Understanding Thermal Stability of
Radiation-Dominated Disks
and
Radiative Efficiency of Global Relativistic
Disks
with
Omer Blaes, Shigenobu Hirose
Scott Noble, John Hawley, Kris Beckwith
Understanding Thermal Stability of
Radiation-Dominated Disks
Radiation-Dominance Is the Natural State of
the Interesting Portions of Bright Disks
Radiation pressure exceeds gas pressure for
r =r g < 170(L =L E ) 16=21 (M =M ¯ ) 2=21
That is, for the most interesting
parts of all bright accretion disks
around black holes
Yet a – Model Predicts Thermal Instability
When pr > Shakura
pg & Sunyaev 1976
Z
$\int dz Q \propto p_r h$$
Z
dz Q »
Energy conservation gives Z
The a model asserts
Z
dz Tr Á »
dz Tr Á
dz p
Z
h/ F =
When radiation pressure dominates,
Z
pr » Qt cool » Q(h=c)¿ » (¿=c) dz Q
And
dz Q
T hermal Inst ability
Dissipation and Pressure Are Correlated
So why doesn’t the thermal instability take place ?
What Does Dimensional Analysis Really Imply?
Pressure and stress are comparable, but
does that mean pressure controls stress?
Orbital shear does work on magnetic field,
magnetic field dissipates, heat becomes radiation---so magnetic energy and stress drive the pressure,
not the other way around!
Evidence from Simulation Data
Magnetic leads
Radiation leads
Magnetic Energy vs. Radiation Energy
Explore with Toy Model
dE B
EB 0
= R(t)
dt
t gr owt h
µ
ER
ER 0
¶n
EB
¡
t diss
dE R
EB
ER
=
¡
dt
t diss t cool
dEB
= R(t)En ¡ EB
R
d¿
In dimensionless form,
¢
dER
EB 0 ¡
=
EB ¡ E1¡ s
R
d¿
ER0
Results Strongly Resemble Simulations
Without any intrinsic
pressure-stress
correlation: n=s=0
Including a Pressure/Magnetic Energy
Correlation --- After the Fact
Thermal balance means
EB / E1¡
R
Independent of n
s
Which Variables Really Control the Stress?
As suggested by the structure of shearingbox simulations, S and W are the truly
fundamental variables wherever the inflow
time is the longest timescale.
Magnetic field intensity, and secondarily, the
pressure, follow, with dissipation of
magnetic energy driving the pressure, as
regulated by the radiative loss rate.
Radiative Efficiency of Global Relativistic
Disks
Origin of Traditional Efficiency Numbers:
the Novikov-Thorne model
•
•
•
•
Full GR
Time-steady, axisymmetric, vertically-integrated
Energy and angular momentum conservation
Boundary conditions—
energy: prompt radiation carries off dissipation
angular momentum: zero-stress at ISCO
h = ut(ISCO)
MHD Stresses Don’t Know to Stop at the ISCO
(Thorne 1974): “In the words of my referee, James M. Bardeen (which
echo verbal warnings that I have received from Ya. B. Zel’dovich and
V.F. Schwartzman), ‘It seems quite possible that magnetic stresses
could cause large deviations from circular orbits in the very inner part
of the accretion disk….’”
It follows that the Novikov-Thorne radiative efficiency numbers may
not be the last word when magnetic stresses are important.
Numerical Procedure
• Extend HARM (GR/MHD, total-energy,
conservative) from 2-d axisymmetric to 3-d
• Introduce toy-model optically thin cooling function:
(1) rapidly radiates (almost) all the heat generated
(2) allows aspect ratio regulation
r
·
L =
½²
º = ¡ Lu
T
º
¹
¹
²
(H ) 2
¡ 1+ j
²
(H ) 2
¸ 1=2
¡ 1j
A First Result
a/M = 0.9
H/r = 0.1
T = 15000 GM/c3
Surface Brightness in the Fluid Frame
averaged over 10000—12000M
Preliminary Summary
• There is noticeable radiation beyond N-T
• Dependence on H/r, a/M to be explored