Solar radius and luminosity variations induced by the internal dynamo magnetic fields

Although the occurrence of solar irradiance variations induced by magnetic surface features (e.g., sunspots, faculae, magnetic network) is generally accepted, the existence of intrinsic luminosity changes due to the internal magnetic fields is still controversial. This additional contribution is expected to be accompanied by radius variations, and to be potentially significant for the climate of the Earth. We aim to constrain theoretically the radius and luminosity variations of the Sun that are due to the effect of the variable magnetic fields in its interior associated with the dynamo cycle. We have extended a one-dimensional stellar evolution code to include several effects of the magnetic fields on the interior structure. We investigate different magnetic configurations, based on both observational constraints and on the output of state-of-the-art mean field dynamo models. We explore both step-like and simply periodic time dependences of the magnetic field peak strength. We find that the luminosity and radius variations are in anti-phase and in phase, respectively, with the magnetic field strength. For peak magnetic field strengths of the order of tens of kilogauss, luminosity variations ranging between 10^{-6} and 10^{-3} (in modulus) and radius variations between 10^{-6} and 10^{-5} are obtained. Modest but significant radius variations (up to 10^{-5} in relative terms) are obtained for magnetic fields of realistic strength and geometry, providing a potentially observable signature of the intrinsic variations. Establishing their existence in addition to the accepted surface effects would have very important implications for the understanding of solar-induced long-term trends on climate.Comment: 18 pages, 7 figures; accepted for publication in Astronomische Nachrichte

The eddy heat-flux in rotating turbulent convection

The three components of the heat-flux vector $F =\rho C_p are numerically computed for a stratified rotating turbulent convection using the NIRVANA code in a flat box. The latitudinal component$F_\theta$proves to be negative (positive) in the northern (southern) hemisphere so that the heat always flows towards the poles. As a surprise, the radial heat-flux$F_r$peaks at the equator rather than at the poles (Taylor numbers O(10^6)). The same behavior is observed for the radial turbulence intensity$ which for \emph{free} turbulence is also believed to peak at the poles (see Eq. (19) below). As we can show, however, the consequences of this unexpected result (also obtained by Kaepylae, Korpi and Tuominen 2004) for the theory of differential rotation are small as mainly the F_\theta$is responsible to solve the `Taylor number puzzle'. In all our simulations the azimuthal component$F_\phi$proves to be negative so that the rotating turbulence produces an westwards directed azimuthal heat-flux which should be observable. Fluctuations with higher temperature are expected to be anticorrelated with their own angular velocity fluctuations. We find this rotation-induced result as understandable as the$F_\phi$ is closely related to the radial \Lambda-effect which is known to be also negative in stratified and rapidly rotating convection zones.Comment: 8 pages, 9 figures, Astron. Astrophys. (subm.

The generalized non-conservative model of a 1-planet system - revisited

We study the long-term dynamics of a planetary system composed of a star and a planet. Both bodies are considered as extended, non-spherical, rotating objects. There are no assumptions made on the relative angles between the orbital angular momentum and the spin vectors of the bodies. Thus, we analyze full, spatial model of the planetary system. Both objects are assumed to be deformed due to their own rotations, as well as due to the mutual tidal interactions. The general relativity corrections are considered in terms of the post-Newtonian approximation. Besides the conservative contributions to the perturbing forces, there are also taken into account non-conservative effects, i.e., the dissipation of the mechanical energy. This dissipation is a result of the tidal perturbation on the velocity field in the internal zones with non-zero turbulent viscosity (convective zones). Our main goal is to derive the equations of the orbital motion as well as the equations governing time-evolution of the spin vectors (angular velocities). We derive the Lagrangian equations of the second kind for systems which do not conserve the mechanical energy. Next, the equations of motion are averaged out over all fast angles with respect to time-scales characteristic for conservative perturbations. The final equations of motion are then used to study the dynamics of the non-conservative model over time scales of the order of the age of the star. We analyze the final state of the system as a function of the initial conditions. Equilibria states of the averaged system are finally discussed.Comment: 37 pages, 13 figures, accepted to Celestial Mechanics and Dynamical Astronom

The maunder minimum as due to magnetic #LAMBDA#-quenching. Rotation law and magnetic field for M dwarf models

A 2D mean-field MHD code for spheres is used to check the nonlinear interplay between dynamo-induced magnetic fields and the differential rotation in convection zones. The magnetic back-reaction is threefold: Lorentz force, #alpha#-quenching and #LAMBDA#-quenching. If only the Malkus-Proctor feedback is used then the dynamo shows an interesting nonperiodic behavior which, however, disappears for alpha-quenching included (cf. Fig. 2). If also a strong #LAMBDA#-quenching is allowed to modify the differential rotation then the dynamo starts its exotic performance again with periodic periods and fluctuating magnetic parities. The Elsasser number has been put to unity whereas the magnetic Prandtl number must be smaller than unity. For too small Prandtl number (e.g. for Pm=0.01), however, the grand minima become very seldom events. (orig.)Available from TIB Hannover: RR 7310(98-32/33) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Nonlinear winding of large-scale magnetic fields in spiral galaxies. Do T Tauri stars rotate differentially?

A new-developed 3D numerical code is applied to an uniform external (primordial) magnetic field subject to a complex flow pattern representing the situation in a turbulent spiral galaxy. The spiral arms are defined by the radial-azimuthal profiles of density and the turbulent velocity, but they do not yet possess any own large-scale velocity field. No dynamo alpha is assumed to exist, but all the known turbulence effects such as eddy diamagnetism and turbulent pumping are involved. In our model the galactic differential rotation leads to a permanent amplification of the toroidal magnetic field component which, however, is limited by the turbulent diffusivity - which itself is nonlinearly modified by the induced magnetic fields. Two different models are followed: the (nonaxisymmetric) external magnetic field is considered as an initial-value and/or as a boundary condition. In the first case the decay of the magnetic field is rather fast. The initial field cannot survive more than 500 Myr. In its early times the magnetic field is concentrated between the spirals but later it is strongly wound up by the differential rotation. Any amplification of the magnetic energy does not appear. The nonlinear diffusivity quenching only plays a role for small eddy diffusivity. If the galaxy is embedded in an external intergalactic magnetic field there is an amplification of the magnetic energy by a factor of 10. But very soon the magnetic spirals have been transformed into rings and after about 1.5 Gyr the galaxy is nearly field-free. Our results confirm the idea that primordial magnetic fields in galaxies are unable to become old. If both the gaseous and the magnetic spirals had a common origin, the gaseous spirals are revealed here as young phenomena. Tuning the pattern speed of the spirals an exceptional amplification of the magnetic field is found in case of 'resonance' of the pattern speed and a magnetic drift velocity. The peak amplification arises from the fact that the turbulence in the interarm regions is assumed as weak hence the diffusion there is strongly reduced. (orig.)SIGLEAvailable from FIZ Karlsruhe / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Lumbar disk prolapse: response to mechanical physiotherapy in the absence of changes in magnetic resonance imaging. Report of 11 cases

BACKGROUND: Lumbar disk prolapses are among the most common neurological conditions. In this open study, we asked whether repeated end-range spinal movements (McKenzie method) as physiotherapy in patients with lumbar disk prolapse induce early changes in location, size and signal intensity of lumbar disc material detectable by magnetic resonance imaging (MRI). We compared clinical with radiographic changes. The clinical efficacy of mechanical physiotherapy according to the McKenzie method within 5 days was documented. METHODS: Eleven consecutive patients with lumbar disk prolapse were included. Patients were treated with repeated end-range spinal movements and MRI was performed before and after 2-5 treatments. RESULTS: All patients achieved a reduction in symptoms and signs of disk prolapse during and after these procedures but none showed any change in the MRI features of the prolapses. CONCLUSIONS: Beneficial effects of specific mechanical physiotherapy in patients with radicular syndromes from lumbar disk prolapse are not paralleled by changes in the MRI appearance of the prolapses. Alternative explanations for the early clinical responses in some patients with lumbar disc prolapse treated according to the McKenzie method must be sought