The Impact of Magnetic Stresses and The Impact of Magnetic Stresses and Inhomogeneities on Accretion Disk Inhomogeneities on Accretion Disk

SpectraSpectraShane DavisShane Davis

IASIAS

Omer BlaesOmer BlaesIvan HubenyIvan HubenyNeal TurnerNeal Turner

Julian KrolikJulian KrolikJim StoneJim StoneShigenobu HiroseShigenobu Hirose

Questions Addressed in This Questions Addressed in This TalkTalk

• How do magnetic fields and associated How do magnetic fields and associated inhomogeneities affect disk spectra? inhomogeneities affect disk spectra? (concentrate on local effects)(concentrate on local effects)

• What can we learn from What can we learn from (local) (local) accretion disk simulations?accretion disk simulations?

• What impact does this have on spin What impact does this have on spin estimates?estimates?

• Assumes simple Assumes simple temperature temperature distribution:distribution:

• Spectrum assumed Spectrum assumed to be color-corrected to be color-corrected blackbody:blackbody:

The Multicolor Disk ModelThe Multicolor Disk Model

F

F

BHSPECBHSPEC

€

i

L/LEdd

MassSpin

Inclination

Model ParametersModel Parameters

= 0= 0

absabs= 1= 1

Spectral FormationSpectral Formation

z = 0z = 0

z = z = absabs

: emissivity; : emissivity; absabs = mean free path to absorption = mean free path to absorption

abs abs = = / / abs abs

= 0= 0

absabs= 1= 1

Spectral FormationSpectral Formation

z = 0z = 0

z = z = absabs

: emissivity; : emissivity; absabs = mean free path to absorption = mean free path to absorption

abs abs = = / / abs abs

= 0= 0

absabs= 1= 1

Spectral FormationSpectral Formation

z = 0z = 0

z = z = absabs

FF = = abs abs = = / / abs abs = B= B(T)(T) : emissivity; : emissivity; absabs = mean free path to absorption = mean free path to absorption

= 0= 0

abs abs = 1= 1

Spectral FormationSpectral Formation

z = 0z = 0

z = z = absabs

: emissivity; : emissivity; absabs, , eses = mean free path to absorption/scattering = mean free path to absorption/scattering

effeff = = es es absabs))1/21/2;; effeff = ( = (absabs eses))1/21/2

es es = 1= 1 z = z = eses

eff eff = 1= 1 z = z = effeff

abs abs = = / / abs abs es es = = / / es es abs abs >> >> eses

= 0= 0

abs abs = 1= 1

Spectral FormationSpectral Formation

z = 0z = 0

z = z = absabs

: emissivity; : emissivity; absabs, , eses = mean free path to absorption/scattering = mean free path to absorption/scattering

effeff = = es es absabs))1/21/2;; effeff = ( = (absabs eses))1/21/2

es es = 1= 1 z = z = eses

eff eff = 1= 1 z = z = effeff

abs abs = = / / abs abs es es = = / / es es abs abs >> >> eses

= 0= 0

abs abs = 1= 1

Spectral FormationSpectral Formation

z = 0z = 0

z = z = absabs

: emissivity; : emissivity; absabs, , eses = mean free path to absorption/scattering = mean free path to absorption/scattering

effeff = = es es absabs))1/21/2;; effeff = ( = (absabs eses))1/21/2

es es = 1= 1 z = z = eses

eff eff = 1= 1 z = z = effeff

FF = = eff eff = = abs abs ((es es //absabs))1/2 1/2 = B= B ((abs abs //eses))1/21/2

Spectral FormationSpectral Formation• Depth of formationDepth of formation **: optical : optical

depth where depth where ((eses absabs))1/21/2~1~1

> > **: absorbed: absorbed

< < **: escape: escape

• Thomson scattering produces Thomson scattering produces modified blackbody:modified blackbody:

• Due to temperature gradients Due to temperature gradients Compton scattering gives a Compton scattering gives a softer Wien spectrum softer Wien spectrum

• Very approximately: Very approximately:

ffcol col ~ T~ T**/T/Teffeff ~ 1.5-1.8 ~ 1.5-1.8

for BHBsfor BHBs

Overall Vertical Structure of Disk Overall Vertical Structure of Disk with Pwith Prad rad ~ ~ PPgasgas

MRI - the source ofMRI - the source ofaccretion poweraccretion power

PhotospherePhotosphere

PhotospherePhotosphere

Parker UnstableParker UnstableRegionsRegions

Parker UnstableParker UnstableRegionsRegions

PPmag mag > P> Prad rad ~ ~ PPgasgas

PPmag mag > P> Prad rad ~ ~ PPgasgas

PPrad rad ~ ~ PPgas gas > P> Pmagmag

r H

z / H

Hirose et al.

Magnetic Pressure: Magnetic Pressure: Vertical StructureVertical Structure

• PPmagmag = B = B22/8/8 taken from taken from simulationssimulations

• Extra magnetic pressure Extra magnetic pressure support increases scale support increases scale height:height:

hhmagmag = P = Pmagmag/(d P/(d Pmagmag/dz) > h/dz) > hgasgas • This leads to density This leads to density reductionreduction

atat **::

* * ~ ~ es es h h soso

~ ~ * * / (/ (eses h) h)

• LowerLower means lower ratio means lower ratio of absorption to scattering:of absorption to scattering:

absabs/ / es es **

which means larger which means larger TT**/T/Teff eff

and larger and larger ffcolcol

No B fieldB field

Simulation

Magnetic Pressure: Magnetic Pressure: SpectrumSpectrum

• Lower Lower ** and higher and higher TT** combine to give a harder combine to give a harder spectrumspectrum

• In this case lower In this case lower ** alters statistical alters statistical equilibrium -- lower equilibrium -- lower recombination rate recombination rate relative to relative to photoionization rate yield photoionization rate yield higher ionization and higher ionization and weaker edgesweaker edges

• Overall effect is an Overall effect is an enhancementenhancement of of ffcolcol by by~~10-15%10-15%

No B field

B field

• Compare 3D with 1D Compare 3D with 1D average: average: dependence is dependence is important:important:

absabs -2-2

eses -1-1

• Non-linear Non-linear dependence of dependence of on on leads to enhanced leads to enhanced emissionemission

• Due to weaker Due to weaker dependence on dependence on , , photons escape photons escape predominantly predominantly through low through low regionsregions

Inhomogeneities: Vertical Inhomogeneities: Vertical StructureStructure

Inhomogeneities: Monte Inhomogeneities: Monte Carlo SpectraCarlo Spectra

• Spectral shape is Spectral shape is approximately approximately unchanged, but flux unchanged, but flux is enhanced by is enhanced by ~~40%40%

• Increased efficiency Increased efficiency allows lower allows lower TT** to to produce equivalent produce equivalent fluxflux

• Would lead to Would lead to reductionreduction of of ffcol col by by ~~15-20% 15-20%

40%

3-D MC1-D

ConclusionsConclusions

• Magnetic pressure support acts to make disk Magnetic pressure support acts to make disk spectra harder -- larger spectra harder -- larger ffcolcol

• Density inhomogeneities will tend to make Density inhomogeneities will tend to make disk spectra softer -- smaller disk spectra softer -- smaller ffcolcol

• These uncertainties should be accounted for in These uncertainties should be accounted for in black hole spin estimates -- approximately black hole spin estimates -- approximately 20% uncertainty for a/M20% uncertainty for a/M ~ ~ 0.8 if 0.8 if ffcol col is off by is off by ~~15%15%