Dynamics of the solar tachocline – I. An incompressible study

Gough & McIntyre have suggested that the dynamics of the solar tachocline are dominated by the advection–diffusion balance between the differential rotation, a large-scale primordial field and baroclinicly driven meridional motions. This paper presents the first part of a study of the tachocline, in which a model of the rotation profile below the convection zone is constructed along the lines suggested by Gough & McIntyre and solved numerically. In this first part, a reduced model of the tachocline is derived in which the effects of compressibility and energy transport on the system are neglected; the meridional motions are driven instead by Ekman–Hartmann pumping. Through this simplification, the interaction of the fluid flow and the magnetic field can be isolated and is studied through non-linear numerical analysis for various field strengths and diffusivities. It is shown that there exists only a narrow range of magnetic field strengths for which the system can achieve a nearly uniform rotation. The results are discussed with respect to observations and to the limitations of this initial approach. A following paper combines the effects of realistic baroclinic driving and stratification with a model that closely follows the lines of work of Gough & McIntyre.     

Modulation and symmetry changes in stellar dynamos

Stellar dynamos are governed by non-linear partial differential equations (PDEs) which admit solutions with dipole, quadrupole or mixed symmetry (i.e. with different parities). These PDEs possess periodic solutions that describe magnetic cycles, and numerical studies reveal two different types of modulation. For modulations of Type 1 there are parity changes without significant changes of amplitude, while for Type 2 there are amplitude changes without significant changes in parity. In stars like the Sun, cyclic magnetic activity is interrupted by grand minima that correspond to Type 2 modulation. Although the Sun's magnetic field has maintained dipole symmetry for almost 300 yr, there was a significant parity change at the end of the Maunder Minimum. We infer that the solar field may have flipped from dipole to quadrupole polarity (and back) after deep minima in the past and may do so again in the future. Other stars, with different masses or rotation rates, may exhibit cyclic activity with dipole, quadrupole or mixed parity. The origins of such behaviour can be understood by relating the PDE results to solutions of appropriate low-order systems of ordinary differential equations (ODEs). Type 1 modulation is reproduced in a fourth-order system while Type 2 modulation occurs in a third-order system. Here we construct a new sixth-order system that describes both types of modulation and clarifies the interactions between symmetry-breaking and modulation of activity. Solutions of these non-linear ODEs reproduce the qualitative behaviour found for the PDEs, including flipping of polarity after a prolonged grand minimum. Thus we can be confident that these patterns of behaviour are robust, and will apply to stars that are similar to the Sun.     

PSR J1012+5307: younger than it looks?

Lorimer et al. have recently reported that the spin-down age (∼7 × 10⁹ yr) of the low-mass binary pulsar PSR J1012+5307 is much higher than the cooling age (3 × 10⁸ yr) of its white dwarf companion. The proposed solutions for this discrepancy are outlined and discussed. In particular, the revised cooling age estimate proposed by Alberts et al. agrees with data from other low-mass binary pulsar systems if a transition to the 'classical' cooling regime occurs between ∼0.14 and ∼0.28 M_⊙. If this transition is excluded, PSR J1012+5307 seems to have finished its accretion phase far from the spin-up line.     

耦合热传导的磁重联的数值模拟

磁重联被认为是太阳耀斑的产生机制,本文数值模拟在日冕中发生在磁重联过程,结果表明耀斑环的表观运动是磁重联的自洽结果;由重联点发出的慢激波对耀斑环的加热有贡献;耀斑环的上升并不意味着重联点的上升。     

The magnetic field and rotational period of 53 Camelopardalis

The magnetic Ap star 53 Cam has been described as the best object for testing theories of elemental diffusion in the presence of a stellar magnetic field. It is thus vital to determine the rotational period of this very important star as accurately as possible. An improved period (8.026 81±0.000 04 d) is derived here by combining new measurements of the effective magnetic field with previously published values.     

Numerical modelling of the impact crater depth-diameter dependence in an acoustically fluidized target

2D numerical modelling of impact cratering has been utilized to quantify an important depth-diameter relationship for different crater morphologies, simple and complex. It is generally accepted that the final crater shape is the result of a gravity-driven collapse of the transient crater, which is formed immediately after the impact. Numerical models allow a quantification of the formation of simple craters, which are bowl-shaped depressions with a lens of rock debris inside, and complex craters, which are characterized by a structural uplift. The computation of the cratering process starts with the first contact of the impactor and the planetary surface and ends with the morphology of the final crater. Using different rheological models for the sub-crater rocks, we quantify the influence on crater mechanics. To explain the formation of complex craters in accordance to the threshold diameter between simple and complex craters, we utilize the Acoustic Fluidization model. We carried out a series of simulations over a broad parameter range with the goal to fit the observed depth/diameter relationships as well as the observed threshold diameters on the Moon, Earth and Venus.     

Calibration of Vector Magnetogram with the Nonlinear Least-squares Fitting Technique

To acquire Stokes profiles from observations of a simple sunspot with the Video Vector Magnetograph at Huairou Solar Observing Station (HSOS), we scanned the FeI λ5324.19A line over the wavelength interval from 150mA redward of the line center to 150 mA blueward, in steps of 10 mA. With the technique of analytic inversion of Stokes profiles via nonlinear least-squares, we present the calibration coefficients for the HSOS vector magnetic magnetogram. We obtained the theoretical calibration error with linear expressions derived from the Unno-Becker equation under weak-field approximation.