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