Carbon Ignition in Type Ia Supernovae: II. A Three-Dimensional Numerical Model

The thermonuclear runaway that culminates in the explosion of a Chandrasekhar mass white dwarf as a Type Ia supernova begins centuries before the star actually explodes. Here, using a 3D anelastic code, we examine numerically the convective flow during the last minute of that runaway, a time that is crucial in determining just where and how often the supernova ignites. We find that the overall convective flow is dipolar, with the higher temperature fluctuations in an outbound flow preferentially on one side of the star. Taken at face value, this suggests an asymmetric ignition that may well persist in the geometry of the final explosion. However, we also find that even a moderate amount of rotation tends to fracture this dipole flow, making ignition over a broader region more likely. Though our calculations lack the resolution to study the flow at astrophysically relevant Rayleigh numbers, we also speculate that the observed dipolar flow will become less organized as the viscosity becomes very small. Motion within the dipole flow shows evidence of turbulence, suggesting that only geometrically large fluctuations (~1 km) will persist to ignite the runaway. We also examine the probability density function for the temperature fluctuations, finding evidence for a Gaussian, rather than exponential distribution, which suggests that ignition sparks may be strongly spatially clustered.Comment: 16 pages, 9 figures, submitted to ApJ. A high resolution version of this paper, as well as movies, can be found at http://www.ucolick.org/~mqk/Carbo

Magnetic Field Saturation in the Riga Dynamo Experiment

After the dynamo experiment in November 1999 had shown magnetic field self-excitation in a spiraling liquid metal flow, in a second series of experiments emphasis was placed on the magnetic field saturation regime as the next principal step in the dynamo process. The dependence of the strength of the magnetic field on the rotation rate is studied. Various features of the saturated magnetic field are outlined and possible saturation mechanisms are discussed.Comment: 4 pages, 8 figure

Numerical simulations of current generation and dynamo excitation in a mechanically-forced, turbulent flow

The role of turbulence in current generation and self-excitation of magnetic fields has been studied in the geometry of a mechanically driven, spherical dynamo experiment, using a three dimensional numerical computation. A simple impeller model drives a flow which can generate a growing magnetic field, depending upon the magnetic Reynolds number, Rm, and the fluid Reynolds number. When the flow is laminar, the dynamo transition is governed by a simple threshold in Rm, above which a growing magnetic eigenmode is observed. The eigenmode is primarily a dipole field tranverse to axis of symmetry of the flow. In saturation the Lorentz force slows the flow such that the magnetic eigenmode becomes marginally stable. For turbulent flow, the dynamo eigenmode is suppressed. The mechanism of suppression is due to a combination of a time varying large-scale field and the presence of fluctuation driven currents which effectively enhance the magnetic diffusivity. For higher Rm a dynamo reappears, however the structure of the magnetic field is often different from the laminar dynamo; it is dominated by a dipolar magnetic field which is aligned with the axis of symmetry of the mean-flow, apparently generated by fluctuation-driven currents. The fluctuation-driven currents have been studied by applying a weak magnetic field to laminar and turbulent flows. The magnetic fields generated by the fluctuations are significant: a dipole moment aligned with the symmetry axis of the mean-flow is generated similar to those observed in the experiment, and both toroidal and poloidal flux expulsion are observed.Comment: 14 pages, 14 figure

Detection of a flow induced magnetic field eigenmode in the Riga dynamo facility

In an experiment at the Riga sodium dynamo facility, a slowly growing magnetic field eigenmode has been detected over a period of about 15 seconds. For a slightly decreased propeller rotation rate, additional measurements showed a slow decay of this mode. The measured results correspond satisfactory with numerical predictions for the growth rates and frequencies

Nonlinear Dynamics of Gravity Wave Driven Flows in the Solar Radiative Interior

We present results of nonlinear numerical simulations of gravity wave driven shear flow oscillations in the equatorial plane of the solar radiative interior. These results show that many of the assumptions of quasi-linear theory are not valid. When only two waves are forced (prograde and retrograde) oscillatory mean flow is maintained; but critical layers often form and are dynamically important. When a spectrum of waves is forced, the non-linear wave-wave interactions are dynamically important, often acting to decrease the maintenance of a mean flow. The (in)coherence of such wave-wave interactions must be taken into account when describing wave driven mean flows.Comment: 21 pages, 10 figures, accepted to MNRAS animations can be found at http://www.solarphysicist.co

The effect of hyperdiffusivity on turbulent dynamos with helicity

In numerical studies of turbulence, hyperviscosity is often used as a tool to extend the inertial subrange and to reduce the dissipative subrange. By analogy, hyperdiffusivity (or hyperresistivity) is sometimes used in magnetohydrodynamics. The underlying assumption is that only the small scales are affected by this manipulation. In the present paper, possible side effects on the evolution of the large scale magnetic field are investigated. It is found that for turbulent flows with helicity, hyperdiffusivity causes the dynamo-generated magnetic field to saturate at a higher level than normal diffusivity. This result is successfully interpreted in terms of magnetic helicity conservation, which also predicts that full saturation is only reached after a time comparable to the large scale magnetic (hyper)diffusion time.Comment: 4 pages, 3 figure

Nonlinear Turbulent Magnetic Diffusion and Mean-Field Dynamo

The nonlinear coefficients defining the mean electromotive force (i.e., the nonlinear turbulent magnetic diffusion, the nonlinear effective velocity, the nonlinear kappa-tensor, etc.) are calculated for an anisotropic turbulence. A particular case of an anisotropic background turbulence (i.e., the turbulence with zero mean magnetic field) with one preferential direction is considered. It is shown that the toroidal and poloidal magnetic fields have different nonlinear turbulent magnetic diffusion coefficients. It is demonstrated that even for a homogeneous turbulence there is a nonlinear effective velocity which exhibits diamagnetic or paramagnetic properties depending on anisotropy of turbulence and level of magnetic fluctuations in the background turbulence. Analysis shows that an anisotropy of turbulence strongly affects the nonlinear mean electromotive force. Two types of nonlinearities (algebraic and dynamic) are also discussed. The algebraic nonlinearity implies a nonlinear dependence of the mean electromotive force on the mean magnetic field. The dynamic nonlinearity is determined by a differential equation for the magnetic part of the alpha-effect. It is shown that for the alpha-Omega axisymmetric dynamo the algebraic nonlinearity alone cannot saturate the dynamo generated mean magnetic field while the combined effect of the algebraic and dynamic nonlinearities limits the mean magnetic field growth. Astrophysical applications of the obtained results are discussed.Comment: 15 pages, REVTEX

A spherical shell numerical dynamo benchmark with pseudo vacuum magnetic boundary conditions

It is frequently considered that many planetary magnetic fields originate as a result of convection within planetary cores. Buoyancy forces responsible for driving the convection generate a fluid flow that is able to induce magnetic fields; numerous sophisticated computer codes are able to simulate the dynamic behaviour of such systems. This paper reports the results of a community activity aimed at comparing numerical results of several different types of computer codes that are capable of solving the equations of momentum transfer, magnetic field generation and heat transfer in the setting of a spherical shell, namely a sphere containing an inner core. The electrically conducting fluid is incompressible and rapidly rotating and the forcing of the flow is thermal convection under the Boussinesq approximation. We follow the original specifications and results reported in Harder & Hansen to construct a specific benchmark in which the boundaries of the fluid are taken to be impenetrable, non-slip and isothermal, with the added boundary condition for the magnetic field <b>B</b> that the field must be entirely radial there; this type of boundary condition for <b>B</b> is frequently referred to as ‘pseudo-vacuum’. This latter condition should be compared with the more frequently used insulating boundary condition. This benchmark is so-defined in order that computer codes based on local methods, such as finite element, finite volume or finite differences, can handle the boundary condition with ease. The defined benchmark, governed by specific choices of the Roberts, magnetic Rossby, Rayleigh and Ekman numbers, possesses a simple solution that is steady in an azimuthally drifting frame of reference, thus allowing easy comparison among results. Results from a variety of types of code are reported, including codes that are fully spectral (based on spherical harmonic expansions in angular coordinates and polynomial expansions in radius), mixed spectral and finite difference, finite volume, finite element and also a mixed Fourier-finite element code. There is good agreement among codes