In this section, output from a short NBODY4 simulation run is listed and briefly interpreted.
For initial conditions a Plummer model (cf. Aarseth's book, p.121) was
adopted and realistic Salpeter mass function with mean stellar mass
of 0.5 solar masses. The cluster moves in a circular Galactic
orbit in the Solar neighbourhood. The resulting tidal force is
included in the equations of motion (cf. Aarseth's book, p.128). The
termination time of 100 time units corresponds to 60 Myr with length
unit RBAR = 1 pc, which is sufficient to illustrate some general
features of the evolution.
Models of this type and size can be
quickly and easily run with NBODY4 (1-2 mins) and NBODY6 (~10
minutes).
For more realistic models of star clusters, stellar evolution should be switched on (KZ19=3) and somewhat longer termination times used. This section concludes with a final snapshot of a run with stellar evolution.
The following is intended only to be an introduction to the extensive output produced by NBODY4. Note that runs made with your version of NBODY4 may not yield the same results, due to differences in software versions, GRAPE libraries, compilers and other factors.
N NFIX NCRIT
NRAND NRUN
1000 1 5
50000 1
ETA DTADJ
DELTAT TCRIT QE
RBAR ZMBAR
2.0E-02 2.0E+00 1.0E+01 1.0E+02
2.2E-05 1.0E+00 5.0E-01
KZ OPTIONS
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
34 35 36 37 38 39 40
0 0 0 0 1 0 6 0 0
0 0 0 0 1 1 1 0 0
0 0 1 0 2 0 1 2 0
0 0 2 0 0 0 0 0 0
1 0 0 0
DTMIN RMIN
ETAU ECLOSE GMIN
GMAX
1.0E-05 1.0E-04 2.0E-01 1.0E+00
1.0E-06 1.0E-03
STANDARD IMF ALPHA = 2.30 BODY1 = 10.0
BODYN = 0.20
SCALING: SX = 0.97 E = -2.58E-01
M(1) = 1.65E-02 M(N) = 3.30E-04 <M> =
1.00E-03
TIME SCALES: TRH = 1.6E+01 TCR = 2.8E+00
2<R>/<V> = 2.3E+00
PHYSICAL SCALING: R* = 1.0 M* =
607.0 V* = 1.615 T* = 0.606 <M> = 0.61
SU = 4.4E+07
TOTAL MASS = 607.0 TIDAL(1&3) = 1.52E-03
-6.07E-03 PC/GM = 2.33E-08
TIDAL PARAMETERS: 5.83E-04 0.00E+00
-2.33E-03 3.27E-02 TSCALE = 6.06E-01 (10**6 YRS)
RTIDE = 11.97
TIME = 0.00 Q =
0.50 DE = 0.000000 E = -0.249563 RMIN =
1.7E-03 DTMIN = 8.9E-05 ECLOSE = 1.00 TC =
0 EB/E = 0.0000 BIN = 0
0
T = 0.0 N = 1000
KS = 0 NM = 0 MM = 0 NS =
1000 NSTEPS =
0 0
DE = 0.000000 E = -0.249563
RUN = 1
M# = 0 CPU = 0.0 DMIN = 1.0E+02
1.0E+02 AMIN = 1.0E+02 RMAX = 0.0E+00 NBLOCK
= 0 NIRECT = 0
NURECT = 0 NEFF = 325
<R> RTIDE RDENS RC
NC MC RHOD RHOM
UN NPT RCM VCM
AZ EB/E EM/E TCR
T6 NTESC
#1 0.78 12.0 0.10
0.240 61 0.070 6.2 34.2
0 0 0.000 0.0000 -0.021152 0.000
0.000 2.84 0
3
NKSTRY NKSREG
NKSHYP NKSPER NPRECT NKSMOD
NTTRY NTRIP NQUAD NCHAIN NMERG NEWHI
NSTEPC NBCALL NTPERT
NWARN NHI
#2
0 0
0 0
0 0
0 0
0 0
0 0
0 804
0 46 0
TWO
MASS GROUPS: NM1 NM2 M1 M2 RM1 RM2
152 848 0.501 0.499 0.736
0.801
TIME = 2.00 Q = 0.51 DE =
0.000000 E = -0.249564 RMIN = 1.7E-03 DTMIN =
9.2E-05 ECLOSE = 1.02 TC = 0 EB/E =
0.0000 BIN = 0
0
TIME = 4.00 Q = 0.52 DE =
0.000000 E = -0.249564 RMIN = 1.7E-03 DTMIN =
8.7E-05 ECLOSE = 1.04 TC = 1 EB/E =
0.0000 BIN = 0
0
TIME = 6.00 Q = 0.53 DE =
0.000000 E = -0.249564 RMIN = 1.8E-03 DTMIN =
9.4E-05 ECLOSE = 1.06 TC = 2 EB/E =
0.0000 BIN = 0
0
TIME = 8.00 Q = 0.50 DE =
0.000000 E = -0.249564 RMIN = 1.7E-03 DTMIN =
9.2E-05 ECLOSE = 1.00 TC = 2 EB/E =
0.0000 BIN = 0
0
TIME = 10.00 Q = 0.52 DE =
0.000000 E = -0.249563 RMIN = 1.7E-03 DTMIN =
9.2E-05 ECLOSE = 1.05 TC = 3 EB/E =
0.0000 BIN = 0
0
T = 10.0 N = 1000 KS
= 0 NM = 0 MM = 0 NS =
1000 NSTEPS = 1535962
614 DE = 0.000000 E = -0.249563
RUN =
1 M# = 0 CPU = 0.2 DMIN =
5.8E-05 5.8E-05 AMIN = 1.0E+02 RMAX = 0.0E+00
NBLOCK = 38547 NIRECT = 0 NURECT
= 0 NEFF = 325
<R>
RTIDE RDENS RC NC
MC RHOD RHOM UN NPT
RCM VCM
AZ EB/E EM/E TCR
T6 NTESC
#1 0.70 12.0 0.10
0.291 72 0.117 4.1 16.3
0 0 0.000 0.0000 -0.020921 0.000
0.000 2.84 6
15
NKSTRY NKSREG
NKSHYP NKSPER NPRECT NKSMOD
NTTRY NTRIP NQUAD NCHAIN NMERG NEWHI
NSTEPC NBCALL NTPERT
NWARN NHI
#2 6407
34 31
0 0
0 0
0 0
0 0
0 0
5055 0
368 0
TWO MASS GROUPS:
NM1 NM2 M1 M2 RM1 RM2 152
848 0.501 0.499 0.632 0.868
TIME
= 12.00 Q = 0.50 DE = 0.000000 E
= -0.249563 RMIN = 1.6E-03 DTMIN = 8.4E-05 ECLOSE =
1.00 TC = 4 EB/E = 0.0000 BIN =
0 0
TIME = 14.00 Q =
0.52 DE = 0.000000 E = -0.249563 RMIN =
1.5E-03 DTMIN = 7.1E-05 ECLOSE = 1.05 TC =
4 EB/E = 0.0000 BIN = 0
0
ESCAPE N = 999
1 0 0.9996 -0.250145 0.01
24.48 0.500 0.00100 996
874
ESCAPE ANGLES
84 7
With
RBAR = 1, RTIDE=12 pc so escapers are removed outside 24 pc.
TIME =
16.00 Q = 0.51 DE = 0.000000 E = -0.250145
RMIN = 1.4E-03 DTMIN = 6.8E-05 ECLOSE = 1.03 TC =
5 EB/E = 0.0000 BIN = 0
0
TIME
= 18.00 Q = 0.53 DE = 0.000000 E
= -0.250145 RMIN = 1.3E-03 DTMIN = 5.8E-05 ECLOSE =
1.06 TC = 6 EB/E = 0.0000 BIN =
0 0
ESCAPE N
= 998 2 0
0.9990 -0.250690 0.01 24.95 0.500
0.00100 994 461
ESCAPE
ANGLES 43
10
TIME = 20.00 Q = 0.55 DE =
0.000000 E = -0.250690 RMIN = 1.0E-03 DTMIN =
4.2E-05 ECLOSE = 1.12 TC = 7 EB/E =
0.0000 BIN = 0
0
T = 20.0 N = 998
KS = 0 NM = 0 MM = 0 NS =
998 NSTEPS = 2881172
2374 DE = 0.000001 E = -0.250690
RUN
= 1 M# = 0 CPU = 0.3
DMIN = 2.0E-05 2.0E-05 AMIN = 1.0E+02 RMAX = 1.3E-02
NBLOCK = 80845 NIRECT = 0 NURECT
= 0 NEFF = 324
<R>
RTIDE RDENS RC NC
MC RHOD RHOM UN NPT
RCM VCM
AZ EB/E EM/E TCR
T6 NTESC
#1 0.83 12.0 0.11
0.085 9 0.074 64.4 142.7
0 0 0.014 0.0008 -0.020246 0.000
0.000 2.81 12
28
NKSTRY NKSREG
NKSHYP NKSPER NPRECT NKSMOD
NTTRY NTRIP NQUAD NCHAIN NMERG NEWHI
NSTEPC NBCALL NTPERT
NWARN NHI
#2 17858
72 59
0 0
0 0
0 0
0 0
0 0
8735 0
679 1
TWO MASS GROUPS:
NM1 NM2 M1 M2 RM1 RM2 151
847 0.499 0.500 0.577 1.096
The
heavy mass group already shows significant mass segregation (mean
radius RM) towards centre. Note first energetic binary next output,
involving two massive members.
TIME =
22.00 Q = 0.60 DE = 0.000002 E = -0.250690
RMIN = 9.4E-04 DTMIN = 3.7E-05 ECLOSE = 0.96 TC =
5 EB/E = 0.3101 BIN = 1
5
ESCAPE N = 997
3 0 0.9984 -0.251049 0.01
24.14 0.500 0.00100 992
426
ESCAPE ANGLES
26 18
TIME = 24.00 Q =
0.58 DE = 0.000001 E = -0.251048 RMIN =
1.1E-03 DTMIN = 4.3E-05 ECLOSE = 0.89 TC =
5 EB/E = 0.3335 BIN = 1
5
ESCAPE N = 996
4 0 0.9978 -0.257011 0.01
25.08 0.500 0.00100 991
452
ESCAPE ANGLES
59 17
TIME = 26.00 Q =
0.53 DE = 0.000012 E = -0.257008 RMIN =
1.1E-03 DTMIN = 4.5E-05 ECLOSE = 0.80 TC =
6 EB/E = 0.3610 BIN = 5
1
NEW CHAIN 1 T =
27.49 H = -5. R = 1.1E-03 M = 0.0277
0.0039 G4 = 3.3E-06 R1 = 8.2E-04 P = 8.8E-05
E1 = 1.764 NP =64
NEW CHAIN N NP E RSUM
RGRAV TCR RMAXS NAM 3 4 -0.07201
1.1E-03 5.4E-04 3.3E-03 5.8E-03
1 5 35
CHAIN
BINARY NAM = 1
5 A = 1.5E-03 E = 0.29 EB = 0.88 GB =
9.3E-03 G4 = 0.0E+00 EB1 = 0.00 E1 = 0.26 ET
= 0.246 DB = 0.9
RECOIL: E E1 PM/A
RD A A1 RP GB IN 0.2859 0.99 0.1
3.5 1.46E-03 7.50E-03 3.80E-03 9.32E-03
105.6
END CHAIN 1 2 3
1 RB = 1.8E-03 R13 = 4.5E-03 R24 = 1.0E+10 DE
= 3.7E-06 TC = 0.3 # 12 2
4 DB = 0.89 EC = 0.280
CHTERM: T I3
I4 NT DT 27.4910 35
35 997 1.9E-06 1.9E-06 1.9E-06
The
first strong (chain) interaction. Note the virial ratio Q=0.61 next
time. This means at least one high-velocity body was produced during
this event. This is connected with increased energy in hard binaries
(or just one).
TIME =
28.00 Q = 0.61 DE = 0.000004 E = -0.257007
RMIN = 1.1E-03 DTMIN = 4.4E-05 ECLOSE = 0.81 TC =
4 EB/E = 0.6347 BIN = 1
5
ESCAPE N = 995
5 0 0.9942 -0.260098 0.10
25.15 0.500 0.00100 989
39
ESCAPE ANGLES
44 45
NEW CHAIN
1 T = 29.67 H = -12. R = 7.5E-04
M = 0.0277 0.0040 G4 = 2.6E-06 R1 = 8.7E-04 P =
8.6E-04 E1 = 0.075 NP = 5
NEW CHAIN
N NP E RSUM RGRAV TCR RMAXS NAM 3 1
-0.10269 1.1E-03 5.3E-04 1.9E-03 6.7E-03
1 5 34
CHAIN
BINARY NAM = 1
5 A = 1.0E-03 E = 0.92 EB = 0.89 GB =
3.4E-03 G4 = 0.0E+00 EB1 = 0.00 E1 = 0.13 ET
= 0.353 DB = 0.1
RECOIL: E E1 PM/A
RD A A1 RP GB IN 0.9190 0.84 0.8
2.7 1.01E-03 5.31E-03 3.85E-03 3.41E-03
145.6
END CHAIN 1 2 3
1 RB = 1.0E-03 R13 = 3.5E-03 R24 = 1.0E+10 DE
= 1.9E-06 TC = 0.5 # 13 1
1 DB = 0.11 EC = 0.395
CHTERM: T I3
I4 NT DT 29.6738 474 474
996 1.9E-06 1.9E-06 1.9E-06
TIME =
30.00 Q = 0.60 DE = -0.000004 E = -0.260099
RMIN = 1.2E-03 DTMIN = 5.4E-05 ECLOSE = 0.75 TC =
4 EB/E = 0.7717 BIN = 5
1
Further
increase of binary energy after another chain interaction. One
binary now has 77 % of the total energy.
T = 30.0
N = 995 KS = 1 NM =
0 MM = 0 NS = 993 NSTEPS =
4060357 166372 DE =
0.000015 E = -0.260099
RUN = 1 M# =
0 CPU = 0.4 DMIN = 1.6E-05 1.6E-05
AMIN = 8.1E-04 RMAX = 1.6E-02 NBLOCK =
150265 NIRECT = 0 NURECT = 0 NEFF =
288
<R> RTIDE RDENS
RC NC MC RHOD
RHOM UN NPT RCM
VCM AZ
EB/E EM/E TCR
T6 NTESC
#1 1.06 12.0 0.21
0.166 13 0.065 26.4 92.5
0 3 0.109 0.0042 -0.022192 0.772
0.000 6.25 18
66
NKSTRY NKSREG
NKSHYP NKSPER NPRECT NKSMOD
NTTRY NTRIP NQUAD NCHAIN NMERG NEWHI
NSTEPC NBCALL NTPERT
NWARN NHI
#2 30743
133 91
61 0
87 78
0 0
2 0
0 25 20389
2200 3129 2
TWO
MASS GROUPS: NM1 NM2 M1 M2 RM1 RM2
150 844 0.497 0.497 0.780
1.408
OR = 0 EX = 0 DB =
0.456 SB = 0.0000 BB = 0.0000 CH =
-0.0390 NC = 1 N(A) = 0
1
<E> = 0.79 EMAX = 0.789 NPOP =
1 0 993 5 0
0 0 0 0 EB/KT = 0 0
0 0 0 0 0
0 0 1
ENERGIES
-0.11411 0.00000 -0.14599 0.01054 0.00000
0.00000 0.00000 0.00000 0.00000 0.00000
ETOT = -0.260099
NEW CHAIN 1
T = 30.90 H = -7. R = 7.8E-04
M = 0.0208 0.0112 G4 = 4.2E-07 R1 = 8.9E-04 P =
1.2E-04 E1 = 4.814 NP =35
NEW CHAIN
N NP E RSUM RGRAV TCR RMAXS NAM 3 1
-0.11572 1.2E-03 6.1E-04 1.7E-03 1.3E-02
1 30 5
EXCHANGE
T NAM E0 E A0 A EB0 EB 30.91
1 30 1
5 0.943 0.831 1.6E-03 9.2E-04 -2.3E-02
-1.0E-01
CHAIN BINARY NAM =
1 5 A = 9.2E-04 E = 0.83 EB
= 0.87 GB = 1.7E-03 G4 = 0.0E+00 EB1 = 0.00
E1 = 0.67 ET = 0.387 DB = 3.5
RECOIL:
E E1 PM/A RD A A1 RP GB IN 0.8309 0.90 0.4
1.9 9.20E-04 4.02E-03 5.10E-03 1.71E-03
99.1
END CHAIN 1 3 2
1 RB = 1.2E-03 R13 = 5.5E-03 R24 = 1.0E+10 DE
= 1.8E-11 TC = 4.0 # 70 7
1 DB = 3.48 EC = 0.445
CHTERM: T I3
I4 NT DT 30.9111 2
2 996 3.8E-06 3.8E-06 3.8E-06
NEW
CHAIN 1 T = 30.92 H
= -14. R = 9.9E-04 M = 0.0277 0.0043 G4 =
2.3E-07 R1 = 1.0E-03 P = 5.0E-04 E1 = 0.164
NP = 3
NEW CHAIN N NP E RSUM RGRAV TCR RMAXS
NAM 3 1 -0.11572 1.2E-03
6.1E-04 1.7E-03 1.3E-02 1
5 30
CHAIN ESCAPE: IESC
NM RI RDOT2 2*M/R VF 3 30
4.0E-03 3.3E+01 1.6E+01 6.7
Following
a temporary exchange of star #30 with the heavier members #1 and #5,
the former is ejected with velocity 6.7 km/s and the binary
increases
its energy by 60 %. In the next strong interaction, the light star
#556 acquires escape velocity of 10.7 km/s.
CHAIN BINARY
NAM = 1 5 A =
6.1E-04 E = 0.68 EB = 1.31 GB = 1.1E-04 G4 =
0.0E+00 EB1 = 0.00 E1 =-0.38 ET = 0.584 DB =
0.6
RECOIL: E E1 PM/A RD A A1 RP GB IN
0.6829 1.28 0.8 5.8 6.09E-04 -1.66E-03
3.98E-03 1.10E-04 109.9
END CHAIN
1 2 3 1 RB = 3.6E-04 R13 = 4.1E-03
R24 = 1.0E+10 DE = 9.7E-12 TC = 0.4 #
19 0 1 DB = 0.59 EC = 0.445
CHTERM:
T I3 I4 NT DT 30.9192 12
12 996 9.5E-07 9.5E-07 9.5E-07
NEW
CHAIN 1 T = 31.47 H
= 0. R = 3.0E-04 M = 0.0118 0.0165
G4 = 8.1E-08 R1 = 5.9E-04 P = 2.0E-04 E1 =******
NP =16
NEW CHAIN N NP E RSUM RGRAV TCR RMAXS
NAM 3 0 -0.15166 1.2E-03
5.8E-04 8.0E-04 1.5E-02 5
556 1
CHAIN ESCAPE:
IESC NM RI RDOT2 2*M/R VF 2 556
5.4E-03 5.4E+01 1.0E+01 10.7
EXCHANGE
T NAM E0 E A0 A EB0 EB 31.47
5 556 5
1 1.000 0.627 5.4E-04 5.7E-04 -7.9E-03
-1.6E-01
CHAIN BINARY NAM =
5 1 A = 5.7E-04 E = 0.63 EB
= 1.07 GB = 4.2E-05 G4 = 0.0E+00 EB1 = 0.00
E1 =-1.42 ET = 0.626 DB =****
RECOIL:
E E1 PM/A RD A A1 RP GB IN 0.6273 1.31 0.4
7.4 5.69E-04 -6.39E-04 5.42E-03 4.22E-05
83.7
END CHAIN 1 3 2
1 RB = 7.5E-04 R13 = 5.7E-03 R24 = 1.0E+10 DE
= 0.0E+00 TC = 2.5 # 83 6
0 DB =***** EC = 0.583
CHTERM: T I3
I4 NT DT 31.4717 2
2 996 9.5E-07 9.5E-07 9.5E-07
NEW
CHAIN 1 T = 31.92 H
= -24. R = 9.2E-04 M = 0.0277 0.0006 G4 =
8.2E-08 R1 = 7.4E-04 P = 6.5E-04 E1 = 0.016
NP = 1
NEW CHAIN N NP E RSUM RGRAV TCR RMAXS
NAM 3 0 -0.16231 1.2E-03
6.1E-04 7.3E-04 1.4E-02 5
1 416
CHAIN ESCAPE: IESC NM RI
RDOT2 2*M/R VF 3 416 6.3E-03
1.1E+01 9.0E+00 2.0
END CHAIN
1 2 3 1 RB = 9.2E-04 R13 = 6.6E-03
R24 = 1.0E+10 DE = 0.0E+00 TC = 2.1 #
31 2 0 DB = 0.00 EC = 0.624
CHTERM:
T I3 I4 NT DT 31.9248 414 414
996 3.8E-06 3.8E-06 3.8E-06
TIME =
32.00 Q = 0.73 DE = 0.000001 E = -0.260098
RMIN = 1.5E-03 DTMIN = 7.2E-05 ECLOSE = 0.74 TC =
2 EB/E = 1.6429 BIN = 5
1
TIME = 34.00 Q = 0.71 DE =
-0.000001 E = -0.260098 RMIN = 1.4E-03 DTMIN =
6.9E-05 ECLOSE = 0.69 TC = 2 EB/E =
1.6344 BIN = 5
1
A
lot of activity leading to quite large binary energy ratio (> 100
% because fast escaping members are still included).
TIME
= 36.00 Q = 0.71 DE = 0.000005 E
= -0.260097 RMIN = 1.4E-03 DTMIN = 6.7E-05 ECLOSE =
0.70 TC = 3 EB/E = 1.6256 BIN =
5 1
ESCAPE N
= 993 7 0
0.9925 -0.270603 0.14 28.77 0.500
0.00100 980 195
556
ESCAPE ANGLES
48 4 45
4
NEW CHAIN 1 T =
37.54 H = -24. R = 8.9E-04 M = 0.0277 0.0012
G4 = 8.8E-07 R1 = 6.4E-04 P = 3.7E-04 E1 =-0.036
NP = 2
NEW CHAIN N NP E RSUM RGRAV TCR RMAXS
NAM 3 4 -0.16262 1.4E-03
7.0E-04 7.7E-04 7.0E-03 5
1 187
END CHAIN 1 2
3 1 RB = 5.6E-04 R13 = 2.9E-03 R24 = 1.0E+10
DE = 1.6E-07 TC = 3.4 # 69
5 4 DB =-0.02 EC = 0.601
CHTERM:
T I3 I4 NT DT 37.5413 186 186
994 1.9E-06 1.9E-06 1.9E-06
NEW
CHAIN 1 T = 37.54 H
= -23. R = 1.1E-03 M = 0.0277 0.0012 G4 =
7.5E-07 R1 = 6.8E-04 P = 2.9E-04 E1 = 0.118
NP = 3
NEW CHAIN N NP E RSUM RGRAV TCR RMAXS
NAM 3 4 -0.16262 1.4E-03
7.0E-04 7.7E-04 7.9E-03 5
1 187
CHAIN ESCAPE: IESC NM RI
RDOT2 2*M/R VF 3 187 3.9E-03
2.2E+01 1.5E+01 4.5
CHAIN BINARY
NAM = 5 1 A =
5.5E-04 E = 0.84 EB = 1.04 GB = 3.8E-05 G4 =
0.0E+00 EB1 = 0.00 E1 =-0.04 ET = 0.622 DB =
0.1
RECOIL: E E1 PM/A RD A A1 RP GB IN
0.8387 1.21 1.1 4.7 5.50E-04 -2.85E-03
3.94E-03 3.83E-05 29.1
END CHAIN
1 2 3 1 RB = 3.7E-04 R13 = 3.8E-03
R24 = 1.0E+10 DE = 1.5E-07 TC = 1.0 #
24 1 4 DB = 0.10 EC = 0.601
CHTERM:
T I3 I4 NT DT 37.5457 186 186
994 1.9E-06 1.9E-06 1.9E-06
NEW
CHAIN 1 T = 37.63 H
= -26. R = 1.0E-03 M = 0.0277 0.0067 G4 =
1.6E-05 R1 = 1.2E-03 P = 1.2E-03 E1 =-0.027
NP = 3
NEW CHAIN N NP E RSUM RGRAV TCR RMAXS
NAM 3 2 -0.16906 1.4E-03
7.0E-04 1.1E-03 5.3E-03 5
1 15
END CHAIN 1
2 3 1 RB = 9.5E-04 R13 = 2.6E-03 R24 =
1.0E+10 DE = 3.6E-06 TC = 0.3 #
15 0 2 DB = 0.03 EC = 0.625
CHTERM:
T I3 I4 NT DT 37.6322 448 448
994 9.5E-07 9.5E-07 9.5E-07
TIME =
38.00 Q = 0.72 DE = 0.000005 E = -0.270602
RMIN = 1.6E-03 DTMIN = 8.2E-05 ECLOSE = 0.69 TC =
2 EB/E = 1.9124 BIN = 5
1
ESCAPE N = 990
10 0 0.9710 -0.324470 0.28
25.18 0.500 0.00098 974
30 35 3
ESCAPE
ANGLES 22
23 25 46
43 24
TIME = 40.00 Q =
0.53 DE = -0.000009 E = -0.324472 RMIN = 1.4E-03
DTMIN = 6.8E-05 ECLOSE = 0.65 TC = 6
EB/E = 1.2301 BIN = 5
1
ESCAPE N = 988
12 0 0.9688 -0.326463 0.27
23.99 0.500 0.00098 971
135 376
ESCAPE ANGLES
53 38 8
24
Note
total energy increase after fast escapers removed. This leads to
almost overall equilibrium (denoted by Q=0.50). At this time,
smallest binary size is AMIN = 5.1E-04. By now, half-mass radius,
<R>, has increased to 1.28 because the binaries have expelled
other members.
T = 40.0
N = 988 KS = 1 NM =
0 MM = 0 NS = 986 NSTEPS =
4896023 413143 DE =
0.000002 E = -0.326463
RUN = 1 M# =
0 CPU = 0.6 DMIN = 1.6E-05 2.2E-05
AMIN = 5.1E-04 RMAX = 1.8E-03 NBLOCK =
206909 NIRECT = 0 NURECT = 0 NEFF =
292
<R> RTIDE RDENS
RC NC MC RHOD
RHOM UN NPT RCM
VCM AZ
EB/E EM/E TCR
T6 NTESC
#1 1.28 11.8 0.28
0.129 6 0.032 69.6 241.6
1 0 0.270 0.0201 -0.013566 1.230
0.000 5.99 24
88
NKSTRY NKSREG
NKSHYP NKSPER NPRECT NKSMOD
NTTRY NTRIP NQUAD NCHAIN NMERG NEWHI
NSTEPC NBCALL NTPERT
NWARN NHI
#2 51295
154 102
8582 0
656 1123 0
0 9
0 0 336
49046 14714 6550
1
TWO MASS GROUPS: NM1 NM2 M1 M2 RM1
RM2 154 833
0.485 0.484 0.918 1.559
OR =
0 EX = 0 DB = 0.721 SB = 0.0000
BB = 0.0000 CH = -0.3548 NC = 1 N(A)
= 0 1
<E> = 0.91 EMAX =
0.911 NPOP = 1 0 986
12 0 0 0 0 0 EB/KT =
0 0 0 0 0
0 0 0 0 0
1
ENERGIES -0.18018 0.00000
-0.14429 0.07690 0.00000 0.00000 0.00000
0.00000 0.00000 0.00000 ETOT = -0.324472
TIME
= 42.00 Q = 0.53 DE = 0.000042 E
= -0.326456 RMIN = 1.6E-03 DTMIN = 8.4E-05 ECLOSE =
0.65 TC = 7 EB/E = 1.2116 BIN =
5 1
ESCAPE N
= 987 13 0 0.9681
-0.327300 0.31 25.35 0.500 0.00098
968 410
ESCAPE ANGLES
43 33
TIME = 44.00 Q =
0.62 DE = -0.000018 E = -0.327305 RMIN = 1.6E-03
DTMIN = 7.9E-05 ECLOSE = 0.81 TC = 7
EB/E = 1.2044 BIN = 5
1
ESCAPE N = 986
14 0 0.9674 -0.327545 0.35
24.39 0.500 0.00098 965
353
ESCAPE ANGLES
42 26
----------
Output from T=46 to T=88 omitted to save space ------------------
T =
90.0 N = 952 KS = 1
NM = 0 MM = 0 NS = 950 NSTEPS
= 7800737 1686032 DE
= 0.000000 E = -0.359742
RUN = 1
M# = 0 CPU = 1.2 DMIN = 1.6E-05
2.7E-04 AMIN = 3.5E-04 RMAX = 4.6E-04 NBLOCK =
480603 NIRECT = 0 NURECT = 0 NEFF =
282
<R> RTIDE RDENS
RC NC MC RHOD
RHOM UN NPT RCM
VCM AZ
EB/E EM/E TCR
T6 NTESC
#1 2.01 11.7 1.90
0.284 10 0.069 31.6 92.7
1 0 1.554 0.0422 0.033596
3.077 0.050 11.62 54
217
NKSTRY NKSREG
NKSHYP NKSPER NPRECT NKSMOD
NTTRY NTRIP NQUAD NCHAIN NMERG NEWHI
NSTEPC NBCALL NTPERT
NWARN NHI
#2 222412
319 127 124750
0 2199 25877
0 0
20 63 0
723 177528 55693
57687 0
TWO MASS GROUPS:
NM1 NM2 M1 M2 RM1 RM2 149
802 0.466 0.465 1.462 2.644
OR
= 0 EX = 0 DB = 1.091 SB =
0.0000 BB = 0.0000 CH = -0.4436 NC = 1
N(A) = 0 0 1
<E> =
0.21 EMAX = 0.206 NPOP = 1 0
950 48 0 0 0 0
0 EB/KT = 0 0 0
0 0 0 0 0
0 0 0 1
ENERGIES
-0.26837 0.00000 -0.08696 0.11019 0.00000
0.00000 0.00000 0.00000 -0.00434 0.00000 ETOT
= -0.359661
TIME = 92.00 Q = 0.53 DE =
-0.000014 E = -0.359743 RMIN = 2.4E-03 DTMIN =
1.5E-04 ECLOSE = 0.45 TC = 7 EB/E =
3.1095 BIN = 5
1
ESCAPE N = 946
54 0 0.9278 -0.360076 1.67
23.67 1.000 0.00098 893
309 902 388 445 526
752
ESCAPE ANGLES
56 5 27
7 19 0
46 4 17
18 18 7
TIME
= 94.00 Q = 0.54 DE = -0.000017 E =
-0.360078 RMIN = 2.2E-03 DTMIN = 1.3E-04 ECLOSE =
0.46 TC = 8 EB/E = 3.0834 BIN =
5 1
ESCAPE N
= 945 55 0 0.9273
-0.360076 1.75 23.54 0.500 0.00098
890 527
ESCAPE ANGLES
61 6
TIME = 96.00 Q
= 0.59 DE = 0.000000 E = -0.360076 RMIN =
1.3E-03 DTMIN = 5.7E-05 ECLOSE = 0.52 TC =
8 EB/E = 3.0802 BIN = 5
1
TIME = 98.00 Q = 0.52 DE =
0.000020 E = -0.360074 RMIN = 1.7E-03 DTMIN =
8.5E-05 ECLOSE = 0.45 TC = 8 EB/E =
3.0768 BIN = 5
1
ESCAPE N = 943
57 0 0.9262 -0.360434 1.89
23.96 1.000 0.00098 887
416 784
ESCAPE ANGLES
6 21 6
1
NEW CHAIN 1 T =
99.84 H = -40. R = 4.3E-04 M = 0.0277 0.0083
G4 = 7.7E-07 R1 = 1.2E-03 P = 2.3E-04 E1 = 0.022
NP = 1
NEW CHAIN N NP E RSUM RGRAV TCR RMAXS
NAM 3 2 -0.27243 1.7E-03
8.3E-04 6.1E-04 1.2E-02 5
1 10
CHAIN ESCAPE: IESC
NM RI RDOT2 2*M/R VF 3 10
3.6E-03 2.6E+01 2.0E+01 3.9
END
CHAIN 1 2 3 1 RB = 3.7E-04
R13 = 3.5E-03 R24 = 1.0E+10 DE = 7.6E-12 TC =
1.1 # 26 1 0 DB = 0.10
EC = 0.756
CHTERM: T I3 I4 NT DT
99.8364 13 13 945
9.5E-07 9.5E-07 9.5E-07
TIME = 100.00
Q = 0.64 DE = 0.000103 E = -0.360422 RMIN =
2.0E-03 DTMIN = 1.1E-04 ECLOSE = 0.39 TC =
4 EB/E = 5.5969 BIN = 5
1
ESCAPE N = 940
60 0 0.9191 -0.365072 1.94
23.68 0.500 0.00098 882
17 592 664
ESCAPE ANGLES
19 33 54
0 82 22
A
total of 60 escapers at T6 = 60 Myr, with <R> = 2.05. Now the
core has decreased to NC = 8 members only. Hence a tightly bound
group has formed so that the average density contrast (RHOD=45) is
large. The CPU time was 1.4 mins on the Cambridge micro-Grape.
Finally there are two hard binaries, with EB/E = 5.6 which is quite
pronounced. Note members #1 & #5 still remain together,
with AMIN = 3.1E-04. Some 8 million direct integration steps were
taken and 2 million regularized steps. Final evolution of the mass
groups shows considerable expansion, mostly of the light bodies.
The highest escape velocities (in file ESC) were 7 and 10 km/s. This
compares with typical initial member velocities of 1.1 km/s which
declined a bit later due to the cluster expansion. Finally, the
actual energy in binaries amounts to -0.29 compared to -0.05 binding
the cluster itself (-0.25 initially), given by ENERGIES below.
T =
100.0 N = 940 KS = 2
NM = 0 MM = 0 NS = 936 NSTEPS
= 8279038 1981903 DE
= 0.000091 E = -0.365072
RUN = 1
M# = 0 CPU = 1.4 DMIN = 1.6E-05
1.8E-05 AMIN = 3.1E-04 RMAX = 2.4E-02 NBLOCK =
548764 NIRECT = 0 NURECT = 0 NEFF =
249
<R> RTIDE RDENS
RC NC MC RHOD
RHOM UN NPT RCM
VCM AZ
EB/E EM/E TCR
T6 NTESC
#1 2.05 11.6 2.32
0.234 8 0.061 45.4 147.6
1 96 1.943 0.0438 0.058436 5.518
0.079 23.67 60 235
NKSTRY NKSREG NKSHYP NKSPER
NPRECT NKSMOD NTTRY NTRIP NQUAD
NCHAIN NMERG NEWHI NSTEPC
NBCALL NTPERT NWARN
NHI
#2 271730 333
129 153001
0 2570 33910
0 0
21 63 0
749 214436 70095
82916 1
TWO MASS GROUPS:
NM1 NM2 M1 M2 RM1 RM2 147
791 0.460 0.459 1.550 2.456
OR
= 0 EX = 0 DB = 1.228 SB =
0.0000 BB = 0.0000 CH = -0.4696 NC = 2
N(A) = 1 0 1
<E> =
0.64 EMAX = 0.885 NPOP = 1 1
936 60 0 0 0 0
0 EB/KT = 0 0 0
0 0 1 0 0
0 0 0 1
ENERGIES
-0.29537 -0.00734 -0.05337 0.11553 0.00000 0.00000
0.00000 0.00000 -0.00434 0.00000 ETOT =
-0.360422
END RUN TIME = 100.0 CPUTOT =
0.0 ERRTOT = 0.000147 DETOT = 0.000019
End
of Plummer model run without stellar evolution
Final snapshot of a run with stellar evolution
Same parameters as standard case, except tolerance QE = 1.0D-04 for last output and KZ19 = 3. The three heaviest stars (above 8 solar masses) have become neutron stars with high escape velocity due to asymmetrical mass loss and there are two white dwarfs. Now the final binary consists of stars #9 & #8 so their dynamical effect is considerably less than before. This leads to somewhat fewer stars escaping. The total mass lost from the stellar evolution represents 34 solar masses out of 607 initially. At T = 60 Myr, stars above 6.3 solar masses (TURN) have evolved off the main sequence. Because of compensating factors, a simulation with stellar evolution is expected to attain a greater age before disruption.
TIME = 100.00 Q = 0.57 DE = -0.000159 E = -0.615727 RMIN = 2.1E-03 DTMIN = 1.2E-04 ECLOSE = 0.40 TC = 6 EB/E = 2.3257 BIN = 9 8
ESCAPE N = 959 41 0 0.9083 -0.629030 0.60 23.60 0.500 0.00095 917 315 282
T = 100.0 N = 959 KS = 1 NM = 0 MM = 0 NS = 957 NSTEPS = 8195483 1540382 DE = -0.000285 E = -0.629030
RUN = 1 M# = 0 CPU = 1.3 DMIN = 8.1E-07 8.6E-05 AMIN = 2.5E-04 RMAX = 9.1E-03 NBLOCK = 433849 NIRECT = 0 NURECT = 0 NEFF = 363
<R> RTIDE RDENS RC NC MC RHOD RHOM UN NPT RCM VCM AZ EB/E EM/E TCR T6 NTESC
#1 2.10 11.6 0.57 0.172 8 0.051 81.6 169.4 1 0 0.599 0.0168 -0.023746 2.328 -0.002 15.71 60 205
NKSTRY NKSREG NKSHYP NKSPER NPRECT NKSMOD NTTRY NTRIP NQUAD NCHAIN NMERG NEWHI NSTEPC NBCALL NTPERT NWARN NHI
#2 215944 342 120 172655 0 5083 30484 0 0 10 42 0 960 201658 69610 77043 0
NMDOT NRG NHE NRS NNH NWD NSN NBH TURN ZMRG ZMHE ZMRS ZMNH ZMWD ZMSN ZMDOT NTYPE
#4 1250 6 6 5 0 2 3 0 6.34 0.0 0.0 0.2 0.0 0.0 21.1 34.5 781 175 0 0 1 0 0 0 0 0 0 0 2
TWO MASS GROUPS: NM1 NM2 M1 M2 RM1 RM2 163 795 0.454 0.454 1.327 2.733
OR = 1 EX = 0 DB = 0.643 SB = 0.0000 BB = 0.0000 CH = -0.1533 NC = 1 N(A) = 0 0 1
<E> = 0.39 EMAX = 0.394 NPOP = 1 0 957 41 0 0 0 0 0 EB/KT = 0 0 0 0 0 0 0 0 0 0 1
ENERGIES -0.16077 0.00000 -0.06812 0.37943 0.00000 0.00000 0.00000 0.00000 0.00014 0.00000 ETOT = -0.615727
END RUN TIME = 100.0 CPUTOT = 0.0 ERRTOT = -0.000336 DETOT = -0.00003