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)How do magnetic fields and associated inhomogeneities affect disk spectra? (concentrate on local effects) What can we learn from (local) accretion disk simulations?What can we learn from (local) accretion disk simulations? What impact does this have on spin estimates?What impact does this have on spin estimates?

Assumes simple temperature distribution:Assumes simple temperature distribution: Spectrum assumed to be color-corrected blackbody:Spectrum assumed to be color-corrected blackbody: The Multicolor Disk Model F F

BHSPEC

L/L Edd Mass Spin Inclination Model Parameters

 = 0  abs = 1 Spectral Formation z = 0 z = abs   : emissivity; abs = mean free path to absorption abs =  /  abs  abs =  /  abs 

 = 0  abs = 1 Spectral Formation z = 0 z = abs   : emissivity; abs = mean free path to absorption abs =  /  abs  abs =  /  abs 

 = 0  abs = 1 Spectral Formation z = 0 z = abs F =   abs =  /  abs  = B (T)   : emissivity; abs = mean free path to absorption

 = 0  abs = 1 Spectral Formation z = 0 z = abs   : emissivity; abs, es = mean free path to absorption/scattering  eff  =  es  abs ) 1/2 ; eff = ( abs es ) 1/2  es = 1 z = es  eff = 1 z = eff abs =  /  abs  es =  /  es  abs >> es  abs =  /  abs  es =  /  es  abs >> es 

 = 0  abs = 1 Spectral Formation z = 0 z = abs   : emissivity; abs, es = mean free path to absorption/scattering  eff  =  es  abs ) 1/2 ; eff = ( abs es ) 1/2  es = 1 z = es  eff = 1 z = eff abs =  /  abs  es =  /  es  abs >> es  abs =  /  abs  es =  /  es  abs >> es 

 = 0  abs = 1 Spectral Formation z = 0 z = abs   : emissivity; abs, es = mean free path to absorption/scattering  eff  =  es  abs ) 1/2 ; eff = ( abs es ) 1/2  es = 1 z = es  eff = 1 z = eff F =   eff =  abs ( es / abs ) 1/2 = B   (  abs /  es ) 1/2

Spectral Formation Depth of formation  * : optical depth where (  es  abs ) 1/2 ~1Depth of formation  * : optical depth where (  es  abs ) 1/2 ~1  >  * : absorbed  >  * : absorbed  <  * : escape  <  * : escape Thomson scattering produces modified blackbody:Thomson scattering produces modified blackbody: Due to temperature gradients Compton scattering gives a softer Wien spectrumDue to temperature gradients Compton scattering gives a softer Wien spectrum Very approximately:Very approximately: f col ~ T * /T eff ~ for BHBs

Overall Vertical Structure of Disk with P rad ~ P gas MRI - the source of accretion power PhotospherePhotosphere Parker Unstable Regions Regions P mag > P rad ~ P gas P rad ~ P gas > P mag r  H z / H Hirose et al.

Magnetic Pressure: Vertical Structure P mag = B 2 /8  taken from simulationsP mag = B 2 /8  taken from simulations Extra magnetic pressure support increases scale height:Extra magnetic pressure support increases scale height: h mag = P mag /(d P mag /dz) > h gas h mag = P mag /(d P mag /dz) > h gas This leads to density reduction at  * :This leads to density reduction at  * :  * ~  es   h so   ~  * / (  es h)   ~  * / (  es h) Lower   means lower ratio of absorption to scattering:Lower   means lower ratio of absorption to scattering:  abs /  es  * which means larger T * /T eff and larger f col No B field B field Simulation

Magnetic Pressure: Spectrum Lower  * and higher T * combine to give a harder spectrumLower  * 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 edgesIn 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 f col byOverall effect is an enhancement of f col by ~ 10-15% No B field B field

Compare 3D with 1D average:  dependence is important:Compare 3D with 1D average:  dependence is important:      abs  -2 es  -1 es  -1 Non-linear dependence of  on  leads to enhanced emissionNon-linear dependence of  on  leads to enhanced emission Due to weaker dependence on , photons escape predominantly through low  regionsDue to weaker dependence on , photons escape predominantly through low  regions Inhomogeneities: Vertical Structure

Inhomogeneities: Monte Carlo Spectra Spectral shape is approximately unchanged, but flux is enhanced by ~ 40%Spectral shape is approximately unchanged, but flux is enhanced by ~ 40% Increased efficiency allows lower T * to produce equivalent fluxIncreased efficiency allows lower T * to produce equivalent flux Would lead to reduction of f col by ~ 15-20%Would lead to reduction of f col by ~ 15-20% 40% 3-D MC 1-D

Conclusions Magnetic pressure support acts to make disk spectra harder -- larger f colMagnetic pressure support acts to make disk spectra harder -- larger f col Density inhomogeneities will tend to make disk spectra softer -- smaller f colDensity inhomogeneities will tend to make disk spectra softer -- smaller f col These uncertainties should be accounted for in black hole spin estimates -- approximately 20% uncertainty for a/M ~ 0.8 if f col is off by ~ 15%These uncertainties should be accounted for in black hole spin estimates -- approximately 20% uncertainty for a/M ~ 0.8 if f col is off by ~ 15%