mike shara department of astrophysics american museum of natural history star cluster dyna mic s or:...
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Mike Shara Department of Astrophysics American Museum of Natural History
STAR CLUSTER DYNAMICSOr:BINARY EVOLUTION onSTEROIDS
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Collaborator: Jarrod Hurley
Thanks to: John Ouellette, Jun MakinoSverre Aarseth
Christopher ToutOnno Pols
Peter Eggleton
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Overview of Talk*How we do it…hardware, software, physics
*M67…Simulating Observations
*Clusters as type Ia SNe factories
*Promiscuous stars (XXX-rated)
*divorced white dwarfs and the Age of the Universe
*Cataclysmic Binaries’ hastened evolution
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1992 - small N (~1000) for Gigaflop boards - 2000 CPU hrs (1000 crossing times) - major restrictions on stellar evolution, binaries, tidal field, etc. (McMillan, Hut & Makino 1990; Heggie & Aarseth 1992)
GRAPE-6:A Teraflop TelescopeHardwired to do GMm r2
2002 - large open clusters (N = 2*104) for Teraflop boards - moderate globulars (N = 2*105) - much more realism - 100-10,000 CPU hrs (1000 crossing times)
1018 to 1019 floating point operations/simulation
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Dear Modest member,
We are happy to announce the public use of NBODY4 on the web.It works in combination with a GRAPE-6a on the websitehttp://www.NBodyLab.org. Short test runs are available on a first-come basis.
Enjoy!
Vicki Johnson and Sverre Aarseth
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NBODY4 software (Aarseth 1999, PASP, 111, 1333)
• includes stellar evolution
• and a binary evolution algorithm
• and as much realism as possible
fitted formulae as opposed to “live evolution” or tables rapid updating of M, R etc. for all stellar types and metallicities done in step with dynamics
tidal evolution, magnetic braking, gravitational radiation, wind accretion, mass-transfer, common-envelope, mergers
perturbed orbits (hardening & break-up), chaotic orbits, exchanges, triple & higher-order subsystems, collisions, etc. … regularization techniques + Hermite integration with GRAPE + block time-step algorithm + external tidal field …
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N-body complicationsOrbit may be, or may become, perturbed -> can’t average mass-transfer over many orbits
-> do a bit of mass-transfer then a bit of dynamics, and so on …-> must work in combination with regularization of orbit
for a description of the binary evolution algorithm
and its implementation in NBODY4
and everything N-body
Hurley, Tout & Pols, 2002, MNRAS, 329, 897
Hurley et al., 2001, MNRAS, 323, 630
“Gravitational N-body Simulations: Tools and Algorithms” Sverre Aarseth, 2003, Cambridge University Press
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more on the binary evolution method …
Detached Evolution - in timestep tupdate stellar masses
changes to stellar spins
orbital angular momentum and eccentricity changes
evolve stars
check for RLOF
set new timestep
repeat
=> semi-detached evolution
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more on the binary evolution method …
Semi-Detached Evolution • Dynamical:
• Steady:
merger or CE (-> merger or binary)
calculate mass-transfer in one orbitdetermine fraction accreted by companionset timestepaccount for stellar windsadjust spins and orbital angular momentumevolve starscheck if donor star still fills Roche-lobecheck for contactrepeat
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Simulation of a Rich Open Cluster: M67 Initial Conditions
12,000 single stars (0.1 - 50 M) 12,000 binaries (a: flat-log, e: thermal, q: uniform) solar metallicity (Z = 0.02)
Plummer sphere in virial equilibrium circular orbit at Rgc= 8 kpc M ~ 18700 M
tidal radius 32 pcTrh ~ 400 Myr ~ 3 km/snc ~ 200 stars/pc3
6-7 Gyr lifetime4-5 weeks of GRAPE-6 cpu
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“A complete N-body model of the old open cluster M67”
Hurley, Pols, Aarseth & Tout, 2005, MNRAS (accepted July 05 … preprint astro-ph/0507239)
also see
“White dwarf sequences in dense star clusters”
Hurley & Shara, 2003, ApJ, 589, 179
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M67 at 4 Gyr? solar metallicity 50% binaries luminous mass 1000 M in 10pc tidal radius 15pc core radius 0.6pc, half-mass radius 2.5pc
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The simulated CMD at 4 Gyear
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M67 Observed CMD N-body Model CMD
NBS/Nms,2to = 0.15 Rh,BS = 1.6pc half in binaries
NBS/Nms,2to = 0.18 Rh,BS = 1.1pc half in binaries
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More than 50% of BSs from dynamical intervention
perturbations/hardeningExchanges (cf Knigge et al 47 Tuc BS + X-ray active MSS)Triples
+ X-ray binary population: RS CVn, BY Drac
+ characteristics of WD population
+ luminosity functions, etc.
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PROMISCUITY: N-body double-WD example
T = 0 Myr: 6.9 M + 3.1 M P = 9500d, e = 0.3
60 Myr: e = 0.0, mass-transfer => 1.3 M WD + 3.1 M
430 Myr: mass-transfer => 1.3 M + 0.8 M WDs
1.3 0.8P = 9100dStandard binary evolution
Merger timescale > 1010 Gyr
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1.3 0.8P = 9100d
… then 200 Myr later
2.0
ResonantExchange
0.8
2.01.3 P = 14000d, e = 0.63
Perturbed: 6000d, e=0.94Tides + mass-transfer => double-WD, P = 0.35 d => merger after 10 Gyr
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16000 Stars, 2000 binaries
500 cases of stellar infidelity730 different stars involved (~15% of
cluster)some stars swapped partner once (494)some did it twice (105) three times (48) four (27)five (14) and even 22 times (1) !!Usually the least massive star was ejected
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SNIa Motivation*SNIa – crucial to cosmology (acceleration)
*Significant corrections to Mv now handled empirically because PROGENITORS ARE UNCERTAIN
1) SuperSoftSources (WD +RG) 2) Double Degenerates (WD +WD) PREDICTION:
Double WD SNIa OCCUR PREFERENTIALLY in STAR CLUSTERS,
DRIVEN TO COALESCENCE BY DYNAMICAL HARDENING
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SINGLE WD DIVORCED WD
BINARY WD OUTER BINARY WD
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BINARY WDs!
FALSE LF PEAK deduce wrong age!!
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CONCLUSIONS – SNIa and DD
*Beware of DD in age-dating the Universe
*HARDENING OF DDs
PREFERENTIALLY MANUFACTURES
“LOADED GUNS” IN CLUSTERS….
Grav. Radiation does the rest
*Look in clusters (eg M67, NGC 188) for
very short period DDs (~5 today)
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Simulation of a “Modest” Globular Cluster Hurley & Shara 2006
95,000 single stars (0.1 - 50 M) (200,000 underway) 5000 binaries (a: flat-log, e: thermal, q: uniform) sub-solar metallicity (Z = 0.001)
Plummer sphere in virial equilibrium circular orbit at Rgc= 8.5 kpc M ~ 51700 M
tidal radius 50 pcTrh ~ 2 Gyr ~ 3 km/snc ~ 1000-10,000 stars/pc3
20 Gyr lifetime6 months of GRAPE-6 cpu
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Central Density
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The evolution of binary fractions in globular clustersIvanova, Belczynski, Fregeau, Rasio
Monthly Notices of the Royal Astronomical Society, Volume 358, Issue 2, pp. 572-584.
• We study the evolution of binary stars in globular clusters using a new Monte Carlo approach combining a population synthesis code (STARTRACK) and a simple treatment of dynamical interactions in the dense cluster core using a new tool for computing three- and four-body interactions (FEWBODY). We find that the combination of stellar evolution and dynamical interactions (binary-single and binary-binary) leads to a rapid depletion of the binary population in the cluster core. The maximum binary fraction today in the core of a typical dense cluster such as 47 Tuc, assuming an initial binary fraction of 100 per cent, is only ~5-10 per cent. We show that this is in good agreement with recent Hubble Space Telescope observations of close binaries in the core of 47 Tuc, provided that a realistic distribution of binary periods is used to interpret the results. Our findings also have important consequences for the dynamical modelling of globular clusters, suggesting that `realistic models' should incorporate much larger initial binary fractions than has usually been the case in the past.
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Binary Fraction
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M67 Binary Fraction
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Exchange Binaries
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Binary Periods
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Hastened CV Evolution
Cluster
FIELDOther CVs: *Premature*Aborted*Frankenstein CVs
*Triple
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NGC 6397-Richer, Rich, Shara, Zurek et al 2006
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Summary- GRAPE6 Nbody • Remarkable simulation realism- at a steep but
worthwhile computational price• M67 models “approaching reality” with
populations and structure mimicing observations VERY well
• Double white dwarfs: SNIa, dating clusters• Stellar promiscuity (M67 and 47 Tuc BS…)• Cataclysmic variables evolve more quickly, can
be aborted or premature