mike shara department of astrophysics american museum of natural history
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STAR CLUSTER DYNA MIC S Or: BINARY EVOLUTION on STEROIDS. Mike Shara Department of Astrophysics American Museum of Natural History. Collaborator: Jarrod Hurley. Thanks to: John Ouellette, Jun Makino Sverre Aarseth Christopher Tout Onno Pols Peter Eggleton. - PowerPoint PPT PresentationTRANSCRIPT
Mike Shara Department of Astrophysics American Museum of Natural History
STAR CLUSTER DYNAMICSOr:BINARY EVOLUTION onSTEROIDS
Collaborator: Jarrod Hurley
Thanks to: John Ouellette, Jun MakinoSverre Aarseth
Christopher ToutOnno Pols
Peter Eggleton
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
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
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
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 …
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
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
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
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
“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
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
The simulated CMD at 4 Gyear
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
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.
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
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
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
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
SINGLE WD DIVORCED WD
BINARY WD OUTER BINARY WD
BINARY WDs!
FALSE LF PEAK deduce wrong age!!
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)
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
Central Density
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.
Binary Fraction
M67 Binary Fraction
Exchange Binaries
Binary Periods
Hastened CV Evolution
Cluster
FIELDOther CVs: *Premature*Aborted*Frankenstein CVs
*Triple
NGC 6397-Richer, Rich, Shara, Zurek et al 2006
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