7. The fundamental unsolved problems - davidar/scholarpedia GitHub Wiki
Analytic models assume the zero torque inner boundary condition:
the viscous torque at the inner edge of a very thin accretion disc
is vanishingly small. This assumption has been challenged by
Krolik and others but
defended by
Paczynski and collaborators.
A very important numerical work that supports
Paczynski's point of view was published in 2008 by
Shafee and others.
It describes the results of three-dimensional
general relativistic magnetohydrodynamical simulations of a
geometrically thin accretion disc around a non-spinning black
hole. The disc has a relative thickness h ~0.005-0.1 over
the radius range <math>(2-20)GM/c^2\ .</math> In steady state, the specific
angular momentum profile of the inflowing magnetized gas deviates
by less than 2% from that of the standard thin disc model with
the zero-inner-torque assumed. In addition, the magnetic torque at
ISCO is only ~2% of the inward flux of the angular momentum
at that radius. Both results indicate that magnetic coupling
across the inner edge is relatively unimportant for geometrically
thin discs around non-spinning black holes, which is in accordance
with Paczynski's ideas. However, until a mathematically
correct analytic model describing thin MHD accretion flows
near the ISCO becomes available, the controversy is likely to
continue.
The unresolved issue of the zero torque inner boundary condition is technically
rather difficult, mostly because the coupled non-linear
differential equations that describe the accretion flow have multiple
critical points near <math>r_{in}\ .</math> The issue is also fundamentally
important because all detailed comparisons between theory and
observations performed to date were based on the correctness of the
zero torque inner boundary condition. A related fundamental problem,
whether a non-zero torque at the event horizon may couple black holes
with infalling matter, is also unresolved.
While some authors claim that an electrodynamic torque is possible,
others argue that "black holes have no hair" and thus, in particular,
do not anchor magnetic fields. Therefore, any change in the three properties
of a black hole (mass, angular momentum, charge) may occur only
by a direct capture of matter by the black hole. Matter may gain some
rotational energy of the black hole only if a particle or photon
with negative energy</i> would cross the event horizon.
Both thin and thick discs models are stationary and axially symmetric. They usually describe matter in the hydrodynamical approximation (with no magnetic field). In addition, however, it is still unknown whether it is physically legitimate to make all these assumptions and suppose that in some "averaged" sense accretion flows may be (approximately) described in terms of stationary and axially symmetric hydrodynamical equilibria. While observations seem to suggest that many real astrophysical sources experience periods in which this may be quite reasonable, several authors point out that results of recent numerical simulations indicate that the MRI and other instabilities could make the accretion flows genuinely non-steady and non-symmetric, and that the very concept of separate timescales may be questionable in the sense that locally it could be <math>t_{dyn} \approx t_{the} \approx t_{vis}\ .</math>
 The observed spectral states may be
caused by a non-stationary transition between Shakura-Sunyaev thin disc
(a solid bar) and adaf (a cloud of dots).
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