43 research outputs found
Hydrodynamic stability in accretion disks under the combined influence of shear and density stratification
The hydrodynamic stability of accretion disks is considered. The particular
question is whether the combined action of a (stable) vertical density
stratification and a (stable) radial differential rotation gives rise to a new
instability for nonaxisymmetric modes of disturbances. The existence of such an
instability is not suggested by the well-known Solberg-Hoiland criterion. It is
also not suggested by a local analysis for disturbances in general
stratifications of entropy and angular momentum which is presented in our
Section 2 confirming the results of the Solberg-Hoiland criterion also for
nonaxisymmetric modes within the frame of ideal hydrodynamics but only in the
frame of a short-wave approximation for small m. As a necessary condition for
stability we find that only conservative external forces are allowed to
influence the stable disk. As magnetic forces are never conservative, linear
disk instabilities should only exist in the magnetohydrodynamical regime which
indeed contains the magnetorotational instability as a much-promising
candidate. To overcome some of the used approximations in a numerical
approach,the equations of the compressible adiabatic hydrodynamics are
integrated imposing initial nonaxisymmetric velocity perturbations with m=1 to
m=200.
Only solutions with decaying kinetic energy are found. The system always
settles in a vertical equilibrium stratification according to pressure balance
with the gravitational potential of the central object. keywords: accretion
disks -- hydrodynamic instabilities -- turbulenceComment: 6 pages, 4 figures, 1 table, Astronomy and Astrophysics (subm.
Stratorotational instability in MHD Taylor-Couette flows
The stability of dissipative Taylor-Couette flows with an axial stable
density stratification and a prescribed azimuthal magnetic field is considered.
Global nonaxisymmetric solutions of the linearized MHD equations with toroidal
magnetic field, axial density stratification and differential rotation are
found for both insulating and conducting cylinder walls. Flat rotation laws
such as the quasi-Kepler law are unstable against the nonaxisymmetric
stratorotational instability (SRI). The influence of a current-free toroidal
magnetic field depends on the magnetic Prandtl number Pm: SRI is supported by
Pm > 1 and it is suppressed by Pm \lsim 1. For too flat rotation laws a smooth
transition exists to the instability which the toroidal magnetic field produces
in combination with the differential rotation. This nonaxisymmetric azimuthal
magnetorotational instability (AMRI) has been computed under the presence of an
axial density gradient. If the magnetic field between the cylinders is not
current-free then also the Tayler instability occurs and the transition from
the hydrodynamic SRI to the magnetic Tayler instability proves to be rather
complex. Most spectacular is the `ballooning' of the stability domain by the
density stratification: already a rather small rotation stabilizes magnetic
fields against the Tayler instability. An azimuthal component of the resulting
electromotive force only exists for density-stratified flows. The related
alpha-effect for magnetic SRI of Kepler rotation appears to be positive for
negative d\rho/dz <0.Comment: 10 pages, 13 figures, submitted to Astron. Astrophy
Three dimensional simulation of the magnetic stress in a neutron star crust
We present the first fully self-consistent three dimensional model of a neutron star’s magnetic field, generated by electric currents in the star’s crust via the Hall effect. We find that the global-scale field converges to a dipolar Hall-attractor state, as seen in recent axisymmetric models, but that small-scale features in the magnetic field survive even on much longer time scales. These small-scale features propagate toward the dipole equator, where the crustal electric currents organize themselves into a strong equatorial jet. By calculating the distribution of magnetic stresses in the crust, we predict that neutron stars with fields stronger than 1014 G can still be subject to starquakes more than 105 yr after their formation
The Occurrence of the Hall--Instability in Crusts of Isolated Neutron Stars
In former papers we showed that during the decay of a neutron star's magnetic
field under the influence of the Hall--drift, an unstable rise of small--scale
field structures at the expense of the large--scale background field may
happen. This linear stability analysis was based on the assumption of a uniform
density throughout the neutron star crust, whereas in reality the density and
all transport coefficients vary by many orders of magnitude. Here, we extend
the investigation of the Hall--drift induced instability by considering
realistic profiles of density and chemical composition, as well as background
fields with more justified radial profiles. Two neutron star models are
considered differing primarily in the assumption on the core matter equation of
state. For their cooling history and radial profiles of density and composition
we use known results to infer the conductivity profiles. These were fed into
linear calculations of a dipolar field decay starting from various initial
configurations. At different stages of the decay, snapshots of the magnetic
fields at the equator were taken to yield background field profiles for the
stability analysis. The main result is that the Hall instability may really
occur in neutron star crusts. Characteristic growth times are in the order of
\lesssim 10^4 ... 10^6 yrs depending on cooling age and background field
strength. The influence of the equation of state and of the initial field
configuration is discussed.Comment: 16 pages, 16 figures, PS, submitted to A&A. Justification/discussion
slightly changed/extended in replying to the referee. Changes on p. 3, 11,
13, framed by XXX mark
Hall drift of axisymmetric magnetic fields in solid neutron-star matter
Hall drift, i. e., transport of magnetic flux by the moving electrons giving
rise to the electrical current, may be the dominant effect causing the
evolution of the magnetic field in the solid crust of neutron stars. It is a
nonlinear process that, despite a number of efforts, is still not fully
understood. We use the Hall induction equation in axial symmetry to obtain some
general properties of nonevolving fields, as well as analyzing the evolution of
purely toroidal fields, their poloidal perturbations, and current-free, purely
poloidal fields. We also analyze energy conservation in Hall instabilities and
write down a variational principle for Hall equilibria. We show that the
evolution of any toroidal magnetic field can be described by Burgers' equation,
as previously found in plane-parallel geometry. It leads to sharp current
sheets that dissipate on the Hall time scale, yielding a stationary field
configuration that depends on a single, suitably defined coordinate. This
field, however, is unstable to poloidal perturbations, which grow as their
field lines are stretched by the background electron flow, as in instabilities
earlier found numerically. On the other hand, current-free poloidal
configurations are stable and could represent a long-lived crustal field
supported by currents in the fluid stellar core.Comment: 8 pages, 5 figure panels; new version with very small correction;
accepted by Astronomy & Astrophysic
Stability of density-stratified viscous Taylor-Couette flows
The stability of density-stratified viscous Taylor-Couette flows is
considered using the Boussinesq approximation but without any use of the
short-wave approximation. The flows which are unstable after the Rayleigh
criterion (\hat \mu<\hat \eta^2, with \hat \mu=\Omega_{out}/\Omega_{in} and
\hat \eta= R_{in}/R_{out}) now develop overstable axisymmetric Taylor vortices.
For the considered wide-gap container we find the nonaxisymmetric modes as the
most unstable ones. The nonaxisymmetric modes are unstable also beyond the
Rayleigh line. For such modes the instability condition seems simply to be
\hat\mu<1 as stressed by Yavneh, McWilliams & Molemaker (2001). However, we
never found unstable modes for too flat rotation laws fulfilling the condition
\hat \mu >\hat \eta. The Reynolds numbers rapidly grow to very high values if
this limit is approached (see Figs. 3 and 4).
Also striking is that the marginal stability lines for the higher do less
and less enter the region beyond the Rayleigh line so that we might have to
consider the stratorotational instability as a 'low- instability'. The
applicability of these results to the stability problem of accretion disks with
their strong stratification and fast rotation is shortly discussed.Comment: 7 pages, 7 figures, Astron. Astrophys. (subm.
On the Origin of X-ray Emission From Millisecond Pulsars in 47 Tuc
The observed spectra and X-ray luminosities of millisecond pulsars in 47 Tuc
can be interpreted in the context of theoretical models based on strong, small
scale multipole fields on the neutron star surface. For multipole fields that
are relatively strong as compared to the large scale dipole field, the emitted
X-rays are thermal and likely result from polar cap heating associated with the
return current from the polar gap. On the other hand, for weak multipole
fields, the emission is nonthermal and results from synchrotron radiation of
pairs created by curvature radiation. The X-ray luminosity, , is
related to the spin down power, , expressed in the form with and for strong and weak
multipole fields respectively. If the polar cap size is of the order of the
length scale of the multipole field, and , the polar cap
temperature is .
A comparison of the X-ray properties of millisecond pulsars in globular
clusters and in the Galactic field suggests that the emergence of relatively
strong small scale multipole fields from the neutron star interior may be
correlated with the age and evolutionary history of the underlying neutron
star.Comment: 25 pages, 2 figures, accepted for publication in Ap