LSST and opportunities of PKU Astrophysics
Beijing, 4 Dec. 2011
Transient activities of supermasive
binary black holes in normal
galactic nuclei
Fukun Liu
Astronomy Department, Peking University
Collaborators
Xian Chen (PKU), Shuo Li (PKU), Xuebing Wu(PKU), John
Magorrian (Oxford), Piero Madau (UCSC), Alberto Sesana (AEI),
Rainer Spurzem (Heidelberg), Peter Berczik (Heidelberg)
Content

The formation and evolution of supermassive
black hole binaries (SMBHBs)

Transient activity of supermassive black hole
in galactic nuclei

Tidal disruption of stars in SMBHBs in galactic
nuclei: rate and light curves

Tidal disruption of stars by gravitational
recoiling SMBHs

Conclusions
• Formation and evolution: hierarchical galaxy formation
in CDM cosmology
Hierarchical structure formation
Volonteri
merge tree
NGC2207
Arp 147
Arp194
Arp272
Frequent galaxy interaction and mergers
• If coalesce: Gravitational wave astronomy
—Laser Interferometer Space Antenna (LISA) (Danzmann 2003)
LISA: 10-4-10-1 Hz (MBH104 -107M⊙)
—Pulsar Timing Array (PTA)
(Lorimer 2005)
• very low frequency GWs
 10-9 — 10-5 Hz
• MBH ~107-1010 M⊙
Pulsar
Earth
LISA & PTA: spatial resolution  1°, Electromagnetic
counterparts are essential to Gravitational Wave detections
• Evolution of MBBHs and observational evidences
(Begelman et al. 1980; Sillapaa et al. 1988; Komossa et al. 2003, 2008; Liu,
Wu, Cao 2003; Liu 2004; Liu, X., et al. 2009,2010)
Evolution timescale
Hard Phase
Hubble time
1010 yr
108 yr
Silllapaa et al
Liu + Merritt &Ekers
gas disk?
two AGNs
Boroson & Lauer
106 yr
Gravitational
Wave Radiation
Dynamical
Friction
~1pc
0.01pc
Komossa et al
1pc
Komossa et al
Distance
Liu et al
100pc
1pc = 3.1x1018 cm
Begelmann, et al. 1980
SMBBHs in normal galaxies?
• Stellar tidal disruption by SMBHs in local galactic nuclei
A dormant SMBH is temporarily activated by tidally disrupting a star
(Hills 1975; Rees 1988; Phinney 1989; Evans & Kochanek 1989; Komossa et al.
2004; Lodato et al. 2009; Strubbe & Quataert 2009; Kasen & Ramirez-Ruiz
2010; etc): γ-ray, X-ray, UV, optical, Radio; LSST surveys
-2.5
stars
-1
Single BH disruption rate (yr )
BH
Loss cone
rg 
2 GM
c
Cusp galaxies
Core galaxies
-3.0
-3.5
-4.0
-4.5
-5.0
-5.5
-6.0
-6.5
5.5
BH
6.5
7.0
7.5
8.0
8.5
9.0
9.5
Log MBH
2
 M BH
rt  r* 
 m*
6.0




1/ 3
8M
M
>10
8M*
MBH
<10
BH
*
rrt<r
g
t>rg
Stellar disruption rate~10-5 yr-1(Wang &
Merritt, 2004), enhanced due to nonspherical (~2), tri-axial (~10-100), or
galaxy mergers (Chen Xian’s talk)
Tidal accretion: falling back model (Rees 1988, Phinney 1988)
• The tidal gas debris with  < 0 moves with a Keplerian orbit
and return to tidal radius after a Keplerian time


3


rap 2

T  2 
 GM BH 


1/2
2
1/2
 GM BH 
3/2
Rp
rap
• Assumptions (Rees 1988):
1. Constant mass distribution of plasma with specific energy
(hydrodynamic simulation for =5/3 by Evans & Kochanek 1989;
etc)
dM/d = constant
2. Once returning to the pericenter, the
material rapidly loses its angular
momentum due to strong shocks at
several tidal radii and circularizes to
form an orbiting torus at
Simulated accretion rate for stars with
Rtorus  2 Rp
=1.4, 1.5, 5/3, 1.8 (Lodato, King, Pringle, 2009)
Observations of tidal flares:
consistent with falling back
model (Rees, 1988): accretion
disk and jets
• Initially radiating with
Eddington luminosity:
LEdd  1.3  10
45

M 

 ergs/s
7
10
M

e 
RX J 1242.6-1119A (Komossa et al. 2004)
• Thermal spectrum of effective
temperature
1/4
Teff
 L

Edd
; 

2
 4 rt  
 r 
 2.4  10  * 
 re 
1/2
5
 m 
*


 Me 
1/6
1/12
M8
K
• Decaying after peak as powerlaw with time

f  t t flare

5/3
• on a timescale:
t flare
 r 
: 1.1yr  * 
 re 
3/2
 m 
*


 Me 
1
1/2
M8
Tidal accretion and jet in SW 1644+57
(Bloom et al. 2011, Zauderer et al. 2011 )
Tidal X-ray flares at center of
NGC 5905 by ROSAT and
Chandra: consistent with falling
back model ~t-5/3 (Halpern,
Gezari, Komossa, 2004, ApJ)
&  T T 
lg M
min
5/3
UV, optical light curve of the tidal
disruption flare candidate D1-9
by CFHTLS (Gezari et al. 2008).
• Effects of SMBHBs on tidal disruption rates
Unbound stars (Chen, Liu, & Magorrian, 2008) and bound stars (Chen,
Madau, Sesana, Liu, 2009; Chen, Sesana, Madau, Liu, 2011):
Interaction of stars and MBHBs: scattering experiments
BH
BH
Three-body Sling-shot effects:
ejecting most of the stars
(Quilan, 1996): decreasing
the tidal disruption rates of
unbound stars
• Cusp destruction of bright galaxy (Merritt 2006)
• hyper-velocity stars in Milk Way (Yu, et al 2003)
• Hyper-velocity binary stars (Lu, Yu, Lin, 2007)
Disruption rates of unbound stars in spherical two-body
relaxation (Chen, Liu, Magorrian, 2008, ApJ)
Single BH
Primary BH
secondary BH
51 elliptical
galaxies: solar
type stars
•Tidal disruption rates of unbound stars by SMBHBs: ~10-7 yr-1
•Possible tidal flares in SMBHBs with mass > 108 M☉
Isothermal cusp
I
Shallower cusp
Tidal disruption rate of bound stars:
• Peak rate: ~10-1 yr-1, insensitive
to e or q
• Very sensitive to the cusp
density profile of galaxies
• During time: t~ 105 yr
II
III
A complete picture for the stellar disruption rate in MBBHs: 3
Phases
• Phase I: shortly after MBHBs becoming bound, high rate, short
duration (Kozai timescale)
• Phase II: after the initial stellar cusp is destroyed, low rate, long
duration (until BHs coalesce)
• Phase III: after BHs coalesce, recovering, relaxation timescale
(Merritt & Wang 2005)
• Effects on the tidal flare light curves: Interruption
(Liu, Li, Chen, 2009, ApJL)
r
r
j
j
• binary black holes and

gas debris consist of a
restricted three-body
system

Chaotic
b
rap
secular
• gas-debris with large bind
2ab
energy || is in the secular
region and fall back to tidal For a restricted three-body system,
the fluid elements with agas < amax
radius to form accretion
consist of hierarchical binary system
• Region with agas > amax are and its orbit changes secularly
chaotic and fluid elements (Mardling & Aarseth 2001):
exchange angular
a
a

 2.8 1  q
 1  e  
a
a
momentum with binary BH
on dynamical time scale,
1  e  1  0.3 / 180 
b
b
gas
max
2/5
out
2/5
b
6/5
b
The fluid elements with larger semimajor axis, agas > amax
do not fall back to tidal radius and BH accretion stops！
Numerical simulation of tidal accretion in SMBHB system
• Simulations: MBH=107M☉,
q=mBH/MBH = 0.1, ab=104 rG
• Interruption at time: Ttr ~ 0.25 Tb
• Ttr/Tb~0.15-0.5: insensitive to
the MBHB parameters: ab and q
&  T T 
lg M
min
5/3
Ttr : Torb / 7 ~ 3yr
Ttr/Tb : Depending on the orbit parameters of the disrupted star
SMBBHs with orbit ab  102 rg (PTA & LISA sources): Ttr~10 days
• Observational signatures of recoiling black holes
SMBHBs get merged due to interaction with stars or gas disk
Any asymmetry in the merging binary system (mass differences,
BH spins) leads to anisotropic gravitational radiation (Peres 1962;
Berkenstein 1973): carrying away momentum  recoil velocity
 Schwarzschild SMBHBs: unequal masses (Fitchett 1983;
Favata et al. 2004; Baker et al. 2006; Gonzalez et al. 2007; etc):
vrecoil  176 km s-1 (symmetric mass  = 0.195)
 Kerr SMBHBs due to BH spins (Campanelli et al. 2007a,b;
Herrmann et al. 2007; Koppitz et al. 2007; Pollney et al. 2007; Rezzolla, et
al. 2008): Vrecoil  4000 km s-1 (or  104 km/s for parabolic orbit)
Elliptical orbit e  0: increase with e
  mM
m  M 
2
• Post-merger: recoiling MBHs in galaxies: N-body
simulations (Li, Liu, Berczik, Chen, Spurzem, 2011, ApJ)
The dynamic evolution of a kicked SMBH in galaxy: two oscillation
phases (Phases I & II) + Brownian motion (Phase III)
Phase I: influence radius of BH oscillation amplitude; as
predication with dynamic friction theory  damping on dynamic
friction timescale

Phase I
Phase II
Phase II: influence radius of BH oscillation
amplitude; deviation from predication
with dynamic friction theory  very slow
damping for much longer time
Direct N-body simulations with NAOC GPU: 106 particles
• Recoiling MBHs: ejecting and oscillating in galaxies: two
phases
• Off-nucleus tidal stellar disruption: 10-6 yr-1 (consistent with
Komossa & Merritt 2008)
• Off-nuclear massive compact stellar global cluster M* ~10-3 MBH
Phase I
Phase II
x10-5 yr-1
• SMBHBs in local galaxies?
X-ray flares at center of local
quiescent galaxies: consistent
with falling-back model
(Komossa, 2004)
&  t  t  t

lg M
D
min 

Normal flare followed by
extremely rapid disappear:
SMBHB in RXJ1624+75 (??)
flare rates vs binary fraction
0.4
0.0
5/3
0.8
• Preliminary survey: tidal
disruption candidates in
inactive galaxies (Komossa
2002, Donley et al. 2002,
Gezari et al. 2006)
Chen, Liu, Magorrian 2008
Conclusions
SMBHBs are products of galaxy formation in CDM
SMBHBs would dramatically the change tidal
disruption rate of stars in galactic nuclei: as high as
~ 0.1 galaxy-1 yr-1
SMBHBs would interrupt the tidal disruption light
curves, which can be used to identify strong
gravitational wave radiation system in galactic
nuclei
Recoiling SMBHB in galactic nuclei may be
identified by observing spatial off-nuclear tidal flare