Transcript No Slide Title

Gravitational Waves from
Massive Black-Hole Binaries
Stuart Wyithe (U. Melb)
NGC 6420
Outline
• The black-hole - galaxy relations.
• Regulation of growth during quasar phase.
• The quasar luminosity function.
• Evolution of the BH mass function.
• Rate of gravity wave detection (LISA).
• The gravity wave back-ground.
• The occupation fraction of SMBHs in halos and
GW predictions.
Black Hole - Galaxy Relations
5/3
Mbh  Mhalo
 vc5
Ferrarese (2002)
The Black Hole-Bulge Relationship
• Quasar hosts at high z are smaller than
at z=0 (Croom et al. 2004).
The Black Hole-Bulge Relationship
• Radio quiet QSOs conform to the Mbh-* with
little dependence on z (Shields et al. 2002).
Model Quasar Luminosity Function
• One quasar episode per major merger.
Three assumptions:
• Accretion at Eddington Rate with median spectrum.
• Hypothesis: Black-Hole growth is regulated by
feedback over the dynamical time.
This hypothesis provides a physical origin for the
Black-Hole mass scaling.
5
5/3
M
bh
 vcir  Mhalo 1  z 
5/2
The dynamical time is identified as the quasar lifetime.
(LB ,z)

0.5M halo
0
dn ps
d2Nmerge
3 t dyn
dMhalo
(M halo
3
5 5.7 10 d(M halo  M halo ) dMhalodt
 M halo
)
Wyithe & Loeb (ApJ 2003)
Model Quasar Luminosity Function.
• The black-hole -- dark matter
halo mass relation agrees with
the evolution of clustering.
• The galaxy dynamical time
reproduces the correct number
of high redshift quasars.
clustering
of quasars
Wyithe & Loeb (ApJ 2003;2004)
Properties of Massive BHs
• Ubiquitous in galaxies >1011Msolar at z~0.
• Tight relation between Mbh and * (or vc, Mhalo).
• Little redshift evolution of Mbh~f(*) to z~3.
• Feedback limited growth describes the
evolution of quasars from z~2-6.
• Massive BHs (Mbh>109Msolar) at z>6.
• Is formation via seed BHs at high z or through
continuous formation triggered by gas cooling?
• What is the expected GW signal?
Evolution of Massive BHs
• Were the seeds of supermassive BHs the
remnant stellar mass
BHs from an initial
episode of metal free
star formation at z~20?
• The BH seeds move into larger halos
through hierachical merging.
Evolution of Massive BHs
• Is super-massive BH
formation ongoing and
triggered by gas cooling
inside collapsing darkmatter halos?
BH Evolution Triggered by Gas
Cooling
• Prior to reionization, cooling of gas inside darkmatter halos is limited by the gas cooling
thresh-hold (104K for H).
• Following reionization the infall of gas into
dark-matter halos is limited by the Jeans Mass.
•
High z
-3/2


1
z
 108
 M solar
 20 
Low z
Reionisation
10  1  z 
 10 

 10 
-3/2
 Tvir 
 5 Msolar
 10 K 
• Reionization may affect BH formation in low
mass galaxies as it does star formation.
Merging Massive BHs
• Satellite in a virialized halo sinks on a timescale
(Colpi et al. 1999)
1 M  M
t sink  0.25H
M
• Allow at most one coalescence per tsink.

• BBHs in some galaxies
will converge within H-1
• Coalescence more rapid in triaxial galaxies.
• Brownian motion of a binary black hole results
in a more rapid coalescence.
• We parameterise the hard binary coalescence
efficiency by mrg.
LISA GW Event Rate
(hc>10-22 at fc=10-3Hz)
2
d Ngw
dtdz



0
dM  dMM,M,fc ,hc ,z  Sz ,M bh ,M bh 
M
0
dn bh

2

dn bh
d2N
d
V


mrg
d
M


4


dM d Mdt M dn ps
1 z dz d



d M 
• An event requires the satellite galaxy to sink,
rapid evolution through hard binary stage, and
a detectable GW signal.
Number counts resulting
from BH seeds
Number counts resulting from
continuous BH formation

Characteristic Strain Spectrum
Sh (f) 


0
dh  0

2
d
d
V
2
dz h
(z)4 
dhdf
dzd 
• hspec<10-14 (current)
• hspec<10-15.5 (PPTA)
Jenet et al. (2006)
hspec (f)  fSh (f)
hspec is Sensitive to the Mbh-vc Relation
2
3
M halo 
M bh
 1.20 12 
 10 
M halo
Ferrarese (2002):
0=10-5.0 =5.5
WL (2002):
0=10-5.4 =5.0
Massive Black-Holes at low z
Dominate GW Back Ground
Sesna et al. (2004)
Black-Hole Mass-Function
• The halo mass-function over predicts the
density of local SMBHs.
• Most GWBG power comes from z<1-2.
Model Over-Predicts Low-z Quasar
Counts at High Luminosities
Galaxy Occupation Fraction
• The occupation
fraction is the galaxy
LF / halo MF
• Assume 1 BH/galaxy
Reduced GW Background
• Inclusion of the
occupation fraction
lowers the predicted
GW background by 2
orders of magnitude.
Conclusions
• The most optimistic limits on the spectrum of
strain of the GW back-ground are close to
expected values. Tighter limits or detection of
the back-ground may limit the fraction of
binary BHs.
• Allowance should be made for the occupation
of SMBHs in halos, which lower estimates of
the GW background based on the halo mass
function by 2 orders of magnitude.
• Models are very uncertain! PTAs will probe the
evolution of the most massive SMBHs at low z.
Limits on the GW Back-Ground
• Pulsar Timing arrays
limit the energy
density in GW.
• gwh2<2x10-9
1 dρGW
ΩGW (f) 
ρcrit dlnf
(Lommen 2002)
Minimum Halo Mass for
Star formation
• Atomic hydrogen
cooling provides the
mechanism for
energy loss that
allows collapse to
high densities.
• This yields a
minimum mass in a
neutral IGM.

3
2
1 z 
M min  10 
 M solar
 10 
8
Minimum Halo Mass for
Baryonic Collapse
• Assume gas settles into hydrostatic
equilibrium after collapse into a DM halo
from an adiabatically expanding IGM.
3
2
 6 Tvir 
b
b  1  1
 1
 5 T 
b

Tvir  17.2T
(b  100)
• This yields a minimum mass in an ionized
IGM.
3

1 z  2
M min  5 10 
 M solar
 10 
9
Minimum Halo Mass for
Baryonic Collapse
z=11
QuickTime™ and a
TIFF (U ncompressed) decompressor
are needed to see this picture.
Qu i c k T i m e ™ a n d a
T IF F (U n c o m p re s s e d ) d e c o m p re s s o r
a re n e e d e d to s e e th i s p i c tu re .
z=2
• A minimum mass
is also seen in
simulations. The
minimum mass is
reduced at high
redshift.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
(Dijkstra et al. 2004)
Median Quasar Spectral Energy Distribution
Elvis et al. (1994); Haiman & Loeb (1999)
• The median SED
can be used to
compute number
counts.
• The SED can also
be used to convert
low luminosity Xray quasar
densities to low
luminosity optical
densities.
Binary BH Detection by LISA
107
106
105
104
10-3.5Hz
10-1.5Hz
Black-holes at high z accrete
near their Eddington Rate
2π 2 3
ΩGW (f) 
f Sh (f )
2
3H0
A BBH in a pair of Merging Galaxies
(NGC 6420; Komossa et al. 2003)
Gravitational Waves from BBHs
• The observable is a strain amplitude
Mbh ΔMbh
f 2/3
 20
16
hc 

10

10
R(z ) Mbh  ΔMbh 1/3
• In-spiral due to gravitational radiation.
 P 
tP   10 P

 1se c
5
5/3
Merger Rates for DM Halos

d2N
(M)
dMdt
crit(z)
Large M
Time
Small M
k
Lacey & Cole (1993)
The Press-Schechter Mass Function
Z=30
Z=0
• Reionization may affect BH formation in low
mass galaxies as it does starformation.
Binary Evolution Timescales
(Yu 2002)
• BBHs in some galaxies will converge within H-1
• Coalescence more rapid in triaxial galaxies.
• Residual massive BH binaries have P>20yrs
and a>0.01pc.
Merging Massive BHs
• Satellite in a virialized halo sinks on a timescale
(Colpi et al. 1999)
t decay
 rvir
 1.2
 vc

M  ΔM

ε 0.4
  ΔM  ln  M  ΔM 
 e   ΔM 
M  ΔM
 0.25H
ΔM
1
• Allow at most one coalescence during the decay
plus coalescence times.
Reduced Event Rate
• Inclusion of the
occupation fraction
lowers the predicted
event rate by an
order of magnitude.