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Dynamical Simulations of Magnetically Channeled Line- Driven Stellar Winds. I. Isotermal, Nonrotating, Radially Driven Flow
ud-Doula, Asif and Owocki, Stanley P

Abstract

We present numerical magnetohydrodynamic (MHD) simulations of the effect of stellar dipole magnetic fields on line-driven wind outflows from hot, luminous stars. Unlike previous fixed-field analyses, the simula- tions here take full account of the dynamical competition between field and flow and thus apply to a full range of magnetic field strength and within both closed and open magnetic topologies. A key result is that the over- all degree to which the wind is influenced by the field depends largely on a single, dimensionless "wind mag- netic confinement parameter" &eta* = (BeqR*)2/[(dM/dt)v&infin], which characterizes the ratio between magnetic field energy density and kinetic energy density of the wind. For weak confinement, &eta* &le 1, the field is fully opened by the wind outflow, but nonetheless, for confinements as small as &eta* = 1/10 it can have a significant back- influence in enhancing the density and reducing the flow speed near the magnetic equator. For stronger con- finement, &eta* > 1, the magnetic field remains closed over a limited range of latitude and height about the equa- torial surface, but eventually is opened into a nearly radial configuration at large radii. Within closed loops, the flow is channeled toward loop tops into shock collisions that are strong enough to produce hard X-rays, with the stagnated material then pulled by gravity back onto the star in quite complex and variable inflow patterns. Within open field flow, the equatorial channeling leads to oblique shocks that are again strong enough to produce X-rays and also lead to a thin, dense, slowly outflowing "disk" at the magnetic equator. The polar flow is characterized by a faster-than-radial expansion that is more gradual than anticipated in pre- vious one-dimensional flow tube analyses and leads to a much more modest increase in terminal speed (less than 30%), consistent with observational constraints. Overall, the results here provide a dynamical ground- work for interpreting many types of observations--e.g., UV line profile variability, redshifted absorption or emission features, enhanced density-squared emission, and X-ray emission--that might be associated with perturbation of hot-star winds by surface magnetic fields.


Summary

This paper provides the mathematical groundwork for future MHD simulations carried out by Owocki and his team. As per &theta1 Ori C, the authors speculate that its large magnetic field may have evolved from an early, convective phase during initial formation. Alternatively, it may have formed as a result of compression of interstellar magnetic flux during initial stellar collapse. This suggestion is made due to the star's relative youth.

The simulations here are "based on an isotermal approximation of the complex energy balance and so can provide only a rough estimate of the level of shock heating and X-ray generation." They use the ZEUS 3D code modified to use spherical polar cooridinates in a 2-dimensional formulation. The critical equations are the time-dependent conservation of mass:

(D&rho/Dt) + &rho&nabla&bull&nu = 0
and the equation of motion:
&rho(D&nu/Dt) = -&nabla p + 1/(4&pi)&bull(&nabla x B) x B -
GM(1-&Gamma)r
r2
 + glines
The authors also go through the details of the numerical specifications for their simulations.

In general, once the authors had the basic simulation set up, they tested their model by varying the wind magnetic confinement parameter &eta* between 0.01 and 10. At low values of &eta*, the magnetic field hardly affects the wind at all. For large &eta*, however, the field has a significant influence on the wind.

The simulations run were time dependent, and essentially consisted of throwing a magnetic field on top of a pre-existing stellar wind structure. These two dynamic states are highly incompatible, and the sudden combination of the two leads to discontinuities in both field and flow. Eventually, the flow opens up the field lines, resulting in sustained, practically radial flow. The authors speculate that once the field lines have opened, "the outflow should keep them open to arbitrarily large distances." A narrow disk of dense, slow outflow is observed at the magnetic equator as well.

The authors point out the interesting fact that, even though the simulation is set up to be entirely symmetric, this initial symmetry is spontaneously broken by material infall. This leads to random, possibly chaotic behavior from that point on.

There are a few interesting consequences as far as observation implications. For instance, the detection of occasional occurrences of redward-shifted features in absorption or emission can be readily explained by the infall of material near the magnetic equator. Such infall is an inevitable outcome of the magnetically-trapped wind material with sufficient wind magnetic confinement (&eta*). In addition, the MHD models provide implications for the detections of variable X-ray emissions from some hot stars. Such X-rays can be produced by the sudden collision of wind material at the magnetic equator. There will be severe compression, which is quickly alleviated by means of radiation within a narrow cooling layer. If the compressions are shock-type, they could easily have enough energy to produce X-rays.


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