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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). - PowerPoint PPT Presentation
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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
Ferrarese (2002)
5c
5/3halobh vMM ∝∝
• Quasar hosts at high z are smaller than at z=0 (Croom et al. 2004).
The Black Hole-Bulge Relationship
The Black Hole-Bulge Relationship
• Radio quiet QSOs conform to the Mbh-* with little dependence on z (Shields et al. 2002).
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Φ(L B, )z = dΔM halo
35ε
tdyn
5.7 ×103
dnps
(d Mhalo
−ΔMhalo)
d2Nmerge
dΔM halodt(M
halo−ΔM
halo)
0
0.5M halo∫
Three assumptions:• One quasar episode per major merger.
• Accretion at Eddington Rate with median spectrum.
• Hypothesis: Black-Hole growth is regulated by feedback over the dynamical time.
Model Quasar Luminosity Function
Wyithe & Loeb (ApJ 2003)
This hypothesis provides a physical origin for the Black-Hole mass scaling.
The dynamical time is identified as the quasar lifetime.
( )5/25/3halo
5cirbh z1MvM +∝∝⇒
Wyithe & Loeb (ApJ 2003;2004)
Model Quasar Luminosity Function.
clustering of quasars
• 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.
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 super-massive 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 dark-matter halos?
BH Evolution Triggered by Gas Cooling
• Prior to reionization, cooling of gas inside dark-matter 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.
•
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≈108 1+ z20 ⎛ ⎝ ⎜
⎞ ⎠ ⎟-3/2
M solar solar5vir
-3/210 M
K10
T
10
z110 ⎟
⎠
⎞⎜⎝
⎛⎟⎠
⎞⎜⎝
⎛ +≈
High z Reionisation Low z
• 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)
• 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 εmrg.
€
tsink ≈0.25H−1 M +ΔMΔM
LISA GW Event Rate (hc>10-22 at fc=10-3Hz)
€
d2Ngw
dtdz= dM dΔMΘ ,M Δ ,M fc,hc,z( )×S ,z M bh,ΔM bh( )
0
M∫0
∞∫
×dnbh
dM× d2N
dΔ MdtM
dnbhdΔ M
dnps
dΔ M
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
εmrg
1+ z4π d2V
dzdΩ
• 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
• hspec<10-14 (current)
• hspec<10-15.5 (PPTA)
€
Sh( )f = dh0
∞∫ dz0
∞∫ h2dΦ
dhdf( )4z π d2V
dzdΩ
(f)fS(f)h hspec =
Jenet et al. (2006)
€
M bh
M halo
=1.2ε0M halo
1012
⎛ ⎝ ⎜
⎞ ⎠ ⎟
23
Ferrarese (2002):ε0=10-5.0 =5.5
WL (2002):ε0=10-5.4 =5.0
hspec is Sensitive to the Mbh-vc Relation
Sesna et al. (2004)
Massive Black-Holes at low z Dominate GW Back Ground
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.
Ωgwh2<2x10-9
(Lommen 2002)
dlnf
dñ
ñ
1(f)Ù GW
critGW =
• Atomic hydrogen cooling provides the mechanism for energy loss that allows collapse to high densities.
• This yields a minimum mass in a neutral IGM.
Minimum Halo Mass for Star formation
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Mmin =108 1+ z
10
⎛
⎝ ⎜
⎞
⎠ ⎟−
3
2Msolar
• Assume gas settles into hydrostatic equilibrium after collapse into a DM halo from an adiabatically expanding IGM.
• This yields a minimum mass in an ionized IGM.
Minimum Halo Mass for Baryonic Collapse
€
δb =ρ b
ρ b−1= 1+
6
5
Tvir
T
⎛
⎝ ⎜
⎞
⎠ ⎟
3
2−1 ⇒ Tvir >17.2T (δb >100)
€
Mmin = 5 ×109 1+ z
10
⎛
⎝ ⎜
⎞
⎠ ⎟−
3
2Msolar
(Dijkstra et al. 2004)
• A minimum mass is also seen in simulations. The minimum mass is reduced at high redshift.
Minimum Halo Mass for Baryonic Collapse
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z=11
z=2
Median Quasar Spectral Energy DistributionElvis 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 X-ray quasar densities to low luminosity optical densities.
Binary BH Detection by LISA
104
107
106
105
10-1.5Hz10-3.5Hz
Black-holes at high z accrete near their Eddington Rate
)(fSf3H
2∂(f)Ù h
320
2
GW =
A BBH in a pair of Merging Galaxies (NGC 6420; Komossa et al. 2003)
Gravitational Waves from BBHs• The observable is a strain amplitude
• In-spiral due to gravitational radiation.
( )1620
1/3bhbh
bhbh2/3
c 1010ÄMM
ÄMM
R(z)
fh −− −≈
+∝
( )5/3
5
1sec
PP10Pt ⎟
⎠
⎞⎜⎝
⎛≈
Merger Rates for DM Halos
(M)Mdtd
Nd2
Δ
k
δ
δcrit(z)
Large M Small M
Time
Lacey & Cole (1993)
The Press-Schechter Mass Function
Z=30Z=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)
• Allow at most one coalescence during the decay plus coalescence times.
ÄM
ÄMM0.25H
å
ÄMÄMM
lne
ÄMÄMM
v
r1.2t
1
0.4
c
virdecay
+≈
⎟⎠⎞
⎜⎝⎛ +
⎥⎦⎤
⎢⎣⎡
+⎟⎟⎠
⎞⎜⎜⎝
⎛≈
−
Reduced Event Rate
• Inclusion of the occupation fraction lowers the predicted event rate by an order of magnitude.