Binary black-hole mergers in magnetized disks: Simulations in full general relativity

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1 Binary black-hole mergers in magnetized disks: Simulations in full general relativity Brian D. Farris, Roman Gold, Vasileios Paschalidis, Zachariah B. Etienne, and Stuart L. Shapiro arxiv: University of Illinois at Urbana-Champaign Midwest Relativity Meeting, September 29 th, 2012

2 Circumbinary disks ˆ Every galaxy core thought to harbor SMBH ˆ We observe galaxies merge SMBH binary coalescence ˆ GW signal from BHBH coalescence: Vacuum BHBH well understood! ˆ BUT: Studies of BHBH in gaseous environment incl. magnetic fields still in its infancy ˆ Goal: Identify EM signatures that accompany GW signal ˆ MHD Accretion flow onto inspiraling/merging BHBH This is intrinsically a GR problem has not been studied in GR before!

3 Circumbinary disks ˆ Magnetorotational instability (MRI) MHD turbulence (effective) viscosity accretion ˆ Balance between viscous torques and binary tidal torques: ˆ viscosity drives matter inward ˆ Binary tidal torques drive matter outward ˆ Equal-mass binary: low-density hollow ˆ Two regimes: ˆ pre-decoupling: t GW >> t vis (can neglect inspiral) ˆ post-decoupling: t GW < t vis (must evolve spacetime) t GW = t vis a d M 13 ( ) ( ) α 2/5 4/5 H/R

4 Computational Challenge: Disparate Length And Time Scales M: total ADM-mass of the binary Length scales Resolve horizons r 10 2 M MRI wavelength λ MRI 10 1 M Horizon r AH r g = M binary separation a 10M disk inner edge r in 20M disk outer edge r out 200M Time scales Time step dt CFL 10 2 M r g /c = M T binary Kepler M TKepler disk & ω 1 MRI 10 3 M t GW 10 3 M (near ρ max :) t vis 10 4 M

5 The Illinois GRMHD (AMR) Code ˆ metric: G µν = 8πT µν (BSSN, moving punctures) ˆ matter: µ T µν = 0; ν (ρ 0 u ν ) = 0 (HRSC) ˆ E&M: µ F µν = 0; F µν u ν = 0 magnetic induction eq (A µ formulation) generalized Lorenz gauge µ A µ = ξn µ A µ ˆ Vacuum BHBH CTS initial data (provided by H. Pfeiffer) ˆ Γ-law equation of state; Γ = 5/3

6 Effective Cooling Scheme ˆ Realistic cooling depends on detailed microphysics ˆ Consider 2 extreme, limiting cases: ˆ no-cooling ˆ cooling ν T µν MHD = νt µν RAD = Λuµ Λ: remove any (shock-)generated entropy on (local) Keplerian timescale ˆ Realistic cooling case bracketed by these 2 cases

7 Pre-decoupling (a > a d ) ˆ Disk: equilibrium solution around single BH of mass M ˆ Spacetime: CTS BHBH metric Stationary in the corotating frame (helical KV) ˆ BHBH evolution: simply rotate CTS metric ˆ Allow disk to relax black: no-cooling green: cooling magenta: initial surface density Σ ˆ no-cooling :disk puffs up; moves outward ˆ cooling : pile-up

8 Phenomenology and motivation Warm-Up Methods Results At Decoupling: Rest-Mass Density log10 (ρ0 /ρ0,max ) 0.5 Y/M X/M

9 Accretion rates & Luminosities Pre-decoupling Post-decoupling black: no-cooling green: cooling ˆ Ṁ BHBH comparable to Ṁ BH t m : merger time black: L Poynting no-cooling green: L Poynting cooling magenta: L Λ (matter cooling) ˆ L Poynting and L Λ peak just after merger!

10 Outflows: log 10 (b 2 /ρ 0,max ) Z/M c X/M

11 Conclusions ˆ GRMHD simulations are now possible! ˆ Full GR effects necessary for all of the following results: ˆ Some matter always present inside hollow ˆ Ṁ BHBH Ṁ BH (predecoupling) ˆ Poynting dominated outflows ˆ Characteristic speed-up of outflows after merger. Note, final BH is spinning. ˆ Aftermath: Total luminosity peak after merger Stay tuned...

12 Thank you for your attention! Reference: ˆ B. D. Farris, R. Gold, V. Paschalidis, Z. B. Etienne, and S. L. Shapiro, ArXiv e-prints(jul. 2012), arxiv: [astro-ph.he]