File:Thick-disc-03.jpg

Equipressure surfaces for a non rotating black hole, and with angular momentum distribution \[ {\ell}(r, \theta) = {\ell}_0\left\{ \frac{{\ell}_K(r)}{{\ell}_0}\right\}^{\beta}(\sin\theta)^{2\gamma} ~\left({\rm for}~~ r \geq r_{ms}\right) ,~~ {\ell}(r, \theta) = {\ell}_{ms}(\sin\theta)^{2\gamma} ~\left({\rm for}~~ r < r_{ms}\right). ~~{\rm Here}~~ {\ell}_0 \equiv \eta\,{\ell}_K(r_{ms}) ~~{\rm and}~~ {\ell}_{ms} = {\ell}_0\left\{\frac{{\ell}_K(r_{ms})}{{\ell}_0}\right\}^{\beta}. \] with \(\gamma = 0.18\), \(\eta = 1.085\), \(\beta = 0.9\). It is compared with global MHD numerical simulations by Fragile et al., 2007, time averaged over a period corresponding to the orbital period at \(25r_G\) (color-coded). Credit: Lei et al., 2008