Many-BodyLaboratories Nicholas Z. Rui (UCB), Kyle Kremer (NU), Fred Rasio (NU)
Two-Body Problem • Two gravitationally-interacting point masses • Has an exact solution: conic sections
Three-Body Problem • Chaotic, analytically intractable
N-body Problem • Even more obviously chaotic • Increasing N: More complexity, less predictability • Is there any hope?
Star Clusters: (N≫1)-body Problem • Globular clusters: 105-106 stars • Evolved relic sandboxes of the universe: >1010 years • Surely there’s no hope. • Is this problem even interesting? • Large N: statistical regime
Emergent Dynamics 1 • In a steady-state, stars move in the potential of all the stars; over a crossing time: • Is there a difference? • Two-body encounters: finite memory over a relaxation time: Star clusters forget.
Emergent Dynamics 2 • Some stars randomly attain high velocities • Fast stars leave the cluster and never come back • “Evaporation” • There are no real stable equilibria Star clusters evaporate.
Emergent Dynamics 3 • More energetic orbits are slower and further in • Consequence: Star clusters have negative heat capacity • Temperature determines direction of energy transfer • Core is hotter: leads to runaway “core collapse” • Globular clusters: Just the right age! Star clusters collapse.
Biggest Supercomputer: The Universe Non-core-collapsed NGC 1261 NGC 6254 NGC 6171 Core-collapsed About 1/6th of clusters NGC 6397 NGC 6681 NGC 6624
QUEST: almost as good • Ideal: N-body • Time-consuming • Cluster Monte Carlo (CMC) yields accurate dynamics • Scientifically feasible runtimes Core-collapsed Non-core-collapsed
A Comprehensive Model Grid • Recent grid of 149 GC models • Virial radius • Galactocentric distance • Metallicity • Stars • Realistic cluster parameters using CMC
Matching Model to Reality • Projected dynamical observables: • Surface brightness profile (SBP) • Velocity dispersion profile (VDP) • Models assume spherical symmetry: “r” • Probabilistically construct SBPs and VDPs by “smearing” stars around sphere of radius r:
Matching Model to Reality • Perform χ2 fit on SBP and VDPs, normalize by number of data points and sum • Only include model snapshots with: • Realistic ages • Accurate metallicity • Accurate galactocentric distance NGC 1261 NGC 6624
Peering Inside • Models: We play “God” • By matching GCs to models, we can make statements about their populations Black holes Millisecond pulsars Cataclysmic variables
Summary • We build a general routine for matching clusters to models • This allows us to look inside the populations of clusters • We can further explore cluster dynamics – the vibrant many-body problem Up next: • Science (the sky’s the limit)