Gravitational-wave spin measurements and massive black hole evolution Emanuele Berti, University of Mississippi CENTRA, Jul 9, 2009

Outline 1) Evidence for BHs and BH binaries 2) Spin in inspiral, merger, ringdown 3) Physics and astrophysics from spin measurements

(Movie courtesy of Reinhard Genzel) The SMBH at the center of our Galaxy

SMBH spin estimates: efficiency and ISCO  =1-(8/9) 1/2 =0.057  =0.42

Continuum spectroscopy: in the “high soft state” gas is optically thick, radiates like a blackbody; from radiation flux, estimate R in cos  /D Line spectroscopy: X-ray observations of “skewing” of the Fe K  Fluorescence line Large uncertainties! EB, Cardoso & Starinets Gravitational wave observations can do better

Radiative efficiency and SMBH spin (Wang, Hu, Li, Chen, King, Marconi, Ho, Yan, Staubert & Zhang, ) Why the spindown? Chaotic accretion? Were mergers more common in the past?

Massive ( M ~ M sun ), metal-free Pop III stars collapse forming primordial, massive BHs in the cores of massive dark-matter halos (Volonteri, Haardt, Madau, Rees) Alternative: Direct collapse of low-angular momentum material in protogalactic discs to form large-mass seeds at large z>12 (Koushiappas et al. ) SMBH binary formation and event rates 1) Black holes sink to the center by dynamical friction 2) Gravitational slingshot interactions (or gas accretion) increase the binary’s binding energy 3) Gravitational radiation drives binary to merger: eccentric binaries coalesce faster 4) Gravitational-wave recoil for unequal-mass binaries may kick BHs out of the host galaxy Bottom line: maybe 10 events/year at 2<z<6; possible SMBH background! Matsubayashi et al., Miller, Portegies-Zwart et al. 05: a few, or up to 100 IMBH-SMBH/yr (~ M sun )

Close SMBH binary candidates 2002: NGC6240: projected distance ~1kpc (Komossa et al., astro-ph/ ) 2006: Radio Galaxy : M tot ~1.5x10 8, projected separation ~7.3pc (Rodriguez et al., astro-ph/ ) 2008: SDSSJ : quasar with two sets of narrow lines,  v~2650km/s (one with associated broad lines) Initial interpretation: recoiling BH (Komossa, Zhou & Lu, ) Binary interpretations: 1)Blueshifted lines from accretion stream within the inner rim of a circumbinary disk q~0.1, m 1 ~10 9 (Bogdanovic et al., ) 2)Blueshifted lines from gas swirling around secondary q~0.3, m 1 ~2x10 9, a~0.34pc, P~370yrs (Dotti et al., ) Superposition of two AGN? (Shields et al., ) Analogous to NGC 1275, large and small galaxy interacting (Heckman et al., ) 2009: SDSSJ : quasar with two sets of broad lines,  v~3500km/s (absoption lines at intermediate velocity) Binary interpretation (Boroson & Lauer, ): q=1/40, m 1 ~8x10 8, a~0.1pc, P~100yrs, may coalesce within a Hubble time No superposition of two AGNs May be analogous to NGC 1275 ?

OJ 287: a SMBH binary near merger? Consistent with gravitational wave emission within 10%, T merge =10 4 yrs (Valtonen et al., Nature, ) M 1 =1.8x10 10 M sun, M 2 =10 8 M sun, e=0.66, a~50M,  =39° Sep 13, 2008

Spin in inspiral, merger and ringdown

Inspiral, merger and ringdown

LISA signal-to-noise ratio for inspiral and ringdown ~ z=0.54 ~ z=10 (EB, Cardoso & Will 06)

Inspiral: (circular) Post-Newtonian waveforms Spin-orbit, 1.5PNSpin-spin, 2PN Brans-Dicke: dipole radiation - best bounds from NS-IMBH Massive graviton: D -dependent delay in wave propagation Best bounds from SMBH binaries Standard Post-Newtonian terms in black can be used to test GR (more later..)

Parameter estimation (in a nutshell) Fisher matrix where the Fisher matrix Errors on and correlations between parameters are given by the correlation matrix: { i } Gravitational-wave signal described by parameters { i } Inspiral: { i } = Inspiral: { i } = masses, spins, sky location, orbital orientation.. Ringdown: { i } = Ringdown: { i } = mass, angular momentum, spin orientation, sky location.. For high SNR, errors have a Gaussian distribution: (see Vallisneri 07 for caveats)

Inspiral: tracking M source (z), J source (z) LISA only measures redshifted combinations of masses and spins of the form M=(1+z)M source J=(1+z) 2 J source Measuring luminosity distance D L (z,cosmology) and assuming cosmology is known, find z(D L ) and remove degeneracy (EB, Buonanno & Will 05) Luminosity distance Angular resolution (steradians) Reduced mass “Chirp” mass

Spin precession Spin precession (Kidder 95)

(Apostolatos, Cutler, Sussman & Thorne 94) Simple precession vs. transitional precession

(Schnittman 04) Spin-orbit induced alignment?

Ringdown: black hole spectroscopy  lmn =  R +i  I =2 p f+i/ t f = (10 6 M sun )/M Hz  = 55 M/(10 6 M sun ) s

Spectroscopy of rotating (Kerr) black holes

Mergers: kick velocities and final spin (Buonanno, Kidder & Lehner 2007) (EB et al. 2007; Rezzolla et al ) Very good agreement (~few %) between different models for aligned/antialigned spins Kicks for spinning binaries as large as 4000 km/s (Campanelli et al., Jena group) Spin expansion: spin and kicks using symmetry arguments and a few simulations (Boyle, Kesden & Nissanke 2007)

Typical final spin from MBH mergers * Without alignment, isotropic mergers (on average) are unlikely to produce spins >0.7 * Alignment (presumably) requires torques from accretion disks (Bogdanovic et al., astro-ph/ )

Physics and astrophysics from spin measurements

Random spins m 1 =10 6 (solid) m 2 =3x10 5 (dashed) m 1 =10 6, m 2 =3x10 5  1 =  2 =0.9 (solid)  1 =  2 =0.1 (dashed) (Lang & Hughes 06)

Errors on single-mode detection with LISA D L =3Gpc,  rd =3% SNR -1 ~  rd -1/2 Errors scale like SNR -1 ~  rd -1/2 (EB, Cardoso & Will 06)

Ringdown: no-hair tests f(M, j ),  (M, j ) M(f,  ), j (f,  )  One-mode detection: Measure of black hole’s mass and angular momentum (Echeverria 89, Finn 92)  Multi-mode detection: First mode yields (M, j ) only In GR, quasinormal frequencies depend only on M and j : second mode yields test that we are observing a rotating black hole Under reasonable assumptions, the test requires SNR~ (EB, Cardoso & Will 06) Test similar in nature to “multipolar mapping” with EMRIs and with advanced LIGO Test should be possible both with LISA and with advanced LIGO (EB et al. 07)

Spin distribution encodes merger history (EB & Volonteri, ) Assume isotropy and zero spins for the “seed” black holes (for this plot only!) Consider for simplicity three scenarios: 1)Inefficient accretion (evolution by mergers only): attractor at spin ~0.7 2)Prolonged accretion (Bardeen-Petterson), producing spinup 3)Chaotic accretion (King & Pringle), producing spindown

Depends on descoping. We considered the 6-link and baseline designs (Arun et al., ) May not lose much in terms of detected merger events, but dramatic loss for source localization and distance determination (and loss of EMRI science) Punchline: descopes would seriously damage the science you can do with LISA LISA science: parameter estimation accuracy

Fundamental physics: the graviton mass (EB, Buonanno & Will, gr-qc/ ; Arun & Will, )

Summary EM observations yield model-dependent spin estimates Inspiral/ringdown: measure spins with accuracy ~1% or better Spin evolution encodes SMBH merger history Seed formation scenarios determine mass evolution/event rates Accretion (efficient/chaotic/inefficient) determines spin distribution Astrophysics: how efficient is alignment? Affects ejection rates (and LISA event rates) Affects LISA parameter estimation accuracy/requirements Fundamental physics with massive black hole binaries Inspiral: graviton mass Ringdown: no-hair tests Inspiral+Ringdown: Hawking’s area theorem