Tracing hierarchical galaxy formation with stellar dynamics...
Transcript of Tracing hierarchical galaxy formation with stellar dynamics...
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Tracing hierarchical galaxy formation with stellar
dynamics: From nuclei to halos
Loren Hoffman
Hebrew University of Jerusalem
UCSC, 8/17/2010
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Dynamical imprint of galaxy formation
-Violent relaxation in mergers is incomplete (Lynden-Bell 1967).
-Memory of ICs encoded in integrals of motion (IOM).
-Time-dependence/perturbations -> diffusion in IOM phase space.
-Crossing of orbital boundaries -> erasure of ICs (relaxation).
-To understand galactic structure and evolution, need to identify macroscopic groups of orbits that conserve qualitatively similar IOM.
Stellar orbits are the building blocksof galaxies (images: Poon & Merritt 2001).
Orbital phase space need not beuniformly populated (image: van den Bosch et al. 2008).
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Dynamical information in real galaxies
Image: http://seds.org/~spider/ngc/ngc.cgi?NGC4365
The stellar population of the NGC 4365 KDC is indistinguishable from that of the outer galaxy.NGC 4365: SAURON image
Gomez et al. 2010
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Proctoret al. 2009
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Binney & Tremaine 2008
Spherical potentials Axisymmetric potentials
-Energy, angular momentumconserved -> orbit confinedto plane
-Rosettes (precessing ellipses) uniformly fill annulus r0 < r < r1
over long times
-Centrifugal barrier shields star from center of potential
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Box Inner long-axis tube Outer long-axis tubeShort-axis tube
3D triaxial potentials
Poon & Merritt 2001
Binney and Spergel 1982;figure from Hoffman et al. 2010
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Imprint of orbitalstructure on kinematics
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Origin of the orbital structure – effect of a CMC
Merritt &Valluri 1997
Kalapotharakoset al. 2004
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Origin of the orbital structure
Hoffman et al. 2010
Hopkins et al. 2009
Hopkins et al. 2009
Barnes & Hernquist 1996,Hopkins et al. 2009
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SAURON data
KDCs in 15-20% gas remnants
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NGC4365 – van den Bosch et al. 2008
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Hopkins et al. 2009:10% “extra light”componentin NGC 4365
NGC 4365 – comparison of 3D structure with simulations
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Constraints from outer kinematics
Emsellem et al. 2004Proctor et al. 2009 Coccato et al. 2009
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Outer kinematics II
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Outerkinematics
III
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NGC 5813
NGC 3414
NGC 5846
NGC 4486
Cappellari et al. 2007
Burkert et al. 2008The SAURON challenge
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More general formation scenarios
Ceverino et al. 2009 Weil & Hernquist 1996
1) Complete exploration of merger phase space
2) Bulge formation throughClump migration in “wild disks”
3) Multiple mergers / cosmologically motivated sequences
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Binary SMBHs in collisionless galactic nuclei
Requirements: Integrate cuspy system with N ≈ 107-8 for up to 500-1000 tdyn ;suppress relaxation enough to be in empty loss cone regime.
Ideal code: Pure triaxial NBSCF (no kicks) until initial spherical loss cone cleared out, switching to MCSCF after that.
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(A)
1) O(N)2) Completely parallel3) No Cartesian
softening
The Self-consistent field (SCF) method
Most astrophysical systems modeled with N-body simulations undergo brief episodes of rapid evolution, long periods of slow evolution (tev >> tdyn).
(B)
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Binary S/IMBHs in collisional nuclei
Milosavljevic & Merritt 2003Sharp phase space gradients near the loss cone.
Requirements: Integrate cuspy system with N ≈ 107 for up to 500-1000 tdyn ; suppress relaxation enough to be in empty loss cone regime and accurately treat 2-body relaxation.
Ideal code: Spherical, triaxial MCSCF with Henon kicks (note: unlike Spitzer MC, Henon method does not require a Maxwellian distribution!).
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Relaxation in N-body simulations
Hernquist & Ostriker 1992
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N = 2.5 x 103
Nmax = 6, lmax = 4
Evolution owing to time fluctuations of coefficients
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Temporal smoothing
1) Initialize {mk, rk, vk}.2) Compute a(r) from eq’n (B).3) Integrate each particle’s orbit
separately through δt=εtrelax,.
4) Apply Henon kicks.5) Go back to step 2.
“Monte-Carlo” implementation
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Energy conservation is currently an issue for long-term integrations of104– 105 dynamical times.
Suppressing relaxation with rare potential updates
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Summary
-Merger model predicts a characteristic, physically intuitive orbital structure (though not necessarily unique), observable with SAURON + SMEAGOL
-Power of direct comparisons with dynamical models of observed systems: Physical intuition, some features detectable only this way
-Need for extension to more general formation models –cosmological merger trees, smooth/clumpy gas accretion, …
-SCF / MC technique ideal for studying nuclear kinematicsof SMBH binary nuclei; code under development.