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 $m$ do less and less enter the region beyond the Rayleigh line so that we might have to consider the stratorotational instability as a 'low-$m$ 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.