Figure 20

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"Foundations of Black Hole Accretion Disk Theory"

Marek A. Abramowicz and P. Chris Fragile

	Abstract
1	Introduction
2	Three Destinations in Kerr’s Strong Gravity
	2.1	The event horizon
	2.2	The ergosphere
	2.3	ISCO: the orbit of marginal stability
	2.4	The Paczyński–Wiita potential
	2.5	Summary: characteristic radii and frequencies
3	Matter Description: General Principles
	3.1	The fluid part
	3.2	The stress part
	3.3	The Maxwell part
	3.4	The radiation part
4	Thick Disks, Polish Doughnuts, & Magnetized Tori
	4.1	Polish doughnuts
	4.2	Magnetized Tori
5	Thin Disks
	5.1	Equations in the Kerr geometry
	5.2	The eigenvalue problem
	5.3	Solutions: Shakura–Sunyaev & Novikov–Thorne
6	Slim Disks
7	Advection-Dominated Accretion Flows (ADAFs)
8	Stability
	8.1	Hydrodynamic stability
	8.2	Magneto-rotational instability (MRI)
	8.3	Thermal and viscous instability
9	Oscillations
	9.1	Dynamical oscillations of thick disks
	9.2	Diskoseismology: oscillations of thin disks
10	Relativistic Jets
11	Numerical Simulations
	11.1	Numerical techniques
	11.2	Matter description in simulations
	11.3	Polish doughnuts (thick) disks in simulations
	11.4	Novikov–Thorne (thin) disks in simulations
	11.5	ADAFs in simulations
	11.6	Oscillations in simulations
	11.7	Jets in simulations
	11.8	Highly magnetized accretion in simulations
12	Selected Astrophysical Applications
	12.1	Measurements of black-hole mass and spin
	12.2	Black hole vs. neutron star accretion disks
	12.3	Black-hole accretion disk spectral states
	12.4	Quasi-Periodic Oscillations (QPOs)
	12.5	The case of Sgr A*
13	Concluding Remarks
	Acknowledgements
	References
	Footnotes
	Figures
	Tables

Figure 20: Left: Time-averaged rest mass density in the $r$ – $z$ plane for four GRMHD simulations with $a = 0$ and various disk thicknesses. The dashed vertical line marks the ISCO. The disk opening angle, $h = H ∕r$ , and effective Shakura–Sunyaev viscosity, $α$ , are reported in each panel. The top three panels have $h ≪ α$ and the inner edge of the disk is located outside the ISCO. The bottom panel has $h ≫ α$ and the density increases monotonically down to the event horizon. Figure from [241]. Right: Various fluxes as functions of radius for a numerical Novikov–Thorne disk simulation. Top: Mass accretion rate. Second panel: Accreted specific angular momentum. Solid line is simulation data; dashed line gives Novikov–Thorne solution; dotted line is ISCO value. Note that the specific angular momentum does not drop significantly inside the ISCO, unlike for thick disks, such as in Figure 17. Third panel: The “nominal” efficiency, which is the total loss of specific energy from the fluid. Bottom panel: Specific magnetic flux. The near constancy of this quantity inside the ISCO is an indication that magnetic stresses are not significant in this region. Image reproduced by permission from [240].