Theoretical  Models  of  X-­‐‑ray  Emission  from  Black  Hole  Accretion  Flows	
Norita Kawanaka
The University of Tokyo
Workshop on “Prospects, Challenges and Evolution of AGN modeling inthe ASTRO-H Era”@Rikkyo University
21-22/10/2015	

Outline	 • Accretion Disk Models (standard, RIAF,supercritical)• Typical X-ray Spectra of AGNs
• How to Explain the X-ray Emission• hot and “cold” accretion flow
• ADAF (RIAF)? disk-corona?
• Disk-corona model• solar corona model• reconnection-heated disk-corona• Fe fluorescence line modeling• Comments on the Supercritical Accretion Flow• Summary

Fundamental  Eqs.  of  a  BH  Accretion  Disk	 Assumptions	 Newtonian, steady, axisymmetric, ~Keplar 	

M! = −4π r ρ H υ rmass conservation	

dd#dΩ &224πρ
Hr
⋅r
Ω⋅υ
=4πρ
Hr
⋅
ν
r
(r)
%$
(' ang. momentum conservation	
dr
dr
dr

p
= Ω2 H 2ρdΩρν r= −α pdrds+−2 ρ H ⋅ T υ r = Qvis
− Qraddrhydrostatic balance	
α-viscosity	
energy balance	−radQ
ρ, T, p(ρ, T), s(ρ, T)	+visQH	Basic  Disk  Solutions	 
Energy balance equation:	

ds−−−
Q = 2 ρ H ⋅ T υ r + Qrad ≡ Qadv + Qrad
dr+visviscous heating	

advective radiativecooling	 cooling	+−−Qvis≈ Qrad>> Qadv
(a disk is efficiently cooled)	

standard disk	 • cool and bright• ~105 K (MBH/108Msun)-1/4	+
vis−
adv

Q ≈Q−
rad>> Q(due to low density)	

radiatively-inefficient accretion flow (RIAF)	
• hot and tenuous• ~109 K	

Standard  Accretion  Disk	 

Shakura & Sunyaev 1973; Novikov & Thorne 1973	+−Q≈Q• radiative cooling is efficient: visrad• geometrically thin, optically-thick disk
• thermal emission (multicolor blackbody)	
−1/4" M BH %5Teff ≈ 10 $ 8'
# 10 M sun &1/4

−3/4

" M! % " r %'$2' $# LEdd / c & # 3rS &• inner radius = Innermost
Stable Circular Orbit (ISCO)• peak energy ~ kBT(rISCO)	

Fν

K ∝ r −3/4

ν1/3(small r)hνRadiatively-­‐‑Ineﬃcient  Accretion  Flow	 Ichimaru 1977; Abramowicz+ 1995	

• Since the density is too low, dissipatedenergy is stored in the disk as internal energy+−Qvis≈ Qadv• Appears below ~0.3α2LEdd /c2	hard X-rayemission	
• synchrotron, bremsstrahlung,inverse Compton• (Roughly) power-law X-rayemission	

Manmoto+ 1996	

Physical  States  of  BH  Accretion  Disks	M!
supercritical accretion flow
optically thick,geometrically thick disk

(Abramowicz et al. 1988)+−Qvis≈ Qadvbecause photons are trapped	

M! Eddstandard disk (gas/rad pressure dominated)
cold, optically thick,geometrically thin disk

(Shakura & Sunyaev 1973, Novikov & Thorne 1973)thermal emission	
BH

radiatively-inefficient accretion flow (RIAF)
hot, optically thin,geometrically thck disk

(Narayan & Yi 1994)

optically-thin emission	Typical  X-­‐‑ray  Spectra  of  AGNs	(broad) iron Kα line

Optical/UV quasithermal bump

power-law X-ray reflection continuum(Fν ~ ν -1)

Magdziarz+ 1998

coexistence of hot gas (~109 K) and “cool” gas (~105 K)	

Fe line = evidence of “cold” gas	emission process	Kα  line	Fe line	reflection
hump	

incident
photon	cold gas (~105 K) 	Incidentcontinuum
Fe line•Iron should be almost neutral (i.e.
irradiated gas should besufficiently “cold”).
• Iron Kα line (～6.4keV forneutral) is the most theoreticallyexpected line emission of all.
Reynolds (1996)

incident
X-ray	

incident  X-­‐‑ray:  thermal  Comptonization	 (steady state) Kompaneets equation	

! kBTe $ 1 d ' 4 ! dn*n
2$0 =#) x # + n + n &, + Q ( x ) −2& 2%+Max (τ es, τ es2 )" mec % x dx ( " dxx = hν/kBTe: the  normalized  photon  energy	

hard photon	n(x) = (c2/2hν3)Iν : photon  occupation  number	τ : electron-­‐‑scaPering  optical  IC	esdepth	y = (4kBTe/mec2) Max (τes , τes2) 	 Compton y-parameter	

soft photon	

If Q(x) ≠ 0 only  below  x <~ xsoft (i.e.  only  soft  photons  are  supplied),  the  emergent  spectrum  will  be  a  power-­‐‑law:	
1/2n∝xm⇒ Iν ∝ ν3+m

3 "9 4%m = − ±$ + '2 #4 y&e.g. y ~ 1⇒ Iν ~ ν -1 	What  is  the  origin  of  X-­‐‑ray-­‐‑emiPing  plasma?	 
two solutions	
(1) inner hot accretion flow 	 (2) disk-corona structure	Liang & Nolan 1984	

(1)  inner  hot  accretion  ﬂow	 
inner RIAF + outer standard disk	
• Hot gas would benaturally produced• Seed photons(synchrotron photons
and/or disk soft photons)
are easily supplied.
• Solid angle of “cold” gas
is not so large?	
tcool >> tacc	

tcool << tacc	

(2)  disk-­‐‑corona  structure	
standard disk sandwiched by hot tenuous plasma(corona)	
• Solid angle of “cold” gas would be enough• Seed photons = thermal disk photons• Why does the corona get so hot? 	
low energy thermal photons	

disk (~105 K)

corona	(~109 K)

high energy photons	

The profile of Fe line emission from anaccretion disk would be relativisticallybroadened	③①②

broadened	①②③

Fe fluorescence line emission(ASCA obs. of MCG-6-30-15;
Tanaka et al. 1995)

The  importance  of  a  broadened  Fe  Line	 
(1) the effects of strong gravitational field	
• test of General Relativity• large gravitational redshift ⇔small ISCO ⇔ large BH spin!
Reynolds & Nowak2003	(2) existence of “cold”
gas at the innermostregion	Disk-corona structure
is favored!	

Disk-Corona Model
Observations of power-law X-ray and broad iron line emission…Hot gas (～109 K) seems to coexist with cold disk gas (～105-6 K)
extending to the innermost region.

Disk-Corona model (Liang & Nolan 1984; Haardt & Maraschi 1991)
X-ray photons are produced in a hot gas (corona) by inverse Compton
scattering of soft photons from an underlying disk.
reflection
continuumiron lineCompton
scattering

hard photon

corona: hot & tenuous, Telec ～ 109K

soft photon

disk body: cool & dense, Telec ～ 105K
BHHowever, the physical process for heating a corona is unknown.

Hint:  Solar  Corona	 

Shibata & Yokoyama 1999	

Emission Measure – T relation	
single power-law frommicroflares to YSO flares 	model	• in corona	magnetic reconnection heating= heat conduction cooling	EM ∝ B-5 T 17/2 	
• in chromosphere	
heat conduction heating= photoevaporation cooling	

ncorona ~ 109 cm-3	

Magnetic Reconnection-Heated Corona Model
Magnetic fields are continuously generated
in the disk by dynamo action.

Liu, Mineshige & Shibata 2002;
Liu, Mineshige & Ohsuga 2003
Magnetic loops

By magnetic buoyancy, magnetic flux loops
emerge into the corona and reconnect withother loops.
Disk
The magnetic energy carried from the disk isreleased in the corona as thermal energy.
reconnection
In the corona, thermal soft photons from thedisk are Compton scattered by hot electrons,
and become hard X-ray photons.

heatingcoolingBasic Assumptions of the Model・ Standard disk with Schwarzschild black hole (Shakura & Sunyaev
1973) … P = P(r , M , M! )・ Equipartition between the magnetic energy and gas thermal energy in!)the disk … B = B(r , M , M
・ energy balance- reconnection heating = Compton cooling in the corona

B24kT
VA ≈nσ T cU radl = ycU rad
24π
mecl : the length of the loop

- conduction heating = evaporation cooling in the chromosphere1/ 2⎛ kT ⎞
k0T 7 / 2γ⎟⎟≈
nkT ⎜⎜lγ −1⎝ mH ⎠

Magnetic loop

X-raysevaporation(enthalpy flux)

disk
9B.H

Tcorona～109 K, ncorona~109 cm-3 , y～1coronaWhy  do  we  have  y ~ 1 ?	 
−coronaConsider the energy balance in corona:	 Q+
corona=Q−
Qcorona~ ycUseed : inverse Compton cooling	
4with	
Useed = aTdisk+++
Qcorona~ fQdisk~ Qdisk: substantial fraction of accretion energy would betransferred from the disk to the corona 	
−4−
Qcorona~ ycUseed ~ y ⋅ σ Tdisk= yQdisk++−
Qcorona~ Qdisk= Qdisk(energy balance in the disk)	

y ~ 1	Continuum Spectrum from a Magnetic
Reconnection-Heated Corona
Liu, Mineshige & Ohsuga 2003

Photons emerged from the disk (thermal, soft) are partially Comptonupscattered in the corona.
Spectrum calculations through Monte Carlo simulationFν ∝ν −α ⇒ α ≈ 1.1…Consistent with the observed
spectra in Seyfert galaxies

How about the iron
fluorescent line profiles?

νmax~ kBTcorona/h	Step 1. Determine the coronal quantities with the model,
and perform Monte Carlo simulation to calculate theillumination spectrum on the disk

Tcorona ≈ 10 9 K, ncorona ≈ 10 9 K
Temperature and density of the corona ishigher in the inner region.
Liu et al. 2003

∵Reconnection heating and chromosphere
evaporation are intensive at small r.

→radiuscorona• disk emission : black body (～105K)• Some photons are Comptonscattered and gain energy from hot
electrons in the corona.

Compton scattering

Thermalsoft photon

ionizing hard photon

diskStep 2. From the illumination spectrum, compute the ironline emissivity distribution on the disk.
George & Fabian (1991) simulated the reflection spectrum from cold gas slab
irradiated by incident X-ray.

the intensity of Fe lime emission

Incident photons with energyaround Fe K edge are most capable
to drive fluorescence line emission.

We used the approximate
functional describing thissimulation result.

the energy of incident X-ray [keV]Step 3. Compute the iron line profile that would be observed
by a distant observer.
• Doppler effects
Taking into account relativistic effects• relativistic beaming• gravitational redshift• photon path deflection

Observer’s screen

I obs = g 4 I intr
Photon path

g=

ν obs
: Energy shiftν intrIntegrate the contribution
from the whole disk andcalculate the line profile
BH accretion disk

Result: line emissivity distribution on the disk

∝r -5
Energy flux per unit surface
area from the disk ∝ r -3×r↓, coronal temperature↑, density↑＝⇒More photons tend to be upscatteredin the corona and gain enough energy toionize iron atoms/ionsr –5 distribution

consistent withobservations	Result: Comparison with the observation ofMCG-6-30-15 by ASCA

1.4e+049

photon flux[arbitrary unit]

1.2e+049
1e+0498e+0486e+0484e+0482e+04803456E[keV]789Corona  in  the  Supercritical  Accretion  Flow	 The existence of hot plasma above the disk isnaturally expected and already seen in the simulation… radiation pressure-driven outflow 	(see also Ohsuga-san’sand Kawashima-san’stalk)	

cf. observations of
Ultraluminous X-ray sources(candidates of supercriticalaccretion flows)… fitted by thermal emission andComptonizing corona with low Te(<<109 K) and large optical depth(τes > 3) (see Vierdayanti+ 2010)	
Kawashima+ 2009	

corona = (optically-thick) outflow?	

Summary  and  Future  Prospects	
• X-ray emission from BH accretion disks• inner RIAF + outer standard disk
• disk-corona structure• coronal heating mechanism is still unclear• magnetic reconnection? dissipation of Alfven
waves? etc.
• conduction and evaporation should be included infuture MHD simulations• broadened Fe line emission• support the disk-corona model• well-reproduced from the disk-corona theory• ASTRO-H• detailed profile of Fe line, cutoff energy of PL,…