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Toward Precise Constraints on the Growth of Massive Black Holes. 陆由俊 ( Youjun Lu ) National Astronomical Observatory of China Feb. 27th, 2009 The 8th Sino-German workshop. Outline. MBHs in nearby galaxies and MBHs mass funtion in the local universe Demography on QSOs and X-ray AGNs

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toward precise constraints on the growth of massive black holes
Toward Precise Constraints on the Growth of Massive Black Holes

陆由俊(Youjun Lu)

National Astronomical Observatory of China

Feb. 27th, 2009

The 8th Sino-German workshop

  • MBHs in nearby galaxies and MBHs mass funtion in the local universe
  • Demography on QSOs and X-ray AGNs
  • Connection between local MBHs and QSOs
  • Constraints on luminosity evolution of individual QSOs and associated basic properties of disk accretion
  • Summary
black holes
Black Holes
  • Parameters to define a BH: mass and spin (Electric charge: irrelevant for astrophysical BHs)

Spin: extremely difficult to measure;

(QPO, spectral modeling or Iron K line)

Mass: can be estimated by motions of stars and gaseous material in the potential of the MBH.


NGC 4258

MBHs in nearby Galaxies: Best cases

The Milky Way


mbhs in nearby galaxies
MBHs in nearby galaxies
  • Stellar dynamics
  • Gas dynamics

(Keplerian rotation in near Keplerian potentials)

It is hard to measure the masses of MBHs in nearby galaxies.

Currently the number of (firmly) detected MBHs in the nuclei of nearby galaxies is only about 40-50, but we are lucky------

relations between mbh mass and galaxy properties
Relations between MBH mass and Galaxy Properties

Tremaine et al. 2002

Ferrarese & Ford 2005

the local black hole mass function
The local black hole mass function

The MBH mass vs Galaxy properties relations +

The galaxy property (velocity dispersion or luminosity) distribution function


Scatters in the relations 

The local black hole mass function

demography of qsos agns
Demography of QSOs/AGNs
  • Measurements: luminosity and redshift;
  • Number density as a function of redshift and luminosity;
  • Other relevant parameters:

(1) total energy, with given bolometric corrections;

(2) accretion rate, provided the MBH mass can be estimated using virial mass estimator(s);


qso luminosity function
QSO luminosity function

Croom et al. 2004

qso luminosity function1
QSO luminosity function

Richards et al. 2006

x ray luminosity function
X-ray luminosity function

La Franca et al. 2005

x ray luminosity function1
X-ray luminosity function

Silverman et al. 2008

  • How do these MBHs in the local universe form and evolve?
  • What is the main mechanism shaping the mass distribution of these MBHs?
  • What is the main mechanism shaping the spin distribution of these MBHs?
different routes
Different Routes
  • Elaborate hierarchical co-evolution model

Rees & Efstathiou 1988; Kauffmann & Haehnelt 2002; Croton et al. 2006, Bower et al. 2006, Malbon et al. 2007, Di Matteo et al. 2005, Hopkins et al. 2006, Somerville et al. 2008

(seeding, feeding and feedback)

State of the art:

Halo merger tree--SAM--BH accretion recipes--AGN feedback (QSO mode and radio mode)

QSO formation and BH growth (Kauffmann & Haehnelt 2000) andAGN feedback (Croton et al. 2006, Bower et al. 2006)

Hierarchical galaxy formation (Cole et al. 2000)

different routes1
Different Routes
  • Clustering of QSO versus halo models

constrain QSO lifetime and/or light curve

(Haiman & Hui 2001, Martini & Weinberger 2001)

  • Global constraints: without details of generation mechanism of QSOs

(1) the local MBHs are the remnant of QSOs (cosmological principle);

(2) QSOs are the phenomena of powerful accretion of material onto MBHs with high radiation efficiency.

What can we learn about the growth of MBHs and the accretion physics from these observational censuses on the local MBHs and QSOs in the distant universe?

the extended soltan argument
The (extended) Soltan argument
  • Faraway galaxies represent history of nearby galaxies (cosmological principle).

 MBHs in local galaxies as QSO remnants(Lynden-Bell 1969; Soltan 1982)


Blandford 2003

Yu & Tremaine 2002; Marconi et al. 2004; Shankar et al. 2004,2008;

Yu & Lu 2004, 2008; Merloni & Heinz 2008

the extended soltan argument1
Local BHs with present-day mass M0:

Triggering history: seed BHs triggered at cosmic timeti;

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

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

(ignoring BH mergers)

QSOLF local BHMF lifetime probability



The extended Soltan argument






seed BH


QSOLF local BHMF lifetime probability

Fourier transformation or Merlin transformation to sovle it

Luminosity evolution:

not uniquely determined by the relation;

assuming models and constraining parameters involved.

Characteristic transition timescaleD =Sp

characteristic increasing timescaleSpSalpeter timescale



I =Sp

involved parameters
Involved parameters
  • Efficiency--;
  • Time-period for the self-regulated accretion set by the Eddington limit -- ;
  • Timescale for the accretion mode transiting from Eddington-limited accretion to self-similar long-term evolution of disk accretion -- ;
  • Power-law index (=-1.2-- -1.3) in the declining phase.

(, , , )

time integral of qso xagn lf
Time-integral of QSO/XAGN LF

Croom et al. 2004; Wolf et al. 2003;

Richards et al. 2006; Jiang et al. 2007;


La Franca et al. 2005;

Silverman et al. 2008

models versus optical data
Models versus Optical data

= 0.16;

= 10;

= 0.2;

= 1.3.

Obscuration is significant and consistent with current observation

effects of mergers
Effects of Mergers
  • Dry mergers: may affect the black hole mass function in the local universe, but typically today red-galaxies only experienced 0.5-2 major mergers, and the effect is not significant compared to other uncertainties;
  • Wet mergers: multiple wet mergers, but the uncertainty introduced by this is only about 20-30% if the masses of MBHs increased substantially during the last wet major merger.

The constraints obtained above are robust!

observations on eddington ratios
Observations on Eddington ratios

Netzer et al. 2007

Kollmeier et al. 2006

eddington ratios
Eddington ratios

Shen et al. 2008

eddington ratio distribution in qsos
Eddington ratio distribution in QSOs

Approximately single Eddington ratio at high luminosity and a broad range of Eddington ratio at low luminosity

Kollmeier et al. 2006;

Shen et al. 2008;

Netzer 2007.

  • Efficiency:
  • Lifetime: a few10^9yr

(but 2-3x10^8yr for Eddington ratio>0.1)

  • The luminosity (or accretion rate) evolution of individual QSOs probably involving two phases:

(1) an initial exponentially increasing phase self-regulated by the Eddington limit when the infall material to feed the central MBHs is over-supplied;

(2) followed by a phase with power-law declining set by the self-similar long-term evolution of disk accretion;

BHMF from 

BHMF from Lhot

  • Other simple luminosity (or accretion rate) evolution models, such as a single Eddington ratio for all MBHs/QSOs or initially exponentially increasing phase followed by an exponentially decay phase are rule out;
  • High luminosity QSOs accrete via a single Eddington ratio (close to 1 but not smaller than 0.5); low luminosity AGN accrete via a much wide range Eddington ratio (10^0.001--1);
  • The timescale for the QSO luminosity declining from its peak luminosity to 10% peak luminosity should be relatively short compared to the Salpeter timescale, which suggests that the infall material deposited in the vicinity of MBHs is consumed by rapid accretion of the central MBHs and at the mean time further deposit of material is efficiently suppressed by some mechanisms, probably the AGN feedback mechanism, on a timescale less than the Salpeter timescale;
  • The fraction of optically obscured QSOs/AGNs inferred from the extended Soltan argument can be as high as 80% at M_B~ -20--- -23 and slightly decrease to at M_B=-24--- -27, and these numbers are consistent with recent observations.
on going work
On going work:

The triggering rates, the down-sizing evolution of massive black holes and galaxies, the evolution of MBH mass function in both quiescent galaxies and active galaxies, etc.