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1.
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2.
We study torsional Alfvén oscillations of magnetars, that is neutron stars with a strong magnetic field. We consider the poloidal and toroidal components of the magnetic field and a wide range of equilibrium stellar models. We use a new coordinate system  ( X , Y )  , where     and     and a 1 is the radial component of the magnetic field. In this coordinate system, the one+two-dimensional evolution equation describing the quasi-periodic oscillations (QPOs), see Sotani et al., is reduced to a one+one-dimensional equation where the perturbations propagate only along the y -axis. We solve the one+one-dimensional equation for different boundary conditions and the open magnetic field lines, that is magnetic field lines that reach the surface and there match up with the exterior dipole magnetic field as well as closed magnetic lines, i.e. magnetic lines that never reach the stellar surface. For the open field lines, we find two families of QPO frequencies: a family of 'lower' QPO frequencies which is located near the x -axis and a family of 'upper' frequencies located near the y -axis. According to Levin, the fundamental frequencies of these two families can be interpreted as the turning point of the continuous spectrum. We find that the upper frequencies are multiples of the lower ones by a constant equalling  2 n + 1  . For the closed lines, the corresponding factor is   n + 1  . By using these relations, we can explain both the lower and the higher observed frequencies in SGR 1806−20 and SGR 1900+14.  相似文献   

3.
We investigate a model for the excitation of high-order oscillations in roAp stars. In this model we assume that the strong concentration of magnetic field about the magnetic poles is enough to suppress convection. Thus the model considered is composed of two polar regions, in which convection is presumed to be suppressed totally, and an equatorial region, where the convection is unaffected. This model is generated by building pairs of locally spherically symmetrical equilibria to represent the polar and equatorial regions of the star, which are patched together below the base of the convection zone. Gravitational settling of heavy elements is taken into account by choosing appropriate chemical composition profiles for both the polar and equatorial regions. Our results indicate that the composite model is unstable against axisymmetric non-radial high-order modes of pulsation that are aligned with the magnetic poles. The oscillations are excited by the κ mechanism acting principally in the hydrogen ionization zones of the polar regions. The effect of the lateral inhomogeneity on the second frequency differences is also investigated; we find that the perturbation to them by the inhomogeneity is of the same order as the second differences themselves, thereby hindering potential attempts to use such differences to identify the degrees of the modes in a straightforward way.  相似文献   

4.
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   

5.
Strong magnetic fields in relativistic stars can be a cause of crust fracturing, resulting in the excitation of global torsional oscillations. Such oscillations could become observable in gravitational waves or in high-energy radiation, thus becoming a tool for probing the equation of state of relativistic stars. As the eigenfrequency of torsional oscillation modes is affected by the presence of a strong magnetic field, we study torsional modes in magnetized relativistic stars. We derive the linearized perturbation equations that govern torsional oscillations coupled to the oscillations of a magnetic field, when variations in the metric are neglected (Cowling approximation). The oscillations are described by a single two-dimensional wave equation, which can be solved as a boundary-value problem to obtain eigenfrequencies. We find that, in the non-magnetized case, typical oscillation periods of the fundamental     torsional modes can be nearly a factor of 2 larger for relativistic stars than previously computed in the Newtonian limit. For magnetized stars, we show that the influence of the magnetic field is highly dependent on the assumed magnetic field configuration, and simple estimates obtained previously in the literature cannot be used for identifying normal modes observationally.  相似文献   

6.
Rapidly oscillating Ap stars constitute a unique class of pulsators with which to study non-radial oscillations under some — even for stars — unusual physical conditions. These stars are chemically peculiar, they have strong magnetic fields and they often pulsate in several high-order acoustic modes simultaneously. We discuss here an excitation mechanism for short-period oscillation modes based on the classical κ mechanism. We particularly stress the conditions that must be fulfilled for successful driving. Specifically, we discuss the roles of the chemical peculiarity and strong magnetic field on the oscillation modes and what separates these pulsators from δ Scuti and Am-type stars.  相似文献   

7.
We compute the continuous part of the ideal-magnetohydrodynamic (ideal-MHD) frequency spectrum of a polar mountain produced by magnetic burial on an accreting neutron star. Applying the formalism developed by Hellsten & Spies, extended to include gravity, we solve the singular eigenvalue problem subject to line-tying boundary conditions. This spectrum divides into an Alfvén part and a cusp part. The eigenfunctions are chirped and anharmonic with an exponential envelope, and the eigenfrequencies cover the whole spectrum above a minimum ωlow. For equilibria with accreted mass  1.2 × 10−6≲ M a/M⊙≲ 1.7 × 10−4  and surface magnetic fields  1011≲ B */G ≲ 1013, ωlow  is approximately independent of   B *  , and increases with M a. The results are consistent with the Alfvén spectrum excited in numerical simulations with the zeus-mp solver. The spectrum is modified substantially by the Coriolis force in neutron stars spinning faster than ∼100 Hz. The implications for gravitational-wave searches for low-mass X-ray binaries are considered briefly.  相似文献   

8.
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.  相似文献   

9.
Cool stars at giant and supergiant evolutionary phases present low-velocity and high-density winds, responsible for the observed high mass-loss rates. Although presenting high luminosities, radiation pressure on dust particles is not sufficient to explain the wind acceleration process. Among the possible solutions to this still unsolved problem, Alfvén waves are, probably, the most interesting for their high efficiency in transfering energy and momentum to the wind. Typically, models of Alfvén wave driven winds result in high-velocity winds if they are not highly damped. In this work, we determine self-consistently the magnetic field geometry and solve the momentum, energy and mass conservation equations, to demonstrate that even a low-damped Alfvén wave flux is able to reproduce the low-velocity wind. We show that the magnetic flux tubes expand with a super-radial factor of S > 30 near the stellar surface, larger than that used in previous semi-empirical models. The rapid expansion results in a strong spatial dilution of the wave flux. We obtained the wind parameter profiles for a typical supergiant star of  16 M⊙  . The wind is accelerated in a narrow region, coincident with the region of high divergence of the magnetic field lines, up to 100 km s−1. For the temperature, we obtained a slight decrease near the surface for low-damped waves, because the wave heating mechanism is less effective than the radiative losses. The peak temperature occurs at   r ≃ 1.5  r 0  reaching 6000 K. Propagating outwards, the wind cools down mainly due to adiabatic expansion.  相似文献   

10.
The theory of polar magnetic burial in accreting neutron stars predicts that a mountain of accreted material accumulates at the magnetic poles of the star, and that, as the mountain spreads equatorward, it is confined by, and compresses, the equatorial magnetic field. Here, we extend previous, axisymmetric, Grad–Shafranov calculations of the hydromagnetic structure of a magnetic mountain up to accreted masses as high as   M a= 6 × 10−4 M⊙  , by importing the output from previous calculations (which were limited by numerical problems and the formation of closed bubbles to   M a < 10−4 M⊙  ) into the time-dependent, ideal-magnetohydrodynamic code zeus-3d and loading additional mass on to the star dynamically. The rise of buoyant magnetic bubbles through the accreted layer is observed in these experiments. We also investigate the stability of the resulting hydromagnetic equilibria by perturbing them in zeus-3d . Surprisingly, it is observed that the equilibria are marginally stable for all   M a≤ 6 × 10−4 M⊙  ; the mountain oscillates persistently when perturbed, in a combination of Alfvén and acoustic modes, without appreciable damping or growth, and is therefore not disrupted (apart from a transient Parker instability initially, which expels <1 per cent of the mass and magnetic flux).  相似文献   

11.
The frequency of the sixth mode observed in HR 1217 cannot currently be understood in the light of the asymptotic theory for high-frequency acoustic modes, valid for adiabatic pulsations in spherically symmetric stars. Deviations from spherical symmetry will change the frequency of the observed oscillations away from the frequencies predicted by the asymptotic theory. Among other things, the presence of a magnetic field in the star will introduce such deviations from spherical symmetry. In the present work we inspect the effect of the magnetic field on the oscillations of HR 1217. Although we model HR 1217 in a rather simplified manner, we believe, as argued in the text, that the essence of the conclusions would not be modified if a more sophisticated model were to be used instead. The results show that the frequency of the sixth mode observed in HR 1217 might be understood if the effect of the magnetic field on the frequencies of the oscillations is fully taken into account. Moreover, we interpret the sixth frequency as a mode of even degree, and explain the absence from the observations of an intermediate l =1 , m =0 mode as the result of large energy losses associated with the coupling of the latter with Alfvénic waves, in the strongly magnetized outer layers of the star. Finally, we show how, in the light of this explanation, the frequency of the sixth mode might be used in order to put constraints on the parameters characterizing the star.  相似文献   

12.
We present XMM–Newton observations of the eclipsing polar V2301 Oph which cover nearly 2.5 binary orbital cycles and two eclipses. This polar is believed to have the lowest magnetic field strength (7 MG) of any known polar. We find evidence for structure in the X-ray eclipse profile which shows a 'standstill' feature lasting  26 ± 4  s. This allows us to place an upper limit on the mass of the white dwarf of  ∼1.2 M⊙  . We find no evidence for quasi-periodic oscillations (QPOs) in the frequency range 0.02–10 Hz. This coupled with the absence of QPOs in RXTE data suggests that, if present, any oscillations in the shock front have a minimal effect on the resultant X-ray flux. We find no evidence for a distinct soft X-ray component in its spectrum – it therefore joins another seven systems which do not show this component. We suggest that those systems which are asynchronous, have low mass-transfer rates or have accretion occurring over a relatively large fraction of the white dwarf are more likely to show this effect. We find that the specific mass-transfer rate has to be close to 0.1 g cm−2 s−1 to predict masses which are consistent with that derived from our eclipse analysis. This may be due to the fact that the low magnetic field strength allows accretion to take place along a wide range of azimuth.  相似文献   

13.
This paper presents the results of a non-adiabatic analysis for axisymmetric non-radial pulsations including the effect of a dipole magnetic field. Convection is assumed to be suppressed in the stellar envelope, and the diffusion approximation is used to radiative transport. As in a previous adiabatic analysis, the eigenfunctions are expanded in a series of spherical harmonics. The analysis is applied to a  1.9-M⊙  , main-sequence model  (log  T eff= 3.913)  . The presence of a magnetic field always stabilizes low-order acoustic modes. All the low-order modes of the model that are excited by the κ-mechanism in the He  ii ionization zone in the absence of a magnetic field are found to be stabilized if the polar strength of the dipole magnetic field is larger than about 1 kG. For high-order p modes, on the other hand, distorted dipole and quadrupole modes excited by the κ-mechanism in the H ionization zone remain overstable, even in the presence of a strong magnetic field. It is found, however, that all the distorted radial high-order modes are stabilized by the effect of the magnetic field. Thus, our non-adiabatic analysis suggests that distorted dipole modes and distorted quadrupole modes are most likely excited in rapidly oscillating Ap stars. The latitudinal amplitude dependence is found to be in reasonable agreement with the observationally determined one for HR 3831. Finally, the expected amplitude of magnetic perturbations at the surface is found to be very small.  相似文献   

14.
Magnetohydrodynamic (MHD) equations are presented for the mixture of superfluid neutrons, superconducting protons and normal electrons believed to exist in the outer cores of neutron stars. The dissipative effects of electron viscosity and mutual friction resulting from electron-vortex scattering are also included. It is shown that Alfvén waves are replaced by cyclotron-vortex waves that have not been previously derived from MHD theory. The cyclotron-vortex waves are analogous to Alfvén waves with the tension arising from the magnetic energy density replaced by the vortex energy density. The equations are then put into a simplified form useful for studying the effect of the interior magnetic field on the dynamics. Of particular interest is the crust–core coupling time, which can be inferred from pulsar glitch observations. The hypothesis that cyclotron-vortex waves play a significant role in the core spin-up during a glitch is used to place limits on the interior magnetic field. The results are compared with those of other studies.  相似文献   

15.
We present new high-speed, multisite photometric observations of the rapidly oscillating Ap star HD 119027 acquired over seven nights during 1996. A frequency analysis of these observations reveals the presence of oscillations at 1835, 1875, 1888, 1913, 1940, 1942 and (possibly) 1953 μHz. These frequencies are consistent with a spacing of either 13 or 26 μHz, depending on the reality of the oscillations at 1875 and 1953 μHz. The data in hand do not permit us to discriminate between the two possible spacings. If the smaller value of the spacing is correct, it suggests that HD 119027 is outside the main-sequence band. Two of the frequencies listed above are separated by only 1.95 μHz, suggesting that they are modes of ( n ,ℓ) and ( n  − 1, ℓ + 2), which in roAp stars is a quantity governed by the internal magnetic field.  相似文献   

16.
We present numerical simulations and explore scalings and anisotropy of compressible magnetohydrodynamic (MHD) turbulence. Our study covers both gas-pressure-dominated (high β) and magnetic-pressure-dominated (low β) plasmas at different Mach numbers. In addition, we present results for super-Alfvénic turbulence and discuss in what way it is similar to sub-Alfvénic turbulence. We describe a technique of separating different magnetohydrodynamic modes (slow, fast and Alfvén) and apply it to our simulations. We show that, for both high- and low-β cases, Alfvén and slow modes reveal a Kolmogorov   k −5/3  spectrum and scale-dependent Goldreich–Sridhar anisotropy, while fast modes exhibit a   k −3/2  spectrum and isotropy. We discuss the statistics of density fluctuations arising from MHD turbulence in different regimes. Our findings entail numerous astrophysical implications ranging from cosmic ray propagation to gamma ray bursts and star formation. In particular, we show that the rapid decay of turbulence reported by earlier researchers is not related to compressibility and mode coupling in MHD turbulence. In addition, we show that magnetic field enhancements and density enhancements are marginally correlated. Addressing the density structure of partially ionized interstellar gas on astronomical-unit scales, we show that the viscosity-damped regime of MHD turbulence that we reported earlier for incompressible flows persists for compressible turbulence and therefore may provide an explanation for these mysterious structures.  相似文献   

17.
We investigate the effect of a strong large-scale magnetic field on the reflection of high-frequency acoustic modes in rapidly oscillating Ap stars. To that end, we consider a toy model composed of an isothermal atmosphere matched on to a polytropic interior and determine the numerical solution to the set of ideal magnetohydrodynamic equations in a local plane-parallel approximation with constant gravity. Using the numerical solution in combination with approximate analytical solutions that are valid in the limits where the magnetic and acoustic components are decoupled, we calculate the relative fraction of energy flux that is carried away in each oscillation cycle by running acoustic waves in the atmosphere and running magnetic waves in the interior. For oscillation frequencies above the acoustic cut-off, we show that most energy losses associated with the presence of running waves occur in regions where the magnetic field is close to vertical. Moreover, by considering the depth dependence of the energy associated with the magnetic component of the wave in the atmosphere we show that a fraction of the wave energy is kept in the oscillation every cycle. For frequencies above the acoustic cut-off frequency, such energy is concentrated in regions where the magnetic field is significantly inclined in relation to the local vertical. Even though our calculations were aimed at studying oscillations with frequencies above the acoustic cut-off frequency, based on our results we discuss what results may be expected for oscillations of lower frequency.  相似文献   

18.
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.   相似文献   

19.
In this paper, we shall study the problem of stability of polar oscillations of a non-rotating Newtonian superfluid star. We find that the stability of the latter system is guaranteed by the positive definiteness of a matrix quantity. We also find conditions which characterize the occurrence of zero-frequency polar modes, which marks the onset of polar instability. We find that the negative definiteness of the mentioned matrix quantity implies instability of the system. We apply our results to show that the polar oscillations of a non-rotating Newtonian superfluid star in the zero-temperature approximation are marginally stable.  相似文献   

20.
Analyses of the widths and shifts of optically thin emission lines in the ultraviolet spectrum of the active dwarf ε Eri (K2 V) are presented. The spectra were obtained using the Space Telescope Imaging Spectrograph on the Hubble Space Telescope and the Far Ultraviolet Spectroscopic Explorer . The linewidths are used to find the non-thermal energy density and its variation with temperature from the chromosphere to the upper transition region. The energy fluxes that could be carried by Alfvén and acoustic waves are investigated, to test their possible roles in coronal heating. Acoustic waves do not appear to be a viable means of coronal heating. There is, in principle, ample flux in Alfvén waves, but detailed calculations of wave propagation are required before definite conclusions can be drawn concerning their viability. The high sensitivity and spectral resolution of the above instruments have allowed two-component Gaussian fits to be made to the profiles of the stronger transition region lines. The broad and narrow components that result share some similarities with those observed in the Sun, but in ε Eri the broad component is redshifted relative to the narrow component and contributes more to the total line flux. The possible origins of the two components and the energy fluxes implied are discussed. On balance our results support the conclusion of Wood, Linsky & Ayres, that the narrow component is related to Alfvén waves reaching to the corona, but the origin of the broad component is not clear.  相似文献   

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