Download in clusters…

Planets, White Dwarfs,
Cataclysmic Variables and SNIa
in Star Clusters:
Changing the Rules
Mike Shara
American Museum of Natural History
M. Shara Sept. 26, 2007
Collaborators
J. Hurley
H. Richer
D. Zurek
R. Mardling
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M. Shara Sept. 26, 2007
Goal: Completely self-consistent
Star Cluster Evolution:
N-body dynamics + Single + Binary Star Evolution-->
to predict stellar populations/ test against HST data
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M. Shara Sept. 26, 2007
Overview
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How we do it: hardware and software
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The evolution of a cluster and it’s Blue Stragglers (M67)
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WDs in clusters…single, divorced, promiscuous
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SNIa (double degenerates) in clusters…enhanced rates
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CVs in Star Clusters - simulations - the tail wags the dog
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Planets in Star Clusters - Making warm Jupiters,
eccentric Earths
M. Shara Sept. 26, 2007
OPEN & GLOBULAR CLUSTERS
Excellent dynamics laboratories
AND
Stellar evolution laboratories
Direct integration = O(N3) cost
Fokker-Planck and Monte Carlo:
Dynamics/Evolution of 106 – 107 SINGLE stars
BUT!
Binaries (even 5%) control real clusters
N-body essential to study cluster populations,
planets
M. Shara Sept. 26, 2007
TeraFlop Computers
1000 Pentiums in a pizza-sized box
“GRAPE-6”:
Hardwired for gravity
simulations: GMm/r2
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1018 to 1019
operations/simulation
M. Shara Sept. 26, 2007
NBODY4 software
(Aarseth 1999, PASP, 111, 1333)
• includes stellar evolution
 fitted formulae as opposed to “live” 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 fieldM.…Shara Sept. 26, 2007
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
=> semi-detached evolution
set new timestep
repeat
M. Shara Sept. 26, 2007
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
M. Shara Sept. 26, 2007
Star Cluster Simulation Procedure
Assumptions
star formation stage is complete
all residual gas has been removed
all stars are coeval and same composition
Initial Conditions
distribute masses (IMF) +brown dwarfs? +planets?
distribute stellar positions & velocities (density + virial)
choose binary fraction and binary masses/separations
lntegration
dynamics (GRAPE ... mostly)
stellar & binary evolution (host)
formation & dissolution of resonances
collisionsmergers or destruction
mass removal, e.g. tidal field
M. Shara Sept. 26, 2007
Shortcomings of Current Models
Initial conditions
*IMF?
*binaries’ mass ratio and separation distributions?
Neutron star retention (Pfahl et al. 2002)
*kick velocity at birth?
Collision and merger products
*interface with hydro code
Uncertainty of binary evolution
parameters
*Real time stellar and binary and merger-product evolution
M. Shara Sept. 26, 2007
Simulation of a Rich Open Cluster
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
M. Shara Sept. 26, 2007
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
M. Shara Sept. 26, 2007
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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
M. Shara Sept. 26, 2007
More than 50% of
Blue Stragglers result from
dynamical intervention
e
perturbations/hardening
exchanges
triples
PERIOD
all observed orbital
combinations
M. Shara Sept. 26, 2007
20K STAR SIMULATIONS
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16,000 single stars
2000 stars with Jupiters
2000 binaries
Kroupa, Tout, Gilmore IMF
Z=0.004, 0.02
q = 0.1  1.0
a from log normal distn, peak at 30 au
Eccentricity from a thermal distn.
Planet separations 0.5  50 au
Galactic tidal field, no shocking
speed ~ 2 km/s, nc ~ 500 stars/pc3
open cluster: 5 Gyr of evolution
M. Shara Sept. 26, 2007
Dynamical Modification of Cluster Populations
aka “Stellar Promiscuity”
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
M. Shara Sept. 26, 2007
NEVER A DULL MOMENT
Over the entire run (t = 0.0  4566.1
Myr):
41 BLUE STRAGGLERS FORMED
5 CATACLYSMIC VARIABLES
48 DOUBLE WD SYSTEMS FORMED…
32/48 ARE NOT PRIMORDIAL BINARIES
8 DD collapses  Likely SN Ia
M. Shara Sept. 26, 2007
SNIa Motivation
*SNIa – crucial to cosmology (acceleration)
*Corrections to Mv now
handled empirically because
PROGENITORS ARE UNCERTAIN
1) SuperSoftSources (WD +RG)
2) Double Degenerates (WD +WD)
PREDICTION: SNIa ENHANCED IN STAR CLUSTERS
M. Shara Sept. 26, 2007
N-body Evolution
Example
Primordial Binary
M1 = 6.88 Msun
M2 = 3.10 Msun
a = 4050 Rsun
After 60 Myr:
M1 = 6.26 on AGB
e = 0.0 (tides)
RLOF => CE
M1 = 1.3 ONeWD
After 434 Myr:
M2 = 2.02 on AGB
M1 = 1.3 (symbiotic)
RLOF => CE
M2 = 0.8 COWD
1.3 ONeWD + 0.8 COWD
a = 2500 Rsun
DWD with t
~ 10 yr
22
grav
a = 2500 Rsun
M. Shara Sept. 26, 2007
and then ...
1.3 WD
DWD
9100 d
630 Myr
SIRIUS-LIKE BINARY!
0.8 WD
Resonant
Exchange
(few Myr)
1.3 WD
2.0MS
14000 d
e = 0.63
perturbed: 6000 d, e = 0.94
CE + CE => DWD (0.35 d) M=1.6
2.0 MS
GR -> merger after 10 Gyr
0.8 WD
Mtot = 1.6 Msun
M. Shara Sept. 26, 2007
dJ/dt
J
= -K
mM(m+M) f(e)
a4
GENERAL RELATIVITY
dP/dt = -k P-5/3
Pcrit ~ 10 hours for ~(1+1) Msun
for gravity waves
8DD =10x expected number of coalescing field double
WDs in a modest open cluster
Expect >n (globular)/n(open) ~ 103 x enhancement in globulars
Are Star Clusters
(the) Type Ia Supernova Factories?
M. Shara Sept. 26, 2007
DDs which Merge in <1010 YR
with Mtot > 1.4 Msun
ID #S
79 80
33 34
75 76
86 8058
63 64
57 58
61 62
95 96
Types
CO CO
CO CO
CO CO
CO ONe
CO CO
ONe CO
CO CO
CO CO
Masses
0.826 0.662
0.989 0.664
0.920 0.642
0.716 1.241
0.972 0.665
1.057 0.574
1.089 0.536
0.832 0.668
Period/d
8.7096E-03
1.0715E-01
4.3652E-02
3.3884E-01
1.1482E-01
1.0715E-01
2.4547E-01
1.1220E-01
NB! 7 of 8 SYSTEMS ARE PRIMORDIAL; WOULD NOT HAVE
MERGED IN THE FIELD
M. Shara Sept. 26, 2007
Strongly Centrally Concentrated
“Loaded Guns”
DD
MS
M. Shara Sept. 26, 2007
SINGLE WD
DIVORCED WD
OUTER BINARY WD
BINARY WD
M. Shara Sept. 26, 2007
M>MChandra
HOW TO FIND “LOADED GUNS”
M. Shara Sept. 26, 2007
The White Dwarf Cooling Age
and Dynamical History of the
Metal-Poor Globular Cluster NGC6397
126 orbits with ACS in Cycle 13 (Mar/Apr 05)
complements previous observations of M4
123 orbits with WFPC2 (Apr 01)
NGC 6397  [Fe/H] = -1.9
 core-collapsed
M4  [Fe/H] = -1.3
 pre-core-collapse
(Hansen et al. 2002, 2004)
M. Shara Sept. 26, 2007
11.9  0.4 Gyr
12.1  0.7 Gyr
M. Shara Sept. 26, 2007
Contamination of the WD luminosity function (and CMD distribution)
30K, 50% binaries  4 Gyr
(Hurley & Shara 2003)
M. Shara Sept. 26, 2007
M. Shara Sept. 26, 2007
M. Shara Sept. 26, 2007
inside Rh
outside Rh
M. Shara Sept. 26, 2007
(small) Globular Cluster Model
100,000 stars, 5% binaries, Z = 0.001, tidal field
20,000 stars at core-collapse (15-16 Gyr)
Rh
Rc
M. Shara Sept. 26, 2007
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binary frequency < 5%
minimal contamination
M. Shara Sept. 26, 2007
Cataclysmic Variable =CV=
Classical Nova or Dwarf Nova=
White Dwarf Accreting From a Red Dwarf Companion
Accretion energy via
Accretion disk
instability L 100x
M. Shara Sept. 26, 2007
“dwarf nova”
L105-6 Lsun
A White Dwarf Forms INSIDE a Red Giant
Sometimes a
companion star
is engulfed
1,000,000 X
denser than
the Sun
M. Shara Sept. 26, 2007
The long-sought Globular cluster
CVs?! (47 Tuc - Grindlay et al)
M. Shara Sept. 26, 2007
HST/FUV NGC 2808
Dieball, Knigge,
Zurek, Shara, long
2005
M. Shara Sept. 26, 2007
Non-standard CV formation and evolution
0.74 M MS
MSS: 0.74 M
+
0.91 M WD
0.71 M MS
WD: 0.91 M
P=4302d, e=0.97
in cluster core
perturbations -> chaos
P=0.52d, circular
RLOF
0.37 M MS
No Common-Envelope!
accelerated CV evolution of
individual systems
M. Shara Sept. 26, 2007
CV orbital periods
Field
Cluster
M. Shara Sept. 26, 2007
Planet Motivation
0 hot Jupiters orbiting 34,000 MSS
in 47 Tuc….expect ~20 (Gilliland et al)
Davies & Sigurdsson, Bonnell et al, Smith
& Bonnell 
Most close planets (<0.3 au) survive
…WHERE ARE THEY?
M. Shara Sept. 26, 2007
N=20,000 STAR SIMULATIONS
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18,000 single stars
Kroupa, Tout, Gilmore IMF
Z= 0.017
100 single stars with Earth +Jupiter OR
Neptune + Jupiter
Initial a, e of planets = Solar System values
2000 binaries with q (mass ratio) = 0.1  1.0
a from log normal distn, peak at 30 au
Stellar Binaries’ eccentricity: a thermal distn.
Galactic tidal field, no shocking
speed ~ 2 km/s, nc ~ 500 stars/pc3
Massive open cluster: 5 Gyr of evolution
M. Shara Sept. 26, 2007
N=2,000 STAR SIMULATIONS
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1400 single stars
600 Binaries
100 single stars with Earth +Jupiter OR
Neptune + Jupiter
Initial a, e of planets = Solar System values
speed ~ 2 km/s, nc ~ 10,000 stars/pc3
Sparse open cluster: 5 Gyr of evolution
M. Shara Sept. 26, 2007
N= 20,000 stars
M. Shara Sept. 26, 2007
N=20,000 stars
M. Shara Sept. 26, 2007
N = 2000 stars
M. Shara Sept. 26, 2007
N= 20,000 Stars
M. Shara Sept. 26, 2007
4 Encounters “ionize” Jupiter
M. Shara Sept. 26, 2007
AND LEAVE BEHIND
AN ECCENTRIC
EARTH e =0.6
Which escapes the
cluster with its host
star
Early Wanderlust by Neptune
M. Shara Sept. 26, 2007
Ionization of Neptune 4.5 Gyr later
M. Shara Sept. 26, 2007
An eccentric Jupiter-Neptune System released into the field at 460 Myr- (from N=2000)
“fossil eccentricity”
Imprinted by previous
cluster environment
M. Shara Sept. 26, 2007
N
JUPITERS
0
2
Log a
4
400 Myr
64 Jupiters
M. Shara Sept. 26, 2007
e
a
SATURN
T Myr
JUPITER
EARTH
M. Shara Sept. 26, 2007
M. Shara Sept. 26, 2007
Conclusions –
Planets in Star Clusters
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The Solar System can escape quite intact from an
N=2000 star cluster (Adams+Laughlin 2001)
MANY Tramp planets MUST EXIST!
More “damage” as N and density increases
Very large eccentricity changes are common during
stellar encounters
Eccentric singles and doubles are released from
clusters into the field (cf Malmberg,Davies et al)
“Tepid” Jupiters are easy to form…a = 3 - 7 AU
No “hot” Jupiters seen yet
Coming: Jupiter + Saturn; 3-4 planets
M. Shara Sept. 26, 2007
CONCLUSIONS – SNIa and DD
*Beware of DD in age-dating the Universe
*HARDENING OF DDs MANUFACTURES
“LOADED GUNS” IN CLUSTERS….
Grav. Radiation does the rest
*Long hardening timescaleNo z peak in
SNIa (J. Tonry)
*Look in clusters (eg M67, NGC 188) for
very short period DDs (~5 today)
M. Shara Sept. 26, 2007
M. Shara Sept. 26, 2007
SINGLE JUPITERS (0.05-50 AU) IN AN OPEN CLUSTER
LIBERATED FROM PARENT
ESCAPING FROM CLUSTER
M. Shara Sept. 26, 2007
N
EARTHS
Log a
400 Myr
22 Earths
M. Shara Sept. 26, 2007
N
Earths
eccentricity
400 Myr
22 Earths
M. Shara Sept. 26, 2007
M. Shara Sept. 26, 2007
PLANET LIBERATION LOCATIONS
M. Shara Sept. 26, 2007
PLANET LIBERATION VELOCITIES
M. Shara Sept. 26, 2007