Literature for Jet study w/ H-AMR



  • Yuan & Narayan 14:
    • 2D simulations do not treat the MRI accurately because of Cowling’s antidynamo theorem (Cowling 1933), which limits the growth of the poloidal magnetic field and causes turbulence to die away. Thus, no steady accretion is possible in 2D, and one has to carefully select a period of time after the disk has become turbulent but before the turbulence dies out. There has been no systematic study of how well the properties of this intermediate period in 2D simulations agree with those of3D simulations with sustained turbulence. Qualitatively, it appears that the differences are not large.

Magnetic field

  • Yuan & Narayan 14:
    • most global simulations start with a weak magnetic field (initial $\beta$ ~ 100), Machida et al. (2000) used a strong initial toroidal field with $\beta$ = 1. There was no MRI in their simulation, but they found the Parker instability, which led to the formation of a magnetized corona.
    • Models with a purely toroidal initial field evolve much more slowly than those with a poloidal initial field, because the former have neither an initial vertical field, which is needed for the linear MRI, nor a radial field, which is needed for field amplification via shear.


  • Yuan & Narayan 14:
    • an idea originally proposed by Bisnovatyi-Kogan & Ruzmaikin (1974), in which a strong vertical bipolar magnetic field is pushed into the central black hole by the thermal and ram pressure of the accreting gas.
    • The MAD state is special in that the flux threading the hole is at its maximum saturation value for the given mass accretion rate $\dot{M}_{\rm BH}$


  • Yuan & Narayan 14:
    • Systems that have not reached the MAD limit have been referred to as SANE (standard and normal evolution) (Narayan et al. 2012b). They span a one-parameter family of models extending from $\Phi = 0$ up to a magnetic flux just below $\Phi_{\rm MAD}$. Structural differences, most notably in the jet, are evident between MAD and SANE models (Narayan et al. 2012b, Sadowski et al. 2013a).


  • Yuan & Narayan 14:
    • Inside the innermost stable circular orbit (ISCO) is the plunging region. Here, the flow spirals in rapidly toward the black hole horizon, and the motion is almost laminar. Although the ISCO is roughly where the turbulent gas in the disk transitions to laminar inflow, there is no other specific signature in the flow dynamics associated with the ISCO. By contrast, in thin disks, the flow changes dramatically across the ISCO (Reynolds & Fabian 2008, Shafee et al. 2008, Penna et al. 2010; but see Noble et al. 2010).


  • Yuan & Narayan 14:
    • For geometrically thin accretion disks, Lense-Thirring precession may cause a tilted disk to align with the spin axis of the black hole out to a fairly large radius (Bardeen & Petterson 1975, Scheuer & Feiler 1996, Lodato & Pringle 2006).
    • Fragile and collaborators have carried out a number of numerical simulations of tilted hot accretion flows (Fragile et al. 2007, 2009; Fragile 2009; Dexter & Fragile 2011, 2013). They found that the disk does not align with the black hole, in agreement with theoretical predictions for a geometrically thick disk (Papaloizou & Lin 1995). Instead, the disk precesses as a whole out to some radius. Alignment does happen when accretion occurs in the MAD regime (Section 3.2.3) and may have observational implications for relativistic jets (McKinney et al. 2013).


  • Yuan & Narayan 14:
    • Simulation results are often given in Heaviside-Lorentz units, whereas numerical estimates in this article are in Gaussian units. The two differ by a factor of $\sqrt{4\pi}$. For instance, the magnetic pressure is $B^{2}/8\pi$ in Gaussian units but $B^{2}/2$ in Heaviside-Lorentz units.