Transcript ppt

STAR CLUSTER DYNAMICS
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
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)
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
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
NBODY4 software
(Aarseth 1999, PASP, 111, 1333)
• includes stellar evolution
 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
• and a binary evolution algorithm
 tidal evolution, magnetic braking, gravitational radiation,
wind accretion, mass-transfer, common-envelope, mergers
• and as much realism as possible
 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 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
Hurley, Tout & Pols, 2002, MNRAS, 329, 897
and its implementation in NBODY4
Hurley et al., 2001, MNRAS, 323, 630
and everything N-body
“Gravitational N-body Simulations: Tools and Algorithms”
Sverre Aarseth, 2003, Cambridge University Press
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
more on the binary evolution method …
Semi-Detached Evolution
• Dynamical: merger or CE (-> merger or binary)
• Steady:
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
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
“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
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The simulated CMD at 4 Gyear
M67 Observed CMD
 NBS/Nms,2to = 0.15
 Rh,BS = 1.6pc
 half in binaries
N-body Model CMD
 NBS/Nms,2to = 0.18
 Rh,BS = 1.1pc
 half in binaries
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.
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
P = 9100d
0.8
=> 1.3 M + 0.8 M WDs
Standard binary evolution
Merger timescale > 1010 Gyr
… then 200 Myr later
0.8
2.0
Resonant
Exchange
1.3
P = 9100d
0.8
1.3
P = 14000d, e = 0.63
2.0
Perturbed: 6000d, e=0.94
Tides + mass-transfer
=> double-WD, P = 0.35 d
=> merger after 10 Gyr
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
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
BINARY WD
DIVORCED 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 pc
Trh ~ 2 Gyr
  ~ 3 km/s
nc ~ 1000-10,000 stars/pc3
20 Gyr lifetime
6 months of GRAPE-6 cpu
Central Density
The evolution of binary fractions in globular clusters
Ivanova, 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 binarybinary) 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
FIELD
Other 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