Stellar Tidal Disruption Flares: an EM Signature of Black Hole Merger and
RecoilNicholas 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)
Post-Newtonian 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
Exception: Kerr BHs, up to ~5x108 M (Beloborodov et al. 1992)
At least half the stellar mass unbound with large spread in energy
Mass fallback rate Supernova-like UV/X-ray
emission, some optical Observed rate ~10-5 /galaxy/yr
Donley et al. 2002
€
rt = R* η 2 MBH
M*
3
€
˙ M ∝ t−5 / 3
Evans & Kochanek 1989
Strubbe & Quataert 2009
Tidal Disruption Rates For a stationary SMBH, governed
by relaxation into 6D loss cone (LC)
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 x × r v 2 = J 2 < Jlc2 ≈ 2GMBH rt
Merritt & Milosavljevic 2003
€
r x × (r v − r v k ) 2 = J 2 < Jlc2 ≈ 2GMBH rt
Our Model Phase space shift could identify recoil in two ways
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
Collisional relaxation (if MBH<107M) Triaxiality
These lead respectively to the following density profiles ρ=kr-γ: 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 , 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
So there is a second decoupling (aJ) when Tgap>TGW
Remove all stars with pericenters rp<aJ
€
Tgap = TrelaxaE
rinf
€
˙ a stars < ˙ a GW
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 post- and 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 Will dynamically produce low-density stellar core
=> no post-kick TDEs? But – two factors could dramatically increase
N<(t) 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:
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
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 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) LSST particularly promising
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
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
super-Eddington 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