1. 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

2. 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

3. Supermassive Black Hole Mergers  SMBH binaries regularly form as consequence of hierarchical galaxy evolution  Final parsec problem:  Dynamical friction can reduce a bin 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 M BH <10 7 M  )  Significant nuclear triaxiality  Presence of accreting gas (also suppresses v k )

4. Black Hole Recoil  Numerical relativity simulations increasingly convergent between groups (Lousto et al. 2010)  Gas accretion can align spins, suppress large v k (Bogdanovic et al 2007)  Post- Newtonian resonances could also align spins (Kesden et al 2010) Lousto 2010 v k distribution: -Unaligned spins -30° alignment -10° alignment

5. Tidal Disruption Events (TDEs)  Tidal disruption radius  Above ~10 8 M , r t ≤r s  Exception: Kerr BHs, up to ~5x10 8 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 Evans & Kochanek 1989 Strubbe & Quataert 2009

6. 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 10 4-5 x stationary SMBH rate Merritt & Milosavljevic 2003

7. 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

8. Dry Mergers  Final parsec problem solved by  Collisional relaxation (if M BH <10 7 M  )  Triaxiality  These lead respectively to the following density profiles ρ =kr - γ :  Joint core-cusp profiles (transition at 0.2r infl )  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

9. Dry Mergers: Pre-Merger Loss Cone  SMBHs decouple from stellar population when, at separation a E  Remove all stars with a<a E  But relaxation in J is faster than in E  To fill a gap in J-space takes  So there is a second decoupling (a J ) when T gap >T GW  Remove all stars with pericenters r p <a J

10. 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

11. 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

12. 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 T GW =T visc  Note that large v k will be suppressed

13. 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

14. 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

15. 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

16. Questions?

17. 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

18. 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 (~10 43-44 erg/s) Strubbe & Quataert 2009

19. A Kinematic Recoil Candidate  Interpretation of this spectra, by Komossa et al. 2008, has since been disputed  Other possibilities:  SMBH binary  Chance quasar superposition

20. 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 v wind >>v kick

21. LISA Localization Capabilities  LISA taskforce estimates:  8.2 events/yr localized to within 10 deg 2  2.2 events/yr localized to within 1 deg 2  Holz & Hughes 2005 provide galaxy column density

22. 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

23. 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)

24. Observational Constraints  Peak optical luminosity ~10 40-42 erg/s for disk, ~10 43-44 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