Lectures King

7/28/2019 Lectures King

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Accretion, black holes,AGN and all that..

Andrew King

Theoretical Astrophysics Group, University of Leicester, UK


2/132

accretion = release of gravitational energy from infalling matter

matter falls in

from distance

energy released as electromagnetic

(or other) radiation

accreting object


3/132

If accretor has mass M and radius R, gravitational energy release/mass is

RGME

acc=!

this accretion yieldincreases with compactness M/R: for a given M

the yield is greatest for the smallest accretor radius R

e.g. for accretion on to a neutron star )10,( kmRMMsun

==

gmergEacc /1020

=!


4/132

compare with nuclear fusion yield (mainly H He)

gmergcEnuc /106007.0 182 !=="

Accretion on to a black hole releases significant fraction of restmass

energy:

2//222cEcGMR

acc!"#!

(in reality use GR to compute binding energy/mass:

typical accretion yield is roughly 10% of rest mass)

This is the most efficient known way of using mass to get energy:


5/132

accretion on to a black hole must power the most luminous

phenomena in the universe

Quasars: sergL/10

46!

== McMR

GML

acc

2!

requiresyrMM

sun/1=

Xray binaries: sergL /1039

! yrMsun /107!

Gammaray bursters: sergL /1052

! sec/1.0sun

M

NB a gammaray burst is (briefly!) as bright as the rest of the universe


6/132

Accretion produces radiation: radiation makes pressure can this

inhibit further accretion?

Radiation pressure acts on electrons; but electrons and ions (protons)cannot separate because of Coulomb force. Radiation pressure force

on an electron is

(in spherical symmetry).

Gravitational force on electronproton pair is

2)(

rmmGMF epgrav

+

=

2

4 cr

LF

T

rad

!

"

=

)(ep

mm >>


7/132

thus accretion is inhibited once gravrad FF ! , i.e. once

sergM

McGMmLL

sunT

p

Edd /104

38==!

"

#

Eddington limit: similar if no spherical symmetry: luminosity

requires

minimum mass

bright quasars must have

brightest Xray binaries

In practice Eddington limit can be broken by factors ~ few, at most.

sunMM8

10>

sunMM 10>


8/132

Eddington implies limit ongrowth rate of mass: since

we must have

where

is the Salpeter timescale

T

pacc

c

GMm

cLM

!"

#

"

4

2


9/132

Emitted spectrum of an accreting object

Accretion turns gravitational energy into electromagnetic radiation.Two extreme possibilities:

(a) all energy thermalized, radiation emerges as a blackbody.

Characteristic temperature , where

i.e. significant fraction of the accretor surface radiates the accretion

luminosity. For a neutron star near the Eddington limit

bT

41

24

!"

#$%

&=

'(R

LT

acc

b

KTkmRsergL b738

1010,/10 !"=!


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(b) Gravitational energy of each accreted electron-proton pair

turned directly into heat at (shock) temperature . Thus

For a neutron star

Hence typical photon energies must lie between

i.e. we expect accreting neutron stars to be Xray or gammaray

sources: similarly stellarmass black holes

sT

RGMmkT

p

s =3

KTs

11105!"

MeVkThkeVkTsb

501 !""= #

Good fit to gross properties of Xray binaries


11/132

cmcGMRMMsun

1328103/2,10 !"="

For supermassive black holes we have

so

and is unchanged. So we expect supermassive BH to be

ultraviolet,Xray and possibly gammaray emitters.

KKMMTsunb

54/17 10)(10 !!

sT

Good fit to gross properties of quasars


12/132

Modelling accreting sources

To model an accreting source we need to

(a) choose nature of compact object black hole, neutron star,

to agree with observed radiation components

(b) choose minimum massMof compact object to agree with

luminosity via Eddington limit

Then we have two problems:

(1) we must arrange accretion rate to provide observed

luminosity, (the feeding problem) and

(2)we must arrange to grow or otherwise create an accretor of

the right massMwithin the available time (the growth problem)

M


13/132

examine both problems in the following

compare accreting binaries and active galactic nuclei (AGN)

for binaries

feeding: binary companion star

growth: accretor results from stellar evolution

for AGN

feeding: galaxy mergers?

growth: accretion on to `seed black hole?

both problems better understood for binaries, so ideasand theory developed here first.


14/132

Modelling Xray binaries

Normal galaxies like Milky Way contain several 100 Xraypoint sources with luminosities up to

Typical spectral components ~ 1 keV and 10 100 keV

Previous arguments suggest accreting neutron stars and black holesBrightest must be black holes.

Optical identifications: some systems are coincident with

luminous hot stars: high mass Xray binaries (HMXB).

But many do not have such companions: low mass Xray binaries

(LMXB).

serg/1039


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Accreting Black Holes in a Nearby

Galaxy (M101)

OPTICAL X-RAY


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Accretion disc formation

Transferred mass does not hit accretor in general, but must orbitit

initial orbit is a rosette, but selfintersections dissipation

energy loss, but no angular momentum loss

Kepler orbit with lowest energy for fixed a.m. is circle.

Thus orbit circularizes with radius such that specific a.m.j is the

same as at 1L


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Thus in general matter orbits accretor. What happens?

Accretion requires angular momentum loss see later: specific a.m.at accretor (last orbit) is smaller than initial by factor

Energy loss through dissipation is quicker than angular momentum

loss; matter spirals in through a sequence of circular Kepler orbits.

This is an accretion disc. At outer edge a.m. removed by tides from

companion star

100)/( 2/1 !circrR


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Accretion discs are universal:

matter usually has far too much a.m. to accrete directly matter

velocity not `aimed precisely at the accretor!

in a galaxy, interstellar gas at radius R from central black hole

has specific a.m. , whereMis enclosed galaxy mass;

farhigher than can accrete to the hole, which is

angular momentum increases in dynamical importance as matter

gets close to accretor: matter may be captured gravitationally at

large radius with `low a.m. (e.g. from interstellar medium) but

still has far too much a.m. to accrete

Capture rate is an upper limit to the accretion rate

2/1)(~ GMR

cGMcGMGMRGM bhbhbhbhbh /)/(~)(~ 2/122/1 =!


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expect theory of accretion discs developed for XRBs to apply

equally to supermassive blackhole accretors in AGN

as well

virtually all phenomena present in both cases


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Thin Accretion Discs

Assume disc is closely confined to the orbital plane with semithickness

H, and surface density

in cylindrical polars . Assume also that

These two assumptions are consistent: both require thatpressure

forces are negligible

!! Hdz 2"=# $%

%&

),,( zR !

2/1)/( RGMvvK==!


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Accretion requires angular momentum transport outwards.

Mechanism is usually called `viscosity, but usual `molecular

process is too weak. Need torque G(R) between neighboring annuli

Discuss further later but functional form must be

with

reason: G(R) must vanish for rigid rotator

Coefficient , where = typical lengthscale andu = typical velocity.

!"#=22)( RRRG $%

dRd /!=!"

)0( =!"

u!" ~ !


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Net torque on disc ring between is

Torque does work at rate

but term

is transport of rotational energy (a divergence, depending only on

boundary conditions).

RRR !+,

RR

G

RGRRG !"

"=#!+ )()(

RGGR

RR

G

!"#$%&' ()*(+

+=!+

+( )(

!""

#

#)(G

R


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Remaining term represents dissipation: per unit area (two disc faces!)

this is

Note that this is positive, vanishing only for rigid rotation. For

Keplerian rotation

and thus

2)(2

1

4)( !"#=

!"= R

R

GRD $

%

2/13)/( RGM=!

389)(

R

GMRD != "


24/132

Assume now that disc matter has a small radial velocity .

Then mass conservation requires

Angular momentum conservation is similar, but we must take

the `viscous torque into account. The result is

Rv

0)( =!"

"+

"

!"

RvR

RtR

R

GRvR

RR

tR

R

!

!="#

!

!+"#

!

!

$2

1)()( 22


25/132

We can eliminate the radial velocity , and using the Kepler

assumption for we get

Diffusion equation for surface density: mass diffuses in, angular

momentum out.

Diffusion timescale is viscous timescale

Rv

!

[ ]!"#

$%&'

(

(

(

(=

(

$( 2/12/13R

RR

RRt)

!/~2

Rtvisc


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For accretion disc equations etc see

Frank et al.(2002) Accretion Power in Astrophysics, 3rd Ed.

For general astrophysical fluid dynamics seePringle & King (2007) Astrophysical Flows


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Steady thin discs

Setting we integrate the mass conservation equation as

Clearly constant related to (steady) accretion rate through

disc as

Angular momentum equation gives

0/=

!! t

constvRR=!

)(2RvRM !"=

#

!! 22

2 CGRvR

R+="#


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where G(R) is the viscous torque and Ca constant.

Equation forG(R) gives

Constant Crelated to rate at which a.m. flows into accretor.

If this rotates with angular velocity


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Putting this in the equation for and using the Kepler form

of angular velocity we get

Using the form of D(R) we find the surface dissipation rate

!"

!!

"

#

$$

%

&!"

#$%

&'=( )

2/1

13 R

RM

*

+

!!

"

#

$$

%

&

!"

#

$%

&

'=

(

2/1

3 18

3

)( R

R

R

GMMRD

)


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Now if disc optically thick and radiates roughly as a blackbody,

so effective temperature given by

Note that is independent of viscosity!

is effectively observable, particularly in eclipsing binaries:

this confirms simple theory.

4

)( bTRD !=

!!

"

#$$

%

&!"

#$%

&'= (

2/1

3

4

18

3

R

R

R

GMMTb

)*

bT

bT

bT


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Condition for a thin disc (H


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With

and , where is the sound speed, we find

Hencefor a thin disc we require that the local Kepler velocity

should be highly supersonic

Since this requires that the disc cancool.

HzHPzP ~,/~/ !!2

~ scP ! sc

Rv

cR

GM

RcH

K

s

s~~

2/1

!

"

#$

%

&

If this holds we can also show that the azimuthal velocity is

close to Kepler

2/1

Tcs!


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thin Keplerian efficiently cooled! !

Eitherall three of these properties hold, ornone do!

Thus for discs,


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Thin discs?

Thin disc conditions hold in many observed cases.

If not, disc is thick, nonKeplerian, and does not cool efficiently.

Pressure is important: disc ~ rapidly rotating `star.

Progress in calculating structure slow: e.g. flow timescales far shorterat inner edge than further out.

One possibility: matter flows inwards without radiating, and can

accrete to a black hole `invisibly (ADAF = advection dominated

accretion flow). Most rotation laws dynamical instability (PP).

Numerical calculations suggest indeed that most of matter flows

out (ADIOS = adiabatic inflowoutflow solution)


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u!" ~

u,!

scuH


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Physical angular momentum transport

A disc has

but

accretion requires a mechanism to transport a.m. outwards, butfirst relationstability against axisymmetric perturbations

(Rayleigh criterion).

Most potential mechanisms sensitive to a.m. gradient, so transport

a.m. inwards!

,0)( 2 >!"

"R

R0!""

0/


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origin of instability:

so

i.e. local accretion rate increases in response to a decrease in

(and vice versa), so local density drops (or rises).

To see condition for onset of instability, recall

!"= M#

0/0/

M

!

4

bTM!!"=

#


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and internal temperature T. Thus stability/instability

decided by sign of along the equilibrium curve

i.e.

C

D

B

A

!b

T!"" /T

T

!

0T

0!

max!

min!

minT

max

T

)(!T

)(!T

0/ =!! tT

0/

0/ >!! tT

0/ =!"! t

A

B

C

D


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Equilibrium

here lies on unstable branch

System is forced to hunt around limit cycle ABCD, unable to reach

equilibrium.

evolution AB on long viscous timescale

evolution BC on very short thermal timescale

evolution CD on moderate viscous timescale

evolution CA on very short thermal timescale

Thus get long low states alternating withshorter high states, with rapid

upwards and downward transitions between them dwarf nova light

curves.

=!! tT / 0/ =!"! t

0/


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origin of wiggles in equilibrium curve is hydrogen

ionization threshold at

If all of disc is hotter than this, disc remains stably in the high

state no outbursts.

Thus unstable discs must have low accretion rates:

where is outer disc radius

)(!TKT

410~

416

3

4

10

8

3K

R

GMMT

out

b


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Xray irradiation by central source: disc is concave or warped

thus not so dominates at

large R (where most disc mass is)

ionization/stability properties controlled by CENTRAL

2/1!"= RTT

irrb

4/3!" RT

visc

M


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Thus an outburst of an irradiated disc cannot be ended by a

cooling wave, but only when central accretion rate drops below a

critical value such that

mass of central disc drops significantlylong!

KTRT ionoutirr 6500)( !=


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K & Ritter (1998): in outburst disc is roughly steadystate, with

the central accretion rate. Mass of hot disc is

Now hot zone mass can change only through central accretion, so

!"3

#$ cM

cM

!

"

32

2

0

hc

R

h

RMRdRM

h

# $%=

ch MM

!=


53/132

thus

i.e.

so central accretion rate, Xrays, drop exponentially for small discs

hh

h MR

M2

3!="

2/3

0

hRt

heMM

!"

=

observation indeed shows that outbursts in small, fully irradiated

discs are exponential (`soft Xray transients)


54/132

size of AGN disc set byselfgravity

vertical component of gravity from central mass is

cf that from selfgravity of disc

3

/~ RGMH

HGHHG !! ~/~23


55/132

Thus selfgravity takes over where , or

disc breaks up into stars outside this

3

/~ RM!

M

R

HHRM

disc~~

2!


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accretion to central object

central object gains a.m. andspins up at rate

reaches maximum spin rate (a ~ M for black hole) after accreting

~Mif starts from low spin. `Centrifugal processes limit spin. ForBH, photon emission limits a/M


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active galactic nuclei

supermassive BH in the centre of every galaxy

how did this huge mass grow?

cosmological picture:

)1010( 96sun

M!


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big galaxy swallows small one

merger


59/132

galaxy mergers

two things happen:

1. black holes coalesce: motion of each is slowed by inertia of

gravitational `wake dynamical friction. Sink to bottom of

potential and orbit each other. GR emissioncoalescence

2. accretion: disturbed potential gas near nuclei destabilized,

a.m. loss accretion: merged black hole grows:

radiationAGN


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black hole coalescence

Hawkings theorem: black hole event horizon area

or

where a.m., , can never decrease

])/([8 2/122242

4

2

GJcMM

c

GA !+=

"

])1(1[ 2/12*2

aMA !+"

2

*/GMcJa ==J


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thus can give up angular momentum and still increase area, i.e.

release rotational energy e.g. as gravitational radiation

then mass M decreases! minimum is (irreducible mass)

start from and spin down to keepingA fixed

coalescence can be bothprograde and retrograde wrt spin of

merged hole, i.e. orbital opposite to spin a.m.

Hughes & Blandford (2003): longterm effect of coalescences

isspindown since last stable circular orbit has larger a.m. in

retrograde case.

2/M

1*=a 0

*=a


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Soltan (1982): total restmass energy of all SMBH

consistent with radiation energy of Universe

if masses grew by luminous accretion (efficiency ~10 %)

black hole accretion

thus ADAFs etc unimportant in growing most massive

black holes


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merger picture of AGN: consequences for accretion

mergers do not know about black hole mass M, so accretion

may be superEddington

mergers do not know about hole spin a, so accretion may be

retrograde

*


64/132

efficiency versus spin parameter


65/132

superEddington accretion:

must have been common as most SMBH grew (z ~2), so

outflows

what do we know about accretion at super (hyper)Eddington rates?


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Hyper-Eddington Accretion: SS433

13.1day binary with huge mass transfer rate (~ 3000 Eddington)

pair of jets (v = 0.26c) precessing with 162day period, at

angle to binary axis

seen in H alpha, radio, Xrays

kinetic luminosity of jets ~ erg/s, but radiative luminosity

less, e.g. erg/s

huge outflow (`stationary H alpha) at 2000 km/s this is

where hyperEddington mass flow goes

this outflow inflates surrounding nebula (W50) and precessing

jets make `ears

3910

3610!

xL

o

20=!


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68/132


69/132

outflowcan be sensitive to outer disc plane if from large enough R


70/132

outflow bends jets parallel to axis of outer disc, since far more

momentum


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Where is the outflow launched?

Shakura & Sunyaev (1973): `spherization radius

==

ss

Edd

outsp RR

M

MR ,

4

27Schwarzschild radius

Outflow velocity is v ~ 2000 km/s, suggesting

cmRv

c

v

GM

R ssp10

2

2

2 107

2

!"""

for 10 Msun black hole


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within accretion rate must drop as ~R, to keep each radius

below Eddington rate. This leads (cf Shakura & Sunyaev, 1973) to

spR

)/ln(28

33 inspEdd

R

R

Eddacc RRLRdR

R

RMGML

sp

in

!"# $

%

%

Now , so logarithm is ~ 10.

Thus a 10 Msun black hole can emit erg/s

insp RR4

10!

4010


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Moreover walls of outflow are very optically thick (tau ~ 80)so all luminosity escapes in narrow cone


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An observer viewing the system down this axis would infer

an isotropic luminosity

erg/s

where b is the collimation factor.

Ultraluminous Xray sources (ULXs) may be (nonprecessing)

systems like this: even with only b = 10% collimation they can reach

the luminosities of observed ULXs.

14010

!

" bL


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outflow is optically thick to scattering: radiation field L LEddtransfers allits momentum to it


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response to superEddington accretion: expel excess

accretion as an outflow with thrustgiven purely by LEdd , i.e.

outflows with Eddington thrust must have been common as SMBH

grew

NB mechanical energy flux requires knowledgeof v or

c

LvM

Edd

out!

&

outM&

c

vL

vM

Edd

out !

2

2

1&


77/132

effect on host galaxylarge: must absorb most of the

outflow momentum and energy galaxies not `optically

thin to matter unlike radiation

e.g. could have accreted at 1Myr-1 for 5107 yr

mechanical energy deposited in this time 1060 erg

cfbinding energy 1059 erg of galactic bulge with

M 1011Mand velocity dispersion 300 km s-1

examine effect of superEddington accretion on growing

SMBH (K 2003)


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model protogalaxy as an isothermal sphere of dark matter:

gas

density is

withfg= baryon/matter' 0.16

so gas mass inside radiusR is

2

2

2)( Gr

f

Rg

!

"

#=

G

RfdrrRM g

R2

02

24)(

!"# == $


79/132

dynamics depend on whether gas cools (`momentumdriven)

or not (`energydriven)

Compton cooling is efficient out to radius Rc such that

M(Rc) 210113200M8

1/2M

where 200

= /200 km s-1, M8 = M/108M

flow is momentumdriven (i.e. gas pressure is unimportant) out to

R = Rc

for flow speeds up because of pressure drivingc

RR >


80/132

swept-up gas

ambient gas outflow

ram press re of o tflo dri es e pansion of s ept p shell:


81/132

ram pressure of outflow drives expansion of swept-up shell:

(usingM(R) = 2fg2 R/G etc)

thus

constG

fc

LR

RGMvMvRRRM

dt

d

gEdd

out

=!=

!==

4

2

222

4

)(4])([

"

#$ &&

2

000

22

2

222

2

RtvRt

cf

GLR

g

Edd++

!!"

#

$$%

&'= (

(


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for small (i.e. smallM),R reaches a maximum

2

022

2

0

2

02

max

2/2R

cfGL

vRR

gEdd

+

!

=

""

in a dynamical time

R cannot grow beyond untilMgrows: expelled

matter is trapped inside bubble

MandR grow on Salpeter timescale ~

maxR

yr7

105!

!/~max

R

EddL


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gas in shell recycled star formation, chemical enrichment

starbursts accompany blackhole growth

AGN accrete gas ofhigh metallicity

ultimately shell too large to cool: drives off gas outside

velocity large:superwind

remaining gas makes bulge stars blackhole bulge mass

relation

no fuel for BH after this, soMfixed:Msigma relation


84/132

4

2!

"

#

G

fM

g=

thusMgrows until

or

!"= MM

4

200

8102 #

for a dispersion of 200 km/s


85/132

4

2!

"

#

G

fM

g=

has no free parameter!

Note: predicted relation


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Msigma is very close to observed relation (Ferrarese & Merritt,

2000; Gebhardt et al., 2000; Tremaine et al, 2002)

only mass inside cooling radius ends as bulge stars, giving

actually

in good agreement with observation

bulMMM

4/1

8

4

107~

!!

"

bulpe McmmM )/()/(~2

!


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argument via Soltan assumes standard accretion efficiency

but mergersmergers imply accretion flows initially counteraligned in

half of all cases, i.e. low accretion efficiency, initialspindown


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how does SMBH react? i.e. what are torques on hole?

two main types: 1. accretion spinup or spindown requireshole to accrete ~ its own mass to change

a/Msignificantly slow

2. LenseThirring from misaligned disc

viscous timescale fast in inner disc

standard argument: alignmentvia LenseThirring occurs

rapidly, hole spins up to keep a ~ M, accretion efficiency is high

but LT also vanishes forcounteralignment

alignment or not? (King, Lubow, Ogilvie & Pringle 05)


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LenseThirring:

plane of circular geodesicprecesses

about black hole spin axis: dissipation causes alignment or

counteralignment


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Torque on hole is pure precession, so orthogonal to spin.

Thus general equation for spin evolution is

HereK1,K2 > 0 depend on disc properties. First term specifies

precession, second alignment.

Clearly magnitudeJh is constant, and vector sum Jt of Jh, Jd is

constant. Thus Jt stays fixed, while tip ofJh moves on a sphereduring alignment.

Using these we have


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Using these, we have

thus

ButJh,Jt are constant, so angle h between them obeys

hole spin always aligns with totalangular momentum


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Can further show thatJd2 always decreases during this process

dissipation

Thus viewed in frame precessing with Jh, Jd,

Jt stays fixed: Jh aligns with it while keeping its length constant

Jd2 decreases monotonically because of dissipation


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Since

there are two cases, depending on whether

or not. If this condition fails, Jt >Jh and alignment follows in

the usual way older treatments implicitly assume

so predicted alignmenthd

JJ >>


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Jh =

Jd =

Jt = Jh + Jd =


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butif does hold,

counteralignment occurs

which requires > /2 andJd < 2Jh,

then Jt


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98/132

small counterrotating discs antialign

large ones align

what happens in general?

consider an initially counteraligned


99/132

consider an initially counteraligned

accretion event (Lodato &

Pringle, 05)


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LT effect first acts on inner disc: less a.m. thanhole, so central disc counteraligns, connected to

outer disc by warp: timescale yr8

10


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but outer disc has more a.m. thanhole, so forces it to align, taking

counteraligned inner disc with it


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104/132

resulting collision of counterrotating gas intense dissipation

high central accretion rate

accretion efficiency initially low (retrograde): a/Mmay be lower

too


105/132

merger origin of AGN superEddington accretion outflows

these can explain

1. Msigma

2. starbursts simultaneous with BH growth3. BHbulge mass correlation

4. matter accreting in AGN has high metallicity

*


106/132

black hole growth

can we grow masses

at redshifts z = 6 (Barth et al., 2003; Willott et al., 2003)?

sunMM

9

105!>

9


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must grow these masses in yr after Big Bang

and is limited by Eddington, i.e.

with

910!

accMM

!=

)1("

M

!

"

#

GMcLMcEddacc

42=$

these combine to give


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these combine to give

with

yr

thus

final mass exponentially sensitive to 1/efficiency

Eddt

MM

!

!"

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