The Impact of Magnetic Stresses and
Inhomogeneities on Accretion Disk Spectra
Shane Davis
IAS
Omer Blaes
Ivan Hubeny
Neal Turner
Julian Krolik
Jim Stone
Shigenobu Hirose
Questions Addressed in This Talk
• How do magnetic fields and associated
inhomogeneities affect disk spectra?
(concentrate on local effects)
• What can we learn from (local) accretion disk
simulations?
• What impact does this have on spin
estimates?
The Multicolor Disk Model
• Assumes simple
temperature
distribution:

• Spectrum assumed to
be color-corrected
blackbody:

BHSPEC
i

Model Parameters
L/LEdd
Inclination
Spin
Mass
Spectral Formation
= 0
z=0
abs= 1
z = abs
abs =  / abs 
: emissivity; abs = mean free path to absorption
Spectral Formation
= 0
z=0
abs= 1
z = abs
abs =  / abs 
: emissivity; abs = mean free path to absorption
Spectral Formation
= 0
z=0
abs= 1
z = abs
F =  abs =  / abs = B(T)
: emissivity; abs = mean free path to absorption
Spectral Formation
= 0
z=0
es = 1
z = es
eff = 1
z = eff
abs = 1
z = abs
abs =  / abs  es =  / es  abs >> es
: emissivity; abs, es = mean free path to absorption/scattering
eff = es abs)1/2; eff = (abs es)1/2
Spectral Formation
= 0
z=0
es = 1
z = es
eff = 1
z = eff
abs = 1
z = abs
abs =  / abs  es =  / es  abs >> es
: emissivity; abs, es = mean free path to absorption/scattering
eff = es abs)1/2; eff = (abs es)1/2
Spectral Formation
= 0
z=0
es = 1
z = es
eff = 1
z = eff
abs = 1
z = abs
F =  eff =  abs (es /abs)1/2 = B(abs /es)1/2
: emissivity; abs, es = mean free path to absorption/scattering
eff = es abs)1/2; eff = (abs es)1/2
Spectral Formation
•
•
•
•
Depth of formation *: optical
depth where (es abs)1/2~1
 > *: absorbed
 < *: escape
Thomson scattering produces
modified blackbody:
Due to temperature gradients
Compton scattering gives a
softer Wien spectrum
Very approximately:
fcol ~ T*/Teff ~ 1.5-1.8
for BHBs
Overall Vertical Structure of Disk with
Prad ~ Pgas
Pmag > Prad ~ Pgas
Parker Unstable
Regions
Prad ~ Pgas > Pmag
MRI - the source of
accretion power
Pmag > Prad ~ Pgas
Parker Unstable
Regions
Photosphere
z/H
Photosphere
r H
Hirose et al.
Magnetic Pressure: Vertical
Structure
•
•
•
•
Pmag = B2/8 taken from
simulations
Extra magnetic pressure support
increases scale height:
hmag = Pmag/(d Pmag/dz) > hgas
This leads to density reduction
at *:
* ~ es  h so
 ~ * / (es h)
Lower means lower ratio of
absorption to scattering:
abs/ es *
which means larger T*/Teff
and larger fcol
No B field
B field
Simulation
Magnetic Pressure: Spectrum
•
•
•
Lower * and higher T*
combine to give a harder
spectrum
In this case lower * alters
statistical equilibrium -lower recombination rate
relative to photoionization
rate yield higher ionization
and weaker edges
Overall effect is an
enhancement of fcol by
~10-15%
No B field
B field
Inhomogeneities: Vertical
Structure
•
•
•
Compare 3D with 1D
average: dependence
is important:
 abs -2
es -1
Non-linear dependence
of  on  leads to
enhanced emission
Due to weaker
dependence on ,
photons escape
predominantly through
low regions
Inhomogeneities: Monte Carlo
Spectra
•
•
•
Spectral shape is
approximately
unchanged, but flux is
enhanced by ~40%
Increased efficiency
allows lower T* to
produce equivalent flux
Would lead to reduction
of fcol by ~15-20%
3-D MC
1-D
40%
Conclusions
• Magnetic pressure support acts to make disk spectra
harder -- larger fcol
• Density inhomogeneities will tend to make disk
spectra softer -- smaller fcol
• These uncertainties should be accounted for in black
hole spin estimates -- approximately 20% uncertainty
for a/M ~ 0.8 if fcol is off by ~15%