Part II: Magnetic to Rest-Mass Density Ratio

1. Introduction
2. B-Fields Following Particles

Introduction

Fig. 1-1: Initial Configuration of Black Hole Magnetized Disk

To demonstrate that BHNS mergers may form an SGRB engine under appropriate conditions, the final disk from the unmagnetized case was seeded with a purely poloidol magnetic field with and average magnetic-to-gas pressure ration of ~0.1%. Though dynamically insignifigant initially, the strength of the fields is sufficient to resolve MRI throughout most of the disk due to the purely poloidal nature of the fields. Within ~.5 orbital periods, magnetic turbulence begins, accretion of the dipole poloidal fields occurs, and inflows diminish. The magnetic-to-rest mass density ratio,B²/2ρ₀, amplifies to a maximum value greater than 100, and mildly relativistic outflows appeat in funnels above and below the black hole.

B-Fields Following Particles

In the clip, the magnetic to rest-mass density ratio of the star is plotted on a logarithmic scale. The final disk from the unmagnetized case is seeded with a purely poloidal field with an average magnetic-to-gas pressure ratio of ~.1%. For steady-state, Poynting-dominated jets, the energy-to-mass flux ratio, in this case approximately equal to B²/2ρ₀, is equal to the maximum possible Lorentz factor in the asymptotic jet. The following images display the density profile in a meridional plane intersecting the black hole centroid. Shown in white are streamlines intersecting a grid of points lying above and below the black hole.

The magnetic fields were drawn through grid points. These grid points were a set of points that lie in circular disks at a certain height above and below the black hole. The motivation for this visualization was to see how well the magnetic fields are able to collimate. To emphasize this, no toroidal fieldlines are rendered. This visualization exhibits similar qualities to those from the visualization above.

The final collimated magnetic fields are rendered in white.

Fig. 2-1: B-field profile at time t/M = 2152	Fig. 2-2: B-field profile at time t/M = 2238
Fig. 2-3: B-field profile at time t/M = 2404	Fig. 2-4: B-field profile at time t/M = 2596

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Poloidal fields in the remnant disk can be amplified exponentially by MRI, driving the initial influx of matter into the black hole to reverse itself and generating an outflow of matter in the regions above and below the black hole. The magnetic to rest-mass density ratio, B²/2ρ₀, with an intial value of ~10^-4, amplifies to a maximum value of over 100 in the funnels above and below the black hole. For steady-state, Poynting-dominated jets, the energy-to-mass flux ratio, in this case approximately equal to B²/2ρ₀, is equal to the maximum possible Lorentz factor in the asymptotic jet. At this time, the Poynting luminosity is 3.5×10^-3 d/dt(M₀c ²) = 1.28×10⁵² ergs/sec, which may be sufficient to power an SGRB.