Sp.-V/AQuan/1999/10/11:10:50
Page 471
Chapter 19
Star Populations and
the Solar Neighborhood
Gerard F. Gilmore and Michael Zeilik
19.1
19.1
The Nearby Stars . . . . . . . . . . . . . . . . . . . . . 471
19.2
The Brightest Stars . . . . . . . . . . . . . . . . . . . . 475
19.3
Stellar Populations . . . . . . . . . . . . . . . . . . . . . 478
19.4
Star Counts at High Latitudes . . . . . . . . . . . . . . 480
19.5
Vertical Stellar Density Profile . . . . . . . . . . . . . . 481
19.6
Main Sequence Field Stellar
Luminosity Function . . . . . . . . . . . . . . . . . . . 485
19.7
White Dwarf Luminosity Function . . . . . . . . . . . 485
19.8
Luminosity Class Distribution for
Nearby Field Stars . . . . . . . . . . . . . . . . . . . . 486
19.9
Mass Density in the Solar Neighborhood . . . . . . . 487
19.10
Stellar Mass Function
19.11
Solar Motion and Kinematics of
Nearby Stars . . . . . . . . . . . . . . . . . . . . . . . . 493
. . . . . . . . . . . . . . . . . . 488
THE NEARBY STARS
Table 19.1 lists the 100 nearest stars to the Earth in order of increasing distance. Positions are calculated
from observed positions with corrections for proper motions; they are given in the FK5 system with
equinox = J2000.0 and epoch = J2000.0. The first column gives the identifier in the Hipparcos
471
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472 / 19
S TAR P OPULATIONS AND THE S OLAR N EIGHBORHOOD
Catalogue [1]; the last column gives the parallax in milliarcsecs with the associated standard deviation
error.
Table 19.1. Nearby stars.
HD
number
α (2000.0)
δ (2000.0)
70890
N/A
71681
128621
71683
128620
87937
N/A
54035
95735
32349
48915
92403
N/A
16537
22049
114046
217987
57548
N/A
104214
201091
37279
61421
104217
201092
91772
173740
91768
173739
1475
1326
108870
209100
8102
10700
5643
N/A
36208
N/A
24186
33793
105090
202560
110893
239960
30920
N/A
72511
N/A
80824
N/A
439
225213
15689
N/A
3829
N/A
72509
N/A
86162
N/A
14 29 42.95
−62 40 46.1
14 39 35.08
−60 50 13.8
14 39 36.50
−60 50 02.3
17 57 48.50
+04 41 36.2
11 03 20.19
+35 58 11.6
06 45 08.92
−16 41 58.0
18 49 49.36
−23 50 10.4
03 32 55.84
−09 27 29.7
23 05 52.04
−35 51 11.1
11 47 44.40
+00 48 16.4
21 06 53.94
+38 44 57.9
07 39 18.12
+05 13 30.0
21 06 55.26
+38 44 31.4
18 42 46.90
+59 37 36.6
18 42 46.69
+59 37 49.4
00 18 22.89
+44 01 22.6
22 03 21.66
−56 47 09.5
01 44 04.08
−15 56 14.9
01 12 30.64
−16 59 56.3
07 27 24.50
+05 13 32.8
05 11 40.58
−45 01 06.3
21 17 15.27
−38 52 02.5
22 27 59.47
+57 41 45.1
06 29 23.40
−02 48 50.3
14 49 34
−26 06 22
16 30 18.06
−12 39 45.3
00 05 24.43
−37 21 26.5
03 22 05.50
−13 16 43.8
00 49 09.90
+05 23 19.0
14 49 31.76
−26 06 42.0
17 36 25.90
+68 20 20.9
HIP
Other name
Sp. type
V magnitude
Abs V
B−V
Parallax
α Cen C
M5 Ve
11.01
15.45
+1.81
772.33 ± 2.42
α Cen B
K1 V
1.35
5.70
+0.88
742.12 ± 1.40
α Cen A
G2 V
−0.01
4.34
+0.71
742.12 ± 1.40
Barnard’s star
M5 V
9.54
13.24
+1.57
549.01 ± 1.58
Gl 411
M2 Ve
7.49
10.46
+1.50
392.40 ± 0.91
α CMa
A1 V
−1.44
1.45
+0.01
379.21 ± 1.58
Gl 729
M4.5 Ve
10.37
13.00
+1.51
336.48 ± 1.82
Eri
K2 V
3.72
6.18
+0.88
310.75 ± 0.85
Gl 887
M2 Ve
7.35
9.76
+1.48
303.90 ± 0.87
Ross 128
M4.5 V
11.12
13.50
+1.75
299.58 ± 2.20
61 Cyg A
K5 Ve
5.20
7.49
+1.07
287.13 ± 1.51
α CMi
F5 IV–V
0.40
2.68
+0.43
285.93 ± 0.88
61 Cyg B
K7 Ve
6.05
8.33
+1.31
285.42 ± 0.72
Gl 725B
M5 V
9.70
11.97
+1.56
284.48 ± 5.01
Gl 725A
M4 V
8.94
11.18
+1.50
280.28 ± 2.57
GX And
M2 V
8.09
10.33
+1.56
280.27 ± 1.05
Ind
K5 Ve
4.69
6.89
+1.06
275.76 ± 0.69
τ Cet
G8 Vp
Gl 54.1
M5.5 Ve
3.49
5.68
+0.73
274.17 ± 0.80
12.10
14.25
+1.85
269.05 ± 7.57
Luyten’s star
M3.5
9.84
11.94
+1.57
263.26 ± 1.43
Kapteyn’s star
M0 V
8.86
10.89
+1.55
255.26 ± 0.86
AX Mic
M0 Ve
6.69
8.71
+1.40
253.37 ± 1.13
Kruger 60
M2 V
9.59
11.58
+1.61
249.52 ± 3.03
Ross 614
M4.5 Ve
11.12
13.05
+1.69
242.89 ± 2.64
N/A
N/A
11.72
13.58
N/A
235.24 ± 22.43
Wolf 1061
M3.5
10.10
11.95
+1.58
234.51 ± 1.82
Gl 1
M4 V
8.56
10.36
+1.46
229.33 ± 1.08
N/A
N/A
12.16
13.94
N/A
227.45 ± 61.79
Van Maanen 2
DG
12.37
14.15
+0.55
226.95 ± 5.35
Gl 563.2
M3
12.07
13.80
+1.52
221.80 ± 69.07
BD +68 946
M3.5 Vvar
9.15
10.81
+1.50
220.85 ± 0.92
Sp.-V/AQuan/1999/10/11:10:50
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19.1 T HE N EARBY S TARS / 473
Table 19.1. (Continued.)
HD
number
α (2000.0)
δ (2000.0)
85523
N/A
114110
N/A
57367
N/A
113020
79210
54211
79211
49908
88230
82725
N/A
85605
N/A
106440
204961
86214
N/A
19849
26965
112460
N/A
88601
165341
97649
187642
1242
N/A
57544
N/A
67155
119850
103039
N/A
21088
N/A
33226
265866
53020
128620
25878
36395
82817
152751
96100
185144
29295
42581
26857
N/A
86990
152751
94761
180617
73184
131977
37766
N/A
76074
155876
3821
4614
84478
156026
117473
156026
17 28 39.95
−46 53 42.7
23 06 39
−14 52 19
11 45 42.92
−64 50 29.5
22 53 16.73
−14 15 49.3
11 05 28.58
+43 31 36.4
10 11 22.14
+49 27 15.3
16 54 32.47
−62 24 12.0
17 29 36.25
+24 39 14.7
21 33 33.98
−49 00 32.4
17 37 03.66
−44 19 09.2
04 15 16.32
−07 39 10.3
22 46 49.73
+44 20 02.4
18 05 27.29
+02 30 00.4
19 50 47.00
+08 52 06.0
00 15 28.11
−16 08 01.7
11 47 41.38
+78 41 28.2
13 45 43.78
+14 53 29.5
20 52 33.02
−16 58 29.1
04 31 11.52
+58 58 37.5
06 54 48.96
+33 16 05.4
10 50 52.06
+06 48 29.3
05 31 27.40
−03 40 38.0
16 55 28.75
−08 20 10.8
19 32 21.59
+69 39 40.2
06 10 34.62
−21 51 52.7
05 42 09.27
+12 29 21.6
17 46 34.23
−57 19 08.6
19 16 55.26
+05 10 08.1
14 57 28.00
−21 24 55.7
07 44 40.17
+03 33 08.8
15 32 12.93
−41 16 32.1
00 49 06.29
+57 48 54.7
17 16 13.36
−26 32 46.1
23 49 12.53
+02 24 04.4
HIP
Abs V
B−V
Parallax
9.38
11.10
+1.55
220.43 ± 1.63
DC
12.24
13.92
−0.17
216.52 ± 18.28
Gl 440
DQ6
11.50
13.18
+0.20
216.40 ± 2.11
Ross 780
M5 V
10.16
11.80
+1.60
212.69 ± 2.10
Gl 412A
M2 Ve
8.82
10.40
+1.54
206.94 ± 1.19
Gl 380
K2 Ve
6.60
8.16
+1.33
205.22 ± 0.81
N/A
N/A
11.72
13.26
N/A
203.01 ± 29.27
N/A
N/A
11.39
12.92
+1.10
202.69 ± 39.48
Gl 832
M1 V
8.66
10.19
+1.52
202.53 ± 1.33
Gl 682
M3.5
10.94
12.43
+1.66
198.32 ± 2.43
ω 2 Eri
K1 Ve
4.43
5.92
+0.82
198.24 ± 0.84
EV Lac
M4.5 Ve
10.29
11.77
+1.54
198.07 ± 2.05
70 Oph
K0 Ve
4.03
5.50
+0.86
196.62 ± 1.38
α Aql
A7 IV–V
0.76
2.20
+0.22
194.44 ± 0.94
L722-22
M4
11.49
12.90
+1.75
191.86 ± 17.24
Gl 445
M4 V
10.80
12.14
+1.57
185.48 ± 1.43
Wolf 498
M4 Ve
8.46
9.79
+1.44
184.13 ± 1.27
N/A
N/A
11.41
12.71
+1.65
182.15 ± 3.68
Gl 169.1A
M4
10.82
12.11
+1.65
181.36 ± 3.67
Wolf 294
M4 V
9.89
11.18
+1.57
181.32 ± 1.87
Wolf 358
M5 V
11.64
12.89
+1.68
177.46 ± 23.00
Wolf 1453
M1.5 V
7.97
9.19
+1.47
175.72 ± 1.20
Wolf 630A
M3 Ve
9.02
10.23
+1.55
174.23 ± 3.90
σ Dra
K0 V
4.67
5.87
+0.79
173.41 ± 0.46
Gl 229
M1 Ve
8.15
9.34
+1.49
173.19 ± 1.12
Ross 47
M4
11.56
12.75
+1.62
172.78 ± 3.88
Gl 693
M3.5
10.75
11.93
+1.66
172.08 ± 2.22
Ross 652
M3.5 Ve
9.12
10.28
+1.46
170.26 ± 1.37
Gl 570A
K5 Ve
5.72
6.86
+1.02
169.32 ± 1.67
YZ CMi
M4.5 Ve
11.19
12.32
+1.60
168.59 ± 2.67
Gl 588
M3
9.31
10.44
+1.52
168.52 ± 1.42
η Cas
G3 V
3.46
4.59
+0.59
167.99 ± 0.62
Gl 664
K5 Ve
6.33
7.45
+1.16
167.56 ± 1.06
Gl 908
M2 Ve
8.98
10.10
+1.46
167.51 ± 1.49
Other name
Sp. type
Gl 674
M3
GJ 293
V magnitude
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474 / 19
S TAR P OPULATIONS AND THE S OLAR N EIGHBORHOOD
Table 19.1. (Continued.)
HIP
HD
number
α (2000.0)
δ (2000.0)
84405
155885
99461
191408
15510
20794
99240
190248
71253
164058
86961
N/A
86963
N/A
45343
79210
99701
191849
116132
N/A
74995
N/A
120005
79211
84140
155876
17 15 20.98
−26 36 10.2
20 11 11.94
−36 06 04.4
03 19 55.65
−43 04 11.2
20 08 43.61
−66 10 55.4
14 34 16.81
−12 31 10.4
17 46 12.63
−32 06 12.8
17 46 14.41
−32 06 08.3
09 14 22.79
+52 41 11.8
20 13 53.40
−45 09 50.5
23 31 52.18
+19 56 14.1
15 19 26.82
−07 43 20.2
09 14 24.70
+52 41 11.0
17 12 07.89
+45 39 57.5
07 10 01.83
+38 31 46.1
11 06 30.65
−53 16 05.5
16 55 25.23
−08 19 21.3
23 13 16.98
+57 10 06.1
16 25 24.62
+54 18 14.8
11 00 04.26
+22 49 58.7
14 51 23.38
+19 06 01.7
21 29 36.81
+17 38 35.8
23 07 19
−32 16 05
22 56 34.81
+16 33 12.4
17 18 57.18
−34 59 23.3
20 53 19.79
+62 09 15.8
02 36 04.89
+06 53 12.7
10 28 55.55
+00 50 27.6
17 09 31.54
+43 40 52.9
00 47 01.46
+11 58 25.9
01 42 29.76
+20 16 06.6
00 25 45.07
−77 15 15.3
14 57 26.54
−21 24 41.5
02 44 15.51
+25 31 24.1
34603
54298
N/A
82809
N/A
114622
219134
80459
191408
53767
72659
131156
106106
N/A
114176
N/A
113296
216899
84709
156384
103096
199305
12114
16160
51317
N/A
83945
N/A
3765
4628
7981
10476
2021
2151
73182
131976
12781
N/A
Abs V
B−V
Parallax
4.33
5.44
+0.86
167.08 ± 1.07
K3 V
5.32
6.41
+0.87
165.24 ± 0.90
e Eri
G8 V
4.26
5.35
+0.71
165.02 ± 0.55
δ Pav
G8 V
3.55
4.62
+0.75
163.73 ± 0.65
Wolf 1481
M3
11.32
12.39
+1.64
163.51 ± 2.77
CD −32 13297
M2 V
10.49
11.53
+1.46
161.77 ± 11.29
CD −32 13298
M2 V
11.39
12.43
+1.44
161.77 ± 11.29
BD +53 1320
M0 Ve
7.64
8.68
+1.41
161.59 ± 5.23
Gl 784
M0 V
7.97
9.01
+1.11
161.17 ± 1.08
BD +19 5116
M0 Ve
10.05
11.07
+1.19
160.06 ± 2.81
Gl 581
M5 V
10.57
11.58
+1.60
159.52 ± 2.27
Gl 338B
M0 Ve
7.70
8.71
+1.42
159.48 ± 6.61
Gl 661A
M3
9.31
10.31
+1.49
158.17 ± 3.26
M4.5 Ve
11.65
12.63
+1.70
157.24 ± 3.32
N/A
11.69
12.65
N/A
155.28 ± 78.30
Wolfe 629
M4
11.73
12.67
+1.70
153.96 ± 4.04
Gl 892
K3 V var
5.57
6.50
+1.00
153.24 ± 0.65
Gl 645
M2 V
10.13
11.04
+1.59
151.93 ± 1.11
Gl 408
M3
10.03
10.92
+1.52
150.96 ± 1.59
ξ Boo
G8 Ve
4.54
5.41
+0.72
149.26 ± 0.76
Gl 829
M4 Ve
10.33
11.19
+1.62
148.29 ± 1.85
N/A
N/A
12.28
13.13
N/A
147.95 ± 13.76
BD+15 4733
M2 Ve
8.68
9.49
+1.51
145.27 ± 1.22
Gl 667A
K3 V
5.91
6.69
+1.08
143.45 ± 17.12
BD +61 2068
M2 Ve
8.55
9.31
+1.48
141.95 ± 0.77
BD +06 398
K3 V
5.69
6.50
+0.92
138.72 ± 1.04
BD +01 2447
M2.5 V
9.65
10.35
+1.51
138.29 ± 2.13
N/A
M3
11.77
12.47
+1.70
137.84 ± 8.95
BD +11 96
G8 II
5.74
6.38
+0.99
134.04 ± 0.86
107 Psc
K1 V
5.24
5.87
+0.84
133.91 ± 0.91
β Hyi
G2 IV
2.82
3.45
+0.62
133.78 ± 0.51
BD −20 4123
M2 V
8.01
8.64
+1.01
133.63 ± 33.56
Gl 109
M3.5 Ve
10.55
11.16
+1.53
132.42 ± 2.48
Other name
Sp. type
36 Oph
K1 Ve
Gl 783A
V magnitude
Sp.-V/AQuan/1999/10/11:10:50
Page 475
19.2 T HE B RIGHTEST S TARS / 475
Table 19.1. (Continued.)
HD
number
α (2000.0)
δ (2000.0)
5336
6582
65859
N/A
01 08 16.39
+54 55 13.2
13 29 59.79
+10 22 37.8
HIP
19.2
Other name
Sp. type
µ Cas
G5 Vp
BD +11 2576
M1 V
Abs V
B−V
Parallax
5.17
5.78
+0.70
132.40 ± 0.60
9.05
9.64
+1.49
131.12 ± 1.29
V magnitude
THE BRIGHTEST STARS
Table 19.2 lists the 100 brightest stars in the sky in order of right ascension. Positions are given in the
FK5 system with equinox = J2000.0 and epoch = J2000.0; they are calculated from observed positions
with corrections for proper motions. Parallaxes are from the Hipparcos Main Catalogue [1] and given
in milliarcseconds with the associated standard deviation error.
Table 19.2. Brightest stars.
HD
number
α (2000.0)
δ (2000.0)
Other
name
Sp. type
Alpheratz
358
α And
B9p
Caph
432
β Cas
CD −77 15
2151
Ankaa
2261
Schedar
3712
Diphda
4128
Cih
5394
Mirach
6860
Achernar
10144
Almach
12533
Hamal
12929
Polaris
8890
Menkar
18884
Algol
19356
Mirfak
20902
Aldeberan
29139
Rigel
34085
Capella
34029
Bellatrix
35468
El Nath
35497
Mintaka
36486
Arneb
36673
Alnilam
37128
00 08 23.26
+29 05 25.6
00 09 10.69
+59 08 59.2
00 25 45.01
−77 15 15.3
00 26 17.05
−42 18 21.5
00 40 30.44
+56 32 14.4
00 43 35.37
−17 59 11.8
00 56 42.53
+60 43 00.3
01 09 43.92
+35 37 14.0
01 37 42.85
−57 14 12.3
02 03 53.95
+42 19 47.0
02 07 10.41
+23 27 44.7
02 31 49.08
+89 15 50.8
03 02 16.77
+04 05 23.0
03 08 10.3
+40 57 20.3
03 24 19.37
+49 51 40.2
04 35 55.24
+16 30 33.5
05 14 32.27
−08 12 05.9
05 16 41.36
+45 59 52.8
05 25 07.86
+06 20 58.9
05 26 17.51
+28 36 28.6
05 32 00.40
−00 17 56.7
05 32 43.82
−17 49 20.3
05 36 12.81
−01 12 06.9
Star name
B−V
V−I
2.07
−0.04
−0.10
33.60 ± 0.73
F2 III–IV
2.28
+0.38
+0.40
59.89 ± 0.56
β Hyi
G2 IV
2.82
+0.62
+0.68
133.78 ± 0.51
α Phe
K0 II I
2.40
+1.08
+1.11
42.14 ± 0.78
α Cas
K0 II–IIIvar
2.24
+1.17
+1.13
14.27 ± 0.57
β Cet
K0 III
2.04
+1.02
+1.00
34.04 ± 0.82
γ Cas
B0 IV
2.15
−0.05
−0.02
5.32 ± 0.56
β And
M0 IIIvar
2.07
+1.58
+1.74
16.36 ± 0.76
α Eri
B3 Vp
0.45
−0.16
−0.17
22.68 ± 0.57
γ And
K3 IIb
2.26
+1.37
+1.37
9.19 ± 0.73
α Ari
K2 I II
2.01
+1.15
+1.13
49.48 ± 0.99
α UMi
F7: Ib–IIv
1.97
+0.64
+0.70
α Cet
M2 III
2.54
+1.63
+1.97
14.82 ± 0.83
β Per
B8 V
2.09
−0.03
+0.02
35.14 ± 0.90
α Per
F5 Ib
1.79
+0.48
+0.63
5.51 ± 0.66
α Tau
K5 III
0.87
+1.54
+1.61
50.09 ± 0.95
β Ori
B8 Ia
0.18
−0.03
+0.03
4.22 ± 0.81
α Aur
M1 III
0.08
+0.80
+0.83
77.29 ± 0.89
γ Ori
B2 III
+1.64
−0.22
−0.22
13.42 ± 0.98
β Tau
B7 III
1.65
−0.13
−0.09
24.89 ± 0.88
δ Ori
O9.5 II
2.25
−0.18
−0.21
3.56 ± 0.83
α Lep
F0 Ib
2.58
+0.21
+0.32
2.54 ± 0.72
Ori
B0 Ia
1.69
−0.18
−0.16
2.43 ± 0.91
V magnitude
Parallax
7.5 6 ± 0.48
Sp.-V/AQuan/1999/10/11:10:50
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476 / 19
S TAR P OPULATIONS AND THE S OLAR N EIGHBORHOOD
Table 19.2. (Continued.)
HD
number
α (2000.0)
δ (2000.0)
Other
name
Sp. type
Alnitak
37742
ξ Ori
O9.5 Ib
Saiph
38771
κ Ori
Betelgeuse
39801
Menkalinan
40183
Mirzam
44743
Canopus
45348
Alhena
47105
Sirius A
48915
Adhara
52089
Wezen
54605
Aludra
58350
Castor
60178
Procyon
61421
Pollux
62509
Naos
66811
CD −46 3847
68273
Avoir
71130
Suhail
78647
Miaplacidus
80007
Scutulum
80404
CPD −54 2219
81188
Alphard
81797
Regulus
87901
Algieba
89484
Merak
95418
Dubhe
95689
Zosma
97603
Denebola
102647
Phe cda
103287
Gienah
106625
Alpha Crucis
108248
Gacrux
10890 3
Muhlifain
110304
Mimosa
111123
05 40 45.53
−01 56 33.3
05 47 45.39
−09 40 10.6
05 55 10.31
+07 24 25.4
05 59 31.72
+44 56 50 .8
06 22 41.99
−17 57 21.3
06 23 57.11
− 52 41 44.4
06 37 42.75
+16 23 57.3
06 45 08.92
−16 41 58.0
06 58 37.55
−28 58 19.5
07 08 23.48
−26 23 35.5
07 24 05.70
−29 18 11.2
07 34 35.86
+31 53 17.8
07 39 18.12
+05 13 30.0
07 45 18.95
+28 01 34.3
08 03 35.05
−40 00 11.3
08 09 31.95
−47 20 11.7
08 22 30.84
−59 30 34.1
09 07 59.76
−43 25 57.4
09 13 11.98
−69 43 01.9
09 17 05.41
−59 16 30.8
09 22 06.82
−55 00 38.4
09 27 35.24
−08 39 31.0
10 08 22.31
+11 58 01.9
10 19 58.35
+19 50 29.4
11 01 50.48
+56 22 56.7
11 03 43.67
+61 45 03.7
11 14 06.50
+20 31 25.4
11 49 03.58
+14 34 19.4
11 53 49.85
+53 41 41.4
12 15 48.37
−17 32 30.9
12 26 35.90
−63 05 56.7
12 31 09.96
−57 06 47.6
12 41 31.04
−48 57 35.6
12 47 43.26
−59 41 19.5
Star name
B−V
V−I
1.74
−0.20
−0.18
3.99 ± 0.79
B0.5 Ivar
2.07
−0.17
−0.14
4.52 ± 0.77
α Ori
M2 Ib
0.45
+1.50
+2.32
7.63 ± 1.64
β Aur
A2 V
1.90
+0.08
+0.05
39.72 ± 0.78
β CMa
B1 II–III
1.98
−0.24
−0.24
6.53 ± 0.66
α Car
F0 Ib
−0.62
+0.16
+0.23
10.43 ± 0.53
γ Gem
A0 IV
1.93
+0.00
+0.04
31.12 ± 2.33
α CMa
A1 V
−1.44
+0.01
−0.02
379.21 ± 1.58
CMa
B2 II
1.50
−0.21
−0.20
7.57 ± 0.57
δ CMa
F8 Ia
1.83
+0.70
+0.67
1.82 ± 0.56
η CMa
B5 Ia
2.45
−0.08
+0.01
1.02 ± 0.57
α Gem
A2 V
1.58
+0.03
+0.05
63.27 ± 1.23
α CMi
F5 IV–V
0.40
+0.43
+0.05
285.93 ± 0.88
β Gem
K0 IIIvar
1.16
+0.99
+0.97
96.74 ± 0.87
ζ Pup
O5 IAf
2.21
−0.27
−0.22
2.33 ± 0.51
γ Vel
WC8
1.75
−0.14
−0.14
3.88 ± 0.53
Car
K3 III
1.86
+1.20
+0.16
5.16 ± 0.49
λ Vel
K4 Ib–II
2.23
+1.67
+1.69
5.69 ± 0.53
β Car
A2 IV
1.67
+0.07
+0.02
29.34 ± 0.47
τ Car
A8 Ib
2.21
+0.19
+0.28
4.71 ± 0.46
κ Vel
B2 IV
2.47
−0.14
−0.17
6.05 ± 0.48
α Hya
K3 III
1.99
+1.44
+1.39
18.40 ± 0.78
α Leo
B7 V
1.36
−0.09
−0.10
42.09 ± 0.79
γ Leo
K0 III
2.01
+1.13
+1.17
25.96 ± 0.83
β UMa
A1 V
2.34
+0.03
+0.02
41.07 ± 0.60
α UMa
F7 V
1.81
+1.06
+1.03
26.38 ± 0.53
δ Leo
A4 V
2.56
+0.13
+0.12
56.52 ± 0.83
β Leo
A3 Vvar
2.14
+0.09
+0.10
90.16 ± 0.89
γ UMa
A0 V SB
2.41
+0.04
+0.06
38.99 ± 0.68
γ Crv
B8 III
2.58
−0.11
−0.10
19.78 ± 0.81
α Cru
B0.5 IV
0.77
−0.24
−0.26
10.17 ± 0.67
γ Cru
M4 III
1.59
+1.60
+2.37
37.09 ± 0.67
γ Cen
A1 IV
2.20
−0.02
−0.01
25.01 ± 1.01
β Cru
B0.5 III
1.25
−0.24
−0.27
9.25 ± 0.61
V magnitude
Parallax
Sp.-V/AQuan/1999/10/11:10:50
Page 477
19.2 T HE B RIGHTEST S TARS / 477
Table 19.2. (Continued.)
HD
number
α (2000.0)
δ (2000.0)
Alioth
112185
Spica
116658
Mizar
116656
CPD −52 6655
118716
Alcaid
120315
CD −46 8949
121263
Agena
122451
Menkent
123139
Arcturus
124897
CD −41 8917
127972
GJ 559B
128621
Rigil Kent
128620
CD −46 9501
129056
Izar
129989
Kochab
131873
Alphecca
139006
Dzuba
143275
Acrab
144217
Antares
148478
BD −10 4350
149757
Atria
150798
CD −34 11285
151680
Sabik
155125
Shaula
158926
Ras-Alhague
159561
CD −42 12312
159532
CD −38 12137
160578
Eltanin
164058
Kaus Australis
169022
Vega
172167
Nunki
175191
Altair
187642
Sadir
194093
Peacock
193924
12 54 01.75
+55 57 35.4
13 25 11.58
−11 09 40.8
13 23 55.54
+54 55 31.3
13 39 53.26
−53 27 59.0
13 47 32.44
+49 18 47.8
13 55 32.39
−47 17 18.2
14 03 49.40
−60 22 22.9
14 06 40.95
−36 22 11.8
14 15 39.67
+19 10 56.7
14 35 30.42
−42 09 26.2
14 39 35.08
−60 50 13.8
14 39 36.50
−60 50 02.3
14 41 55.76
−47 23 17.5
14 44 59.21
+27 04 27.4
14 50 42.33
+74 09 19.8
15 34 41.27
+26 42 52.9
16 00 20.01
−22 37 18.2
16 05 26.27
−19 48 19.6
16 29 24.46
−26 25 55.2
16 37 09.54
−10 34 01.5
16 48 39.89
−69 01 39. 8
16 50 09.81
−34 17 35.6
17 10 22.69
−15 43 29.7
17 33 36.52
−37 06 13.8
17 34 56.07
+12 33 36.1
17 37 19.13
−42 59 52.2
17 42 29.27
−39 01 47.9
17 56 36.37
+51 29 20.0
18 24 10.32
−34 23 04.6
18 36 56.34
+38 47 01.3
18 55 15.93
−26 17 48.2
19 50 47.0
+08 52 06.0
20 22 13.70
+40 15 24.0
20 25 38.86
−56 44 06.3
Star name
Other
name
Sp. type
UMa
A0p
α Vir
B−V
V−I
1.76
−0.02
−0.04
40.30 ± 0.62
B1 V
0.98
−0.24
−0.25
12.44 ± 0.86
ζ UMa
A2 V
2.23
+0.06
+0.07
41.73 ± 0.61
Cen
B1 III
2.29
−0.17
−0.23
8.68 ± 0.77
η UMa
B3 V
1.85
−0.10
−0.08
32.39 ± 0 .74
ζ Cen
B2.5 IV
2.55
−0.18
−0.18
8.48 ± 0.74
β Cen
B1 III
0.61
−0.23
−0.25
6.21 ± 0.56
θ Cen
K0 IIIb
2.06
+1.01
+1.01
53.52 ± 0.79
α Boo
K2 II Ip
−0.05
+1.24
+1.22
88.85 ± 0.74
η Cen
B1 Vn
2.33
−0.16
−0.17
10 .57 ± 0.83
α Cen B
K1 V
1.35
+0.90
+0.88
742.12 ± 1.40
α Cen A
G2 V
−0.01
+0.71
+0.69
742.12 ± 1.40
α Lup
B1.5 III
2.30
−0.15
−0.21
5.95 ± 0.76
Boo
K0 II–III
2.35
+0.97
+0.95
15.55 ± 0.78
β UMi
K4 IIIvar
2.07
+1.46
+1.46
25.79 ± 0.52
α CrB
A0 V
2.22
+0.03
+0.05
43.65 ± 0.79
δ Sco
B0.2 IV
2.29
−0.12
−0.09
8.12 ± 0.88
β Sco
B0.5 V
2.56
−0.06
−0.04
6.15 ± 1.12
α Sco
M1 Ib
1.06
+1.87
+2.90
5.40 ± 1.68
ζ Oph
O9.5 V
2.54
+0.04
+0.10
7.12 ± 0.71
α TrA
K2 IIb
1.91
+1.45
+1.45
7.85 ± 0.63
Sco
K2 II Ib
2.29
+1.14
+1.10
49.85 ± 0.81
η Oph
A2.5 Va
2.43
+0.06
+0.06
38.77 ± 0.86
λ Sco
B1.5 IV
1.62
−0.23
−0.24
4.64 ± 0.90
α Oph
A5 III
2.08
+0.16
+0.17
69.84 ± 0.88
θ Sco
F1 II
1.86
+0.41
+0.02
11.99 ± 0.84
κ Sco
B1.5 III
2.39
−0.17
−0.22
7.03 ± 0.73
γ Dra
K5 III
2.24
+1.52
+1.54
22.10 ± 0.46
Sgr
B9.5 III
1.79
−0.03
+0.01
22.55 ± 1.02
α Lyr
A0 Vvar
0.03
+0.00
−0.01
128.93 ± 0.55
σ Sgr
B2.5 V
2.05
−0.13
−0.13
14.54 ± 0.88
α Aql
A7 IV–V
0.76
+0.22
+0.27
194.44 ± 0.94
γ Cyg
F8 Ib
2.14
+0.67
+0.65
2.14 ± 0.51
α Pav
B2 IV
1.94
−0.12
−0.10
17.80 ± 0.70
V magnitude
Parallax
Sp.-V/AQuan/1999/10/11:10:50
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S TAR P OPULATIONS AND THE S OLAR N EIGHBORHOOD
Table 19.2. (Continued.)
HD
number
α (2000.0)
δ (2000.0)
Other
name
Sp. type
Deneb
197345
α Cyg
A2 Ia
Gienar
197989
Cyg
Alderamin
203280
Enif
206778
Al Na’ir
209952
CD −47 14308
214952
Fomalhaut
216956
Scheat
217906
Markab
218045
20 41 25.91
+45 16 49.2
20 46 12.68
+33 58 12.9
21 18 34.77
+62 35 08.1
21 44 11.16
+09 52 30.0
22 08 13.99
−46 57 39.5
22 42.40.05
−46 53 04.5
22 57 39.05
−29 37 20.1
23 03 46.46
+28 04 58.0
23 04 45.65
+15 12 19.0
Star name
19.3
B−V
V−I
1.25
+0.09
+0.16
1.01 ± 0.57
K0 III
2.48
+1.02
+1.00
45.26 ± 0.53
α Cep
A7 IV–V
2.45
+0.26
+0.26
66.84 ± 0.49
Peg
K2 Ibvar
2.38
+1.52
+1.42
4.85 ± 0.84
α Gru
B7 IV
1.73
−0.07
−0.05
32.16 ± 0.82
β Gru
M5 III
2.07
+1.61
+2.60
19.17 ± 0.75
α PsA
A3 V
1.17
+0.14
+0.16
130.08 ± 0.92
β Peg
M2 II–IIIvar
2.44
+1.66
+2.31
16.37 ± 0.72
α Peg
B9.5 III
2.49
−0.03
+0.00
23.36 ± 0.76
V magnitude
Parallax
STELLAR POPULATIONS
The concept of stellar populations arose on observational grounds [2], and was rapidly extended as the
underlying astrophysical processes were identified [3–5]. In modern usage the sequence of populations
is essentially that of time, with the boundaries between population classes being poorly defined or
definable, and often internally inconsistent. The classical scheme and current usage for both the Milky
Way and external galaxies are summarized in the first and second parts of Table 19.3. A complementary
presentation in astrophysical units is summarized in Table 19.4. It remains uncertain if there is a single
sequence of stellar populations in the Milky Way, or two separate sequences, halo–bulge and thick
disk–young disk. The age ranges are in units of τu , the age of the Universe.
The top part of Table 19.3 presents the classical view of stellar populations in the Milky Way. Each
of the three basic population divisions is further subdivided, with defining examples of observed classes
of objects listed. The combinations of spatial distributions, spectral types, kinematics, and chemical
abundances are all correlated. It is this set of correlations which provides the evidence for the basic
physical validity of the population concept. The bottom line of the top part illustrates schematically
a classical extension of the populations concept to external galaxies. The bottom part illustrates the
current appreciation of stellar populations. The format is similar to that of the top part, as are the
essential features. Many more details are shown, together with a finer subdivision. The essential
features of the population concept however remain little modified.
In each panel of Table 19.4, the vertical axis represents an observable which is closely related
to the physical processes of galaxy evolution. The horizontal axis represents a monotonic, though not
necessarily linear, evolutionary sequence related to time. Only in the panel showing the distributions of
specific angular momentum is an apparently clear evolutionary connection between stellar populations
evident.
Sp.-V/AQuan/1999/10/11:10:50
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19.3 S TELLAR P OPULATIONS / 479
Table 19.3. Classical (top) and current (lower) concepts of stellar populations
Population II
Characteristic
objects
and
properties
Scale height (pc)
central
concentration
τ/τu
σW
Z /Z External Galaxies
Halo Pop II
subdwarfs
globular clusters
RR Lyrae
P > 0.d 4
Intermediate
stars with
Vz ≥ 30 km s−1
LPV’s, P < 250d
2000
500
strong
strong
1.0
1.0–0.8
75 km s−1
25 km s−1
0.1
0.25
← Ellipticals →
Extreme Pop II
“halo”
subdwarfs
globular
clusters
with [Fe/H] < −1
RR Lyrae
S > 4
BHB stars
Characteristic
objects
and
properties
Vrot σU :σV :σW
Z /Z τ/τu
External Galaxies
Disk
30
130:100:85
0.03
1.0–0.9
dE
galactic
nucleus
RR Lyrae
P < 0.d 4
weak-line stars
300
strong
0.8–0.25
17 km s−1
0.5
← Bulges →
Intermediate Pop II
“thick disk”
globular
clusters
with [Fe/H] > −1
RR Lyrae, c-type
LPV’s, P ∼ 250d
RHB stars
Bulge/Pop II
“bulge”
SMR stars
= “IR bulge”
planetary
nebulae
= “optical
bulge”
RR Lyrae
S < 4
tri-axial (?)
170
60
60:45:40
120:120:120
0.3
0.1–2
0.9–0.8
1.0–0.5 (?)
Sa →← SO → gE
Population I
Old Pop I
A stars
Me dwarfs
strong-line
stars
Extreme Pop I
gas, spiral
structure
supergiants
Cepheids
100
60
little
little
0.25–0.05
0.05–0.00
10 km s−1
8 km s−1
0.75
1.0
← Spiral disks, Irr’s →
Pop I
“old disk”
intermediate
age disk
stars
Extreme Pop I
“young disk”
young stars
spiral
structure
Cepheids
200
220
38:25:20
20:10:8
0.9
1
0.9–0.1
0.1–0.0
← Sbcd, Irr’s →
Table 19.4. Astrophysical representation of stellar populations.
−2
Halo
−1
Thick disk
0
Bulge →
[Fe/H]
Old disk →
Young
disk
+1
time →
0
Bulge
Half
mass
radius
(kpc)
2
Halo
4
6
Thick disk
Old disk
Young disk
time →
Sp.-V/AQuan/1999/10/11:10:50
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S TAR P OPULATIONS AND THE S OLAR N EIGHBORHOOD
Table 19.4. (Continued.)
−2
Halo
−1
Thick disk
[Fe/H]
Old disk
0
Young disk
Bulge
+1
log mass →
Bulge
100
Vertical
velocity
disp.
(km/s)
Halo
80
Thick disk
40
Old disk
0
Young disk
[Fe/H] →
0
Halo
Angular
mom.
per
mass
(km/s
kpc)
Bulge
103
Thick disk
Old disk
Young disk
2 × 103
19.4
[Fe/H] →
STAR COUNTS AT HIGH LATITUDES [6–12]
Counts of stars in selected color ranges in the V and photographic B J magnitude bands are given for
the north galactic pole in Tables 19.5 and 19.6. Similar data are given in Table 19.7 for the south
galactic pole.
Table 19.5. The stellar color–magnitude distribution at b = +90◦ (stars per square degree per mag.).
V
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
B − V ≤ 0.2
0.5
0.2
0.5
1
1
2
0.3
0.5
1
1
1
2
10
0.5
6
8
9
9
21
26
0.7
8
14
24
35
34
29
0.9
3
8
13
16
22
21
1.1
2
2
6
9
13
15
1.3
1
2
3
8
13
19
1.5
0
1
3
6
16
27
1.7
0.5
0
0.5
1
3
10
≥ 1.9
0.5
0.5
0
0
0
0
Total
5
11
20
36
60
86
125
159
Sp.-V/AQuan/1999/10/11:10:50
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19.5 V ERTICAL S TELLAR D ENSITY P ROFILE / 481
Table 19.6. B J magnitude star counts at the north
galactic pole (stars per square degree per mag.).
BJ
Blue
15.5
16.5
17.5
18.5
19.5
20.5
21.5
50
160
180
Red
Total
200
240
450
60
100
125
160
250
400
630
Table 19.7. V magnitude star counts at the south galactic pole (stars per square degree per mag.).
V
B − V ≤ 0.4
0.4 ≤ B − V ≤ 0.8
0.8 ≤ B − V ≤ 1.2
1.2 ≤ B − V ≤ 1.6
1.6 ≤ 1.6
Total
16–17
17–18
18–19
19–20
20–21
21–22
3
17
31
14
10
24
55
90
72
93
186
234
17
62
59
66
79
169
21
86
79
148
245
341
0
0
14
48
69
141
97
255
255
369
590
910
There is an excess of stars toward b = −90◦ over b = +90◦ which is consistent with a location of
the Sun at z = +40 pc, a scale error in the data, or differential reddening.
19.5
VERTICAL STELLAR DENSITY PROFILE
The vertical structure of the disk is approximately exponential. Near the plane the scale height is low,
as young stars are significant. Far from the plane, the thick disk dominates. Details are in Table 19.8.
Table 19.8. Stellar density structure.
Vertical distance
range (pc)
0z
0z
0z
0z
250 z
50
200
300
500
750
Apparent exponential
scale height (pc)
∼ constant density
120
175
225
260
For distances between 300 and 4000 pc the density profile is describable by
ρ
−z
−z
+ 0.041 exp
.
= 0.959 exp
ρ0
250
1000
Beyond ∼ 4 kpc, the density law is a galactocentric power law of index ∼ −3, axis ratio c/a ∼ 0.75,
or a deprojected r 1/4 law with effective radius re ∼ 2.7 kpc, axis ratio c/a ∼ 0.75, with c/a probably
varying with radius, being smallest in the center. Table 19.9 gives the scale heights as a function of the
star luminosity for disk stars.
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S TAR P OPULATIONS AND THE S OLAR N EIGHBORHOOD
Table 19.9. Absolute magnitude–scale height relation.
Absolute magnitude
MV
Scale height
(pc)
≤ +2
+3
+4
+5
19.5.1
90
150
200
250
The Standard Model of the Optical Stellar Galaxy
This standard model given in Table 19.10 is in reasonable agreement with data for |b| 30◦ , |l| 30◦ ,
10 V 22. It predicts too few stars within ∼ 30◦ of the galactic center.
Table 19.10. Standard model of optical stellar galaxy.a,b
Old disk
Radial density profile
Vertical density profilec
Radial scale length
Vertical scale length
Thick disk
Bulge
Halo
exponential
exponential
3000 pc
1000 pc
power law
power law
500 pc
300 pc
r 1/4 or power law
metal-rich
globular
(?)
metal-rich
globular
−0.2
0.4
—
—
120:120:120 km/s
mean globular
60 km/s at R < 1
kpc
Stellar luminosity function
exponential
exponential
3000 pc
dwarfs = 300 pc
giants = 250 pc
local field
Local stellar density
Color–magnitude relation
tabulated
old open cluster
Mean metallicity
Metallicity dispersion
Radial metallicity gradient
Vertical metallicity gradient
Velocity dispersions
σU , σV , σW
Mean rotation
−0.1
0.3
−0.04 dex/kpc
−0.3 dex/kpc
38:25:20 km/s
metal-rich
globular
0.02 × disk
metal-rich
globular
−0.6
0.3
0: dex/kpc
0: dex/kpc
60:45:40 km/s
200 km/s
170 km/s
2700 pc
2000 pc
0.002 × disk
metal-poor
globular
−1.6
0.5
−0.02: dex/kpc
−0.03: dex/kpc
130:100:85 km/s
30 km/s
Notes
a Solar position (R, δ) = (8000, +20) pc.
b Extinction: In projection, Sandage cosec law, distributed constant density in radius, and vertical exponential
scale height = 100 pc.
c See the scale height versus distance and scale height versus M relations given.
V
Tables 19.11 and 19.12 give typical star counts for the standard galaxy model in the V and I bands.
This first table also includes data from the previous Astrophysical Quantities edition.
Table 19.11. Model log N (V ) (stars per square degree) averaged over galactic longitude and over
the whole sky.
V
b=0
b=5
b = 10
b = 20
b = 30
b = 60
b = 90
Sky
AQ3a
12.0
13.0
14.0
1.751
2.275
2.708
1.752
2.267
2.694
1.743
2.218
2.618
1.665
2.085
2.450
1.544
1.935
2.279
1.234
1.603
1.925
1.160
1.524
1.838
1.556
1.994
2.372
1.76
2.17
2.56
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19.5 V ERTICAL S TELLAR D ENSITY P ROFILE / 483
Table 19.11. (Continued.)
V
b=0
b=5
b = 10
b = 20
b = 30
b = 60
b = 90
Sky
AQ3a
15.0
16.0
17.0
18.0
19.0
20.0
21.0
22.0
23.0
24.0
25.0
3.105
3.485
3.842
4.170
4.474
4.776
5.078
5.342
5.536
5.684
5.813
3.085
3.460
3.809
4.130
4.428
4.722
5.011
5.262
5.448
5.594
5.722
2.985
3.331
3.648
3.939
4.210
4.468
4.705
4.903
5.059
5.195
5.319
2.781
3.089
3.363
3.612
3.845
4.057
4.236
4.382
4.510
4.633
4.749
2.591
2.875
3.124
3.349
3.559
3.748
3.909
4.046
4.168
4.286
4.393
2.209
2.458
2.673
2.869
3.052
3.226
3.389
3.538
3.665
3.772
3.863
2.110
2.347
2.553
2.744
2.924
3.092
3.245
3.382
3.500
3.604
3.695
2.719
3.047
3.350
3.632
3.897
4.156
4.406
4.626
4.797
4.937
5.061
2.94
3.29
3.64
3.95
4.20
4.5
4.7
Note
a From Allen, C.W. 1973, Astrophysical Quantities (Athlone Press, London).
Table 19.12. Model log N (I ) (stars per square degree) averaged over galactic longitude
and over the whole sky.
19.5.2
I
b=0
b=5
b = 10
b = 20
b = 30
b = 60
b = 90
Sky
12.0
13.0
14.0
15.0
16.0
17.0
18.0
19.0
20.0
21.0
22.0
23.0
24.0
25.0
2.466
2.922
3.316
3.650
3.951
4.243
4.548
4.868
5.191
5.479
5.710
5.909
6.092
6.258
2.434
2.877
3.262
3.594
3.897
4.191
4.494
4.807
5.120
5.398
5.623
5.816
5.991
6.150
2.279
2.671
3.023
3.344
3.653
3.955
4.247
4.530
4.802
5.039
5.234
5.400
5.546
5.669
2.011
2.355
2.678
2.991
3.301
3.594
3.861
4.103
4.326
4.515
4.673
4.806
4.916
5.002
1.799
2.138
2.461
2.772
3.069
3.341
3.584
3.804
4.005
4.173
4.313
4.430
4.528
4.606
1.450
1.816
2.149
2.445
2.702
2.926
3.133
3.327
3.503
3.649
3.770
3.874
3.970
4.055
1.374
1.728
2.045
2.326
2.575
2.799
3.005
3.191
3.353
3.488
3.604
3.706
3.797
3.875
2.001
2.396
2.753
3.075
3.376
3.663
3.947
4.230
4.510
4.761
4.967
5.145
5.308
5.453
Surface Brightness
The surface brightness of the sky, excluding solar system and terrestrial sources, has been measured
by Pioneer 10 in two bands (Table 19.13). 3950 Å < λ < 4850 Å (“blue”) and 5900 Å < λ < 6900 Å
(“red”) [13]. Contributions from stars with V 6.5 have been removed. The flux is quoted in units of
the equivalent number of stars of V = 10, type G2 V, per square degree, S10 (V ).
−1
S10 (V ) = 1.16 × 10−9 erg cm−2 s−1 sr−1 Å
−9
= 1.07 × 10
erg cm
−2
−2 −1
S10 (V ) (blue band) ≡ 0.265L ,B pc
≡ 28.49Bmag. arcsec−2 .
s
sr
−1
−1
Å
blue band
red band,
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S TAR P OPULATIONS AND THE S OLAR N EIGHBORHOOD
Table 19.13. Pioneer 10 sky brightness measurements.
Region
NCP
NEP
NGP
SCP
SEPa
SGP
α (1950)
δ
l II
bII
—
+90◦
+67◦
+27◦
−90◦
−67◦
−27◦
123◦
96◦
—
303◦
277◦
—
27◦
30◦
90◦
−27◦
−30◦
−90◦
18h 0m
12h 50m
—
6h 0m
0h 50m
S10 (V )
Blue
Red
56
66
29
74
128
26
77
82
31
94
125
36
Blue–red
(mag.)
1.43 ± 0.08
1.32 ± 0.08
1.18 ± 0.15
1.34 ± 0.07
1.06 ± 0.06
1.41 ± 0.14
Note
a The SEP beam included part of the LMC.
The full data set has been analyzed [13, 14] to derive a surface brightness map of the Milky Way
Galaxy with the following properties:
Surface brightness at galactic poles:
µ B = 24.55 ± 0.1 B mag. arcsec−2
= 10.1 ± 1.0L ,B pc−2 ,
µV = 23.71 ± 0.1V mag. arcsec−2
= 12.0 ± 1.5L ,V pc−2 .
Color of poles:
B − V = 0.76 ± 0.15.
Face-on disk central surface brightness:
µ0 = 95 ± 30L ,B pc−2
= 22.1 ± 0.3 B mag. arcsec−2 .
Integrated disk color:
B − V = 0.84 ± 0.15.
Integrated disk luminosity:
L tot = (1.8 ± 0.3) × 1010 L ,B .
Old disk color:
B − V = 0.95 ± 0.15.
Old disk luminosity:
L tot = (1.1 ± 0.2) × 1010 L ,B .
Integrated halo luminosity:
L = 2 × 109 L ,B .
Halo color:
B − V = 0.8 ± 0.1.
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19.7 W HITE DWARF L UMINOSITY F UNCTION
/ 485
19.6 MAIN SEQUENCE FIELD STELLAR
LUMINOSITY FUNCTION [15–22]
Table 19.14 gives the main sequence stellar luminosity function.
Table 19.14. log (MV ) stars pc−3 MV−1 .
MV
Single
stars
Unresolved
binary/triple
systems
−7
−6
−5
−4
−3
−2
−1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
−7.98
−7.60
−7.27
−6.72
−6.05
−5.43
−4.80
−4.18
−3.60
−3.16
−2.89
−2.63
−2.49
−2.44
−2.52
−2.41
−2.32
−2.14
−1.99
−1.82
−1.9
−2.0
−2.0
−2.1
−2.1
−2.2
7.98
−7.60
−7.27
−6.72
−6.05
−5.43
−4.80
−4.18
−3.60
−3.16
−2.89
−2.63
−2.49
−2.44
−2.52
−2.42
−2.48
−2.26
−2.01
−1.95
−2.25
−2.53
−2.69
−2.67
−2.67
−2.67
Mean globular cluster
Principal
sequence
−5.61
−4.77
−4.39
−4.19
−3.89
−3.59
−2.84
−2.49
−2.44
−2.24
−2.24
−2.14
−1.80
−1.80
−1.90
−2.00
−2.10
−2.20
BHB
RR Lyrae
−3.49
−3.49
There is no significant evidence for variation in the field luminosity function from place to place,
while systematic changes with metallicity are consistent with those expected from the metallicity
dependence of the mass–luminosity relation for a constant initial mass function. The globular cluster
values are the mean of published data. The specific frequency of RR Lyraes varies considerably from
cluster to cluster, although the mean value is correct for field halo stars.
19.7
WHITE DWARF LUMINOSITY FUNCTION [23]
The space density of white dwarfs is given in Table 19.15.
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S TAR P OPULATIONS AND THE S OLAR N EIGHBORHOOD
Table 19.15. The V magnitude and bolometric white dwarf luminosity function.
MV
log (stars pc−3 MV−1 )
9.5
10.0
10.5
11.0
11.5
12.0
12.5
13.0
13.5
14.0
14.5
15.0
15.5
16.0
16.5
17.0
−5.91 (+0.18, −0.31)
−5.00 (+0.14, −0.21)
−4.67 (+0.13, −0.18)
−4.02 (+0.12, −0.16)
−3.92 (+0.11, −0.15)
−3.82 (+0.11, −0.16)
−3.54 (+0.11, −0.16)
−3.22 (+0.20, −0.39)
−3.06 (+0.18, −0.30)
−2.93 (+0.17, −0.29)
−3.03 (+0.26, −0.76)
−2.98 (+0.18, −0.30)
−3.09 (+0.15, −0.23)
−4.14 (+0.25, −0.64)
−4.50 (+0.30, −∞)
?
Mbol
log −1
(stars pc−3 Mbol
)
5.50
6.88
7.84
8.92
10.12
11.24
11.98
12.55
13.25
13.75
14.25
14.75
15.25
15.75
−5.91 (+0.18, −0.31)
−5.00 (+0.14, −0.21)
−4.67 (+0.13. −0.18)
−4.02 (+0.12, −0.16)
−3.92 (+0.11, −0.15)
−3.82 (+0.11, −0.16)
−3.54 (+0.11, −0.16)
−3.22 (+0.20, −0.39)
−3.18 (+0.20, −0.38)
−2.95 (+0.18, −0.30)
−3.00 (+0.25, −0.60)
−2.78 (+0.13, −0.19)
−3.35 (+0.19, −0.35)
−4.47 (+0.30, −∞)
19.8 LUMINOSITY CLASS DISTRIBUTION FOR
NEARBY FIELD STARS [24]
The fraction of the stellar luminosity from the disk and halo versus luminosity is given in Table 19.16.
Table 19.16. Main sequence fraction.
19.8.1
MV
Disk
Thick disk and halo
−6
−5
−4
−3
−2
−1
0
1
2
3
4
0.40
0.42
0.43
0.44
0.45
0.47
0.51
0.56
0.66
0.82
1.00
0
0
0
0
0
0
0
0
0
0
1
Relative Number of Stars by MK Class to V = 8 . 5 in HD Catalogue [24]
The relative fraction of stars in the MK spectral classes is given in Table 19.17.
Table 19.17. Fraction of stars in MK spectral classes.
MK type
% Stars
0
1
B
10
A
22
F
19
G
14
K
31
M
3
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19.9 M ASS D ENSITY IN THE S OLAR N EIGHBORHOOD
19.9
/ 487
MASS DENSITY IN THE SOLAR NEIGHBORHOOD [25–32]
Observed volume mass density
Interstellar matter (ISM)
Main Sequence Stars:
0.08 ≤ M/M < 1.0
1.0 ≤ M/M < 100
Halo stars
Evolved stars:
White dwarfs
Dark extended halo, local density
Total
0.04 ± 0.02
M pc−3
0.036
0.014
0.0001
M pc−3
M pc−3
M pc−3
0.005
0.01
0.10 ± 0.03
M pc−3
M pc−3
M pc−3
Note that 0.01M pc−3 is 0.3 Gev cm−3 .
Observed column mass densities, to |z| = 1.1 kpc
Neutral ISM
Ionized ISM
Molecular ISM
ISM total
Stars:
Disk main sequence
Disk white dwarfs
Thick disk
Halo subdwarfs
Stellar total
Observed total
Extended dark halo
|z| < 1.1 kpc
Total
8
2
3
13 ± 3
M
M
M
M
pc−2
pc−2
pc−2
pc−2
30
3
2
<1
35 ± 5
48 ± 8
M
M
M
M
M
M
pc−2
pc−2
pc−2
pc−2
pc−2
pc−2
23
71 ± 6
M pc−2
M pc−2
K dwarfs (z 160 pc) ρ0 = 0.10 ± 0.03M pc−3 .
All determinations are consistent with each other and with zero local unidentified matter at the ∼ 1.5 σ
level.
Dynamical analysis of the column mass density, M pc−2
K dwarfs
(300 z 2000 pc)
(z
= 71 ± 6M pc−2 ,
tot ≤ 1.1 kpc)
= 48 ± 9M pc−2 ,
disk
= 23M pc−2 ,
dark halo
Unidentified disk dark matter = 0 ± 12M pc−2 .
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S TAR P OPULATIONS AND THE S OLAR N EIGHBORHOOD
Limit on scale height/local volume density of dark disk matter with scale height H (pc):
ρ0,dark
H
0.017
300 pc
−1
M pc−3
Local luminosity density = 0.10L ,V pc−3 .
Mass-to-light ratio for all stars:
M/L|stars = 0.5M/L|,V .
Mass-to-light ratio for all local matter:
M/L|local = 1.0M/L|,V .
Surface brightness in a column:
= 12.0L ,V pc−2 .
Mass density in column, stars, and ISM:
= 48M pc−2 .
Mass-to-light ratio of identified mass:
= 4.0M/L|,V
= 9.5M/L|,B .
Extended halo mass, |z| < 1.1 kpc:
= 23M pc−2 .
Identified matter in a column:
= 48M pc−2
= 100 g/sq. meter (gsm)
= 0.010 g cm−2
= 6 × 1021 H atoms/cm2 .
19.10
STELLAR MASS FUNCTION [28]
The single star and system luminosity functions are consistent with a single stellar initial mass function
(IMF):

0.035M−1.3(±0.6) , 0.08 ≤ M ≤ 0.50,
ξ(M) = 0.019M−2.2 ,
0.50 < M ≤ 1.0,

0.019M−2.7 ,
1.00 < M ≤ 100,
where ξ(M)dM is the number of stars in the mass interval M to M + dM in units of M .
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19.10 S TELLAR M ASS F UNCTION
/ 489
Some properties of the IMF are as follows:
Binary fraction ∼ 50%.
Binary primary: secondary ratio—uncorrelated.
Total mass density in IMF at Sun 0.05 ± 0.01M pc−3 .
Mass density in stars with M ≤ 1M = 0.036M pc−3 .
Extrapolation of IMF to zero mass (brown dwarfs) from 0.085M = 0.0085M pc−3 .
Fraction of all stars with 0.08 ≤ M ≤ 0.5M (M dwarfs) = 77 ± 10%.
Local stellar number density:
−3
Total = 0.087 stars M−1
pc ,
0.08 ≤ M ≤ 1M = 0.13 stars pc−3 ,
1 ≤ M ≤ 60M = 0.011 stars pc−3 .
19.10.1
Mass–Luminosity Relation [19, 28]
The mass function ξ(M) is related to the luminosity function φ(MV ) by ξ(M) =
(dM/dMV )(MV ). The mass–luminosity relation for solar main sequence stars is tabulated in
Table 19.18 to allow this transformation.
Table 19.18. Mass luminosity relation.a
MV
M/M
MV
M/M
MV
M/M
MV
M/M
18.00
16.96
16.13
15.45
14.87
14.36
13.93
13.54
13.21
12.92
12.67
12.47
12.29
12.13
11.99
11.86
11.73
11.60
11.47
11.34
11.21
11.08
10.93
10.79
10.64
10.48
10.31
10.14
0.0700
0.0854
0.101
0.116
0.132
0.147
0.163
0.178
0.193
0.209
0.224
0.240
0.255
0.271
0.286
0.301
0.317
0.332
0.348
0.363
0.379
0.394
0.409
0.425
0.440
0.456
0.471
0.487
8.77
8.56
8.35
8.14
7.92
7.71
7.51
7.31
7.11
6.93
6.75
6.59
6.43
6.28
6.14
6.01
5.88
5.75
5.63
5.52
5.40
5.29
5.19
5.08
4.98
4.88
4.78
4.68
0.595
0.610
0.626
0.641
0.656
0.672
0.687
0.703
0.718
0.734
0.749
0.764
0.780
0.795
0.811
0.826
0.842
0.857
0.872
0.888
0.903
0.919
0.934
0.950
0.965
0.980
0.996
1.011
4.09
4.02
3.95
3.88
3.82
3.75
3.69
3.63
3.57
3.51
3.46
3.40
3.35
3.30
3.25
3.20
3.15
3.10
3.05
3.01
2.96
2.92
2.87
2.83
2.79
2.75
2.71
2.67
1.119
1.135
1.150
1.166
1.181
1.196
1.212
1.227
1.243
1.258
1.274
1.289
1.304
1.320
1.335
1.351
1.366
1.382
1.397
1.412
1.428
1.443
1.459
1.474
1.490
1.505
1.521
1.536
0.0
−1.0
−2.0
−3.0
−4.0
−5.0
−6.0
−7.0
3.467
5.248
7.943
12.023
18.197
26.915
41.687
63.1
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S TAR P OPULATIONS AND THE S OLAR N EIGHBORHOOD
Table 19.18. (Continued.)
MV
M/M
MV
M/M
MV
M/M
9.96
9.78
9.59
9.39
9.19
8.99
0.502
0.517
0.533
0.548
0.564
0.579
4.58
4.49
4.41
4.32
4.24
4.17
1.027
1.042
1.058
1.073
1.088
1.104
2.63
2.59
2.56
2.52
2.00
1.00
1.551
1.567
1.582
1.598
1.862
2.512
MV
M/M
Note
a Three significant figures are provided because the derivative of this relation is
important and not because any particular value is that significant.
Table 19.19 presents the mass and the luminosity (in magnitude units, in each of the V, I, and K
bands) associated with the stellar mass function. These values are the luminosity functions in V, I, and
K bands corresponding to the tabulated mass function.
Table 19.19. Masses and luminosities of the stellar mass function.
Mass (M )
center of
increment
M/M
Mass
increment
M
Mass in
that
increment
mass/n
Luminosity
(mag.)
MV + 2.5 log n
I-band
luminosity
(mag.)
MI + 2.5 log n
K-band
luminosity
(mag.)
MK + 2.5 log n
0.015
0.055
0.095
0.155
0.205
0.255
0.305
0.355
0.405
0.455
0.505
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
10.4 × 10−3
9.7 × 10−3
8.2 × 10−3
7.1 × 10−3
6.5 × 10−3
6.1 × 10−3
5.8 × 10−3
5.5 × 10−3
5.3 × 10−3
5.1 × 10−3
4.9 × 10−3
—
—
19.1
17.50
16.72
16.34
16.13
15.93
15.68
15.35
14.95
—
—
15.0
14.11
13.71
13.52
13.45
13.38
13.26
13.08
12.84
—
—
12.0
11.50
11.30
11.24
11.25
11.25
11.21
11.11
10.98
0.525
0.625
0.725
0.825
0.925
0.05
0.05
0.05
0.05
0.05
2.4 × 10−2
1.9 × 10−2
1.6 × 10−2
1.4 × 10−2
1.2 × 10−2
13.05
12.13
11.17
10.46
9.97
11.02
10.50
9.93
9.53
9.27
9.20
8.92
8.58
8.36
8.24
1.05
1.25
1.55
1.75
2.05
2.25
2.55
0.10
0.10
0.10
0.10
0.10
0.10
0.10
2.0 × 10−2
1.5 × 10−2
1.0 × 10−2
8.4 × 10−3
6.4 × 10−3
5.5 × 10−3
4.4 × 10−3
8.75
8.35
8.07
8.00
7.94
7.90
7.85
8.28
8.16
8.15
8.21
8.30
8.35
8.43
7.40
7.40
7.59
7.72
7.91
8.02
8.17
Sp.-V/AQuan/1999/10/11:10:50
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19.10 S TELLAR M ASS F UNCTION
Table 19.19. (Continued.)
Mass (M )
center of
increment
M/M
Mass
increment
M
Mass in
that
increment
mass/n
Luminosity
(mag.)
MV + 2.5 log n
I-band
luminosity
(mag.)
MI + 2.5 log n
K-band
luminosity
(mag.)
MK + 2.5 log n
2.75
3.05
3.25
3.55
3.75
4.05
5.05
6.05
7.05
8.05
9.05
9.95
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
3.9 × 10−3
3.3 × 10−3
2.9 × 10−3
2.5 × 10−3
2.3 × 10−3
2.0 × 10−3
1.4 × 10−3
1.0 × 10−3
7.9 × 10−4
6.3 × 10−4
5.1 × 10−4
4.4 × 10−4
7.83
7.80
7.79
7.81
7.83
7.87
7.99
8.09
8.17
8.24
8.30
8.35
8.48
8.55
8.60
8.69
8.76
8.85
9.13
9.36
9.55
9.71
9.86
9.97
8.26
8.40
8.48
8.61
8.70
8.83
9.20
9.51
9.76
9.98
10.18
10.34
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
4.0 × 10−3
2.1 × 10−3
1.3 × 10−3
8.8 × 10−4
6.5 × 10−4
5.0 × 10−4
4.0 × 10−4
3.3 × 10−4
2.8 × 10−4
2.4 × 10−4
2.0 × 10−4
1.5 × 10−4
1.3 × 10−4
1.0 × 10−4
8.7 × 10−5
5.87
6.08
6.21
6.28
6.38
6.48
6.57
6.64
6.70
6.75
6.79
6.9
6.9
7.0
7.0
7.54
8.03
8.36
8.60
8.83
9.04
9.21
9.36
9.50
9.61
9.71
9.9
10.1
10.2
10.3
7.92
8.58
9.04
9.38
9.69
9.95
10.18
10.38
10.56
10.72
10.86
11.1
11.3
11.5
11.7
10.5
15.5
20.5
25.5
30.5
35.5
40.5
45.5
50.5
55.5
60.5
70.5
80.5
90.5
99.5
These data in a similar format are plotted in Figure 19.1.
/ 491
log 10 (mass/n) (M ) in δm = 0.05M
MI + log 10 (n) in δm = 0.05M
18
16
14
12
10
8
-6
-5
-4
-3
-2
-1
-1
-1
2
2
MV + log 10 (n) in δm = 0.05M
18
16
14
12
10
8
-1
-1
Figure 19.1. Mass–luminosity relations.
0
1
log 10 (m) (M )
0
1
log 10 (m) (M )
18
16
14
12
10
8
0
1
log 10 (m) (M )
0
1
log 10 (m) (M )
2
2
492 / 19
MK + log 10 (n) in δm = 0.05M
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S TAR P OPULATIONS AND THE S OLAR N EIGHBORHOOD
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19.11 S OLAR M OTION AND K INEMATICS OF N EARBY S TARS / 493
19.11 SOLAR MOTION AND KINEMATICS OF
NEARBY STARS [33, 34]
The local standard of rest (LSR) is defined as the origin of a velocity system corrected for solar peculiar
motion. It is defined empirically, from the mean motion of nearby stars, the kinematic definition, or
from the local circular velocity, the dynamical definition. The standard solar motion is an implicit
kinematic definition of the LSR from the mean motion of nearby gas and stars. The basic solar motion
is an implicit kinematic definition of the LSR from the maximum in the kinematics of nearby stars.
The peculiar solar motion is a dynamical definition, derived from extrapolation of the asymmetric
drift–velocity dispersion relation to zero dispersion. These motions are given in Table 19.20.
Table 19.20. Standard, basic, and peculiar solar motion.
U
v
W
Apex of motion
(km s−1 )
Solar motion
Standard
Basic
Peculiar
V
10.0
9
9
5.2
11
12
7.2
6
7
α
270◦
267.◦ 4
267.◦ 0
13
15.4
16.6
δ
(1900)
(1950)
(1950)
+30◦
+25◦
+28◦
The sign convention U is positive toward the galactic center, V is positive in the direction of the
galactic rotation, and W is positive toward the North Galactic Pole.
19.11.1 Solar Motion and Velocity Dispersion for Stars
of Various Spectral Types [33, 35]
Table 19.21 gives the solar motion and velocity dispersion of stars of various spectral classes.
Table 19.21. Solar motion relative to stars of various spectral types.
Spectral type
Solar motion (km s−1 )
U
V
W
Velocity dispersion (km s−1 )
σU
σV
σW
σu (km s−1 )
ψ (deg)
Supergiants
gO-gB5
gF-gM
+9.0
+7.9
+13.4
+11.7
+3.7
+6.5
12
13
gA
gF
gG
gK0
gK3
gM
+13.4
+19.7
+7.2
+10.6
+9.0
+4.5
+11.6
+18.5
+11.1
+18.6
+17.6
+18.3
+10.3
9.5
+6.9
+6.5
+6.4
+6.2
22
28
26
31
31
31
B0
dA0
dA5
dF0
dF5
dG0
+9.6
+7.3
+8.5
+11.2
+10.1
+14.5
+14.5
+13.7
+7.8
+10.8
+12.3
+21.1
+6.7
+7.2
+7.4
+7.3
+6.2
+6.4
11
9
9
7
19
17
+36
+18
13
15
18
21
21
23
9
9
15
16
17
16
27
33
35
41
41
42
+27
+14
+12
+21
+14
+7
9
9
9
13
17
18
6
9
9
10
17
20
15
20
24
29
36
37
−50
+15
+19
+21
+13
+2
Giants
Main sequence
10
15
20
24
27
26
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494 / 19
S TAR P OPULATIONS AND THE S OLAR N EIGHBORHOOD
Table 19.21. (Continued.)
Solar motion (km s−1 )
Spectral type
U
V
W
Velocity dispersion (km s−1 )
σU
σV
σW
dG5
dK0
dK5
dM0
dM5
+8.1
+10.8
+9.5
+6.1
+9.8
+22.1
+14.9
+22.4
+14.6
+19.3
+4.3
+7.4
+5.8
+6.9
+8.6
32
28
35
32
31
17
16
20
21
23
σu (km s−1 )
15
11
16
19
16
39
34
43
43
42
ψ (deg)
+14
+3
+11
+8
−7
19.11.2 Solar Motion and Velocity Dispersion for
Groups of Selected Objects [36–42]
Table 19.22 gives the solar motion for groups of selected objects.
Table 19.22. Solar motion relative to groups of selected objects.a
Objects
Interstellar H I
Interstellar Ca II
Classical Cepheids
Carbon stars
White dwarfs
RR Lyraes
c-type
ab, s < 5
s ≥ 5
all ab’s
Miras, by period P
P < 148d
145 < P < 200d
200 < P < 250d
250 < P < 300d
300 < P < 350d
350 < P < 400d
P < 410d
Solar motion (km s−1 )
U
V
W
Velocity dispersion (km s−1 )
σU
σV
σW
σu
+12
+11
+11
+10
+10
+15
+14
+12
+12
+15
+9
+8
+10
+5
+7
(
(
8
30
42
5.7
6
7
20
22
)b
)b
5
14
18
0
0
0
0
120
120
180
155
0
0
0
0
100
130
160
160
70
120
110
120
50
80
90
90
60
90
—
60
45
45
—
40
145
70
60
40
25
—
—
60
—
—
35
23
—
33
111
61
33
32
23
15
10
10
12
39
50
81
180
101
88
69
58
50
Notes
a Missing values have very large errors.
b The values for the interstellar gas are line-of-sight velocity dispersions, and
cannot be deconvolved into orthogonal components reliably. It is probable that the
velocity dispersions are nearly isotropic, so are similar in each component.
19.11.3
Velocity–Age Relation for Disk Stars
The total velocity dispersion σV as a function of stellar age τ is adequately described by
σV3 (τ )
=
3
σV,τ
=0
+
3
2 αV δ2 Tδ
τ
exp
Tδ
−1 ,
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19.11 S OLAR M OTION AND K INEMATICS OF N EARBY S TARS / 495
with
σV,τ =0 , the velocity dispersion at age zero, = 10 km/s,
αV , a parameter describing the rotation curve, ≈ 2.95,
Tδ , a timescale, = 5 × 109 yr,
δ2 , a diffusion coefficient, = 3.7 × 10−6 (km/s)3 yr,
τ
δV3 (τ ) = 1000 + 5.4575 × 105 exp
−1 .
τδ
19.11.4
Velocity Dispersions of Stars as a Function of Age [34, 41, 42]
Table 19.23 presents velocity dispersions of groups of differing ages.
Table 19.23. Velocity dispersions of groups with differing ages.
At z = 0
(0)
σU
Group of stars
Classical Cepheids
McCormick K + M dwarfs
HK +8/+3
HK +2
HK +1
HK 0
HK −1
HK −2/−5
All McCormick stars
Integrated over z
(0)
(0)
σV
σW
(km s−1 )
18
21
29
38
40
66
39
10
16
17
23
27
27
23
8
13
15
20
26
23
20
σU
σV
σW
(km s−1 )
στ
Age
τ (109 yr)
8
7
5
12
0.05
20
22
30
40
40
67
48
10
17
16
21
34
29
29
6
13
15
21
34
25
25
23
31
37
50
63
77
62
0.3
1.4
3.0
5.2
7.2
9.0
5.0
Table 19.24 gives the eigenvalues for nine color ranges of the velocity dispersion tensor and, in the
last row, for the reddest stars.
Table 19.24. Eigenvalues of σ 2 for the nine color bins and all stars beyond Parenago’s discontinuity.a
Bin
(B − V )min,max
σ1b
σ1 /σ2b
σ1 /σ3b
cv
1
−0.238
0.139
14.40+0.49
−0.40
1.52+0.16
−0.14
2.62+0.91
−0.28
30.3+4.7
−5.3
2
0.139
0.309
20.23+0.50
−0.43
2.10+0.13
−0.28
2.50+0.81
−0.10
22.8+2.8
−3.0
3
0.309
0.412
22.40+0.56
−0.47
1.88+0.13
−0.20
2.39+0.65
−0.14
19.8+3.2
−3.4
4
0.412
0.472
26.33+0.80
−0.60
1.65+0.12
−0.15
2.15+0.60
−0.14
10.2+4.8
−5.1
5
0.472
0.525
30.45+0.96
−0.69
1.66+0.13
−0.15
2.27+0.76
−0.18
6.8+5.0
−5.3
6
0.525
0.582
33.02+1.08
−0.75
1.51+0.12
−0.12
2.18+0.63
−0.19
1.9+6.0
−6.0
7
0.582
0.641
37.73+1.37
−0.94
1.60+0.07
−0.18
1.77+0.47
−0.04
10.2+5.6
−6.0
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496 / 19
S TAR P OPULATIONS AND THE S OLAR N EIGHBORHOOD
Table 19.24. (Continued.)
Bin
(B − V )min,max
σ1b
σ1 /σ2b
σ1 /σ3b
cv
8
0.641
0.719
38.23+1.19
−0.85
1.59+0.08
−0.15
1.83+0.38
−0.06
7.6+5.2
−5.5
9
0.719
1.543
37.28+1.40
−0.93
1.43+0.12
−0.12
2.04+0.60
−0.16
13.1+6.7
−7.5
—
0.620
1.543
37.97+0.81
−0.64
1.52+0.08
−0.09
1.91+0.24
−0.09
9.8+3.9
−4.1
Notes
a Units are mag., km s−1 , and degrees for B − V , σ , and , respectively. The errors given correspond
v
i
to the 15.7 and 84.3 percentiles, i.e., 1σ error.
b σ , σ , σ are the roots of the largest, middle, and smallest eigenvalue of the velocity dispersion
1 2 3
tensor σ 2 .
c is the vertex deviation.
v
The diffusion of stellar orbits in our Galaxy is given in Table 19.25.
Table 19.25. Radial diffusion of stellar orbits.
19.11.5
Age τ (yr)
1 × 108
2 × 108
5 × 108
1 × 109
2 × 109
5 × 109
1010
R 2 1/2 (kpc)
±0.3
±0.4
±0.7
±0.9
±1.3
±2.1
±2.9
Local Vertical Velocity–Height Relation [31]
Table 19.26 gives the height variation of the velocity dispersion.
Table 19.26. Vertical velocity versus height.
Vδ at δ = 0 (km/s)
Vmax (pc)
0
8
16
22
27
32
37
41
45
48
52
59
68
83
0
100
200
300
400
500
600
700
800
900
1000
1200
1500
2000
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19.11 S OLAR M OTION AND K INEMATICS OF N EARBY S TARS / 497
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