Evolution of Accretion Disks around Massive Black Holes: Constraints from

the Demography of Active Galactic Nuclei

Qingjuan YuUC Berkeley

April 21, 2006

(2005, ApJ, 634, 901, Qingjuan Yu, Youjun Lu, & Guinevere Kauffmann)

Introduction • QSOs are powered by gas accretion onto MBHs.• Most nearby galaxies host MBHs at their centers.

• Mass growth of MBHs comes mainly from gas accretion due to QSO/AGN phases.

(Lynden-Bell 1969; Rees 1984; Soltan 1982; Small & Blandford 1992; Kormendy & Richstone 1995; Magorrian et al. 1998; Yu & Tremaine 2002 etc.)

Quasar PKS 2349 (HST)

M87 (HST)Quasar PKS 2349 (HST) M87 (HST)

Galactic center

NGC 4258

(Tremaine et al. 2002)

• How does the accretion/luminosity evolve?

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

()

&M ( ) =(1−ε)L ( )

εc2

M ( ) =M i + &M ( ')0

∫ d '

Evolution after the nuclear activityof a QSO/AGN is triggered

• Cosmological evolution of comoving number density of the QSO population:

• Evolution of the characteristic luminosity of the QSO population:

Not meaning

Extracting evolution of accretion from observations

• A single AGN may only represent one specific period in a prolonged phase of nuclear activity.

• A large sample of AGNs with different ages will span all phases of this activity and allow us to extract information about evolution.

• In addition to age, other physical parameters may be important in determining how AGNs evolve, and a statistical method may help to clarify these.

2dF

SDSS

Statistical methods involving a largesample of QSOs/AGNs are required.

Extracting ()

• Local BHs with present-day mass M0:– Triggering history: seed BHs triggered at cosmic time ti;

– Luminosity evolution (M0,) as a function of =t-ti;

tO

QSOLF

ψ (L,t)dt

0

t0∫ = nM (M0 ,t0 ) life(M0 )P(L |M0 )dM00

∞

∫QSOLF local BHMF lifetime probability

(Yu & Lu 2004)

(ignoring BH mergers)

• (M0,) is isolated by connecting QSOLF with local BHs:

(M0,)

life

LL+dL

ψ (L,t)dt

0

t0∫ = nM (M0 ,t0 ) life(M0 )P(L |M0 )dM00

∞

∫QSOLF local BHMF lifetime probability

Luminosity evolution of individual triggered nuclei

seed BHtriggered

(M0,)

LL+dL

ψ (L,t)dt

0

t0∫ = nM (M0 ,t0 ) life(M0 )P(L |M0 )dM00

∞

∫QSOLF local BHMF lifetime probability

P(L | M0) or

life(M0 )P(L |M0 )

seed BHtriggered

Accretion rate distribution of SDSS nearby AGNs

(Yu, Lu & Kauffmann 2005)

Accretion rate distribution of SDSS nearby AGNs

Normalized mass accretion rate:

&m[OIII] ≡ fL[OIII]

LEdd(M f )

f : average bolometric correction

between L[OIII] and Lbol;

M f (σ ) : average final mass.

SDSS sample: (Kauffmann et al. 2003; Heckman et al. 2004)

z < 0.3;binning &m[OIII] and σ;

σ : 70 → 200km/ s; M f (σ ) : 2.0 ×106 → 1.3×108 Msun.

Accretion rate distribution of SDSS nearby AGNs

Accretion rate evolution &M bol ( ) P( &Mbol |M f )dlog10

&Mbol

≡( &Mbol ln10)dlog10

&Mbol

d &M bol ( ) d =k

k∑

k: solutions of &M bol ( ) = &Mbol

(k=1,2,...).

-Assumed accretion rate evolution:

&M ∝

expτ

τ Sp

⎛

⎝⎜

⎞

⎠⎟, 0 < τ < τ I ;

τ − τ I + τ D

τ D

⎛

⎝⎜⎞

⎠⎟

−γ

, τ ≥ τ I .

⎧

⎨

⎪⎪

⎩

⎪⎪

III

I

Accretion rate distribution of SDSS nearby AGNs

-Assumed accretion rate evolution:

&M bol ∝

expSp

⎛

⎝⎜

⎞

⎠⎟, 0 < < I ;

− I +D

D

⎛

⎝⎜⎞

⎠⎟

−γ

, ≥ I .

⎧

⎨

⎪⎪

⎩

⎪⎪

III

I

γ =1.3 ± 0.1,

τ D = 3.1 ± 1τ Sp .

(Yu, Lu & Kauffmann 2005)

Evolution model of accretion disks:

• Evolution of surface mass density:

• Self-similar solutions (Pringle 1974):

Σ(R,τ )

Σ0

=τ

τ 0

⎛

⎝⎜⎞

⎠⎟

η

fR

R0

⎛

⎝⎜⎞

⎠⎟τ

τ 0

⎛

⎝⎜⎞

⎠⎟

ξ⎡

⎣⎢⎢

⎤

⎦⎥⎥

∂Σ∂

=3

R

∂

∂RR1/2 ∂

∂R(νΣR1/2 )⎡

⎣⎢⎤⎦⎥, ν ∝ ΣmRn;

&M disk ∝−38+18a+4b32+17a+2b ∝

−1.18 , (a=b=0;Thomson opacity); −1.25 , (a=1,b=7 / 2;Kramers opac.)

⎧⎨⎩

opacity :κ (ρ,T ) ∝ ρaT−b

(Cannizzo, Lee, & Goodman 1990)

Evolution model of accretion disks:

• Diffusion timescale

• Consistency of observations with simple theoretical expectations suggests that the accretion process in nearby AGNs follows a self-similar evolutionary pattern.

0 =R0

2

ν (R0 , Σ0 )= (0.1 − 1.6) × 108 yr

R0

0.3 − 1pc

⎛⎝⎜

⎞⎠⎟

7 /3M BH

107 M sun

⎛

⎝⎜⎞

⎠⎟

1/3α

0.1⎛⎝⎜

⎞⎠⎟

−4 /3 M d ,0

107 M sun

⎛

⎝⎜⎞

⎠⎟

−2/3

T Tauri star

• Disk accretion: self-similar evolution

&M disk ∝ −η

(Hartmann et al. 1998)

Diversity of Eddington ratios (Lbol/Ledd) in QSOs/AGNs

(Mclure & Dunlop 2004)

(Woo & Urry 2002)

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

The diversity in the Eddington ratios is a natural result of the long-term evolutionof accretion disks in AGNs.

Discussions

• Further issues related to long-term evolution of accretion disks:– Disk winds, infalling material deposited onto the disk, instabilities, self-gravitating disks, star formation …

• Binary black holes and coevolution of galaxies and QSOs/AGNs

Discussions

• Adding the effect of an evolving accretion disk in unified models of AGNs– Lack of a torus in very weak AGNs

– Radiatively inefficient accretion

Summary • The accretion rates in most nearby Seyfert galaxies (with host galaxy velocity dispersion sigma~70-200km/s, z<0.3) are declining with time in a power-law form and the accretion process follows a self-similar evolutionary pattern as simple theoretical models predict.

• Some other issues deserves of further investigation, such as the long-term evolution of accretion disks, the evolution of BBHs in QSOs/AGNs, coevolution of galaxies and QSOs/AGNs, and the unification picture of AGNs.

Alternative explanation for the accretion rate

distribution• Fueling low-level AGN activity through the stochastic accretion of cold gas, astro-ph/0603180, Hopkins & Hernquist– Feed-back driven model in a large-scale context

But how can the evolution of accretion disks be avoidable?