1. Constraining Supermassive Black Hole
evolution through continuity equation
Marco Tucci
University of Geneva
In collaboration with Marta Volonteri (IAP)
2. Overview of the AGN population
Radiative−mode AGN
Type 2
Type 1
Accretion
Broad line
Narrow line Weak narrow
line region
thin disk
Dominant
Radio Jet
Dusty obscuring
structure
region
disk
region
Radio
jet
Truncated
Radio−quiet
Radio−loud
Advection−dominated
inner accretion flow
Jet−mode AGN
Black hole
Dust?
Black hole
Heckman&Best14
Quasar-mode AGN Radio-mode AGN
Little radiation, energy output in form of
kinetic energy transported in two-sided jets.
Low accretion rate (𝝀<0.01)
Efficient conversion of the potential energy
of the gas to radiation. In small fraction
powerful jets are present.
High accretion rate (𝝀⪆0.01)
3. (1) galaxies may affect how SMBHs grow because they control BH feeding via
global processes;
(2) SMBHs may affect galaxy properties via energy and momentum feedback.
Feedback processes influence star formation and intracluster medium.
Coevolution of SMBHs and galaxies
• Local observations of massive early-type
galaxies strongly support the presence of
supermassive black holes.
• Correlation between the SMBH mass and
properties of the host galaxy bulge (e.g.,
luminosity, stellar velocity dispersion,
bulge mass).
• SMBH growth seems to be mirrored
in the cosmic star formation history
BH accretion rate vs SFR
4. Empirical scaling relations between SMBH mass and host galaxy
properties are used to estimate the BH mass in the local universe.
Evolution in scaling relations?
For type-1 AGN, viral mass estimates used beyond local universe.
McConnell&Ma 2013
MBH-𝜎 MBH-Mbulge
5. Determination of the local MF using different methods, scaling
relations and data. Uncertainties are mainly due to the scaling relations
Local SMBH mass function
Shankar+09 (blue)
Vika+09 (points)
Li+11 (green)
revised estimates (dashed areas)
Shankar+13
Ueda+14
We adopt a Schecter function
convolved by a Gaussian scatter
of 0.3 and 0.5 dex (Merloni&Heinz08).
Local mass density of SMBHs
M = ?
M
M?
!1+↵
exp 1
M
M?
!
⇢BH = 4.3 6.6 ⇥ 105
M Mpc 3
6. Standard method to describe evolution of SMBH Mass
Function (Cavaliere+71, Small&Blandford92, and widely used in literature)
•Bolometric luminosity
•Eddington ratio
•Average accretion rate:
SMBH evolution via continuity equation
h ˙Mi
M
=
(1 ✏)`
✏c2
U(M, t)
Z
d log P( |M, t)
@ BH
@t
(M, t) = M
@
@M
"
h ˙Mi(M, t) BH(M, t)
M
#
= L/LEdd / L/MBH
L = ✏ ˙Maccc2
=
✏
1 ✏
˙Mc2
7. (1) Average radiative efficiency 𝜀: expected to be between
𝜀=0.05-0.40 (standard accretion disc theory; “Soltan argument”).
We assume constant, independent of BH mass.
(2) Active SMBHs (or AGN) if 𝝀 ≥ 10-4 and Duty cycle
We assume a parametric function for the duty cycle,
12 parameters for U(M,z) that are determined by conditions on the
observational quasar luminosity function.
Main Ingredients of the model
U(M, t) =
AGN (M, t)
BH(M, t)
U(M, z) = min
A(z)
(M/M0)↵l(z) + (M/M0)↵k(z)
, 1
!
with M0 = 107.5
M
X(z) = aX + bX z + cX z2
+ dX z3
with X = A, ↵l, ↵k
8. (3) Eddington Ratio Distribution P(𝝀,z)
-8
-6
-4
-2
z = 0.40z = 0.40 z = 0.60z = 0.60 z = 0.80z = 0.80 z = 1.00z = 1.00
-8
-6
-4 z = 1.20z = 1.20 z = 1.40z = 1.40 z = 1.60z = 1.60 z = 1.80z = 1.80
-8
-6
-4 z = 2.15z = 2.15 z = 2.65z = 2.65
-1.0 -0.5 0.0 0.5
z = 3.20z = 3.20
-1.0 -0.5 0.0 0.5 1.0
z = 3.75z = 3.75
-1.5 -1.0 -0.5 0.0 0.5
-10
-8
-6
-4 z = 4.25z = 4.25
-1.0 -0.5 0.0 0.5 1.0
z = 4.75z = 4.75
log L / LEdd
Kelly&Shen13
type-1 (or unobscured) quasar from
SDSS at redshifts 0.3-5
➔ P(𝝀,z) for type-1 AGN modelled
by a log-normal distribution
peaks at 𝝀 = 0.03 — 0.8
depending on z
Aird+12
sample of type-2 X-ray AGN at 0.2<z<1
For type-2 AGN we use a
truncated power-law distribution
slope 𝛂 = -0.6 at z≤0.6
flattening at z>0.6
9. Given the duty cycle (a set of the 12 param.) the continuity equation
is solved
• backwards in time from now to z=4
• the local SMBH mass function is the boundary condition
• the bolometric luminosity function is computed by
and compared to the observational LF from Hopkins+07
• the best-fit duty cycle parameters are found by a MCMC method
Our approach to the continuity equation
(L, z) =
Z
d log P( |M, z) AGN (M, z)
Best results:
𝜀 = 0.05, 0.07 and local BHMF with 0.5dex scatter
𝜀 = 0.1 and local BHMF with 0.3dex scatter
14. ⇢BH =
Z
log(M)M BH(M)
Mass Function for
type-1 AGN
and
type-2 AGN
BH Mass density
SMBHs
type-1 AGN
type-2 AGN
15. Comparison with Observations
Type-1 AGN
Mass Function
Data from: Kelly&Shen13;
Nobuta+12; Schulze+15
type1
AGN (M) = AGN (M) an(M)
Z 1
log min
d log funo(L)P1( )
16. Comparison with Observations
Type-1 AGN
Eddington ratio
distribution
Data from: Kelly&Shen13;
Nobuta+12; Schulze+15
type1
AGN ( ) = P1( )
Z 11
log Mmin
d log M an(M)funo(L) AGN (M)
17. • Models give tight predictions on the
evolution of active SMBHs, due to the
strong constraints from quasar LF.
• SMBH mass function depends on 𝜀.
Values of 𝜀>0.1 disfavoured, no
evolution in the SMBH mass function.
• Anti-hierarchical growth of SMBHs
and AGN (cosmic downsizing).
• Different scenarios for SMBH seeds:
1) low 𝜀, compatible with stellar mass
progenitors; 2) high 𝜀, with direct
collapse of supermassive stars.
Conclusions
• Information on P(𝝀,z) are still incomplete and uncertain. Imply an
increase of the uncertainties of model predictions, but not dramatic.
