Stellar Tidal Disruption Flares: an
EM Signature of Black Hole Merger
and Recoil
Nicholas Stone in collaboration with Avi Loeb
GWPAW – Milwaukee – 1/28/11
Motivation


EM counterpart necessary to study host galaxy properties,
SMBH population statistics
If EM counterpart exists, BH mergers could be used as
standard sirens




Precision cosmology independent of the standard cosmological
distance ladder (Holz & Hughes 2005)
Previous proposed EM counterparts require uncertain premerger
accretion flows
We propose flares from tidally disrupted stars as prompt and
perhaps repeating EM signatures for a wide class of SMBH
mergers
Key numerical relativity prediction: high-velocity (>100 km/s)
recoils as generic feature of black hole mergers
Supermassive Black Hole Mergers


SMBH binaries regularly form as consequence of
hierarchical galaxy evolution
Final parsec problem:



Dynamical friction can reduce abin to ~pc scales
But GW emission only merges in less than a Hubble time on
≤mpc scales
Possible solutions (Milosavljevic & Merritt 2003):



Collisional relaxation (effective only for MBH<107M)
Significant nuclear triaxiality
Presence of accreting gas (also suppresses vk)
Black Hole Recoil

Numerical relativity simulations increasingly convergent
between groups (Lousto et al. 2010)


Gas accretion
can align spins,
suppress large
vk (Bogdanovic
et al 2007)
PostNewtonian
resonances
could also align
spins (Kesden
et al 2010)
Lousto 2010 vk distribution:
-Unaligned spins
-30° alignment
-10° alignment
Tidal Disruption Events (TDEs)


Tidal disruption radius
Above ~108 M, rt≤rs





M BH
rt  R 
M*
*3
2
Exception: Kerr BHs, up to ~5x108
M (Beloborodov et al. 1992)
At least half thestellar mass
unbound with large spread in
energy
Ý  t 5 / 3
Mass fallback rate M
Supernova-like UV/X-ray emission,
some optical
Observed rate ~10-5 /galaxy/yr


Evans & Kochanek 1989
Donley et al. 2002
Strubbe & Quataert 2009
Tidal Disruption Rates

For a stationary SMBH, governed by
relaxation into 6D loss cone (LC)
r r2
x  v  J 2  J lc2  2GMBH rt
Theoretical estimates 10-4 – 10-6
stars/yr

 Rates highest in small, cuspy galaxies
 SMBH recoil instantaneously shifts
phase space and refills loss cone



Loss cone drains on a dynamical time
(<< relaxational time)
TDE rate up to 104-5 x stationary SMBH
rate
r r r 2
x  (v  v k )  J 2  J lc2  2GMBH rt
Merritt & Milosavljevic 2003
Our Model

Phase space shift could identify recoil in two ways





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TDE signal after LISA signal
Repeating TDEs within one galaxy
Use pre-coalescence distribution functions of stars, f(J, E)
Then shift coordinates in velocity space, and integrate
over new loss cone to get total number of draining stars
Cuts in energy limit us to short period (<100 yr) stars
Two models for f(J, E)


Wet merger
Dry merger
Dry Mergers

Final parsec problem solved by



These lead respectively to the
following density profiles ρ=kr-γ:




Collisional relaxation (if MBH<107M)
Triaxiality
Joint core-cusp profiles (transition at
0.2rinfl)
Cores
Therefore we consider both core
galaxies (γ=1) and the joint (γ=1,
1.75) result of Merritt et al 2007
Salpeter mass function
Dry Mergers: Pre-Merger Loss Cone



SMBHs decouple from stellar
population when aÝstars  aÝGW , at
separation aE
Remove all stars with a<aE
But relaxation
in J is faster than

in E




To fill a gap in J-space takes
aE
Tgap  Trelax
rinf
So there is a second decoupling
(aJ) when Tgap>TGW
Remove all stars with
pericenters rp<aJ
Dry Mergers: Results



N<(t) is the number of
stars disrupted < t years
after SMBH merger
As mass increases:
 More stars in post-kick
LC
 Orbital periods in
post-kick LC increase
As velocity increases:
 Overlap between postand pre-kick LCs
shrink
 Fewer stars remain on
bound orbits
Dry Mergers: Results

The first post-merger
TDEs occurs sooner for:




Higher kicks (up to a
point)
Lighter SMBHs
The opposite
characteristics lead to
more total post-merger
TDEs
Pure core models
produce negligible TDEs
Wet Mergers

Large accretion flows can solve final parsec problem


But – two factors could dramatically increase N<(t)





Will dynamically produce low-density stellar core => no postkick TDEs?
Star formation
Disk migration
We model f(J,E) with a simple power-law cusp
We set the inner boundary for pericenters to where
TGW=Tvisc
Note that large vk will be suppressed
Wet Mergers: Results



Much higher values of
N<(100)
Sequential TDEs
detectable on timescale
of years
Significantly more
uncertainties in this
model




Star formation
Resonances with disk
Wide range of disk
parameters
Note that we assume
(M, R) for all stars
Other Factors

Cosmological enhancement



Higher rate, longer delay until first event?
Unequal mass SMBH binaries
Resonance in dry mergers



Resonant capture can in principal migrate stars inward as
binary hardens
Demonstrated for the 1:1 Trojan resonance by Seto & Muto
2010
Could be relevant for higher-order mean-motion resonances
also – we are currently investigating this
Conclusions

The phase space shift caused by BH recoil will:




The dry merger rates could be dramatically enhanced if MMRs
can migrate 10s-100s of stars
Time domain surveys in LISA era can use this effect for
localization of SMBH merger



Produce TDEs at a time t~10s of years after GW signal for dry
mergers
Perhaps produce repeating TDEs for wet mergers at t~few years
after GW signal
Confirm strong GR predictions
Precision cosmology (standard sirens)
Independent confirmation of recoil possible if repeating TDEs
observed

Calibration of LISA event rate
Questions?
Observational Constraints

Time-domain surveys expected to observe ~10s-1000s of
TDEs/yr (Gezari et al. 2009, Strubbe & Quataert 2009)


Spatial offsets: we assume LSST resolution ~0.8”



LSST particularly promising
With photometric subtraction of bulge astrometric precision is
FWHM/SNR
We assume SNR~10 in our calculations, so detectable offsets of
~0.08”
Kinematic offsets:



UV spectral followup ideal, but uncertain in LSST era
Next best is X-ray, we consider SXS (ASTRO-H) as example
7eV resolution at 10 keV => ~200 km/s offsets detectable if wind
velocity is small or can be firmly modeled
Tidal Disruption Flares

Recent work (Strubbe & Quataert 2009, 2010) models
lightcurves/spectra in more detail





Accretion torus radiates in the UV/soft X-ray for ~months to ~years
Becomes bluer with time
Optical and line emission from unbound gas
Possible super-Eddington outflow lasting ~weeks
Dynamics not settled, but super-Eddington outflows potentially
highly luminous in optical (~1043-44 erg/s)
Strubbe &
Quataert
2009
A Kinematic Recoil Candidate


Interpretation of this
spectra, by Komossa et al.
2008, has since been
disputed
Other possibilities:


SMBH binary
Chance quasar
superposition
Absorption in Super-Eddington Outflows


Predicted by Strubbe & Quataert 2010 (SQ) and Loeb &
Ulmer 1997 (LU) for very different super-Eddington
models
LU scenario: radiation pressure isotropizes returning
debris



Radiation pressure supports quasi-spherical envelope with
smaller accretion disk in center
X-ray/UV absorption lines on surface of envelope, thermally
broadened ~10s km/s
SQ scenario: super-Eddington fallback launches polar wind


Wind speed highly uncertain, but features X-ray/UV absorption
lines
Spectral detection not feasible if vwind>>vkick
LISA Localization Capabilities

LISA taskforce estimates:



8.2 events/yr localized to
within 10 deg2
2.2 events/yr localized to
within 1 deg2
Holz & Hughes 2005
provide galaxy column
density
Eliminating Sources of Confusion

Triple SMBH systems with gravitational slingshot




Presence of 1 or more SMBH in galactic center (Civano et al.
2010)
Host galaxies have very large mass deficits, velocity anisotropy
(Iwasawa et al 2008)
No GW signal
SMBH binaries




Very hard (<pc) scale binaries will display interrupted tidal
flares
Wider binaries potentially resolvable (spatially or spectrally)
No TDE kinematic offset for Kozai scenario
No GW signal
Observability

Time-domain sky surveys expected to observe ~10s-1000s of
TDEs/yr (Gezari et al. 2009, Strubbe & Quataert 2009)



LSST particularly promising
Higher numbers (1000s/yr) if super-Eddington outflows behave
as in Strubbe & Quataert 2009
Two ways to verify a recoil-associated TDE


Spatial offsets
Spectral offset between host galaxy and absorption lines in superEddington outflow (less certain)
Observational Constraints


Peak optical luminosity ~1040-42 erg/s for disk, ~1043-44 for
super-Eddington outflows
Spatial offsets: we assume LSST resolution ~0.8”



With photometric subtraction of bulge astrometric precision is
FWHM/SNR
We assume SNR~10 in our calculations, so detectable offsets
of ~0.08”
Kinematic offsets:



UV spectral followup ideal, but uncertain in LSST era
Next best is X-ray, we consider SXS (ASTRO-H) as example
7eV resolution at 10 keV => ~200 km/s offsets detectable if
wind velocity is small or can be firmly modeled