arXiv subjects

G. Rüdiger

Publications and source records attributed to G. Rüdiger.

39 records · Page 3Linked to original sources

arXiv2001

Meridional flow and differential rotation by gravity darkening in fast rotating solar-type stars

An explanation is presented for the rather strong total surface differential rotation of the observed very young solar-type stars like AB Dor and PZ Tel. Due to its rapid rotation a nonuniform energy flux leaves the stellar core so that the outer convection zone is nonuniformly heated from below. Due to this `gravity darkening' of the equator a meridional flow is created flowing equatorwards at the surface and thus accelerating the equatorial rotation. The effect linearly grows with the normalized pole-equator difference, ε, of the heat-flux at the bottom of the convection zone. A rotation rate of about 9 h leads to ε=0.1 for a solar-type star. In this case the resulting equator-pole differences of the angular velocity at the stellar surface, δΩ, varies from unobservable 0.005/day to the (desired) value of 0.03 day$^{-1}$ when the dimensionless diffusivity factors $c_ν$ and c_χvary between 1 and 0.1 (standard value c_ν\simeq c_χ\simeq 0.3, see Table 1.) In all cases the related temperature differences between pole and equator at the surface are unobservably small. The (clockwise) meridional circulation which we obtain flows opposite to the (counterclockwise) circulation appearing as a byproduct in the Λ-theory of the nonuniform rotation in outer convection zones. The consequences of this situation for those dynamo theories of stellar activity are discussed which work with the meridional circulation as the dominant magnetic-advection effect in latitude to produce the solar-like form of the butterfly diagram. Key words: Hydrodynamics, Star: rotation, Stars: pre-main sequence, Stellar activity

astro-ph↗

arXiv2001

MHD Instability in cylindric Taylor-Couette flow

The linear marginal instability of an axisymmetric MHD Taylor-Couette flow of infinite vertical extension is considered. For flows with a resting outer cylinder there is a well-known characteristic Reynolds number even without magnetic field but for sufficiently weak magnetic fields there are solutions with smaller Reynolds numbers so that a characteristic minimum exists. The minimum only exists, however, for not too small magnetic Prandtl numbers. For small magnetic Prandtl numbers one only finds the typical magnetic suppression of the instability. We are here particularly interested in the case where the outer cylinder rotates so fast that the Rayleigh criterion for hydrodynamic stability is fulfilled. We find that for given magnetic Prandtl number now always a magnetic field amplitude exists where the characteristic Reynolds number is minimal. These critical values are computed for different magnetic Prandtl numbers. In all cases the Reynolds numbers are running with 1/Pm so that for the small magnetic Prandtl numbers of sodium (10^-5) or gallium (10^-6) the critical Reynolds numbers exceed values of 10^6 or 10^, resp.

astro-ph↗

arXiv2001

MHD instability in differentially rotating cylindric flows

The possibility that the magnetic shear-flow instability (MRI, Balbus-Hawley instability) might give rise to turbulence in a cylindric Couette flow is investigated through numerical simulations. The study is linear and the fluid flow is supposed to be incompressible and differentially rotating with a simple velocity profile with $Ω= a+b/R^2$. The simplicity of the model is counterbalanced by the fact that the study is fully global in all three spatial directions with boundaries on each side; finite diffusivities are also allowed. The investigation is also carried out for several values of the azimuthal wavenumber of the perturbations in order to analyse whether non-axisymmetric modes might be preferred, which might produce, in a non-linear extension of the study, a self-sustained magnetic field. We find that with magnetic field the instability is easier to be excited than without magnetic field. The critical Reynolds number for Pm$=1$ is of order 50 independent of whether the nonmagnetic flow is stable or not. Also we find that i) the magnetic field strongly reduces the number of Taylor vortices, ii) the angular momentum is transported outwards and iii) for finite c ylinders a netto dynamo-alpha effect results which is negative for the upper part of the cylinder and which is positive for the lower part of the cylinder. For magnetic Prandtl number smaller than unity the critical Reynolds number scales with Pm$^{-0.65}$. If this was true even for very small magnetic Prandtl number (e.g. liquid sodium) the critical Reynolds number should reach the value 10$^5$ which is, however, also characteristic for nonlinear fi nite-amplitude hydrodynamic Taylor-Couette turbulence -- so that we easily have to expect the simultaneous existence of both sorts of instabi lities in cold accretion disks.

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