Forming and Feeding Super-massive Black Holes

in the Young Universe

Wolfgang J. Duschl

Institut für Theoretische Astrophysik

Universität Heidelberg

Kyoto – 30 October 2003

Plan of talk

• Evidence for massive black holes in the (very) young Universe – Quasars

• Physics of accretion disks: Self-gravity and viscosity

• The parallel evolution of super-massive black holes and of nuclear (quasar/AGN) activity

Kyoto – 30 October 2003

The need for SMBHs in the early Universe

High redshift objects, i.e., young Universe objects:

High luminosity objects (almost entirely from their centre):

Large accretion rate objects:

Large central mass objects:

45 48 -1 12 1510 erg s 10 LQL » »L Le

min max 2apot a Black

min hole

1 1 12

1

10 M yr

r r GMML M MGM Mc

r r

LM

c

h

h- + -

æö÷ç= DF = D » =÷ç ÷çè ø

® = =

=

Le

&& & &

&

7.5 10.5a4 10

M 3.92 10 LM L

>×

L

e e

A

L: Luminosity

Ma: accreting mass

M: mass flow rate

pot: potential energy

r (rmin): (inner) radius

accretion efficiency

.

Fan et al. (2003; SDSS):QSO @ z = 6.4

Then the Universewas less than a billion years old.

Kyoto – 30 October 2003

The need for SMBHs in the early Universe

• How can one transport such large masses (up to at least 10 M yr-1) to a central black hole?

• How can such large central masses exist at all so early in the Universe? How can they be formed so quickly?

• Where have all the quasars gone? (... and why are there no new ones?)

Kyoto – 30 October 2003

The need for SMBHs in the early Universe

A scenario for the formation of super-massive black holes in quasars:

• First, tidal forces due to galaxy-galaxy interactions drive large amounts of ISM very quickly to small radii of a few 102 pc (observations: Sanders et al. 2001 …; models: e.g., Barnes & Hernquist 1996, 1999; Barnes 2002 …), until – because of the angular momentum – it gets stuck at some 102 pc.

• Subsequently, accretion – hopefully – allows to bridge the last few 102 pc, and to do so quickly (within less than 109 years).

• The two original (proto-)galaxies may or may not harbour a ((super-)massive) black hole already.

In a broader context: Post-merger evolution of the ISM in the very center of the newly formed object.

Kyoto – 30 October 2003

Plan of talk

• Evidence for massive black holes in the (very) young Universe – Quasars

• Physics of accretion disks: Self-gravity and viscosity

• The parallel evolution of super-massive black holes and of nuclear (quasar/AGN) activity

Kyoto – 30 October 2003

Accretion disk mass flow rategr, gs, gz gravitational acceleration

in r, s und z directionvs, v velocity in s und direction angular velocity in directionM* mass of accretorsa outer disk radiussi inner disk radius

density surface densityh thickness of diskT temperaturecS sound velocity viscosity time scales

Reynolds number2dz hr r+¥

- ¥

S = »ò

{s, , z; t} cylindrical coordinate system

r2 = s2 + z2

v

vs

M*, si

sa

s

z

M&

Â

Kyoto – 30 October 2003

Evolution of vicous disks

Conservation of mass and angular momentum may be combined into a single equation describing the evolution of such disks:

( )( )

3 3

Kepler

2

1 3s s

s s t s st s s s s ss

s

w wn

nw

é ùæ ö¶ ¶ ¶÷çê úS - S÷ç ÷ç é ù¶S ¶ ¶ ¶è øê ú¶ ¶ ¶= - = Sê úê ú¶ ê ú¶ ¶ ¶ ¶ê ú ë ûê ú¶ê úë û

Relevant time scales: - dynamical - viscousdyn

1t

w=

2

visc

st

n=

Kyoto – 30 October 2003

Self-gravity

Three classes of accretion disks:• Non self-gravitating (NSG)*:

– gravitational forces in the vertical and in the radial direction are dominated by the central body:

• Keplerian self-gravitating (KSG): – Self-gravity is irrelevant in the radial direction, but dominates in

the vertical direction:

• Fully self-gravitating (FSG):– Self-gravity dominates in both directions:

disk *

hM M

s=

* disk *

hM M M

s³?

* diskM M£

*: In NSG disks Shakura & Sunyaev´s a parameterization has proven to be very successful: = h cs

Kyoto – 30 October 2003

Self-gravity

Fully or Keplerian self-gravitating -disks:

i.e., the radial temperature distribution becomes independent of central mass, location within the disk, etc.

This is unphysical.

Reason: In a self-gravitating -disk the local and the global disk structure decouple.

3S

20

3dT

c GMdr

pa

= Þ =&

Kyoto – 30 October 2003

Generalized viscosity ansatz

Reynolds number based turbulence:

(Duschl, Strittmatter, Biermann 2000)

Critical issues:• Scaling parameter:

– Critical Reynolds number:– Observed velocities:

• Relation to -viscosity: Limiting case for massless disks• Linear stability: non-linear instability (e.g., Grossmann

2000; Longaretti et al. 2002); experiments (e.g., Wendt 1933; Taylor 1936)

2 3 2 3crit 10 10b - -Â = Â = Þ =L L

1with

svsvj

jn b bn

 = Þ = =Â

2turb turb( / )v v v vj jb b= Þ =

Kyoto – 30 October 2003

Plan of talk

• Evidence for massive black holes in the (very) young Universe – Quasars

• Physics of accretion disks: Self-gravity and viscosity

• The parallel evolution of super-massive black holes and of nuclear (quasar/AGN) activity

Kyoto – 30 October 2003

The three phases of quasar evolution

A numerical example in detail (Duschl & Strittmatter 2003):

• Disk extends from 10-2 to 102 pc

• Initial disk mass: 1010 MSun

• Viscosity parameter : 10-3

• Seed black hole: 103 MSun

• Initial mass distribution ~ s-1

Kyoto – 30 October 2003

The three phases of quasar evolution

Kyoto – 30 October 2003

The three phases of quasar evolution

Kyoto – 30 October 2003

The three phases of quasar evolution

Kyoto – 30 October 2003

The “final” mass of the black hole

Kyoto – 30 October 2003

The evolution time scale

Kyoto – 30 October 2003

The mass flow rate

Kyoto – 30 October 2003

The quasar regime

Kyoto – 30 October 2003

Summary

• Black holes in quasars may be formed as a result of galaxy-galaxy interactions – but it needs a major event, not just a fly-by type of interaction.

• In today‘s Universe there are too few galaxy-galaxy interactions to form many new quasars, and the old ones have used up all their “fuel”.

Kyoto – 30 October 2003

Summary

• It takes only a few 102 million years to form a suitably massive black hole and to switch the quasar on.

• For the subsequent few 102 million years it acts as a “normal” quasar.

• After altogether only ~109 years the quasar phase comes to an end for good (unless ...)

Kyoto – 30 October 2003

Thank you very much

for your attention !