High Resolution Simulations of the Plunging Region in a Pseudo-Newtonian Potential: Dependence on Numerical Resolution and Field Topology

New three dimensional magnetohydrodynamic simulations of accretion disk dynamics in a pseudo-Newtonian Paczynski-Wiita potential are presented. These have finer resolution in the inner disk than any previously reported. Finer resolution leads to increased magnetic field strength, greater accretion rate, and greater fluctuations in the accretion rate. One simulation begins with a purely poloidal magnetic field, the other with a purely toroidal field. Compared to the poloidal initial field simulation, a purely toroidal initial field takes longer to reach saturation of the magnetorotational instability and produces less turbulence and weaker magnetic field energies. For both initial field configurations, magnetic stresses continue across the marginally stable orbit; measured in units corresponding to the Shakura-Sunyaev alpha parameter, the stress grows from ~0.1 in the disk body to as much as ~10 deep in the plunging region. Matter passing the inner boundary of the simulation has ~10% greater binding energy and ~10% smaller angular momentum than it did at the marginally stable orbit. Both the mass accretion rate and the integrated stress fluctuate widely on a broad range of timescales.Comment: Accepted for publication in the Astrophysical Journal. For Web version with mpeg animations see http://www.astro.virginia.edu/VITA/papers/plunge

Hysteresis between distinct modes of turbulent dynamos

Nonlinear mean-field models of the solar dynamo show long-term variability, which may be relevant to different states of activity inferred from long-term radiocarbon data. This paper is aimed to probe the dynamo hysteresis predicted by the recent mean-field models of Kitchatinov \& Olemskoy (2010) with direct numerical simulations. We perform three-dimensional simulations of large-scale dynamos in a shearing box with helically forced turbulence. As initial condition, we either take a weak random magnetic field or we start from a snapshot of an earlier simulation. Two quasi-stable states are found to coexist in a certain range of parameters close to the onset of the large-scale dynamo. The simulations converge to one of these states depending on the initial conditions. When either the fractional helicity or the magnetic Prandtl number is increased between successive runs above the critical value for onset of the dynamo, the field strength jumps to a finite value. However, when the fractional helicity or the magnetic Prandtl number is then decreased again, the field strength stays at a similar value (strong field branch) even below the original onset. We also observe intermittent decaying phases away from the strong field branch close to the point where large-scale dynamo action is just possible. The dynamo hysteresis seen previously in mean-field models is thus reproduced by 3D simulations. Its possible relation to distinct modes of solar activity such as grand minima is discussed.Comment: Published in Ap

3D global simulations of RIAFs: convergence, effects of azimuthal extent and dynamo

We study the long-term evolution of non-radiative geometrically thick ($H/R\approx 0.5$) accretion flows using 3D global ideal MHD simulations and a pseudo-Newtonian gravity. We find that resolving the scale height with 42 grid points is adequate to obtain convergence with the product of quality factors $\langle \langle Q_{\theta} \rangle \rangle \langle \langle Q_{\phi} \rangle \rangle \geq 300$ and magnetic tilt angle $\theta_B \sim 13^{\circ}-14^{\circ}$. Like previous global isothermal thin disk simulations, we find stronger mean magnetic fields for the restricted azimuthal domains. Imposing periodic boundary conditions with the azimuthal extent smaller than $2\pi$ make the turbulent field at low $m$ appear as a mean field in the runs with smaller azimuthal extent. But unlike previous works, we do not find a monotonic trend in turbulence with the azimuthal extent. We conclude that the minimum azimuthal extent should be $\geq \pi/2$ to capture the flow structure, but a full $2 \pi$ extent is necessary to study the dynamo. We find an intermittent dynamo cycle, with $\alpha$-quenching playing an important role in the nonlinear saturated state. Unlike previous local studies, we find almost similar values of kinetic and magnetic $\alpha$-s, giving rise to an irregular distribution of dynamo-$\alpha$. The effects of dynamical quenching are shown explicitly for the first time in global simulations of accretion flows.Comment: 24 pages, 27 figures, 4 tables. Accepted in MNRAS. We welcome comments and suggestion

The effect of magnetic topology on thermally-driven winds: towards a general formulation of the braking law

Stellar winds are thought to be the main process responsible for the spin down of main-sequence stars. The extraction of angular momentum by a magnetized wind has been studied for decades, leading to several formulations for the resulting torque. However, previous studies generally consider simple dipole or split monopole stellar magnetic topologies. Here we consider in addition to a dipolar stellar magnetic field, both quadrupolar and octupolar configurations, while also varying the rotation rate and the magnetic field strength. 60 simulations made with a 2.5D, cylindrical and axisymmetric set-up and computed with the PLUTO code were used to find torque formulations for each topology. We further succeed to give a unique law that fits the data for every topology by formulating the torque in terms of the amount of open magnetic flux in the wind. We also show that our formulation can be applied to even more realistic magnetic topologies, with examples of the Sun in its minimum and maximum phase as observed at the Wilcox Solar Observatory, and of a young K-star (TYC-0486- 4943-1) whose topology has been obtained by Zeeman-Doppler Imaging (ZDI).Comment: 17 pages, 13 figures, accepted for publication in ApJ (10/29/2014

Off-center ignition in type Ia supernova: I. Initial evolution and implications for delayed detonation

The explosion of a carbon-oxygen white dwarf as a Type Ia supernova is known to be sensitive to the manner in which the burning is ignited. Studies of the pre-supernova evolution suggest asymmetric, off-center ignition, and here we explore its consequences in two- and three-dimensional simulations. Compared with centrally ignited models, one-sided ignitions initially burn less and release less energy. For the distributions of ignition points studied, ignition within two hemispheres typically leads to the unbinding of the white dwarf, while ignition within a small fraction of one hemisphere does not. We also examine the spreading of the blast over the surface of the white dwarf that occurs as the first plumes of burning erupt from the star. In particular, our studies test whether the collision of strong compressional waves can trigger a detonation on the far side of the star as has been suggested by Plewa et al. (2004). The maximum temperature reached in these collisions is sensitive to how much burning and expansion has already gone on, and to the dimensionality of the calculation. Though detonations are sometimes observed in 2D models, none ever happens in the corresponding 3D calculations. Collisions between the expansion fronts of multiple bubbles also seem, in the usual case, unable to ignite a detonation. "Gravitationally confined detonation" is therefore not a robust mechanism for the explosion. Detonation may still be possible in these models however, either following a pulsation or by spontaneous detonation if the turbulent energy is high enough.Comment: 13 pages, 10 figures (resolution of some figures reduced to comply with astro-ph file size restriction); submitted to the Astrophysical Journal on 8/3/200

A theoretical study of the build-up of the Sun's polar magnetic field by using a 3D kinematic dynamo model

We develop a three-dimensional kinematic self-sustaining model of the solar dynamo in which the poloidal field generation is from tilted bipolar sunspot pairs placed on the solar surface above regions of strong toroidal field by using the SpotMaker algorithm, and then the transport of this poloidal field to the tachocline is primarily caused by turbulent diffusion. We obtain a dipolar solution within a certain range of parameters. We use this model to study the build-up of the polar magnetic field and show that some insights obtained from surface flux transport (SFT) models have to be revised. We present results obtained by putting a single bipolar sunspot pair in a hemisphere and two symmetrical sunspot pairs in two hemispheres.We find that the polar fields produced by them disappear due to the upward advection of poloidal flux at low latitudes, which emerges as oppositely-signed radial flux and which is then advected poleward by the meridional flow. We also study the effect that a large sunspot pair, violating Hale's polarity law would have on the polar field. We find that there would be some effect---especially if the anti-Hale pair appears at high latitudes in the mid-phase of the cycle---though the effect is not very dramatic.Comment: 18 pages, 18 figures, published in Ap

Total edge irregularity strength of complete graphs and complete bipartite graphs

AbstractA total edge irregular k-labelling ν of a graph G is a labelling of the vertices and edges of G with labels from the set {1,…,k} in such a way that for any two different edges e and f their weights φ(f) and φ(e) are distinct. Here, the weight of an edge g=uv is φ(g)=ν(g)+ν(u)+ν(v), i. e. the sum of the label of g and the labels of vertices u and v. The minimum k for which the graph G has an edge irregular total k-labelling is called the total edge irregularity strength of G.We have determined the exact value of the total edge irregularity strength of complete graphs and complete bipartite graphs