5. Discussion

5.3 Stress at the marginally stable orbit

Since the pseudo-Newtonian potential is used for these simulations, we can examine the evolution of the stress and specific angular momentum in the region of the marginally stable orbit. The cylindrical simulations demonstrate that the stress is continuous at rms; indeed, there is nothing special at the precise location of rms in any disk quantity. In the present simulations the slope of the specific angular momentum $d\ell/dR$ inside the marginally stable orbit is smaller than seen in the fully global thick disk simulations of Hawley (2000) or HK. The slope is close to that reported by ARC from their simulations of cylindrical Keplerian disks. What then determines the degree to which $\ell $ is reduced inside of rms? In each case there is some nonzero stress inside of rms. Naturally, larger stresses have a larger effect. The question becomes what circumstances produce those larger stresses?

A reduced angular computational domain lowers the observed stress levels, but only by about 10%. The use of an isothermal versus adiabatic equation of state apparently has even less influence, at least when the temperatures at rms are comparable. The internal pressure may have a greater influence, by increasing the radial distance inside of rms where the flow remains subsonic, however there is only circumstantial evidence for this in the results to date. The simulations run here were about half as hot as those of HK, and comparable to the fiducial runs of ARC. ARC also ran a simulation with the sound speed cut in half but did not report any significant differences in the results.

Possibly the most important approximation is the use of cylindrical geometry in lieu of full stratification. Stratified simulations find that the largest magnetic field strengths and Alfvén speeds occur in the lower density regions surrounding the equator (Miller & Stone 2000). In the thick disk simulation of HK the specific angular momentum was nearly constant inside of rms along the equator. The strongest fields and stresses were located above and below the equator, and this is where the greatest reduction in $\ell $ occurred. To investigate this further there appears to be no substitute for stratified global simulations.

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