The Lagrange Points in a Binary BH System: Applications to Electromagnetic Signatures Jeremy Schnittman NASA Goddard Space Flight Center RIT CCRG Seminar November 22, 2010
Motivation Observing supermassive black hole mergers will teach us about Relativity High-energy Astrophysics Radiation Hydrodynamics Cosmology Galaxy Formation and Evolution Stellar Evolution Dark Matter Extra-solar Planets (really!)
What do we know? galaxy mergers + ubiquitous SMBHs Kormendy & Richstone (1995) remarkably few binary AGN, no triples SDSS phases of BH binary evolution stellar dynamical friction Begelman et al. (1980) gas dynamical friction (final parsec?) Milosavljevic & Merritt (2001) GW loss post-newtonian + numerical relativity kick formula for known masses, spins GSFC, RIT, etc.
What do we need to know? galaxy merger rates (dependence on masses, mass ratio, gas fraction, etc.) BH parameters BH masses BH spins: amplitude and orientation BH environment prior to merger quantity and quality of gas stellar distribution and age/metallicity properties of circumbinary disk
What we will learn galaxy environs: gas vs stars high-velocity end of kick distribution time delay between galaxy, BH merger w/ LISA: merger rates, masses, spins, but only for M 10 6 7 M L D vs z out to z 1
What we will not learn Even with LISA, it will be difficult to measure BH mass function for M 10 7 M L D vs z for z > 1 low-velocity end of kick distribution
Diversity of Merger Signatures (theorist) 10 6 10 3 galaxy mergers dual AGN galaxy cores (scouring) X shaped radio lobes occup. fraction diffuse gas M sigma galaxy cores (recoil) stars accretion disks hot gas R(pc) 10 0 10 3 10 6 binary quasars circumbinary disks GW s (pulsar timing) variable accretion enhanced accretion GRMHD LISA off centered/ Doppler shifted quasars HCSSs X ray/uv/ir afterglows tidal disruption suppressed DM annihilation accretion Bondi accretion delayed quasar dark matter 10 9 yr 10 6 yr 10 3 yr 0 yr 103 yr 106yr 10 9 yr time since merger GWs
angular size (arcsec) Diversity of Merger Signatures (observer) 10 2 10 0 10 2 10 4 10 6 galaxy mergers dual AGN galaxy cores (scouring) binary quasars circumbinary disks variable accretion enhanced accretion GW s GRMHD 10 10 (pulsar timing) LISA X ray/uv/ir afterglows suppressed accretion X shaped radio lobes occup. fraction diffuse gas M sigma galaxy cores (recoil) off centered/ Doppler shifted HCSSs quasars tidal disruption DM annihilation Bondi accretion delayed quasar gam ray 10 9 yr 10 6 yr 10 3 yr 0 yr 103 yr 106yr 10 9 yr time since merger (lifetime of source) radio IR O/UV X ray GW
GW counterparts Analytic Newtonian hydro Relativistic hydro Shields & Bonning (2008) JS & Krolik (2008) Lippai et al. (2008) Kocsis & Loeb (2008) Krolik (2010) Chang et al. (2009) Tanaka & Menou (2010) Haiman et al. (2010) Shapiro (2010) Armitage & Natarajan (2002) Palenzuela et al. (2009) Hayasaki et al. (2008) Bode et al. (2009) MacFadyen & Milos. (2008) van Meter et al. (2010) O Neill et al. (2009) Farris et al. (2010) Corrales et al. (2009) Megevand et al. (2009) Rossi et al. (2010) Palenzuela et al. (2010) Anderson et al. (2010) Mosta et al. (2010) Zanotti et al. (2010) Astro 2010 white papers Bloom et al. (2009) Demorest et al. (2009) Jenet et al. (2009) Madau et al. (2009) Miller et al. (2009) Nandra et al. (2009) Owen (2009) Phinney (2009) Prince (2009) Schutz et al. (2009) Stamatikos et al. (2009) NS mergers: Rasio & Shapiro (1992) Rasio & Shapiro (1994) Zhuge et al. (1994) Ruffert et al. (1996) Janka et al. (1999) Faber & Rasio (2000) Faber & Rasio (2001) Shibata et al. (2003) Anderson et al. (2008ab)...
Lagrange points in classical restricted 3-body problem µ 2 = 0.2 µ 2 = 0.02 JS (2010) arxiv:1006.0182 µ crit 0.0385
Equations of motion in co-rotating frame [ ẍ = 2nẏ + n 2 x + µ 2 x + ṅy µ 1 [ ÿ = 2nẋ + n 2 µ1 y ṅx [ µ1 z = r1 3 + µ ] 2 r2 3 z ṅ = 96 5 µ 1µ 2 n 11/3 r 3 1 r 3 1 + µ 2 r 3 2 ] x µ 1 + µ 2 ] y r 3 2
Intro/Motivation Sources 3-body Dynamics Astrophysical Applications Next Steps/Conclusion 70-50 65-55 60-60 55 µ2=0.038 µ2=0.03 µ2=0.02 µ2=0.01 50 45 40 φ(l5) φ(l4) Linear stability of L4 and L5 with radiation reaction 5 10 15 20 binary separation -65 µ2=0.038 µ2=0.03 µ2=0.02 µ2=0.01-70 -75 25 30-80 5 10 15 20 binary separation The Lagrange Points in a Binary BH System: Applications to Electromagnetic Signatures 25 30 Jeremy Schnittman
Intro/Motivation Sources 3-body Dynamics Astrophysical Applications Next Steps/Conclusion 70-50 65-55 60-60 55 µ2=0.038 µ2=0.03 µ2=0.02 µ2=0.01 50 45 40 φ(l5) φ(l4) Linear stability of L4 and L5 with radiation reaction 5 10 15 20 binary separation -65 µ2=0.039 µ2=0.03 µ2=0.02 µ2=0.01-70 -75 25 30-80 5 10 15 20 binary separation The Lagrange Points in a Binary BH System: Applications to Electromagnetic Signatures 25 30 Jeremy Schnittman
Global stability is complicated by resonance 1.0 1.0 1.0 f bound 0.8 0.6 0.4 µ 2 =0.01 L 4 L 5 0.8 0.6 0.4 µ 2 =0.02 L 4 L 5 0.8 0.6 0.4 µ 2 =0.038 L 4 L 5 0.2 0.2 0.2 0.0 0.0 0.0 0.4 5 10 15 20 25 30 35 0.4 5 10 15 20 25 30 35 0.4 5 10 15 20 25 30 35 <δr> bound /a 0.3 0.2 0.1 0.3 0.2 0.1 0.3 0.2 0.1 0.0 0.0 5 10 15 20 25 30 35 binary separation (GM/c 2 ) 5 10 15 20 25 30 35 binary separation (GM/c 2 ) 0.0 5 10 15 20 25 30 35 binary separation (GM/c 2 )
Fate of test particles µ 2 = 0.01 µ 2 = 0.02 µ 2 = 0.038 f (L 4 ) 0.13 0.11 0.13 f (L 5 ) 0.20 0.12 0.21 f (L 4 M 1 ) 0.16 0.33 0.19 f (L 5 M 1 ) 0.15 0.05 0.10 f (L 4 M 2 ) 0.14 0.27 0.18 f (L 5 M 2 ) 0.21 0.11 0.20
Astrophysical Applications formation mechanisms: tidal capture of GC+IMBH supermassive star formation in accretion disk gas leaking from circumbinary disk IMBH+MS star observables: tidal disruption events hyper-velocity stars enhanced star formation highly-shifted emission lines accretion burst prior to merger effect on gravitational waveforms
Intro/Motivation Sources 3-body Dynamics Astrophysical Applications Next Steps/Conclusion Formation mechanisms: IMBH+GC Holley-Bockelmann et al. (2010); fig: Cole Miller IMBH-SMBH mergers? The Lagrange Points in a Binary BH System: Applications to Electromagnetic Signatures Jeremy Schnittman
Formation mechanisms: IMBH+GC, con t R infl = GM σ 2 a h = q R infl (1 + q) 2 4 ( ) M ( σ ) 2 1.1 pc 10 7 M 200 km s 1 Merritt (2006) ( a h 5 10 3 µ2 ) ( ) M ( σ ) 2 pc 0.02 10 7 M 200 km s 1 ( a GW,Hubble 3 10 3 µ2 ) ( ) 1/4 M 3/4 pc 0.02 10 7 10 4 M M
Star formation in quasar accretion disks Goodman & Tan (2004)
Tidal disruption of stars during inspiral R td, = 2R ( MBH M ) 1/3 M 1 = 10 6 M, µ 2 = 1/50 M 1 = 10 7 M, µ 2 = 1/50 10 14 10 14 R td, O/B R td, O/B 10 13 10 13 R td, sun a (cm) R td, sun a (cm) 10 12 10 12 R td, WD R td, WD 10 11 0.01 0.10 1.00 10.00 100.00 1000.0010000.00 days before merger 10 11 0.01 0.10 1.00 10.00 100.00 1000.0010000.00 days before merger
Ultra-mega-hyper-velocity stars large galactic surveys have found 20 stars in galactic halo with radial velocities > 300 km/s Brown et al. (2009) relatively massive and thus young origin consistent with galactic center at v ej = 0.05c, B-type star reaches 150 kpc in MS lifetime N/N eject 0.30 0.25 0.20 0.15 0.10 0.05 80<a<100 60<a<80 40<a<60 20<a<40 5<a<20 0.00 0.00 0.05 0.10 0.15 0.20 0.25 v /c
What do we do next theory cosmological N-body plus hydro high-resolution N-body simulations of galactic nuclei Newtonian regime: grid-based code vs. geodesics/sph good initial conditions for circumbinary disk full NR+MHD radiation post-processing
What do we do next observations dual AGN: HST imaging, field integral spectroscopy binary AGN: SDSS + long-term spectroscopic followups pulsar timing: more pulsars, 10 ns resolution afterglows: wide-field multi-band surveys cores/star clusters: HST imaging + hires spectra LISA counterparts/precursors: wide-field time domain surveys (Pan-STARRS, LSST, MAXI, WFXT, etc.)
Summary/Conclusions EM signatures of BH mergers are valuable as: Probes of strong-field GR (mass loss, kicks) Probes of accretion disk properties Cosmological observations M BH, M bulge, σ bulge relationships galaxy formation and evolution SMBH growth (mergers vs. accretion) mass/spin distribution functions LISA counterparts distance ladder in a single step luminosity-redshift to 1% LIGO counterparts: GW confirmation