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

Summary Report for Concentrating Solar Power Thermal Storage Workshop: New Concepts and Materials for Thermal Energy Storage and Heat-Transfer Fluids, May 20, 2011

This document summarizes a workshop on thermal energy storage for concentrating solar power (CSP) that was held in Golden, Colorado, on May 20, 2011. The event was hosted by the U.S. Department of Energy (DOE), the National Renewable Energy Laboratory, and Sandia National Laboratories. The objective was to engage the university and laboratory research communities to identify and define research directions for developing new high-temperature materials and systems that advance thermal energy storage for CSP technologies. This workshop was motivated, in part, by the DOE SunShot Initiative, which sets a very aggressive cost goal for CSP technologies -- a levelized cost of energy of 6 cents per kilowatt-hour by 2020 with no incentives or credits

Can the Earth's dynamo run on heat alone?

The power required to drive the geodynamo places significant constraints on the heat passing across the core-mantle boundary and the Earth's thermal history. Calculations to date have been limited by inaccuracies in the properties of liquid iron mixtures at core pressures and temperatures. Here we re-examine the problem of core energetics in the light of new first-principles calculations for the properties of liquid iron. There is disagreement on the fate of gravitational energy released by contraction on cooling. We show that only a small fraction of this energy, that associated with heating resulting from changes in pressure, is available to drive convection and the dynamo. This leaves two very simple equations in the cooling rate and radioactive heating, one yielding the heat flux out of the core and the other the entropy gain of electrical and thermal dissipation, the two main dissipative processes. This paper is restricted to thermal convection in a pure iron core; compositional convection in a liquid iron mixture is considered in a companion paper. We show that heat sources alone are unlikely to be adequate to power the geodynamo because they require a rapid secular cooling rate, which implies a very young inner core, or a combination of cooling and substantial radioactive heating, which requires a very large heat flux across the core-mantle boundary. A simple calculation with no inner core shows even higher heat fluxes are required in the absence of latent heat before the inner core formed

Physical processes leading to surface inhomogeneities: the case of rotation

In this lecture I discuss the bulk surface heterogeneity of rotating stars, namely gravity darkening. I especially detail the derivation of the omega-model of Espinosa Lara & Rieutord (2011), which gives the gravity darkening in early-type stars. I also discuss the problem of deriving gravity darkening in stars owning a convective envelope and in those that are members of a binary system.Comment: 23 pages, 11 figure, Lecture given to the school on the cartography of the Sun and the stars (May 2014 in Besan\c{c}on), to appear in LNP, Neiner and Rozelot edts V2: typos correcte

Why dynamos are prone to reversals

In a recent paper (Phys. Rev. Lett. 94 (2005), 184506; physics/0411050) it was shown that a simple mean-field dynamo model with a spherically symmetric helical turbulence parameter alpha can exhibit a number of features which are typical for Earth's magnetic field reversals. In particular, the model produces asymmetric reversals, a positive correlation of field strength and interval length, and a bimodal field distribution. All these features are attributable to the magnetic field dynamics in the vicinity of an exceptional point of the spectrum of the non-selfadjoint dynamo operator. The negative slope of the growth rate curve between the nearby local maximum and the exceptional point makes the system unstable and drives it to the exceptional point and beyond into the oscillatory branch where the sign change happens. A weakness of this reversal model is the apparent necessity to fine-tune the magnetic Reynolds number and/or the radial profile of alpha. In the present paper, it is shown that this fine-tuning is not necessary in the case of higher supercriticality of the dynamo. Numerical examples and physical arguments are compiled to show that, with increasing magnetic Reynolds number, there is strong tendency for the exceptional point and the associated local maximum to move close to the zero growth rate line. Although exemplified again by the spherically symmetric alpha^2 dynamo model, the main idea of this ''self-tuning'' mechanism of saturated dynamos into a reversal-prone state seems well transferable to other dynamos. As a consequence, reversing dynamos might be much more typical and may occur much more frequently in nature than what could be expected from a purely kinematic perspective.Comment: 11 pages, 10 figure

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

Gross thermodynamics of two-component core convection

We model the inner core by an alloy of iron and 8 per cent sulphur or silicon and the outer core by the same mix with an additional 8 per cent oxygen. This composition matches the densities of seismic model, Preliminary Reference Earth Model (PR-EM). When the liquid core freezes S and Si remain with the Fe to form the solid and excess 0 is ejected into the liquid. Properties of Fe, diffusion constants for S, Si, 0 and chemical potentials are calculated by first-principles methods under the assumption that S, 0, and Si react with the Fe and themselves, however, not with each other. This gives the parameters required to calculate the power supply to the geodynamo as the Earth's core cools. Compositional convection, driven by light O released at the inner-core boundary on freezing, accounts for half the entropy balance and 15 per cent of the heat balance. This means the same magnetic field can be generated with approximately half the heat throughput needed if the geodynamo were driven by heat alone. Chemical effects are significant: heat absorbed by disassociation of Fe and 0 almost nullify the effect of latent heat of freezing in driving the dynamo. Cooling rates below 69 K Gyr(-1) are too low to maintain thermal convection everywhere; when the cooling rate lies between 35 and 69 K Gyr(-1) convection at the top of the core is maintained compositionally against a stabilizing temperature gradient; below 35 K Gyr(-1) the dynamo fails completely. All cooling rates freeze the inner core in less than 1.2 Gyr, in agreement with other recent calculations. The presence of radioactive heating will extend the life of the inner core, however, it requires a high heat flux across the core-mantle boundary. Heating is dominated by radioactivity when the inner core age is 3.5 Gyr. We, also, give calculations for larger concentrations of O in the outer core suggested by a recent estimation of the density jump at the inner-core boundary, which is larger than that of PREM. Compositional convection is enhanced for the higher density jumps and overall heat flux is reduced for the same dynamo dissipation, however, not by enough to alter the qualitative conclusions based on PREM. Our preferred model has the core convecting near the limit of thermal stability, an inner-core age of 3.5 Gyr and a core heat flux of 9 TW or 20 per cent of the Earth's surface heat flux, 80 per cent of which originates from radioactive heating

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