotating general relativistic stars are computed along equilibrium sequences from non-rotating to maximally rotating models. The eigenfrequencies of these modes are decreasing functions of the rotational frequency. The eigenfrequency curve of each mode as a function of the rotational frequency has discontinuities, which arise from the avoided crossing with other curves of axisymmetric modes. 相似文献
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José A. Font Harald Dimmelmeier Anshu Gupta Nikolaos Stergioulas 《Monthly notices of the Royal Astronomical Society》2001,325(4):1463-1470
Axisymmetric pulsations of rotating neutron stars can be excited in several scenarios, such as core collapse, crust- and core-quakes or binary mergers, and could become detectable in either gravitational waves or high-energy radiation. Here, we present a comprehensive study of all low-order axisymmetric modes of uniformly and rapidly rotating relativistic stars. Initial stationary configurations are appropriately perturbed and are numerically evolved using an axisymmetric, non-linear relativistic hydrodynamics code, assuming time-independence of the gravitational field (Cowling approximation). The simulations are performed using a high-resolution shock-capturing finite-difference scheme accurate enough to maintain the initial rotation law for a large number of rotational periods, even for stars at the mass-shedding limit. Through Fourier transforms of the time evolution of selected fluid variables, we compute the frequencies of quasi-radial and non-radial modes with spherical harmonic indices l =0 , 1, 2 and 3, for a sequence of rotating stars from the non-rotating limit to the mass-shedding limit. The frequencies of the axisymmetric modes are affected significantly by rotation only when the rotation rate exceeds about 50 per cent of the maximum allowed. As expected, at large rotation rates, apparent mode crossings between different modes appear. In addition to the above modes, several axisymmetric inertial modes are also excited in our numerical evolutions. 相似文献
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B. Haskell N. Andersson A. Passamonti 《Monthly notices of the Royal Astronomical Society》2009,397(3):1464-1485
We develop a new perturbative framework for studying the r modes of rotating superfluid neutron stars. Our analysis accounts for the centrifugal deformation of the star, and considers the two-fluid dynamics at linear order in the perturbed velocities. Our main focus is on a simple model system where the total density profile is that of an n = 1 polytrope. We derive a partially analytic solution for the superfluid analogue of the classical r mode. This solution is used to analyse the relevance of the vortex-mediated mutual friction damping, confirming that this dissipation mechanism is unlikely to suppress the gravitational-wave-driven instability in rapidly spinning superfluid neutron stars. Our calculation of the superfluid r modes is significantly simpler than previous approaches, because it decouples the r mode from all other inertial modes of the system. This leads to the results being clearer, but it also means that we cannot comment on the relevance of potential avoided crossings (and associated 'resonances') that may occur for particular parameter values. Our analysis of the mutual friction damping differs from previous studies in two important ways. First, we incorporate realistic pairing gaps which means that the regions of superfluidity in the star's core vary with temperature. Secondly, we allow the mutual friction parameters to take the whole range of permissible values rather than focusing on a particular mechanism. Thus, we consider not only the weak drag regime, but also the strong drag regime where the fluid dynamics are significantly different. 相似文献