The solar dynamo continues to pose a challenge to observers and theoreticians. Observations of the solar surface reveal a magnetic field with a complex, hierarchical structure consisting of widely different scales. Systematic features such as the solar cycle, the butterfly diagram, and Hale's polarity laws point to the existence of a deep-rooted large-scale magnetic field. At the other end of the scale are magnetic elements and small-scale mixed-polarity magnetic fields. In order to explain these phenomena, dynamo theory provides all the necessary ingredients including the $\alpha$ effect, magnetic field amplification by differential rotation, magnetic pumping, turbulent diffusion, magnetic buoyancy, flux storage, stochastic variations and nonlinear dynamics. Due to advances in helioseismology, observations of stellar magnetic fields and computer capabilities, significant progress has been made in our understanding of these and other aspects such as the role of the tachocline, convective plumes and magnetic helicity conservation. However, remaining uncertainties about the nature of the deep-seated toroidal magnetic field and the $\alpha$ effect, and the forbidding range of length scales of the magnetic field and the flow have thus far prevented the formulation of a coherent model for the solar dynamo. A preliminary evaluation of the various dynamo models that have been proposed seems to favor a buoyancy-driven or distributed scenario. The viewpoint proposed here is that progress in understanding the solar dynamo and explaining the observations can be achieved only through a combination of approaches including local numerical experiments and global mean-field modeling.

In a recent paper numerical simulations of a 2D mean-field model where shown to produce grand minima, typical of the long-term behavior of solar magnetic activity. The model consisted of a dynamo that features an α effect based on the buoyancy instability of magnetic flux tubes, which gives rise to the switching back and forth from grand minima to "regular" solar behavior. In this Letter, we report evidence from a time-series analysis of the model for the presence of crisis-induced intermittency due to attractor-widening. We support this finding by showing that the average duration of the minima, τ , follows the theoretically predicted scaling τ ∼ (C δα − C * δα ) −γ , where C δα is the bifurcation parameter of interest, together with other strong statistical evidence. As far as we are aware, this is the first time concrete and detailed evidence has been produced for the occurrence of this type of crisis-induced intermittency -due to attractor widening -for such dynamo models.

The role of the dynamo layer for dynamo action in solar-type stars is discussed. As a result of instabilities, magnetic flux is expelled from the dynamo layer into the convection zone above it. The resulting partial evacuation of the dynamo layer and amplification of the deep-seated toroidal magnetic field is investigated in an illustrative 3D numerical simulation. The simulation is performed with a finite-difference code that solves the anelastic MHD equations for a Cartesian geometry. It is found that the field strength in the dynamo layer is amplified by a factor of up to about 7.

We show that toroidal magnetic uxtubes can provide ane ect only if they are unstable to small displacements, a criterium that is met for uxtubes in the solar overshoot layer with eld strengths larger than about 10 5 G. A magnetic threshold for the -e ect can lead to dynamo action with on/o -states. Transitions across the threshold can result from external triggering, possibly by random downdrafts carrying ux produced by a separate weak-eld dynamo in the convection zone. In order to illustrate such an on/o -dynamo, we perform 2D mean-eld simulations, and we nd qualitative agreement with long-term behaviour of solar activity, including grand minima.

The origin of the solar magnetic field remains a stubborn challenge of astrophysics. At the solar surface the magnetic field assumes a complex, hierarchical structure in space and time. Systematic features such as the solar cycle and the butterfly diagram point to the existence of a deep-rooted large-scale predominantly toroidal magnetic field. In this review of solar dynamo theory new developments in our understanding of processes relevant for the solar dynamo are discussed. In recent years there has been significant progress with regard to tachocline physics, magnetic helicity conservation, the alpha effect, magnetic pumping, and the storage and amplification of the magnetic field. Remaining uncertainties about the nature of the deep-seated magnetic field and the alpha effect have thus far prevented the formulation of a coherent model for the solar dynamo. It is proposed that further progress is best achieved through a combination of approaches including high-resolution numerical simulations and global mean-field modeling. Along these lines some recent numerical simulations of magnetic pumping and flux expulsion in a magnetic layer are presented. The computations were performed with a new anelastic Cartesian finitedifference MHD code, which is the appropriate tool for studying processes near the base of stellar convection zones with a high spatial resolution. Possible implications for the solar dynamo are discussed.

Lattice gas automata are used to model transport phenomena in random media with static disorder. If the interactions are repulsive, there is a large probability of backscattering or retracing collision sequences. In that case the Boltzmann equation or mean field theory breaks down, even in the limit of a low concentration of scatterers. Here sequences of uncorrelated and retracing collisions are of equal importance. The repeated ring approximation is used to resum the retracing trajectories, and the renormalized transport coefficients are calculated in the low-density limit, not only for hard core scatterers (diamonds, hexagons, triangles), but also for mixed point scatterers (mirrors, rotators, reflectors). The results are compared with extensive computer simulations.

We present numerical simulations of three-dimensional compressible magnetoconvection in a rotating rectangular box that represents a section of the solar convection zone. The box contains a convectively unstable layer, surrounded by stably stratified layers with overshooting convection. The magnetic Reynolds number, Rm, is chosen subcritical, thus excluding spontaneous growth of the magnetic field through dynamo action, and the magnetic energy is maintained by introducing a constant magnetic field into the box, once convection has attained a statistically stationary state. Under the influence of the Coriolis force, the advection of the magnetic field results in a non-vanishing contribution to the mean electric field, given by u × b . From this electric field, we calculate the α-effect, separately for the stably and the unstably stratified layers, by averaging over time and over suitably defined volumes. From the variation of α we derive an error estimate, and the dependence of α on rotation and magnetic field strength is studied. Evidence is found for rotational quenching of the vertical α effect, and for a monotonic increase of the horizontal α effect with increasing rotation. For Rm ≈ 30, our results for both vertical and horizontal α effect are consistent with magnetic quenching by a factor [1 + Rm (B0/Beq) 2 ] −1 . The signs of the small-scale current helicity and of the vertical component of α are found to be opposite to those for isotropic turbulence.

We study the pumping of magnetic flux in three-dimensional compressible magnetoconvection in the context of stellar dynamos. The simulation domain represents a rectangular section from the lower part of a stellar convection zone plus the underlying stably stratified layer, with a total depth of up to five pressure scale heights. Once convection has attained a statistically stationary state, a magnetic field is introduced. The magnetic field is subsequently modified by the convective motions, and the resulting pumping effects are isolated by calculating various coefficients of the expansion of the electromotive force, u × b, in terms of components of the mean magnetic field. The dependence of the pumping effects on rotation, latitude and other parameters is studied. First numerical evidence is found for the existence of pumping effects in the horizontal directions. Evidence is found that the pumping effects act differently on different components of the mean magnetic field. Latitudinal pumping is mainly equatorward for a toroidal field, and can be poleward for a poloidal field. Longitudinal pumping is mainly retrograde for the radial field but prograde for the latitudinal field. The pumping effect in the vertical direction is found to be dominated by the diamagnetic effect, equivalent to a predominating downward advection with a maximum speed in the turbulent case of about 10% of the rms convective velocity. Where possible, an attempt is made to identify the physical origin of the effect. Finally, some consequences of the results for stellar dynamos are discussed.

In der Seleukidenzeit waren die Tempel Babyloniens Zentren der Gelehrsamkeit, wo sich spezialisierte Schreiber mit Astronomie, Astrologie, und anderen Bereichen der mesopotamischen Wissenskultur beschäftigten. Die Kolophone der gelehrten Texte aus Uruk, sowie Information aus juristischen Urkunden und anderen Dokumenten ermöglichen eine partielle Rekonstruktion der Biographien der Astronomen dieser Stadt, und des Netzwerks ihrer Interaktionen. In diesem Beitrag werden beispielhaft die Biographien von zwei Astronomen vorgestellt, die am Rēš, dem Tempel des Himmelsgottes Anu und seiner Gemahlin Antu, tätig waren; weiters wird das Netzwerk, an dem sie beteiligt waren, rekonstruiert. Ziel ist es, das Verständnis des sozialen und institutionellen Kontextes der babylonischen Astronomie in der Seleukidenzeit zu vertiefen. Darüber hinaus zeigt sich, dass die Ergebnisse beitragen können zu einer genaueren Bestimmung von Status und Funktion der Bibliothek des Rēš-Tempels. Wie bei jeder Untersuchung zur babylonischen Astronomie, so ist auch hier unübersehbar, dass an vielen Stellen angeknüpft wird an den Arbeiten von Hermann Hunger. In diesem Fall ist das besonders offensichtlich, da die Kolophone der astronomischen Texte im Mittelpunkt stehen.

Numerical simulations of a 2D mean-field model are presented which show that grand minima, typical for the longterm behaviour of solar magnetic activity, can be produced by a dynamo that features an alpha effect based on the buoyancy instability of magnetic fluxtubes. The buoyancy-driven alpha effect functions only if the magnetic field strength exceeds a minimal value necessary for instability. It opens the possibility of dynamo action within the solar overshoot layer, where a strong magnetic field, B ≈ 10 5 G, is thought to be stored. The existence of a magnetic threshold for dynamo action can lead to interruptions of the magnetic cycle, similar to the grand minima of solar activity. Transitions across the instability threshold are triggered by magnetic-flux injections from the convection zone. This is modelled by allowing for a small-scale kinematic alpha effect in the convection zone, and convective downdrafts that penetrate the overshoot layer.

Aims. The Strouhal number (St), which is a nondimensional measure of the correlation time, is determined from numerical models of convection. The Strouhal number arises in the mean-field theories of angular momentum transport and magnetic field generation, where its value determines the validity of certain widely used approximations, such as the first order smoothing (hereafter FOSA). More specifically, the relevant transport coefficients can be calculated by means of a cumulative series expansion if St < St crit ≈ 1. Methods. We define the Strouhal number as the ratio of the correlation and turnover times, which we determine separately, the former from the autocorrelation of velocity, and the latter by following test particles embedded in the flow. Results. We find that the Strouhal numbers are, generally, of the order of 0.1 to 0.4 which is close to the critical value above which deviations from FOSA become significant. Increasing the rotational influence tends to shorten both timescales in such a manner that St decreases. However, we do not find a clear trend as a function of the Rayleigh number for the parameter range explored in the present study.

We show that the cycle periods (P cyc ) of slowly rotating lower main-sequence stars with well-defined periodic chromospheric activity can be parametrized by the rotation period P rot and the convective turnover time τ c through a relation of the form P cyc ∝ P b rot τ c c , with b = 2.0 ± 0.3 and c = −2.0 ± 0.3. This suggests a common dynamo mechanism for slowly rotating stars lower main-sequence stars. Using a simple linear meanfield dynamo model, we are able to reproduce the observed relation if ∆Ω, the total difference in angular velocity along the radial direction, scales as ∆Ω ∝ P p rot with p = 1.1 ± 0.2, and if the α-coefficient scales as α ∝ Ro q with q = −5.1 ± 0.6. This would suggest that, with increasing rotation rate, differential rotation decreases while |α| rapidly increases.

Like no other cultural achievement, astronomy stands out as a legacy of Babylon. The Chaldaean astronomer, a stock character of the biblical and classical literature, is the personification of that legacy. 1 In this contribution I investigate the astronomers of Babylonia as participants of a network of interacting scholars. With this approach I hope to expand our knowledge of the practice and context of Babylonian astronomy, which is still rather limited. Babylonian astronomers created a large and diverse body of literature consisting of observational astronomy, mathematical astronomy, zodiacal astrology, and omen astrology. 2 Especially the observational texts, by far the most numerous group, imply that astronomy was the collaborative effort of a community of scholars. Since most astronomical diaries contain observations for 6 months, they must have been compiled from individual reports of different scholars. The same holds for other compilations extracted from the diaries, some of which contain data for many decades. Also the fact that observational texts, unlike other scholarly texts, are anonymous (with very few exceptions; cf. below), can be viewed as a consequence of the collaborative effort by which they were produced. Astronomical diaries and related texts are therefore testimonies of a systematic, collaborative program of observation. This program is believed to have existed continuously from the Neo-Babylonian era, perhaps as early as the middle of the 8th c. BC, until the very end of cuneiform writing in the 1st c. AD.