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 The Nearby ...... 471 19.2 The Brightest Stars ...... 475 19.3 Stellar Populations ...... 478 19.4 Counts at High Latitudes ...... 480 19.5 Vertical Stellar Density Profile ...... 481 19.6 Field Stellar Function ...... 485 19.7 Luminosity Function ...... 485 19.8 Luminosity Class Distribution for Nearby Field Stars ...... 486 19.9 Density in the Solar Neighborhood ...... 487 19.10 Function ...... 488 19.11 Solar Motion and Kinematics of Nearby Stars ...... 493

19.1 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 = J2000.0. The first column gives the identifier in the Hipparcos

471 Sp.-V/AQuan/1999/10/11:10:50 Page 472

472 / 19 STAR POPULATIONS AND THE SOLAR NEIGHBORHOOD

Catalogue [1]; the last column gives the in milliarcsecs with the associated standard deviation error.

Table 19.1. Nearby stars.

HD α (2000.0) HIP number δ (2000.0) Other name Sp. type V magnitude Abs VB− V Parallax

70890 N/A 14 29 42.95 α Cen C M5 Ve 11.01 15.45 +1.81 772.33 ± 2.42 −62 40 46.1 71681 128621 14 39 35.08 α Cen B K1 V 1.35 5.70 +0.88 742.12 ± 1.40 −60 50 13.8 71683 128620 14 39 36.50 α Cen A G2 V −0.01 4.34 +0.71 742.12 ± 1.40 −60 50 02.3 87937 N/A 17 57 48.50 Barnard’s star M5 V 9.54 13.24 +1.57 549.01 ± 1.58 +04 41 36.2 54035 95735 11 03 20.19 Gl 411 M2 Ve 7.49 10.46 +1.50 392.40 ± 0.91 +35 58 11.6 32349 48915 06 45 08.92 α CMa A1 V −1.44 1.45 +0.01 379.21 ± 1.58 −16 41 58.0 92403 N/A 18 49 49.36 Gl 729 M4.5 Ve 10.37 13.00 +1.51 336.48 ± 1.82 −23 50 10.4 16537 22049 03 32 55.84  Eri K2 V 3.72 6.18 +0.88 310.75 ± 0.85 −09 27 29.7 114046 217987 23 05 52.04 Gl 887 M2 Ve 7.35 9.76 +1.48 303.90 ± 0.87 −35 51 11.1 57548 N/A 11 47 44.40 Ross 128 M4.5 V 11.12 13.50 +1.75 299.58 ± 2.20 +00 48 16.4 104214 201091 21 06 53.94 61 Cyg A K5 Ve 5.20 7.49 +1.07 287.13 ± 1.51 +38 44 57.9 37279 61421 07 39 18.12 α CMi F5 IVÐV 0.40 2.68 +0.43 285.93 ± 0.88 +05 13 30.0 104217 201092 21 06 55.26 61 Cyg B K7 Ve 6.05 8.33 +1.31 285.42 ± 0.72 +38 44 31.4 91772 173740 18 42 46.90 Gl 725B M5 V 9.70 11.97 +1.56 284.48 ± 5.01 +59 37 36.6 91768 173739 18 42 46.69 Gl 725A M4 V 8.94 11.18 +1.50 280.28 ± 2.57 +59 37 49.4 1475 1326 00 18 22.89 GX And M2 V 8.09 10.33 +1.56 280.27 ± 1.05 +44 01 22.6 108870 209100 22 03 21.66  Ind K5 Ve 4.69 6.89 +1.06 275.76 ± 0.69 −56 47 09.5 8102 10700 01 44 04.08 τ Cet G8 Vp 3.49 5.68 +0.73 274.17 ± 0.80 −15 56 14.9 5643 N/A 01 12 30.64 Gl 54.1 M5.5 Ve 12.10 14.25 +1.85 269.05 ± 7.57 −16 59 56.3 36208 N/A 07 27 24.50 Luyten’s star M3.5 9.84 11.94 +1.57 263.26 ± 1.43 +05 13 32.8 24186 33793 05 11 40.58 Kapteyn’s star M0 V 8.86 10.89 +1.55 255.26 ± 0.86 −45 01 06.3 105090 202560 21 17 15.27 AX Mic M0 Ve 6.69 8.71 +1.40 253.37 ± 1.13 −38 52 02.5 110893 239960 22 27 59.47 Kruger 60 M2 V 9.59 11.58 +1.61 249.52 ± 3.03 +57 41 45.1 30920 N/A 06 29 23.40 Ross 614 M4.5 Ve 11.12 13.05 +1.69 242.89 ± 2.64 −02 48 50.3 72511 N/A 14 49 34 N/A N/A 11.72 13.58 N/A 235.24 ± 22.43 −26 06 22 80824 N/A 16 30 18.06 Wolf 1061 M3.5 10.10 11.95 +1.58 234.51 ± 1.82 −12 39 45.3 439 225213 00 05 24.43 Gl 1 M4 V 8.56 10.36 +1.46 229.33 ± 1.08 −37 21 26.5 15689 N/A 03 22 05.50 N/A N/A 12.16 13.94 N/A 227.45 ± 61.79 −13 16 43.8 3829 N/A 00 49 09.90 Van Maanen 2 DG 12.37 14.15 +0.55 226.95 ± 5.35 +05 23 19.0 72509 N/A 14 49 31.76 Gl 563.2 M3 12.07 13.80 +1.52 221.80 ± 69.07 −26 06 42.0 86162 N/A 17 36 25.90 BD +68 946 M3.5 Vvar 9.15 10.81 +1.50 220.85 ± 0.92 +68 20 20.9 Sp.-V/AQuan/1999/10/11:10:50 Page 473

19.1 THE NEARBY STARS / 473

Table 19.1. (Continued.)

HD α (2000.0) HIP number δ (2000.0) Other name Sp. type V magnitude Abs VB− V Parallax

85523 N/A 17 28 39.95 Gl 674 M3 9.38 11.10 +1.55 220.43 ± 1.63 −46 53 42.7 114110 N/A 23 06 39 GJ 293 DC 12.24 13.92 −0.17 216.52 ± 18.28 −14 52 19 57367 N/A 11 45 42.92 Gl 440 DQ6 11.50 13.18 +0.20 216.40 ± 2.11 −64 50 29.5 113020 79210 22 53 16.73 Ross 780 M5 V 10.16 11.80 +1.60 212.69 ± 2.10 −14 15 49.3 54211 79211 11 05 28.58 Gl 412A M2 Ve 8.82 10.40 +1.54 206.94 ± 1.19 +43 31 36.4 49908 88230 10 11 22.14 Gl 380 K2 Ve 6.60 8.16 +1.33 205.22 ± 0.81 +49 27 15.3 82725 N/A 16 54 32.47 N/A N/A 11.72 13.26 N/A 203.01 ± 29.27 −62 24 12.0 85605 N/A 17 29 36.25 N/A N/A 11.39 12.92 +1.10 202.69 ± 39.48 +24 39 14.7 106440 204961 21 33 33.98 Gl 832 M1 V 8.66 10.19 +1.52 202.53 ± 1.33 −49 00 32.4 86214 N/A 17 37 03.66 Gl 682 M3.5 10.94 12.43 +1.66 198.32 ± 2.43 −44 19 09.2 19849 26965 04 15 16.32 ω 2 Eri K1 Ve 4.43 5.92 +0.82 198.24 ± 0.84 −07 39 10.3 112460 N/A 22 46 49.73 EV Lac M4.5 Ve 10.29 11.77 +1.54 198.07 ± 2.05 +44 20 02.4 88601 165341 18 05 27.29 70 Oph K0 Ve 4.03 5.50 +0.86 196.62 ± 1.38 +02 30 00.4 97649 187642 19 50 47.00 α Aql A7 IVÐV 0.76 2.20 +0.22 194.44 ± 0.94 +08 52 06.0 1242 N/A 00 15 28.11 L722-22 M4 11.49 12.90 +1.75 191.86 ± 17.24 −16 08 01.7 57544 N/A 11 47 41.38 Gl 445 M4 V 10.80 12.14 +1.57 185.48 ± 1.43 +78 41 28.2 67155 119850 13 45 43.78 Wolf 498 M4 Ve 8.46 9.79 +1.44 184.13 ± 1.27 +14 53 29.5 103039 N/A 20 52 33.02 N/A N/A 11.41 12.71 +1.65 182.15 ± 3.68 −16 58 29.1 21088 N/A 04 31 11.52 Gl 169.1A M4 10.82 12.11 +1.65 181.36 ± 3.67 +58 58 37.5 33226 265866 06 54 48.96 Wolf 294 M4 V 9.89 11.18 +1.57 181.32 ± 1.87 +33 16 05.4 53020 128620 10 50 52.06 Wolf 358 M5 V 11.64 12.89 +1.68 177.46 ± 23.00 +06 48 29.3 25878 36395 05 31 27.40 Wolf 1453 M1.5 V 7.97 9.19 +1.47 175.72 ± 1.20 −03 40 38.0 82817 152751 16 55 28.75 Wolf 630A M3 Ve 9.02 10.23 +1.55 174.23 ± 3.90 −08 20 10.8 96100 185144 19 32 21.59 σ Dra K0 V 4.67 5.87 +0.79 173.41 ± 0.46 +69 39 40.2 29295 42581 06 10 34.62 Gl 229 M1 Ve 8.15 9.34 +1.49 173.19 ± 1.12 −21 51 52.7 26857 N/A 05 42 09.27 Ross 47 M4 11.56 12.75 +1.62 172.78 ± 3.88 +12 29 21.6 86990 152751 17 46 34.23 Gl 693 M3.5 10.75 11.93 +1.66 172.08 ± 2.22 −57 19 08.6 94761 180617 19 16 55.26 Ross 652 M3.5 Ve 9.12 10.28 +1.46 170.26 ± 1.37 +05 10 08.1 73184 131977 14 57 28.00 Gl 570A K5 Ve 5.72 6.86 +1.02 169.32 ± 1.67 −21 24 55.7 37766 N/A 07 44 40.17 YZ CMi M4.5 Ve 11.19 12.32 +1.60 168.59 ± 2.67 +03 33 08.8 76074 155876 15 32 12.93 Gl 588 M3 9.31 10.44 +1.52 168.52 ± 1.42 −41 16 32.1 3821 4614 00 49 06.29 η Cas G3 V 3.46 4.59 +0.59 167.99 ± 0.62 +57 48 54.7 84478 156026 17 16 13.36 Gl 664 K5 Ve 6.33 7.45 +1.16 167.56 ± 1.06 −26 32 46.1 117473 156026 23 49 12.53 Gl 908 M2 Ve 8.98 10.10 +1.46 167.51 ± 1.49 +02 24 04.4 Sp.-V/AQuan/1999/10/11:10:50 Page 474

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Table 19.1. (Continued.)

HD α (2000.0) HIP number δ (2000.0) Other name Sp. type V magnitude Abs VB− V Parallax

84405 155885 17 15 20.98 36 Oph K1 Ve 4.33 5.44 +0.86 167.08 ± 1.07 −26 36 10.2 99461 191408 20 11 11.94 Gl 783A K3 V 5.32 6.41 +0.87 165.24 ± 0.90 −36 06 04.4 15510 20794 03 19 55.65 e Eri G8 V 4.26 5.35 +0.71 165.02 ± 0.55 −43 04 11.2 99240 190248 20 08 43.61 δ Pav G8 V 3.55 4.62 +0.75 163.73 ± 0.65 −66 10 55.4 71253 164058 14 34 16.81 Wolf 1481 M3 11.32 12.39 +1.64 163.51 ± 2.77 −12 31 10.4 86961 N/A 17 46 12.63 CD −32 13297 M2 V 10.49 11.53 +1.46 161.77 ± 11.29 −32 06 12.8 86963 N/A 17 46 14.41 CD −32 13298 M2 V 11.39 12.43 +1.44 161.77 ± 11.29 −32 06 08.3 45343 79210 09 14 22.79 BD +53 1320 M0 Ve 7.64 8.68 +1.41 161.59 ± 5.23 +52 41 11.8 99701 191849 20 13 53.40 Gl 784 M0 V 7.97 9.01 +1.11 161.17 ± 1.08 −45 09 50.5 116132 N/A 23 31 52.18 BD +19 5116 M0 Ve 10.05 11.07 +1.19 160.06 ± 2.81 +19 56 14.1 74995 N/A 15 19 26.82 Gl 581 M5 V 10.57 11.58 +1.60 159.52 ± 2.27 −07 43 20.2 120005 79211 09 14 24.70 Gl 338B M0 Ve 7.70 8.71 +1.42 159.48 ± 6.61 +52 41 11.0 84140 155876 17 12 07.89 Gl 661A M3 9.31 10.31 +1.49 158.17 ± 3.26 +45 39 57.5 34603 07 10 01.83 M4.5 Ve 11.65 12.63 +1.70 157.24 ± 3.32 +38 31 46.1 54298 N/A 11 06 30.65 N/A 11.69 12.65 N/A 155.28 ± 78.30 −53 16 05.5 82809 N/A 16 55 25.23 Wolfe 629 M4 11.73 12.67 +1.70 153.96 ± 4.04 −08 19 21.3 114622 219134 23 13 16.98 Gl 892 K3 V var 5.57 6.50 +1.00 153.24 ± 0.65 +57 10 06.1 80459 191408 16 25 24.62 Gl 645 M2 V 10.13 11.04 +1.59 151.93 ± 1.11 +54 18 14.8 53767 11 00 04.26 Gl 408 M3 10.03 10.92 +1.52 150.96 ± 1.59 +22 49 58.7 72659 131156 14 51 23.38 ξ Boo G8 Ve 4.54 5.41 +0.72 149.26 ± 0.76 +19 06 01.7 106106 N/A 21 29 36.81 Gl 829 M4 Ve 10.33 11.19 +1.62 148.29 ± 1.85 +17 38 35.8 114176 N/A 23 07 19 N/A N/A 12.28 13.13 N/A 147.95 ± 13.76 −32 16 05 113296 216899 22 56 34.81 BD+15 4733 M2 Ve 8.68 9.49 +1.51 145.27 ± 1.22 +16 33 12.4 84709 156384 17 18 57.18 Gl 667A K3 V 5.91 6.69 +1.08 143.45 ± 17.12 −34 59 23.3 103096 199305 20 53 19.79 BD +61 2068 M2 Ve 8.55 9.31 +1.48 141.95 ± 0.77 +62 09 15.8 12114 16160 02 36 04.89 BD +06 398 K3 V 5.69 6.50 +0.92 138.72 ± 1.04 +06 53 12.7 51317 N/A 10 28 55.55 BD +01 2447 M2.5 V 9.65 10.35 +1.51 138.29 ± 2.13 +00 50 27.6 83945 N/A 17 09 31.54 N/A M3 11.77 12.47 +1.70 137.84 ± 8.95 +43 40 52.9 3765 4628 00 47 01.46 BD +11 96 G8 II 5.74 6.38 +0.99 134.04 ± 0.86 +11 58 25.9 7981 10476 01 42 29.76 107 Psc K1 V 5.24 5.87 +0.84 133.91 ± 0.91 +20 16 06.6 2021 2151 00 25 45.07 β Hyi G2 IV 2.82 3.45 +0.62 133.78 ± 0.51 −77 15 15.3 73182 131976 14 57 26.54 BD −20 4123 M2 V 8.01 8.64 +1.01 133.63 ± 33.56 −21 24 41.5 12781 N/A 02 44 15.51 Gl 109 M3.5 Ve 10.55 11.16 +1.53 132.42 ± 2.48 +25 31 24.1 Sp.-V/AQuan/1999/10/11:10:50 Page 475

19.2 THE BRIGHTEST STARS / 475

Table 19.1. (Continued.)

HD α (2000.0) HIP number δ (2000.0) Other name Sp. type V magnitude Abs VB− V Parallax

5336 6582 01 08 16.39 µ Cas G5 Vp 5.17 5.78 +0.70 132.40 ± 0.60 +54 55 13.2 65859 N/A 13 29 59.79 BD +11 2576 M1 V 9.05 9.64 +1.49 131.12 ± 1.29 +10 22 37.8

19.2 THE BRIGHTEST STARS

Table 19.2 lists the 100 brightest stars in the sky in order of . 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. are from the Hipparcos Main Catalogue [1] and given in milliarcseconds with the associated standard deviation error.

Table 19.2. Brightest stars.

HD α (2000.0) Other Star name number δ (2000.0) name Sp. type V magnitude B − VV− I Parallax

Alpheratz 358 00 08 23.26 α And B9p 2.07 −0.04 −0.10 33.60 ± 0.73 +29 05 25.6 Caph 432 00 09 10.69 β Cas F2 IIIÐIV 2.28 +0.38 +0.40 59.89 ± 0.56 +59 08 59.2 CD −77 15 2151 00 25 45.01 β Hyi G2 IV 2.82 +0.62 +0.68 133.78 ± 0.51 −77 15 15.3 Ankaa 2261 00 26 17.05 α Phe K0 II I 2.40 +1.08 +1.11 42.14 ± 0.78 −42 18 21.5 Schedar 3712 00 40 30.44 α Cas K0 IIÐIIIvar 2.24 +1.17 +1.13 14.27 ± 0.57 +56 32 14.4 Diphda 4128 00 43 35.37 β Cet K0 III 2.04 +1.02 +1.00 34.04 ± 0.82 −17 59 11.8 Cih 5394 00 56 42.53 γ Cas B0 IV 2.15 −0.05 −0.02 5.32 ± 0.56 +60 43 00.3 Mirach 6860 01 09 43.92 β And M0 IIIvar 2.07 +1.58 +1.74 16.36 ± 0.76 +35 37 14.0 Achernar 10144 01 37 42.85 α Eri B3 Vp 0.45 −0.16 −0.17 22.68 ± 0.57 −57 14 12.3 Almach 12533 02 03 53.95 γ And K3 IIb 2.26 +1.37 +1.37 9.19 ± 0.73 +42 19 47.0 Hamal 12929 02 07 10.41 α Ari K2 I II 2.01 +1.15 +1.13 49.48 ± 0.99 +23 27 44.7 Polaris 8890 02 31 49.08 α UMi F7: IbÐIIv 1.97 +0.64 +0.70 7.5 6 ± 0.48 +89 15 50.8 Menkar 18884 03 02 16.77 α Cet M2 III 2.54 +1.63 +1.97 14.82 ± 0.83 +04 05 23.0 Algol 19356 03 08 10.3 β Per B8 V 2.09 −0.03 +0.02 35.14 ± 0.90 +40 57 20.3 Mirfak 20902 03 24 19.37 α Per F5 Ib 1.79 +0.48 +0.63 5.51 ± 0.66 +49 51 40.2 Aldeberan 29139 04 35 55.24 α Tau K5 III 0.87 +1.54 +1.61 50.09 ± 0.95 +16 30 33.5 34085 05 14 32.27 β Ori B8 Ia 0.18 −0.03 +0.03 4.22 ± 0.81 −08 12 05.9 Capella 34029 05 16 41.36 α Aur M1 III 0.08 +0.80 +0.83 77.29 ± 0.89 +45 59 52.8 35468 05 25 07.86 γ Ori B2 III +1.64 −0.22 −0.22 13.42 ± 0.98 +06 20 58.9 El Nath 35497 05 26 17.51 β Tau B7 III 1.65 −0.13 −0.09 24.89 ± 0.88 +28 36 28.6 36486 05 32 00.40 δ Ori O9.5 II 2.25 −0.18 −0.21 3.56 ± 0.83 −00 17 56.7 Arneb 36673 05 32 43.82 α Lep F0 Ib 2.58 +0.21 +0.32 2.54 ± 0.72 −17 49 20.3 37128 05 36 12.81  Ori B0 Ia 1.69 −0.18 −0.16 2.43 ± 0.91 −01 12 06.9 Sp.-V/AQuan/1999/10/11:10:50 Page 476

476 / 19 STAR POPULATIONS AND THE SOLAR NEIGHBORHOOD

Table 19.2. (Continued.)

HD α (2000.0) Other Star name number δ (2000.0) name Sp. type V magnitude B − VV− I Parallax

Alnitak 37742 05 40 45.53 ξ Ori O9.5 Ib 1.74 −0.20 −0.18 3.99 ± 0.79 −01 56 33.3 38771 05 47 45.39 κ Ori B0.5 Ivar 2.07 −0.17 −0.14 4.52 ± 0.77 −09 40 10.6 39801 05 55 10.31 α Ori M2 Ib 0.45 +1.50 +2.32 7.63 ± 1.64 +07 24 25.4 Menkalinan 40183 05 59 31.72 β Aur A2 V 1.90 +0.08 +0.05 39.72 ± 0.78 +44 56 50 .8 Mirzam 44743 06 22 41.99 β CMa B1 IIÐIII 1.98 −0.24 −0.24 6.53 ± 0.66 −17 57 21.3 Canopus 45348 06 23 57.11 α Car F0 Ib −0.62 +0.16 +0.23 10.43 ± 0.53 − 52 41 44.4 Alhena 47105 06 37 42.75 γ Gem A0 IV 1.93 +0.00 +0.04 31.12 ± 2.33 +16 23 57.3 A 48915 06 45 08.92 α CMa A1 V −1.44 +0.01 −0.02 379.21 ± 1.58 −16 41 58.0 Adhara 52089 06 58 37.55  CMa B2 II 1.50 −0.21 −0.20 7.57 ± 0.57 −28 58 19.5 Wezen 54605 07 08 23.48 δ CMa F8 Ia 1.83 +0.70 +0.67 1.82 ± 0.56 −26 23 35.5 Aludra 58350 07 24 05.70 η CMa B5 Ia 2.45 −0.08 +0.01 1.02 ± 0.57 −29 18 11.2 Castor 60178 07 34 35.86 α Gem A2 V 1.58 +0.03 +0.05 63.27 ± 1.23 +31 53 17.8 61421 07 39 18.12 α CMi F5 IVÐV 0.40 +0.43 +0.05 285.93 ± 0.88 +05 13 30.0 Pollux 62509 07 45 18.95 β Gem K0 IIIvar 1.16 +0.99 +0.97 96.74 ± 0.87 +28 01 34.3 Naos 66811 08 03 35.05 ζ Pup O5 IAf 2.21 −0.27 −0.22 2.33 ± 0.51 −40 00 11.3 CD −46 3847 68273 08 09 31.95 γ Vel WC8 1.75 −0.14 −0.14 3.88 ± 0.53 −47 20 11.7 Avoir 71130 08 22 30.84  Car K3 III 1.86 +1.20 +0.16 5.16 ± 0.49 −59 30 34.1 Suhail 78647 09 07 59.76 λ Vel K4 IbÐII 2.23 +1.67 +1.69 5.69 ± 0.53 −43 25 57.4 Miaplacidus 80007 09 13 11.98 β Car A2 IV 1.67 +0.07 +0.02 29.34 ± 0.47 −69 43 01.9 Scutulum 80404 09 17 05.41 τ Car A8 Ib 2.21 +0.19 +0.28 4.71 ± 0.46 −59 16 30.8 CPD −54 2219 81188 09 22 06.82 κ Vel B2 IV 2.47 −0.14 −0.17 6.05 ± 0.48 −55 00 38.4 Alphard 81797 09 27 35.24 α Hya K3 III 1.99 +1.44 +1.39 18.40 ± 0.78 −08 39 31.0 Regulus 87901 10 08 22.31 α Leo B7 V 1.36 −0.09 −0.10 42.09 ± 0.79 +11 58 01.9 Algieba 89484 10 19 58.35 γ Leo K0 III 2.01 +1.13 +1.17 25.96 ± 0.83 +19 50 29.4 Merak 95418 11 01 50.48 β UMa A1 V 2.34 +0.03 +0.02 41.07 ± 0.60 +56 22 56.7 Dubhe 95689 11 03 43.67 α UMa F7 V 1.81 +1.06 +1.03 26.38 ± 0.53 +61 45 03.7 Zosma 97603 11 14 06.50 δ Leo A4 V 2.56 +0.13 +0.12 56.52 ± 0.83 +20 31 25.4 Denebola 102647 11 49 03.58 β Leo A3 Vvar 2.14 +0.09 +0.10 90.16 ± 0.89 +14 34 19.4 Phe cda 103287 11 53 49.85 γ UMa A0 V SB 2.41 +0.04 +0.06 38.99 ± 0.68 +53 41 41.4 Gienah 106625 12 15 48.37 γ Crv B8 III 2.58 −0.11 −0.10 19.78 ± 0.81 −17 32 30.9 Alpha Crucis 108248 12 26 35.90 α Cru B0.5 IV 0.77 −0.24 −0.26 10.17 ± 0.67 −63 05 56.7 10890 3 12 31 09.96 γ Cru M4 III 1.59 +1.60 +2.37 37.09 ± 0.67 −57 06 47.6 Muhlifain 110304 12 41 31.04 γ Cen A1 IV 2.20 −0.02 −0.01 25.01 ± 1.01 −48 57 35.6 111123 12 47 43.26 β Cru B0.5 III 1.25 −0.24 −0.27 9.25 ± 0.61 −59 41 19.5 Sp.-V/AQuan/1999/10/11:10:50 Page 477

19.2 THE BRIGHTEST STARS / 477

Table 19.2. (Continued.)

HD α (2000.0) Other Star name number δ (2000.0) name Sp. type V magnitude B − VV− I Parallax

Alioth 112185 12 54 01.75  UMa A0p 1.76 −0.02 −0.04 40.30 ± 0.62 +55 57 35.4 116658 13 25 11.58 α Vir B1 V 0.98 −0.24 −0.25 12.44 ± 0.86 −11 09 40.8 Mizar 116656 13 23 55.54 ζ UMa A2 V 2.23 +0.06 +0.07 41.73 ± 0.61 +54 55 31.3 CPD −52 6655 118716 13 39 53.26  Cen B1 III 2.29 −0.17 −0.23 8.68 ± 0.77 −53 27 59.0 Alcaid 120315 13 47 32.44 η UMa B3 V 1.85 −0.10 −0.08 32.39 ± 0 .74 +49 18 47.8 CD −46 8949 121263 13 55 32.39 ζ Cen B2.5 IV 2.55 −0.18 −0.18 8.48 ± 0.74 −47 17 18.2 Agena 122451 14 03 49.40 β Cen B1 III 0.61 −0.23 −0.25 6.21 ± 0.56 −60 22 22.9 Menkent 123139 14 06 40.95 θ Cen K0 IIIb 2.06 +1.01 +1.01 53.52 ± 0.79 −36 22 11.8 Arcturus 124897 14 15 39.67 α Boo K2 II Ip −0.05 +1.24 +1.22 88.85 ± 0.74 +19 10 56.7 CD −41 8917 127972 14 35 30.42 η Cen B1 Vn 2.33 −0.16 −0.17 10 .57 ± 0.83 −42 09 26.2 GJ 559B 128621 14 39 35.08 α Cen B K1 V 1.35 +0.90 +0.88 742.12 ± 1.40 −60 50 13.8 Rigil Kent 128620 14 39 36.50 α Cen A G2 V −0.01 +0.71 +0.69 742.12 ± 1.40 −60 50 02.3 CD −46 9501 129056 14 41 55.76 α Lup B1.5 III 2.30 −0.15 −0.21 5.95 ± 0.76 −47 23 17.5 Izar 129989 14 44 59.21  Boo K0 IIÐIII 2.35 +0.97 +0.95 15.55 ± 0.78 +27 04 27.4 Kochab 131873 14 50 42.33 β UMi K4 IIIvar 2.07 +1.46 +1.46 25.79 ± 0.52 +74 09 19.8 Alphecca 139006 15 34 41.27 α CrB A0 V 2.22 +0.03 +0.05 43.65 ± 0.79 +26 42 52.9 Dzuba 143275 16 00 20.01 δ Sco B0.2 IV 2.29 −0.12 −0.09 8.12 ± 0.88 −22 37 18.2 Acrab 144217 16 05 26.27 β Sco B0.5 V 2.56 −0.06 −0.04 6.15 ± 1.12 −19 48 19.6 Antares 148478 16 29 24.46 α Sco M1 Ib 1.06 +1.87 +2.90 5.40 ± 1.68 −26 25 55.2 BD −10 4350 149757 16 37 09.54 ζ Oph O9.5 V 2.54 +0.04 +0.10 7.12 ± 0.71 −10 34 01.5 Atria 150798 16 48 39.89 α TrA K2 IIb 1.91 +1.45 +1.45 7.85 ± 0.63 −69 01 39. 8 CD −34 11285 151680 16 50 09.81  Sco K2 II Ib 2.29 +1.14 +1.10 49.85 ± 0.81 −34 17 35.6 Sabik 155125 17 10 22.69 η Oph A2.5 Va 2.43 +0.06 +0.06 38.77 ± 0.86 −15 43 29.7 Shaula 158926 17 33 36.52 λ Sco B1.5 IV 1.62 −0.23 −0.24 4.64 ± 0.90 −37 06 13.8 Ras-Alhague 159561 17 34 56.07 α Oph A5 III 2.08 +0.16 +0.17 69.84 ± 0.88 +12 33 36.1 CD −42 12312 159532 17 37 19.13 θ Sco F1 II 1.86 +0.41 +0.02 11.99 ± 0.84 −42 59 52.2 CD −38 12137 160578 17 42 29.27 κ Sco B1.5 III 2.39 −0.17 −0.22 7.03 ± 0.73 −39 01 47.9 Eltanin 164058 17 56 36.37 γ Dra K5 III 2.24 +1.52 +1.54 22.10 ± 0.46 +51 29 20.0 Kaus Australis 169022 18 24 10.32  Sgr B9.5 III 1.79 −0.03 +0.01 22.55 ± 1.02 −34 23 04.6 Vega 172167 18 36 56.34 α Lyr A0 Vvar 0.03 +0.00 −0.01 128.93 ± 0.55 +38 47 01.3 Nunki 175191 18 55 15.93 σ Sgr B2.5 V 2.05 −0.13 −0.13 14.54 ± 0.88 −26 17 48.2 Altair 187642 19 50 47.0 α Aql A7 IVÐV 0.76 +0.22 +0.27 194.44 ± 0.94 +08 52 06.0 Sadir 194093 20 22 13.70 γ Cyg F8 Ib 2.14 +0.67 +0.65 2.14 ± 0.51 +40 15 24.0 Peacock 193924 20 25 38.86 α Pav B2 IV 1.94 −0.12 −0.10 17.80 ± 0.70 −56 44 06.3 Sp.-V/AQuan/1999/10/11:10:50 Page 478

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Table 19.2. (Continued.)

HD α (2000.0) Other Star name number δ (2000.0) name Sp. type V magnitude B − VV− I Parallax

Deneb 197345 20 41 25.91 α Cyg A2 Ia 1.25 +0.09 +0.16 1.01 ± 0.57 +45 16 49.2 Gienar 197989 20 46 12.68  Cyg K0 III 2.48 +1.02 +1.00 45.26 ± 0.53 +33 58 12.9 Alderamin 203280 21 18 34.77 α Cep A7 IVÐV 2.45 +0.26 +0.26 66.84 ± 0.49 +62 35 08.1 Enif 206778 21 44 11.16  Peg K2 Ibvar 2.38 +1.52 +1.42 4.85 ± 0.84 +09 52 30.0 Al Na’ir 209952 22 08 13.99 α Gru B7 IV 1.73 −0.07 −0.05 32.16 ± 0.82 −46 57 39.5 CD −47 14308 214952 22 42.40.05 β Gru M5 III 2.07 +1.61 +2.60 19.17 ± 0.75 −46 53 04.5 Fomalhaut 216956 22 57 39.05 α PsA A3 V 1.17 +0.14 +0.16 130.08 ± 0.92 −29 37 20.1 Scheat 217906 23 03 46.46 β Peg M2 IIÐIIIvar 2.44 +1.66 +2.31 16.37 ± 0.72 +28 04 58.0 Markab 218045 23 04 45.65 α Peg B9.5 III 2.49 −0.03 +0.00 23.36 ± 0.76 +15 12 19.0

19.3 STELLAR POPULATIONS

The concept of stellar populations arose on observational grounds [2], and was rapidly extended as the underlying astrophysical processes were identified [3Ð5]. 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 and external 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, haloÐbulge and thick diskÐyoung 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 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 Page 479

19.3 STELLAR POPULATIONS / 479

Table 19.3. Classical (top) and current (lower) concepts of stellar populations

Population II Disk Population I Halo Pop II Intermediate Old Pop I Extreme Pop I Characteristic subdwarfs stars with galactic A stars gas, spiral −1 objects globular clusters Vz ≥ 30 km s nucleus Me dwarfs structure and RR Lyrae LPV’s, P < 250d RR Lyrae strong-line supergiants properties P > 0.d4 P < 0.d4 stars Cepheids weak-line stars Scale height (pc) 2000 500 300 100 60 central concentration strong strong strong little little τ/τu 1.0 1.0Ð0.8 0.8Ð0.25 0.25Ð0.05 0.05Ð0.00 −1 −1 −1 −1 −1 σW 75 km s 25 km s 17 km s 10 km s 8kms Z/Z 0.1 0.25 0.5 0.75 1.0 External Galaxies ← Ellipticals →←Bulges →←Spiral disks, Irr’s →

Extreme Pop II Intermediate Pop II Bulge/Pop II Pop I Extreme Pop I Characteristic “halo”“”“bulge”“old disk”“young disk” objects subdwarfs globular SMR stars intermediate young stars and globular clusters = “IR bulge” age disk spiral properties clusters with [Fe/H] > −1 planetary stars structure with [Fe/H] < −1 RR Lyrae, c-type nebulae Cepheids RR Lyrae LPV’s, P ∼ 250d = “optical S > 4 RHB stars bulge” BHB stars RR Lyrae S < 4 tri-axial (?) Vrot 30 170 60 200 220 σU :σV :σW 130:100:85 60:45:40 120:120:120 38:25:20 20:10:8 Z/Z 0.03 0.3 0.1Ð2 0.9 1 τ/τu 1.0Ð0.9 0.9Ð0.8 1.0Ð0.5 (?) 0.9Ð0.1 0.1Ð0.0 External Galaxies dE Sa →← SO → gE ← Sbcd, Irr’s →

Table 19.4. Astrophysical representation of stellar populations. −2 Halo −1 Thick disk [Fe/H] Old disk → 0 Bulge → Young disk +1 time → 0 Bulge Half 2 mass Halo radius 4 (kpc) 6 Thick disk Old disk Young disk time → Sp.-V/AQuan/1999/10/11:10:50 Page 480

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Table 19.4. (Continued.)

−2 Halo −1 Thick disk [Fe/H] Old disk 0 Young disk Bulge +1 log mass →

Bulge 100 Vertical Halo velocity 80 disp. Thick disk (km/s) 40 Old disk 0 Young disk [Fe/H] → 0 Halo Bulge Angular mom. per 103 Thick disk mass Old disk (km/s Young disk kpc) 2 × 103 [Fe/H] →

19.4 STAR COUNTS AT HIGH LATITUDES [6Ð12]

Counts of stars in selected color ranges in the V and photographic BJ 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.). VB− V ≤ 0.2 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 ≥ 1.9 Total

10.5 5 11.5 11 12.5 0.5 0.56832100.50.520 13.5 0.2 1 8 14822100.536 14.5 0.5 1 9 24 13 6 3 3 0.5 0 60 15.5 1 1 9 35 16 9 8 6 1 0 86 16.5 1 2 21 34 22 13 13 16 3 0 125 17.5 2 10 26 29 21 15 19 27 10 0 159 Sp.-V/AQuan/1999/10/11:10:50 Page 481

19.5 VERTICAL STELLAR DENSITY PROFILE / 481

Table 19.6. BJ magnitude star counts at the north galactic pole (stars per square degree per mag.).

BJ Blue Red Total 15.5 60 16.5 100 17.5 125 18.5 160 19.5 50 200 250 20.5 160 240 400 21.5 180 450 630

Table 19.7. V magnitude star counts at the south galactic pole (stars per square degree per mag.). VB− V ≤ 0.40.4 ≤ B − V ≤ 0.80.8 ≤ B − V ≤ 1.21.2 ≤ B − V ≤ 1.61.6 ≤ 1.6 Total

16Ð17 3 55 17 21 0 97 17Ð18 17 90 62 86 0 255 18Ð19 31 72 59 79 14 255 19Ð20 14 93 66 148 48 369 20Ð21 10 186 79 245 69 590 21Ð22 24 234 169 341 141 910

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 Apparent exponential range (pc) scale height (pc)

0  z  50 ∼ constant density 0  z  200 120 0  z  300 175 0  z  500 225 250  z  750 260

For distances between 300 and 4000 pc the density profile is describable by     ρ −z −z = 0.959 exp + 0.041 exp . ρ0 250 1000 Beyond ∼ 4 kpc, the density law is a galactocentric power law of index ∼−3, axis ratio c/a ∼ 0.75, 1/4 or a deprojected r 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. Sp.-V/AQuan/1999/10/11:10:50 Page 482

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Table 19.9. –scale height relation.

Absolute magnitude Scale height MV (pc) ≤+290 +3 150 +4 200 +5 250

19.5.1 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 .

, Table 19.10. Standard model of optical stellar galaxy.a b

Old disk Thick disk Bulge Halo / Radial density profile exponential exponential power law r1 4 or power law Vertical density profilec exponential exponential power law Radial scale length 3000 pc 3000 pc 500 pc 2700 pc Vertical scale length dwarfs = 300 pc 1000 pc 300 pc 2000 pc giants = 250 pc Stellar luminosity function local field metal-rich metal-rich mean globular globular globular Local stellar density tabulated 0.02 × disk (?) 0.002 × disk ColorÐmagnitude relation old metal-rich metal-rich metal-poor globular globular globular Mean −0.1 −0.6 −0.2 −1.6 Metallicity dispersion 0.3 0.3 0.4 0.5 Radial metallicity gradient −0.04 dex/kpc 0: dex/kpc — −0.02: dex/kpc Vertical metallicity gradient −0.3 dex/kpc 0: dex/kpc — −0.03: dex/kpc Velocity dispersions 38:25:20 km/s 60:45:40 km/s 120:120:120 km/s 130:100:85 km/s σU , σV , σW Mean rotation 200 km/s 170 km/s 60 km/s at R < 1 30 km/s kpc

Notes aSolar position (R,δ)= (8000, +20) pc. bExtinction: 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 MV relations given.

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.

Vb= 0 b = 5 b = 10 b = 20 b = 30 b = 60 b = 90 Sky AQ3a 12.0 1.751 1.752 1.743 1.665 1.544 1.234 1.160 1.556 1.76 13.0 2.275 2.267 2.218 2.085 1.935 1.603 1.524 1.994 2.17 14.0 2.708 2.694 2.618 2.450 2.279 1.925 1.838 2.372 2.56 Sp.-V/AQuan/1999/10/11:10:50 Page 483

19.5 VERTICAL STELLAR DENSITY PROFILE / 483

Table 19.11. (Continued.)

Vb= 0 b = 5 b = 10 b = 20 b = 30 b = 60 b = 90 Sky AQ3a

15.0 3.105 3.085 2.985 2.781 2.591 2.209 2.110 2.719 2.94 16.0 3.485 3.460 3.331 3.089 2.875 2.458 2.347 3.047 3.29 17.0 3.842 3.809 3.648 3.363 3.124 2.673 2.553 3.350 3.64 18.0 4.170 4.130 3.939 3.612 3.349 2.869 2.744 3.632 3.95 19.0 4.474 4.428 4.210 3.845 3.559 3.052 2.924 3.897 4.20 20.0 4.776 4.722 4.468 4.057 3.748 3.226 3.092 4.156 4.5 21.0 5.078 5.011 4.705 4.236 3.909 3.389 3.245 4.406 4.7 22.0 5.342 5.262 4.903 4.382 4.046 3.538 3.382 4.626 23.0 5.536 5.448 5.059 4.510 4.168 3.665 3.500 4.797 24.0 5.684 5.594 5.195 4.633 4.286 3.772 3.604 4.937 25.0 5.813 5.722 5.319 4.749 4.393 3.863 3.695 5.061

Note aFrom 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.

Ib= 0 b = 5 b = 10 b = 20 b = 30 b = 60 b = 90 Sky 12.0 2.466 2.434 2.279 2.011 1.799 1.450 1.374 2.001 13.0 2.922 2.877 2.671 2.355 2.138 1.816 1.728 2.396 14.0 3.316 3.262 3.023 2.678 2.461 2.149 2.045 2.753 15.0 3.650 3.594 3.344 2.991 2.772 2.445 2.326 3.075 16.0 3.951 3.897 3.653 3.301 3.069 2.702 2.575 3.376 17.0 4.243 4.191 3.955 3.594 3.341 2.926 2.799 3.663 18.0 4.548 4.494 4.247 3.861 3.584 3.133 3.005 3.947 19.0 4.868 4.807 4.530 4.103 3.804 3.327 3.191 4.230 20.0 5.191 5.120 4.802 4.326 4.005 3.503 3.353 4.510 21.0 5.479 5.398 5.039 4.515 4.173 3.649 3.488 4.761 22.0 5.710 5.623 5.234 4.673 4.313 3.770 3.604 4.967 23.0 5.909 5.816 5.400 4.806 4.430 3.874 3.706 5.145 24.0 6.092 5.991 5.546 4.916 4.528 3.970 3.797 5.308 25.0 6.258 6.150 5.669 5.002 4.606 4.055 3.875 5.453

19.5.2 Surface Brightness

The surface brightness of the sky, excluding and terrestrial sources, has been measured by Pioneer 10 in two bands (Table 19.13). 3950 Aû <λ<4850 A(û “blue”) and 5900 Aû <λ<6900 Aû (“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 ).

−9 −2 −1 −1 −1 S10(V ) = 1.16 × 10 erg cm s sr Aû blue band − − − − −1 = 1.07 × 10 9 erg cm 2 s 1 sr 1 Aû red band, −2 S10(V )(blue band) ≡ 0.265L,B pc −2 ≡ 28.49Bmag. arcsec . Sp.-V/AQuan/1999/10/11:10:50 Page 484

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Table 19.13. Pioneer 10 sky brightness measurements.

S10(V ) BlueÐred Region α (1950) δ lII bII Blue Red (mag.) ◦ ◦ ◦ NCP — +90 123 27 56 77 1.43 ± 0.08 ◦ ◦ ◦ NEP 18h 0m +67 96 30 66 82 1.32 ± 0.08 ◦ ◦ NGP 12h 50m +27 — 90 29 31 1.18 ± 0.15 ◦ ◦ ◦ SCP — −90 303 −27 74 94 1.34 ± 0.07 ◦ ◦ ◦ SEPa 6h 0m −67 277 −30 128 125 1.06 ± 0.06 ◦ ◦ SGP 0h 50m −27 — −90 26 36 1.41 ± 0.14

Note aThe 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: −2 µB = 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 . Color of poles: B − V = 0.76 ± 0.15. Face-on disk central surface brightness: −2 µ0 = 95 ± 30L,B pc − = 22.1 ± 0.3Bmag. arcsec 2. Integrated disk color: B − V = 0.84 ± 0.15. Integrated disk luminosity: 10 Ltot = (1.8 ± 0.3) × 10 L,B. Old disk color: B − V = 0.95 ± 0.15. Old disk luminosity: 10 Ltot = (1.1 ± 0.2) × 10 L,B. Integrated halo luminosity: 9 L = 2 × 10 L,B. Halo color: B − V = 0.8 ± 0.1. Sp.-V/AQuan/1999/10/11:10:50 Page 485

19.7 WHITE DWARF LUMINOSITY FUNCTION / 485

19.6 MAIN SEQUENCE FIELD STELLAR LUMINOSITY FUNCTION [15Ð22]

Table 19.14 gives the main sequence stellar luminosity function.

( ) −3 −1 Table 19.14. log MV stars pc MV . Mean Unresolved Single binary/triple Principal MV stars systems sequence BHB RR Lyrae −7 −7.98 7.98 −6 −7.60 −7.60 −5 −7.27 −7.27 −4 −6.72 −6.72 −3 −6.05 −6.05 −2 −5.43 −5.43 −5.61 −1 −4.80 −4.80 −4.77 0 −4.18 −4.18 −4.39 1 −3.60 −3.60 −4.19 −3.49 −3.49 2 −3.16 −3.16 −3.89 3 −2.89 −2.89 −3.59 4 −2.63 −2.63 −2.84 5 −2.49 −2.49 −2.49 6 −2.44 −2.44 −2.44 7 −2.52 −2.52 −2.24 8 −2.41 −2.42 −2.24 9 −2.32 −2.48 −2.14 10 −2.14 −2.26 −1.80 11 −1.99 −2.01 −1.80 12 −1.82 −1.95 −1.90 13 −1.9 −2.25 −2.00 14 −2.0 −2.53 −2.10 15 −2.0 −2.69 −2.20 16 −2.1 −2.67 17 −2.1 −2.67 18 −2.2 −2.67

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 massÐluminosity 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. Sp.-V/AQuan/1999/10/11:10:50 Page 486

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Table 19.15. The V magnitude and bolometric white dwarf luminosity function.

log  log  −3 −1 −3 −1 MV (stars pc MV ) Mbol (stars pc Mbol ) 9.5 −5.91 (+0.18, −0.31) 5.50 −5.91 (+0.18, −0.31) 10.0 −5.00 (+0.14, −0.21) 6.88 −5.00 (+0.14, −0.21) 10.5 −4.67 (+0.13, −0.18) 7.84 −4.67 (+0.13. −0.18) 11.0 −4.02 (+0.12, −0.16) 8.92 −4.02 (+0.12, −0.16) 11.5 −3.92 (+0.11, −0.15) 10.12 −3.92 (+0.11, −0.15) 12.0 −3.82 (+0.11, −0.16) 11.24 −3.82 (+0.11, −0.16) 12.5 −3.54 (+0.11, −0.16) 11.98 −3.54 (+0.11, −0.16) 13.0 −3.22 (+0.20, −0.39) 12.55 −3.22 (+0.20, −0.39) 13.5 −3.06 (+0.18, −0.30) 13.25 −3.18 (+0.20, −0.38) 14.0 −2.93 (+0.17, −0.29) 13.75 −2.95 (+0.18, −0.30) 14.5 −3.03 (+0.26, −0.76) 14.25 −3.00 (+0.25, −0.60) 15.0 −2.98 (+0.18, −0.30) 14.75 −2.78 (+0.13, −0.19) 15.5 −3.09 (+0.15, −0.23) 15.25 −3.35 (+0.19, −0.35) 16.0 −4.14 (+0.25, −0.64) 15.75 −4.47 (+0.30, −∞) 16.5 −4.50 (+0.30, −∞) 17.0 ?

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.

MV Disk Thick disk and halo −6 0.40 0 −5 0.42 0 −4 0.43 0 −3 0.44 0 −2 0.45 0 −1 0.47 0 0 0.51 0 1 0.56 0 2 0.66 0 3 0.82 0 4 1.00 1

19.8.1 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 0 B A F G K M % Stars 1 10 22 19 14 31 3 Sp.-V/AQuan/1999/10/11:10:50 Page 487

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19.9 MASS DENSITY IN THE SOLAR NEIGHBORHOOD [25Ð32]

Observed volume mass density − Interstellar matter (ISM) 0.04 ± 0.02 M pc 3 Main Sequence Stars: − 0.08 ≤ M/M < 1.0 0.036 M pc 3 − 1.0 ≤ M/M < 100 0.014 M pc 3 − Halo stars 0.0001 M pc 3 Evolved stars: − White dwarfs 0.005 M pc 3 − Dark extended halo, local density 0.01 M pc 3 − Total 0.10 ± 0.03 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 8 M pc 2 − Ionized ISM 2 M pc 2 − Molecular ISM 3 M pc 2 − ISM total 13 ± 3 M pc 2 Stars: − Disk main sequence 30 M pc 2 − Disk white dwarfs 3 M pc 2 − Thick disk 2 M pc 2 − Halo subdwarfs < 1 M pc 2 − Stellar total 35 ± 5 M pc 2 − Observed total 48 ± 8 M pc 2 Extended dark halo − |z| < 1.1 kpc 23 M pc 2 − Total 71 ± 6 M pc 2 −3 Kdwarfs(z  160 pc) ρ0 = 0.10 ± 0.03M pc .

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) ( ≤ . = ± M −2 tot z 1 1 kpc) 71 6  pc , = ± M −2 disk 48 9  pc , = M −2 dark halo 23  pc , − Unidentified disk dark matter = 0 ± 12M pc 2. Sp.-V/AQuan/1999/10/11:10:50 Page 488

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Limit on scale height/local volume density of dark disk matter with scale height H (pc):   −1 H −3 ρ ,  0.017 M pc 0 dark 300 pc

−3 Local luminosity density = 0.10L,V pc . 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:

−2 = 12.0L,V pc .

Mass density in column, stars, and ISM:

−2 = 48M pc .

Mass-to-light ratio of identified mass:

= 4.0M/L|,V = 9.5M/L|,B.

Extended halo mass, |z| < 1.1 kpc:

−2 = 23M pc .

Identified matter in a column:

−2 = 48M pc = 100 g/sq. meter (gsm) − = 0.010gcm 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) = . M−2.2, . < M ≤ . , 0 019 0 50 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. Sp.-V/AQuan/1999/10/11:10:50 Page 489

19.10 STELLAR MASS FUNCTION / 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:

−1 −3 Total = 0.087 stars M pc , −3 0.08 ≤ M ≤ 1M = 0.13 stars pc , −3 1 ≤ M ≤ 60M = 0.011 stars pc .

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 massÐluminosity 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 0.0700 8.77 0.595 4.09 1.119 0.0 3.467 16.96 0.0854 8.56 0.610 4.02 1.135 −1.0 5.248 16.13 0.101 8.35 0.626 3.95 1.150 −2.0 7.943 15.45 0.116 8.14 0.641 3.88 1.166 −3.0 12.023 14.87 0.132 7.92 0.656 3.82 1.181 −4.0 18.197 14.36 0.147 7.71 0.672 3.75 1.196 −5.0 26.915 13.93 0.163 7.51 0.687 3.69 1.212 −6.0 41.687 13.54 0.178 7.31 0.703 3.63 1.227 −7.0 63.1 13.21 0.193 7.11 0.718 3.57 1.243 12.92 0.209 6.93 0.734 3.51 1.258 12.67 0.224 6.75 0.749 3.46 1.274 12.47 0.240 6.59 0.764 3.40 1.289 12.29 0.255 6.43 0.780 3.35 1.304 12.13 0.271 6.28 0.795 3.30 1.320 11.99 0.286 6.14 0.811 3.25 1.335 11.86 0.301 6.01 0.826 3.20 1.351 11.73 0.317 5.88 0.842 3.15 1.366 11.60 0.332 5.75 0.857 3.10 1.382 11.47 0.348 5.63 0.872 3.05 1.397 11.34 0.363 5.52 0.888 3.01 1.412 11.21 0.379 5.40 0.903 2.96 1.428 11.08 0.394 5.29 0.919 2.92 1.443 10.93 0.409 5.19 0.934 2.87 1.459 10.79 0.425 5.08 0.950 2.83 1.474 10.64 0.440 4.98 0.965 2.79 1.490 10.48 0.456 4.88 0.980 2.75 1.505 10.31 0.471 4.78 0.996 2.71 1.521 10.14 0.487 4.68 1.011 2.67 1.536 Sp.-V/AQuan/1999/10/11:10:50 Page 490

490 / 19 STAR POPULATIONS AND THE SOLAR NEIGHBORHOOD

Table 19.18. (Continued.)

MV M/M MV M/M MV M/M MV M/M 9.96 0.502 4.58 1.027 2.63 1.551 9.78 0.517 4.49 1.042 2.59 1.567 9.59 0.533 4.41 1.058 2.56 1.582 9.39 0.548 4.32 1.073 2.52 1.598 9.19 0.564 4.24 1.088 2.00 1.862 8.99 0.579 4.17 1.104 1.00 2.512

Note aThree 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. and of the stellar mass function.

Mass (M) Mass in I-band K-band center of Mass that Luminosity luminosity luminosity increment increment increment (mag.) (mag.) (mag.) M/M M mass/nMV + 2.5 log nMI + 2.5 log nMK + 2.5logn − 0.015 0.01 10.4 × 10 3 ——— − 0.055 0.01 9.7 × 10 3 ——— − 0.095 0.01 8.2 × 10 3 19.1 15.0 12.0 − 0.155 0.01 7.1 × 10 3 17.50 14.11 11.50 − 0.205 0.01 6.5 × 10 3 16.72 13.71 11.30 − 0.255 0.01 6.1 × 10 3 16.34 13.52 11.24 − 0.305 0.01 5.8 × 10 3 16.13 13.45 11.25 − 0.355 0.01 5.5 × 10 3 15.93 13.38 11.25 − 0.405 0.01 5.3 × 10 3 15.68 13.26 11.21 − 0.455 0.01 5.1 × 10 3 15.35 13.08 11.11 − 0.505 0.01 4.9 × 10 3 14.95 12.84 10.98 − 0.525 0.05 2.4 × 10 2 13.05 11.02 9.20 − 0.625 0.05 1.9 × 10 2 12.13 10.50 8.92 − 0.725 0.05 1.6 × 10 2 11.17 9.93 8.58 − 0.825 0.05 1.4 × 10 2 10.46 9.53 8.36 − 0.925 0.05 1.2 × 10 2 9.97 9.27 8.24 − 1.05 0.10 2.0 × 10 2 8.75 8.28 7.40 − 1.25 0.10 1.5 × 10 2 8.35 8.16 7.40 − 1.55 0.10 1.0 × 10 2 8.07 8.15 7.59 − 1.75 0.10 8.4 × 10 3 8.00 8.21 7.72 − 2.05 0.10 6.4 × 10 3 7.94 8.30 7.91 − 2.25 0.10 5.5 × 10 3 7.90 8.35 8.02 − 2.55 0.10 4.4 × 10 3 7.85 8.43 8.17 Sp.-V/AQuan/1999/10/11:10:50 Page 491

19.10 STELLAR MASS FUNCTION / 491

Table 19.19. (Continued.)

Mass (M) Mass in I-band K-band center of Mass that Luminosity luminosity luminosity increment increment increment (mag.) (mag.) (mag.) M/M M mass/nMV + 2.5 log nMI + 2.5 log nMK + 2.5logn − 2.75 0.10 3.9 × 10 3 7.83 8.48 8.26 − 3.05 0.10 3.3 × 10 3 7.80 8.55 8.40 − 3.25 0.10 2.9 × 10 3 7.79 8.60 8.48 − 3.55 0.10 2.5 × 10 3 7.81 8.69 8.61 − 3.75 0.10 2.3 × 10 3 7.83 8.76 8.70 − 4.05 0.10 2.0 × 10 3 7.87 8.85 8.83 − 5.05 0.10 1.4 × 10 3 7.99 9.13 9.20 − 6.05 0.10 1.0 × 10 3 8.09 9.36 9.51 − 7.05 0.10 7.9 × 10 4 8.17 9.55 9.76 − 8.05 0.10 6.3 × 10 4 8.24 9.71 9.98 − 9.05 0.10 5.1 × 10 4 8.30 9.86 10.18 − 9.95 0.10 4.4 × 10 4 8.35 9.97 10.34 − 10.5 1.0 4.0 × 10 3 5.87 7.54 7.92 − 15.5 1.0 2.1 × 10 3 6.08 8.03 8.58 − 20.5 1.0 1.3 × 10 3 6.21 8.36 9.04 − 25.5 1.0 8.8 × 10 4 6.28 8.60 9.38 − 30.5 1.0 6.5 × 10 4 6.38 8.83 9.69 − 35.5 1.0 5.0 × 10 4 6.48 9.04 9.95 − 40.5 1.0 4.0 × 10 4 6.57 9.21 10.18 − 45.5 1.0 3.3 × 10 4 6.64 9.36 10.38 − 50.5 1.0 2.8 × 10 4 6.70 9.50 10.56 − 55.5 1.0 2.4 × 10 4 6.75 9.61 10.72 − 60.5 1.0 2.0 × 10 4 6.79 9.71 10.86 − 70.5 1.0 1.5 × 10 4 6.9 9.9 11.1 − 80.5 1.0 1.3 × 10 4 6.9 10.1 11.3 − 90.5 1.0 1.0 × 10 4 7.0 10.2 11.5 − 99.5 1.0 8.7 × 10 5 7.0 10.3 11.7

These data in a similar format are plotted in Figure 19.1. Sp.-V/AQuan/1999/10/11:10:50 Page 492

492 / 19 STAR POPULATIONS AND THE SOLAR NEIGHBORHOOD (m) (M ) (m) (M ) 10 10 log log -1012 -1012 8 8

10 12 14 16 18 10 12 14 16 18

10 K 10 V

m = 0.05M = m in (n) log + M m = 0.05M = m in (n) log + M δ δ luminosity relations. Ð Mass Figure 19.1. (m) (M ) (m) (M ) 10 10 log log -1012 -1012 8

-1 -2 -3 -4 -5 -6

10 12 14 16 18

10 I 10

m = 0.05M = m in (n) log + M m = 0.05M = m in ) (M (mass/n) log δ δ Sp.-V/AQuan/1999/10/11:10:50 Page 493

19.11 SOLAR MOTION AND KINEMATICS OF NEARBY STARS / 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 driftÐvelocity 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 v Apex of motion − Solar motion (km s 1) αδ ◦ ◦ Standard 10.0 5.2 7.2 13 270 (1900) +30 ◦ ◦ Basic 9 11 6 15.4 267. 4 (1950) +25 ◦ ◦ Peculiar 9 12 7 16.6 267. 0 (1950) +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. − − Solar motion (km s 1) Velocity dispersion (km s 1) −1 Spectral type U V W σU σV σW σu (km s )ψ(deg) Supergiants gO-gB5 +9.0 +13.4 +3.7 12 11 9 19 +36 gF-gM +7.9 +11.7 +6.5 13 9 7 17 +18 Giants gA +13.4 +11.6 +10.3 22 13 9 27 +27 gF +19.7 +18.5 9.5 28 15 9 33 +14 gG +7.2 +11.1 +6.9 26 18 15 35 +12 gK0 +10.6 +18.6 +6.5 31 21 16 41 +21 gK3 +9.0 +17.6 +6.4 31 21 17 41 +14 gM +4.5 +18.3 +6.2 31 23 16 42 +7 Main sequence B0 +9.6 +14.5 +6.7 10 9 6 15 −50 dA0 +7.3 +13.7 +7.2 15 9 9 20 +15 dA5 +8.5 +7.8 +7.4 20 9 9 24 +19 dF0 +11.2 +10.8 +7.3 24 13 10 29 +21 dF5 +10.1 +12.3 +6.2 27 17 17 36 +13 dG0 +14.5 +21.1 +6.4 26 18 20 37 +2 Sp.-V/AQuan/1999/10/11:10:50 Page 494

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Table 19.21. (Continued.) − − Solar motion (km s 1) Velocity dispersion (km s 1) −1 Spectral type U V W σU σV σW σu (km s )ψ(deg) dG5 +8.1 +22.1 +4.3 32 17 15 39 +14 dK0 +10.8 +14.9 +7.4 28 16 11 34 +3 dK5 +9.5 +22.4 +5.8 35 20 16 43 +11 dM0 +6.1 +14.6 +6.9 32 21 19 43 +8 dM5 +9.8 +19.3 +8.6 31 23 16 42 −7

19.11.2 Solar Motion and Velocity Dispersion for Groups of Selected Objects [36Ð42]

Table 19.22 gives the solar motion for groups of selected objects.

Table 19.22. Solar motion relative to groups of selected objects.a − − Solar motion (km s 1) Velocity dispersion (km s 1) Objects U V W σU σV σW σu

Interstellar H I +12 +15 +9 ( 5.7 )b 10 Interstellar Ca II +11 +14 +8( 6 )b 10 Classical Cepheids +11 +12 +10 8 7 5 12 Carbon stars +10 +12 +530201439 White dwarfs +10 +15 +742221850 RR Lyraes c-type 0 120 0 100 70 50 ab, s < 5 0 120 0 130 120 80 s ≥ 5 0 180 0 160 110 90 all ab’s 0 155 0 160 120 90 Miras, by period P P < 148d 33 60 40 — 81 145 < P < 200d 111 90 145 60 180 200 < P < 250d 61 — 70 — 101 250 < P < 300d 33 60 60 — 88 300 < P < 350d 32 45 40 35 69 350 < P < 400d 23 45 25 23 58 P < 410d 15 ——— 50

Notes aMissing values have very large errors. bThe 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   τ σ 3 (τ) = σ 3 + 3 α δ − , V V,τ=0 V 2Tδ exp 1 2 Tδ Sp.-V/AQuan/1999/10/11:10:50 Page 495

19.11 SOLAR MOTION AND KINEMATICS OF NEARBY STARS / 495

with

σV,τ=0, the velocity dispersion at age zero, = 10 km/s, αV , a parameter describing the rotation curve, ≈ 2.95, 9 Tδ, a timescale, = 5 × 10 yr, δ , , = . × −6 ( / )3 , 2 a diffusion coefficient 3 7 10  km s yr τ δ3 (τ) = + . × 5 − . V 1000 5 4575 10 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 Integrated over z Age σ (0) σ (0) σ (0) σU σV σW στ τ U V − W − Group of stars (km s 1) (km s 1) (109 yr) Classical Cepheids 8 7 5 12 0.05 McCormick K + M dwarfs HK +8/+3 18 10 8 20 10 6 23 0.3 HK +2 211613221713311.4 HK +1 291715301615373.0 HK0 382320402121505.2 HK −1 402726403434637.2 HK −2/−5 662723672925779.0 All McCormick stars 39 23 20 48 29 25 62 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

( − ) σ b σ /σ b σ /σ b c Bin B V min,max 1 1 2 1 3 v

− . . +0.49 . +0.16 . +0.91 . +4.7 1 0 238 0.139 14 40−0.40 1 52−0.14 2 62−0.28 30 3−5.3 . +0.50 . +0.13 . +0.81 . +2.8 2 0.139 0.309 20 23−0.43 2 10−0.28 2 50−0.10 22 8−3.0 . +0.56 . +0.13 . +0.65 . +3.2 3 0.309 0.412 22 40−0.47 1 88−0.20 2 39−0.14 19 8−3.4 . +0.80 . +0.12 . +0.60 . +4.8 4 0.412 0.472 26 33−0.60 1 65−0.15 2 15−0.14 10 2−5.1 . +0.96 . +0.13 . +0.76 . +5.0 5 0.472 0.525 30 45−0.69 1 66−0.15 2 27−0.18 6 8−5.3 . +1.08 . +0.12 . +0.63 . +6.0 6 0.525 0.582 33 02−0.75 1 51−0.12 2 18−0.19 1 9−6.0 . +1.37 . +0.07 . +0.47 . +5.6 7 0.582 0.641 37 73−0.94 1 60−0.18 1 77−0.04 10 2−6.0 Sp.-V/AQuan/1999/10/11:10:50 Page 496

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Table 19.24. (Continued.)

( − ) σ b σ /σ b σ /σ b c Bin B V min,max 1 1 2 1 3 v

. +1.19 . +0.08 . +0.38 . +5.2 8 0.641 0.719 38 23−0.85 1 59−0.15 1 83−0.06 7 6−5.5 . +1.40 . +0.12 . +0.60 . +6.7 9 0.719 1.543 37 28−0.93 1 43−0.12 2 04−0.16 13 1−7.5 . +0.81 . +0.08 . +0.24 . +3.9 — 0.620 1.543 37 97−0.64 1 52−0.09 1 91−0.09 9 8−4.1

Notes a −1 Units are mag., km s , and degrees for B − V , σi , and v, respectively. The errors given correspond to the 15.7 and 84.3 percentiles, i.e., 1σ error. b σ1, σ2, σ3 are the roots of the largest, middle, and smallest eigenvalue of the velocity dispersion tensor σ 2. cv is the vertex deviation.

The diffusion of stellar in our Galaxy is given in Table 19.25.

Table 19.25. Radial diffusion of stellar orbits. Age τ (yr) 1 × 108 2 × 108 5 × 108 1 × 109 2 × 109 5 × 109 1010 / R2 1 2 (kpc) ±0.3 ±0.4 ±0.7 ±0.9 ±1.3 ±2.1 ±2.9

19.11.5 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) 00 8 100 16 200 22 300 27 400 32 500 37 600 41 700 45 800 48 900 52 1000 59 1200 68 1500 83 2000 Sp.-V/AQuan/1999/10/11:10:50 Page 497

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