Mike Shara Department of Astrophysics American Museum of Natural History

1. STAR CLUSTER DYNAMICS Or: BINARY EVOLUTION on STEROIDS Mike Shara Department of Astrophysics American Museum of Natural History

2. Collaborator: Jarrod Hurley Thanks to: John Ouellette, Jun Makino Sverre Aarseth Christopher Tout Onno Pols Peter Eggleton

3. 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

4. 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) 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 GRAPE-6: A Teraflop Telescope Hardwired to do GMm r2

5. 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 website http://www.NBodyLab.org. Short test runs are available on a first-come basis. Enjoy! Vicki Johnson and Sverre Aarseth

6. 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 …

7. N-body complications • Orbit 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

8. more on the binary evolution method … Detached Evolution - in timestep t • update stellar masses • changes to stellar spins • orbital angular momentum and eccentricity changes • evolve stars • check for RLOF • set new timestep • repeat => semi-detached evolution

9. more on the binary evolution method … Semi-Detached Evolution • Dynamical: • Steady: • merger or CE (-> merger or binary) • calculate mass-transfer in one orbit • determine fraction accreted by companion • set timestep • account for stellar winds • adjust spins and orbital angular momentum • evolve stars • check if donor star still fills Roche-lobe • check for contact • repeat

10. 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 pc • Trh ~ 400 Myr •  ~ 3 km/s • nc ~ 200 stars/pc3 • 6-7 Gyr lifetime • 4-5 weeks of GRAPE-6 cpu

11. “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

12. 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 

13. The simulated CMD at 4 Gyear

14. 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

15. More than 50% of BSs from dynamical intervention • perturbations/hardening • Exchanges (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.

16. 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 • Standard binary evolution • Merger timescale > 1010 Gyr 1.3 P = 9100d 0.8

17. … then 200 Myr later 0.8 2.0 Resonant Exchange P = 14000d, e = 0.63 2.0 1.3 P = 9100d 0.8 1.3 • Perturbed: 6000d, e=0.94 • Tides + mass-transfer => double-WD, P = 0.35 d => merger after 10 Gyr

18. 16000 Stars, 2000 binaries 500 cases of stellar infidelity 730 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

19. 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

20. DIVORCED WD SINGLE WD OUTER BINARY WD BINARY WD

22. BINARY WDs! FALSE LF PEAK  deduce wrong age!!

23. 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)

24. 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 pc • Trh ~ 2 Gyr •  ~ 3 km/s • nc ~ 1000-10,000 stars/pc3 • 20 Gyr lifetime • 6 months of GRAPE-6 cpu

25. Central Density

26. The evolution of binary fractions in globular clusters Ivanova, Belczynski, Fregeau, RasioMonthly 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.

27. Binary Fraction

28. M67 Binary Fraction

29. Exchange Binaries

30. Binary Periods

31. Hastened CV Evolution Other CVs: *Premature *Aborted *Frankenstein CVs *Triple Cluster FIELD

32. NGC 6397-Richer, Rich, Shara, Zurek et al 2006

34. 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