Supermassive Black Hole Binaries as Galactic Blenders Balša Terzić University of Florida January 30, 2004 Supermassive Black Hole Binaries as Galactic Blenders Kandrup, Sideris, Terzić & Bohn, 2003, ApJ, 597, 111
Dedicated to the memory of Henry E. Kandrup (1955 2003)
Motivation: explaining central minimum in surface brightness profiles NGC 3706 (Lauer et al. 2002, AJ, 124, 1975)
Supermassive Black Hole Binary NGC 6240
Density and Potential Density: Nuker law (Lauer et al. 1995, AJ, 110, 2622) ρ 0 r = ρ c r γ 1 r α γ β /α double power-law Potential: choose =2, β=4 and γ=0 V 0 r = 2 π arctan r r binary in a circular orbit: radius r h, frequency ω, mass M V t, x, y, z =V 0 x, y, z M r r 1 t M r r 2 t, x 1 = x 2 =r h cos ωt, y 1 = y 2 =r h sin ωt, z 1 =z 2 =0,
Numerical Scheme (1) generate N-body realization with density ρ 0 (r) divide space into N c =100 shells with N=300 ICs each (2) insert a binary: M 1 =M 2 =M, circular orbit ω 2 = (2M+M(r h ))/(2r h ) 3 (3) integrate orbits for t=512 (~ Hubble time) record Δ i t = N t N i δ r,t ρ r,t =[1 δ r,t ] ρ N 0 r (4) from ρ(r,t) compute μ(r,t) μ R,t = 2 ρ r,t r R Y d r, r 2 R 2 Y-- mass/light ratio 1
Binary Induces Chaos In the presence of the time-dependent binary, large fraction of orbits become chaotic via: gravitational scattering -- close encounters dynamical friction resonant chaotic phase mixing binary frequency ω resonates with natural frequencies of orbits affects orbits which are away from the binary sphere of influence of the binary is much larger than its radius Chaotic orbits cause systematic changes in density
Systematic Changes in Density Triaxial Nuker γ=1, =1, β=4, M=0.01, r h =0.05, axis ratio 1.25: 1.00: 0.75, E=-0.7, N=4800 ω=(20) ½ ω=0 t=0 t=16 t=32 t=64 t=128
General Implications: Resonant Vs. 'regular' chaotic phase mixing time-independent: regular phase mixing time-dependent: resonant phase mixing resonant chaotic phase mixing is much more efficient than regular energy is no longer an integral of motion rapid shuffling of orbits on and between constant-energy hypsersurfaces energy shuffling for chaotic orbits is not exponential but diffusive ω= 10 ω=0 t=0 t=8 t=16 t=32 δe t p, σ δe t q, ½ < p < 1, ¼ < q < ½ t=64
Spherical Nuker, =2, β=4, γ=0, M=0.005, r h =0.15, ω=0.6086, M(r=2.26)=0.75M rel. density fluct. density surface brightness t=128 t=256 t=384 t=512
NGC 3706 Vs. spherical Nuker, =2, β=4, γ=0, M=0.005, r h =0.085, ω=1.567 fit relative error t=32 t=64 t=128 t=256
NGC 3706 Vs. spherical Nuker, =2, β=4, γ=0, M=0.005, t=256 r h =0.025, ω=8.968 r h =0.085, ω=1.567
How General is This Model? Underlying assumptions: 1) BHs execute circular orbits 2) BHs have equal mass 3) binary is in the x-y plane Relaxing these assumptions does not appreciably change the dynamics
Goodness of Fit Model fit the data for NGC 3706 qualitatively: reproduces the 'dip' and 'bulge' quantitatively: goodness of fit is significantly better than Nuker Similar fits found for other galaxies listed in Lauer et al. 2002 Uniqueness is not assured: weak dependence on r h and ω Nuker potential is restrictive fixed values of =2 and β=4 even better fit expected for other, more flexible potentials new density/potential model (Terzić & Graham, in preparation) Important: first model to explain central minima in surface brightness
Conclusion and Discussion Binary causes systematic readjustment in density distribution weakly dependent of the potential and parameters orbital frequency of the binary must be in the certain range leads to formation of 'dips' and 'bulges' in s.b. profiles (NGC 3706) Binary facilitates efficient resonant chaotic phase mixing generic in pulsating, time-dependent dynamical systems low-amplitude perturbation can have significant effects at large r more efficient than ordinary chaotic phase mixing violent relaxation in galaxy formation and collisions halo formation in charged particle beams
Auxiliary Information Potential computed via V r = 4 π[ 1 r 0 r ρ R R 2 dr r ρ R R dr ] Mass contained within r for spherical Nuker, =2, β=4, γ=0 M r = 2 arctan r r 2 π 1 r Other potentials investigated Anisotropic oscillator Dehnen (Nuker =1, β=4)» V 0 x, y, z = 1 2 m2 V 0 x, y, z = 2 γ [ 1 2 γ] 1 m2 γ 1 m = m a 2 2 x b 2 y c 2 z, Time-scale 6[ M t=1 1.46 10 10 11 M ] 2[ 1 a 1 kpc ]3 2 yr
Auxiliary Information From μ(r,t) to ρ(r,t): ρ r,t = 1 π r I R,t R 2 r 2 dr, I R =10 μ R /2.5
ENERGY DIFFUSION Triaxial Oscillator, 1.3:1:0.8, M=0.05, r h =0.3, N=1600 ω=0.5 ω=1 ω=2 ω=4 ω=8
Varying M and r h Dehnen γ=1, E=-0.7, <r> 0.33, N=1600 a 2 :b 2 :c 2 r h =0.05 M 1 =M 2 =0.01 1.00:1.00:1.00 spherical 0.90:0.90:1.21 prolate 1.21:1.21:0.64 oblate 1.10:1.00:0.90 mildly triaxial 1.25:1.00:0.75 strongly triaxial
Varying orbital eccentricity and BH mass ratio Dehnen γ=1, E=-0.7, <r> 0.33, N=1600 a 2 :b 2 :c 2 eccentricity mass ratio 1.00:1.00:1.00 spherical 0.90:0.90:1.21 prolate 1.21:1.21:0.64 oblate 1.10:1.00:0.90 mildly triaxial 1.25:1.00:0.75 strongly triaxial