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