The astrophysical behavior of open clusters along the Milky Way Galaxy

NRIAG Journal of Astronomy and Geophysics (2014) 3, 88–100

National Research Institute of Astronomy and Geophysics

NRIAG Journal of Astronomy and Geophysics www.elsevier.com/locate/nrjag

The astrophysical behavior of open clusters along the Milky Way Galaxy A.L. Tadross

*

National Research Institute of Astronomy & Geophysics, NRIAG, Elmarsad St., 11421 Helwan, Cairo, Egypt Received 3 March 2014; revised 25 May 2014; accepted 1 June 2014 Available online 19 July 2014

KEYWORDS Galaxy: open clusters and associations; Astrometry; Stars; Astronomical databases: catalogs

Abstract The main aim of this paper is to study the astrophysical behaviour of open clusters’ properties along the Milky Way Galaxy. Near-IR JHKS (2MASS) photometry has been used for getting a homogeneous Catalog of 263 open clusters’ parameters, which are randomly selected and studied by the author through the last five years; most of them were studied for the first time. The correlations between the astrophysical parameters of these clusters have been achieved by morphological way and compared with the most recent works. ª 2014 Production and hosting by Elsevier B.V. on behalf of National Research Institute of Astronomy and Geophysics.

1. Introduction Open star clusters are very important objects in solving problems of star formation, stellar evolution, and improving our knowledge about the distance scale and the kinematic properties of the Milky Way Galaxy. This kind of study requires a large set of homogeneous data on the positions and ages of open star clusters, which are estimated in a precision way from their Colour-Magnitude Diagrams (CMDs). However, it is useful to re-investigate the properties and structures of the Milky Way Galaxy using the most recent Near–IR JHKS photometric data from the 2-Micron All Sky Survey ð2MASSÞ Point Source * Tel.: +20 2 25560645/25560046, mobile: +20 122 4095523; fax: +20 2 25548020. E-mail address: [email protected]. Peer review under responsibility of National Research Institute of Astronomy and Geophysics.

Production and hosting by Elsevier

Catalogue of Skrutskie (2006). In this context, we used a sample of 263 open star clusters (most of them are studied for the first time) that have been analysed by the author, in a series of papers; Tadross (2008–2012); see Tables 1 and 2. Our aim is to repeat the work we have done 12 years ago, Tadross (2001, 2002), to study such relations using NIR observations instead of UBV. This paper is organized as follows. In Section 2, a historical review of the present study is obtained. In Section 3, data analysis of the clusters under investigation is presented. The limiting and core radii are given in Section 4. The main photometric parameters are obtained in Section 5. Ages and locations, distribution are presented in Section 6. Reddening distribution is presented in Section 7. The diameters and ages’ relations are given in Sections 8 and 9, respectively. Sections 10 and 11 describe the spiral arms and warp of the Galaxy respectively. The conclusions are obtained in Section 12. 2. Historical review Recently, Bukowiecki (2011) determined new coordinates of the centres, angular sizes and radial density profiles for 849

2090-9977 ª 2014 Production and hosting by Elsevier B.V. on behalf of National Research Institute of Astronomy and Geophysics. http://dx.doi.org/10.1016/j.nrjag.2014.06.001

Cluster

NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC

Rlim:

Rc

Age

EBV

R

Rgc

X

Y

Z

h

m

s



0

00

0

0

Gyr

mag

pc

kpc

pc

pc

pc

00 00 01 01 02 04 03 04 05 04 05 05 05 05 05 05 05 05 05 05 06 06 06 06 06 06 06 06 06 06 06 06 07 07 07 07 07 07 07 07

27 51 43 58 32 00 57 13 03 58 10 20 21 44 39 43 44 42 46 55 11 12 23 21 27 29 34 32 38 41 58 59 06 07 03 10 13 13 20 40

25 24 21 37 30 18 51 11 32 35 43 12 25 01 17 12 00 42 43 18 04 09 44 11 28 24 35 48 03 41 47 27 59 47 03 48 31 05 46 09

71 35 55 60 44 12 76 70 49 68 16 39 35 55 17 20 08 34 08 59 51 01 04 44 12 16 26 05 01 11 10 13 27 05 67 08 10 24 07 71

23 49 50 09 35 00 47 28 29 50 31 21 44 47 50 08 41 00 46 54 40 03 40 45 35 41 18 02 28 54 17 41 15 43 24 35 29 02 33 39

00 54 11 18 36 54 42 18 30 40 18 00 24 36 48 00 30 34 54 36 36 54 36 30 36 00 16 00 24 18 42 54 42 12 42 36 12 18 00 18

11.0 3.2 3.0 4.0 5.0 3.8 3.6 13.0 8.0 3.0 9.0 4.0 10.0 3.0 6.0 8.0 5.0 9.0 6.0 12.0 5.0 7.0 3.5 6.5 7.0 14.0 1.5 2.0 10.0 6.0 3.8 10.0 7.0 3.5 5.0 9.0 5.0 3.0 6.5 14.0

0.60 0.29 0.90 0.26 0.64 0.68 0.50 0.10 0.80 0.25 0.46 0.08 0.14 0.32 0.69 0.38 0.36 0.96 0.80 0.38 0.44 0.78 0.30 0.40 0.44 0.84 0.16 0.29 0.55 0.60 0.18 0.21 0.04 0.21 0.33 0.55 0.49 0.90 0.50 0.45

0:90:04 2:50:10 1.6±0.11 0.5±0.02 1.0±0.04 1.6±0.11 2.0±0.08 3.0±0.12 0.6±0.02 0.5±0.02 1.0±0.04 0.16±0.12 2.0±0.05 1.5±0.06 1.6±0.11 0.55±0.02 1.2±0.05 2.1±0.08 1.3±0.05 1.65±0.12 1.5±0.06 0.8±0.03 0.8±0.03 3.0±0.12 0.01±0.00 0.8±0.03 1.0±0.04 0.6±0.02 0.01±0.00 0.3±0.01 0.33±0.01 0.05±0.00 1.7±0.12 0.55±0.02 1.8±0.07 0.75±0.03 0.24±0.01 0.12±0.00 0.2±0.01 3.0±0.12

0:460:10 0.06±0.02 0.34±0.05 0.95±0.20 0.10±0.05 0.04±0.02 0.06±0.01 0.11±0.05 0.57±0.10 0.06±0.02 0.32±0.05 0.97±0.20 0.03±0.02 0.23±0.05 0.06±0.02 0.60±0.10 0.32±0.05 0.03±0.01 0.32±0.05 0.06±0.02 0.23±0.05 0.39±0.05 0.40±0.08 0.06±0.01 1.00±0.25 0.51±0.10 0.23±0.05 0.48±0.10 1.25±0.20 0.48±0.10 0.16±0.05 0.65±0.05 0.06±0.02 0.48±0.05 0.13±0.05 0.61±0.10 0.92±0.25 0.32±0.15 0.31±0.05 0.03±0.00

115053 1068±50 1372±63 1618±75 1455±67 1020±47 775±36 1055±49 1437±66 3080±140 960±44 1545±71 860±40 1100±51 1120±52 1418±65 920±42 542±25 1525±70 974±45 1445±67 1869±86 2023±93 1170±54 2415±111 1617±75 1740±80 1795±83 1985±90 2160±100 2245±103 1335±62 1285±59 1800±83 1070±48 1628±75 1882±87 1750±81 1919±88 1133±52

9.14 9.12 9.44 9.64 9.68 9.44 8.25 8.31 9.85 8.52 9.46 10.02 8.96 9.52 9.37 9.91 9.38 8.79 9.97 8.58 9.89 10.19 10.24 8.92 10.81 10.07 10.23 10.02 10.23 10.54 10.58 9.48 9.77 9.95 8.42 9.76 9.93 9.57 10.00 9.44

585 517 881 1065 1097 680 227 197 1332 437 928 1513 364 981 767 1401 863 246 1430 19 1328 1641 1660 322 2284 1555 1707 1456 1667

975 172 798 486 1041 151 1217 46 883 367 297 700 587 452 805 653 526 121 2477 1777 99 224 310 34 624 467 426 255 681 450 178 125 273 164 409 256 445 285 842 490 427 377 853 268 1118 292 1020 475 785 23 434 79 226 250 1031 201 1071 126 781 123 928 246 958 104 210 337 1154 32 969 432 1106 10 1325 2 1455 191 1307 101 585 557 (continued on next

a

110 272 657 743 956 1498 1520 1557 1724 1785 1807 1857 1891 2013 2017 2026 2039 2061 2063 2132 2165 2189 2219 2220 2224 2234 2248 2250 2260 2265 2312 2318 2331 2338 2348 2349 2351 2352 2364 2408

d

2030 924 1222 1381 139 1195 1336 953 1401 794

Ref.

6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 page)

Astrophysical behavior of open clusters

Table 1 The astrophysical main parameters for the studied clusters, derived by the author. Columns display, respectively, cluster name, equatorial positions, angular limiting radius, core radius, age, reddening, distance from the sun R , distance from the Galactic centre Rgc , the projected distances on the Galactic plane from the sun X ; Y ; Z, and the reference for each cluster.

89

(continued) a

2455 2459 2587 2609 2666 2678 2932 2995 3231 3446 3520 3909 4230 5155 5269 5299 5381 5800 5925 5998 6334 6357 6360 6374 6421 6437 6507 6525 6573 6588 6595 6605 6625 6645 6647 6659 6698 6724 6735 6737 6743 6773 6775 6795

Rlim:

Rc

00

0

0

06 24 30 36 12 18 36 48 55 54 24 06 06 30 54 54 12 06 42 18 12 06 18 00 36 00 00 24 06 30 54 42 42 00 56 42 42 42 30 59 36 54 24 54

4.0 2.7 2.0 2.5 5.5 6.5 10.5 3.5 3.5 7.5 1.5 8.0 5.0 8.5 1.5 16.5 5.5 6.0 12.0 4.5 15.5 2.5 2.5 1.8 4.0 7.5 6.6 6.5 0.9 2.5 2.0 8.5 7.7 7.4 6.5 7.0 5.5 3.0 6.0 4.4 3.5 4.3 1.2 4.0

0.24 0.04 0.11 0.06 0.30 0.60 0.07 0.70 0.47 0.97 0.24 0.99 0.07 0.08 0.02 0.29 0.67 0.14 0.12 0.65 0.99 0.20 0.74 0.15 0.12 0.31 0.45 0.88 0.15 0.13 0.27 0.46 0.22 0.79 0.75 0.11 0.40 0.13 0.03 0.41 0.08 0.12 0.07 0.78

d

h

m

s



0

07 07 08 08 08 08 09 09 10 10 11 11 12 13 13 13 14 15 15 15 17 17 17 17 17 17 17 18 18 18 18 18 18 18 18 18 18 18 19 19 19 19 19 19

49 52 23 29 49 50 35 44 26 52 07 49 17 29 44 50 00 01 27 49 20 24 24 32 45 48 59 02 13 20 17 18 22 32 32 33 48 56 00 02 01 15 16 26

01 02 25 32 47 02 28 04 58 12 08 49 20 35 44 26 41 47 26 34 49 43 27 18 44 24 50 06 41 33 04 21 50 37 50 59 04 46 37 20 20 03 48 22

21 09 29 61 44 11 46 54 66 45 18 48 55 63 62 59 59 51 54 28 36 34 29 32 33 35 17 11 22 63 19 14 11 16 17 23 25 10 00 18 29 04 00 03

18 33 30 06 42 20 48 46 48 08 01 15 06 25 54 56 35 55 31 35 06 12 52 36 41 21 27 01 07 48 51 56 57 53 13 35 52 25 28 32 16 52 55 30

Age

EBV

R

Rgc

X

Y

Z

Gyr

mag

pc

kpc

pc

pc

pc

0.18±0.01 1.6±0.11 0.1±0.00 0.8±0.03 3.2±0.13 2.3±0.09 0.5±0.02 0.05±0.00 1.4±0.06 1.0±0.04 3.2±0.13 2.0±0.08 1.7±0.12 1.5±0.18 0.16±0.11 2.0±0.08 1.6±0.11 0.9±0.04 0.25±0.01 2.2±0.09 0.5±0.02 0.4±0.02 0.02±0.00 1.3±0.05 0.17±0.01 0.2±0.01 0.40±0.02 2.0±0.08 0.01±0.00 1.6±0.11 0.45±0.02 0.6±0.02 0.50±0.03 0.40±0.03 1.60±0.05 4.0±0.16 1.9±0.07 0.9±0.03 0.5±0.02 0.50±0.02 1.4±0.05 0.1±0.00 0.9±0.03 0.95±0.04

0.54±0.10 0.03±0.02 0.23±0.10 0.23±0.10 0.03±0.01 0.03±0.01 0.55±0.10 1.94±0.30 0.02±0.00 0.16±0.05 0.03±0.00 0.13±0.05 0.23±0.10 0.06±0.02 0.52±0.10 0.19±0.05 0.06±0.02 0.62±0.10 0.58±0.10 0.16±0.05 1.06±0.25 1.35±0.30 1.11±0.20 0.48±0.05 1.26±0.20 0.71±0.05 0.85±0.09 0.14±0.03 2.48±0.20 0.10±0.03 0.94±0.10 0.52±0.10 1.21±0.13 0.36±0.07 0.54±0.10 0.10±0.03 0.32±0.05 1.00±0.10 0.87±0.15 0.76±0.11 0.19±0.05 1.16±0.20 0.48±0.05 0.45±0.05

2650±122 1300±60 1740±80 1320±61 860±40 900±41 1525±70 380±17 715±33 1485±68 1245±57 1100±50 1445±67 1070±49 1410±65 1111±50 1170±54 2146±99 1040±48 981±45 1025±47 1205±55 1337±62 900±41 1505±69 943±43 1230±55 1436±66 460±21 960±44 1640±76 889±40 1335±60 1245±55 2200±100 1155±53 1150±53 1105±51 1466±68 2120±95 1111±51 2160±100 1185±55 1320±61

10.14 9.64 9.26 8.46 9.36 9.24 8.59 8.46 9.07 8.32 8.57 8.14 7.92 7.9 7.69 7.83 7.77 6.92 7.68 7.56 7.49 7.3 7.17 7.6 7.0 7.56 7.3 7.46 8.05 7.68 6.90 7.65 7.25 7.31 6.4 7.85 7.37 7.73 7.34 6.51 8.01 6.98 7.58 7.54

1389 1060 609 138 664 621 47 53 401 298 13 409 673 647 886 717 776 1692 845 886 1013 1196 1333 897 1500 936 1203 1097 454 783 1607 855 1262 1195 2119 682 1115 809 1209 1988 539 1653 947 1004

2254 640 1624 1280 47 452 1521 376 314 1417 978 989 1265 852 1096 847 874 1301 606 257 158 143 76 73 107 91 246 838 72 437 325 244 435 338 577 888 182 750 828 624 948 1386 705 845

107 397 136 291 544 469 103 8 502 329 771 254 187 16 16 40 43 222 31 332 8 19 73 7 63 69 65 393 17 342 49 5 19 82 137 282 215 69 47 392 211 113 108 141

Ref.

6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 1 6 6 6 6 6 1 1 1 6 6 6 6 1 6 6 6 6

A.L. Tadross

NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC

90

Table 1 Cluster

6815 6832 6837 6839 6840 6843 6846 6847 6856 6858 6859 6873 6895 6904 6938 6950 7005 7011 7023 7024 7037 7050 7055 7071 7084 7093 7127 7129 7134 7175 7193 7352 7394 7429 7686 7708 7795 7801 7826 7833 1 6 26 37 43 45

19 19 19 19 19 19 19 19 19 20 20 20 20 20 20 20 21 21 21 21 21 21 21 21 21 21 21 21 21 21 22 22 22 22 23 23 23 00 00 00 00 01 06 07 19 19

40 48 53 54 55 56 56 56 59 02 03 07 16 21 34 41 01 01 01 06 10 15 19 26 32 34 43 42 48 58 03 39 50 56 30 35 58 00 05 06 09 51 50 20 15 19

44 15 08 33 18 06 28 37 17 56 49 13 29 48 42 04 57 49 35 09 54 12 30 39 33 21 41 59 55 46 03 43 23 00 07 01 37 21 17 31 36 11 18 24 36 12

26 59 11 17 12 12 32 30 56 11 00 21 50 25 22 16 12 47 68 41 33 36 57 47 17 45 54 66 12 54 10 57 52 59 49 72 60 50 20 27 60 61 05 01 11 15

45 25 41 56 07 09 20 12 07 15 26 06 13 44 12 37 52 21 10 29 45 10 34 55 30 57 37 06 58 49 48 23 08 58 08 50 02 44 41 38 28 03 45 06 13 43

30 18 54 18 36 48 54 48 48 30 36 06 48 24 54 06 50 12 12 18 48 24 12 12 30 54 48 48 24 06 06 42 06 24 00 00 06 30 30 30 30 40 00 00 00 00

15.0 12.0 2.3 3.0 3.0 2.5 2.4 10.0 1.6 5.0 5.0 7.5 8.0 4.0 3.6 7.5 2.0 2.2 7.2 2.5 3.0 3.5 2.5 4.0 8.0 6.5 2.5 3.5 1.5 16.0 6.5 4.5 4.5 7.0 8.0 12.0 10.5 4.0 10.0 1.3 2.5 3.0 2.6 3.5 4.5 3.5

0.10 0.11 0.94 0.90 0.04 0.26 0.12 0.74 0.08 0.59 0.07 0.90 0.85 0.69 0.29 0.41 0.22 0.14 0.33 0.23 0.01 0.45 0.08 0.15 0.90 0.04 0.15 0.21 0.10 0.18 0.39 0.03 0.20 0.06 0.80 0.90 0.19 0.98 0.80 0.10 0.14 0.15 0.13 0.69 0.57 0.14

0.15±0.01 3.0±0.12 1.0±0.04 1.4±0.05 1.3±0.04 1.3±0.04 0.55±0.02 0.5±0.02 1.8±0.06 2.5±0.10 3.0±0.12 0.88±0.04 1.0±0.04 1.0±0.04 1.3±0.04 1.8±0.05 2.5±0.10 0.4±0.01 0.12±0.00 0.5±0.02 2.1±0.08 2.0±0.08 0.8±0.03 0.3±0.01 1.5±0.06 0.9±0.04 0.4±0.02 0.12±0.01 3.3±0.13 0.25±0.01 4.5±0.18 0.05±0.00 0.6±0.02 0.04±0.00 2.0±0.08 2.0±0.08 0.45±0.02 1.7±0.12 2.2±0.09 2.0±0.08 0.4±0.03 0.1±0.00 0.6±0.03 0.9±0.04 0.4±0.03 0.6 ±0.03

1.10±0.20 0.10±0.02 0.25±0.02 0.29±0.05 0.25±0.05 0.30±0.05 0.68±0.05 0.58±0.05 0.16±0.02 0.13±0.02 0.19±0.05 0.35±0.05 0.35±0.05 0.39±0.05 0.13±0.05 0.06±0.02 0.03±0.01 1.08±0.10 1.10±0.10 1.10±0.10 0.16±0.05 0.16±0.05 1.10±0.10 1.14±0.20 0.10±0.05 0.61±0.05 0.90±0.05 0.97±0.05 0.06±0.02 0.87±0.05 0.03±0.00 1.10±0.20 0.35±0.05 1.16±0.10 0.20±0.05 0.42±0.05 1.00±0.10 0.17±0.05 0.03±0.01 0.06±0.02 0.78±0.06 0.78±0.05 0.54±0.05 0.12±0.02 1.52±0.14 0.82±0.05

2024±93 1750±81 943±43 1410±65 1970±90 1945±90 1445±67 1894±87 1704±79 1310±60 1335±62 1250±58 1141±53 1355±62 1250±58 1070±49 1033±48 1236±57 560±26 1760±81 1485±68 1179±54 1275±59 1684±78 765±35 1785±82 1445±67 1070±49 1065±49 1930±89 1080±50 2550±117 1310±60 1190±55 1534±71 1607±74 2105±97 1275±60 620±29 1410±65 2420±110 2300±105 2720±120 4555±210 1355±60 2300±105

7.76 8.74 7.93 7.8 7.42 7.44 8.09 7.95 8.66 7.75 7.56 7.96 8.5 8.05 8.05 8.04 7.69 8.55 8.65 8.51 8.35 8.41 8.76 8.71 8.27 8.72 8.82 8.84 7.74 9.03 8.2 9.52 8.92 8.96 9.13 9.35 9.62 9.11 8.23 9.10 9.9 10.1 11.0 12.4 7.6 7.2

945 59 594 783 1223 1203 525 743 9 805 957 613 81 545 521 499 689 40 132 175 276 171 165 42 239 32 199 280 558 326 304 698 332 387 502 726 935 523 62 416 1128 1481 2407 3605 947 1477

1788 1678 721 1166 1518 1501 1345 1742 1657 1007 856 1081 1126 1232 1112 904 497 1235 527 1747 1437 1152 1258 1682 655 1780 1431 1016 502 1902 839 2452 1259 1125 1416 1401 1885 1136 117 1090 2139 1759 1262 2740 969 1763 (continued

72 6 493 6 131 6 127 6 283 6 284 6 48 6 26 6 398 6 234 6 364 6 134 6 164 6 149 6 233 6 281 6 588 6 13 6 137 6 119 6 252 6 180 6 124 6 59 6 315 6 135 6 29 6 184 6 755 6 3 6 608 6 47 6 147 6 6 6 307 6 301 6 79 6 250 6 606 6 792 6 84 2 38 2 112 2 470 2 4 2 46 2 on next page)

Astrophysical behavior of open clusters

NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC Berkeley Berkeley Berkeley Berkeley Berkeley Berkeley

91

92

Table 1

(continued)

Cluster

47 49 50 51 61 63 72 76 84 89 90 91 95 97 100 101 102 103 2 3 5 12 13 18 23 25 28 52 54 55 57 58 59 60 68 72 73 74 80 84 85 1 2 3

Rlim:

Rc

Age

EBV

R

Rgc

X

Y

Z

00

0

0

Gyr

mag

pc

kpc

pc

pc

pc

06 48 00 06 00 00 00 00 18 00 00 12 00 00 48 30 00 00 12 00 00 52 44 18 14 41 34 18 01 12 17 17 53 44 23 27 55 37 48 49 11 30 00 00

2.0 2.4 3.5 1.5 3.5 3.6 3.5 4.5 1.1 2.5 2.5 1.7 2.4 2.0 2.2 2.2 3.3 2.5 2.5 1.0 3.5 1.4 1.2 4.0 0.9 0.8 0.75 1.2 0.8 1.1 2.2 0.25 1.0 1.6 2.2 2.0 1.2 1.1 1.7 2.2 1.5 2.5 5.8 2.4

0.03 0.17 0.12 0.13 0.19 0.35 0.08 0.96 0.06 0.08 0.22 0.13 0.29 0.10 0.29 0.23 0.28 0.36 0.08 0.03 0.08 0.17 0.08 0.36 0.15 0.10 0.09 0.06 0.11 0.07 0.16 0.01 0.04 0.12 0.18 0.23 0.09 0.05 0.16 0.19 0.11 0.12 0.08 0.14

0.16 ±0.01 0.16 ±0.01 0.25 ±0.01 0.15 ±0.02 0.8 ±0.05 0.5 ±0.02 0.6 ±0.02 0.8 ±0.04 0.12 ±0.01 0.85 ±0.05 0.1 ±0.01 0.5 ±0.02 0.15 ±0.02 0.02 ±0.00 0.16 ±0.01 0.7 ±0.05 0.6 ±0.03 0.5 ±0.02 0.10±0.00 1.60±0.11 0.16±0.02 0.16±0.02 0.40±0.01 0.10±0.00 0.10±0.01 0.05±0.00 0.40±0.01 0.13±0.01 0.25±0.02 0.40±0.02 0.16±0.02 0.16±0.02 0.10±0.00 0.80±0.03 0.20±0.03 0.50±0.02 0.40±0.02 1.00±0.04 0.70±0.03 0.60±0.02 0.30±0.01 0.005±0.00 0.10±0.01 0.10±0.01

1.06±0.10 1.57±0.30 0.97±0.07 1.66±0.14 1.09±0.11 0.90±0.09 0.79±0.07 0.73±0.05 0.76±0.05 1.03±0.10 1.15±0.10 1.00±0.09 1.21±0.12 0.75±0.05 1.21±0.11 1.11±0.10 0.69±0.05 1.00±0.11 1.10 ±0.10 0.38±0.08 2.10±0.40 0.97±0.05 1.13±0.11 1.29±0.12 1.35±0.12 1.32 ±0.11 2.26±0.42 2.45±0.44 0.94±0.04 1.13±0.11 1.06±0.09 1.35±0.12 0.84±0.11 0.84±0.11 2.19±0.40 0.55±0.08 0.97±0.05 0.87±0.05 1.29±0.10 0.61±0.07 1.00 ±0.10 1.23±0.11 0.74±0.12 1.42±0.14

1420±65 2035±110 2100±100 3200±145 3335±150 3305±150 3810±175 2505±115 2025±95 3005±135 2430±70 2400±110 1900±85 1800±85 3355±155 2500±115 2600±120 2100±95 3065±140 1870±85 615±30 1775±80 1380±65 3250±150 1740±80 1220±55 550±25 705±30 1715±80 1260±60 1295±60 1515±70 780±35 1960±90 710±30 1055±50 1695±80 1760±80 1355±60 1075±50 1525±70 2530±115 1775±80 1410±65

7.7 8.1 8.1 8.1 10.7 11.0 12.3 10.4 8.1 8.7 8.6 8.8 9.2 9.2 10.3 9.8 9.8 9.6 5.6 7.3 8.2 10.3 7.7 11.7 9.2 7.3 8.4 8.3 8.0 9.1 8.3 8.3 8.4 10.5 8.2 8.3 8.2 8.2 8.7 8.7 9.1 9.9 9.6 9.4

863 662 633 981 1794 2231 3783 1764 661 357 216 2.7 507 516 1345 1036 1013 872 2934 1324 273 1753 902 3197 601 1169 165 268 612 559 328 295 144 1953 270 271 458 462 69 117 497 1177 939 794

1127 1922 2002 3046 2800 2434 419 1770 1912 2973 2415 2400 1830 1724 3070 2272 2384 1908 887 1299 551 271 1044 584 1633 348 524 652 1602 1129 1253 1484 766 6.6 567 1019 1632 1698 1352 1068 1440 2239 1504 1165

1.4 91 31 16 252 144 171 87 45 253 160 5.5 40 12 144 115 219 91 1.5 240 17 74 24 1.9 0.44 10 18 10.5 15.5 15 11 69.5 0.05 162 3.1 39 37 18 66 21 76 42 84 1.4

d

h

m

s



0

19 19 20 20 00 02 05 07 20 20 20 21 22 22 23 23 23 23 18 19 19 06 19 05 23 18 20 19 20 23 20 20 20 06 20 20 20 20 21 21 07 00 00 01

28 59 10 11 48 19 50 06 04 24 35 10 28 39 25 32 38 45 21 39 46 14 25 18 05 22 06 58 03 53 23 20 23 04 00 12 13 17 11 35 58 07 43 03

36 31 24 54 30 36 18 40 43 36 18 52 18 30 58 47 42 12 19 00 05 16 15 36 59 40 32 08 08 09 58 48 50 10 36 19 47 57 50 32 21 38 42 06

17 34 34 34 67 63 22 11 33 46 46 48 59 59 63 64 56 59 14 06 27 22 13 37 60 14 35 30 31 62 36 41 40 31 30 37 36 36 52 53 34 61 60 62

22 38 58 24 12 43 12 44 54 03 50 32 08 01 46 12 38 18 17 46 50 29 56 37 15 43 34 53 58 47 36 12 08 29 35 53 44 45 22 30 46 28 09 47

Ref.

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4

A.L. Tadross

Berkeley Berkeley Berkeley Berkeley Berkeley Berkeley Berkeley Berkeley Berkeley Berkeley Berkeley Berkeley Berkeley Berkeley Berkeley Berkeley Berkeley Berkeley Kronberger Kronberger Kronberger Kronberger Kronberger Kronberger Kronberger Kronberger Kronberger Kronberger Kronberger Kronberger Kronberger Kronberger Kronberger Kronberger Kronberger Kronberger Kronberger Kronberger Kronberger Kronberger Kronberger Czernik Czernik Czernik

a

4 5 6 7 10 11 12 14 15 16 17 25 26 30 37 38 39 42 44 45 1 2 3 4 5 6 7 8 9 10 11 13 15 16 24 135 137 138 142 168 169 171 9 10 11 19

01 01 02 02 02 02 02 03 03 03 03 06 06 07 17 18 19 22 23 23 02 05 05 05 16 16 17 17 18 20 20 07 07 07 07 17 18 17 18 17 17 18 20 20 20 05

35 55 02 02 33 36 39 16 23 30 52 13 30 31 53 49 07 39 33 56 47 23 33 35 27 45 10 26 08 05 51 08 19 23 31 58 00 59 32 52 59 32 25 26 26 23

24 06 00 24 54 35 12 54 12 48 24 06 48 18 17 42 44 48 30 18 30 4 42 54 24 24 36 12 48 48 00 03 33 10 54 12 16 56 11 46 22 11 42 18 30 42

61 61 62 62 60 59 54 58 52 52 61 06 04 09 27 04 04 59 61 64 17 11 26 25 38 38 15 24 31 40 35 25 19 19 12 11 25 24 12 28 24 16 41 40 41 08

26 20 50 15 10 38 55 36 15 39 57 59 13 58 22 1 56 20 54 57 33 16 28 29 57 04 21 32 11 32 32 57 52 38 28 45 39 13 40 13 26 46 02 56 07 27 11

00 00 00 00 00 00 00 00 00 00 00 00 00 00 0 00 00 54 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 39 57 47 00 01 59 00 00 00 00

2.6 1.5 2.6 2.5 2.2 3.0 3.0 2.0 2.4 5.0 3.6 5.0 2.7 3.6 1.8 5.0 2.5 3.5 4.0 2.5 7.0 5.0 4.5 12.0 15.0 4.0 3.0 8.0 12.0 2.5 3.0 4.5 5.5 3.5 5.0 3.0 2.8 3.0 3.3 2.6 2.6 5.7 3.0 1.8 2.5 12.0

0.77 0.15 0.66 0.31 0.06 0.26 0.85 0.03 0.21 0.55 0.39 0.60 0.08 0.32 0.10 0.11 0.04 0.46 0.08 0.19 0.16 0.38 0.19 0.26 0.55 0.53 0.88 0.90 0.30 0.07 0.40 0.07 0.32 0.31 0.54 0.50 0.25 0.21 0.03 0.80 0.14 0.26 0.72 0.32 0.27 0.40

0.10±0.01 0.70±0.04 0.25±0.06 0.10±0.01 0.20±0.02 0.35±0.03 0.40±0.02 0.25±0.07 0.02±0.00 0.20±0.03 0.40±0.04 0.13±0.02 0.17±0.02 0.13±0.01 0.60±0.03 0.01±0.00 0.01±0.00 0.01±0.00 0.16±0.04 0.02±0.00 5.00±0.25 0.80±0.03 0.40±0.02 0.10±0.00 2.0±0.09 5.0±0.26 2.0±0.11 3.0±0.12 2.3±0.10 1.0±0.05 2.0±0.11 1.00±0.05 0.50±0.03 0.16±0.02 0.06±0.00 0.50±0.02 0.80±0.06 2.00±0.11 0.40±0.04 2.00±0.12 1.00±0.05 3.20±0.15 0.02±0.00 0.25±0.05 0.40±0.03 0.16±0.05

1.06±0.10 1.23±0.10 1.00±0.10 1.19±0.11 1.71±0.13 1.00±0.10 0.45±0.07 1.71±0.13 1.00±0.10 1.29±0.10 0.87±0.05 0.58±0.07 0.45 ±0.06 0.35 ±0.04 1.03 ±0.10 2.03±0.36 2.90±0.45 1.74±0.12 1.48±0.10 1.45±0.11 0.10 ±0.03 0.65 ±0.11 0.77 ±0.13 1.10 ±0.18 0.02 ±0.00 0.03 ±0.00 0.13 ±0.02 0.06 ±0.00 0.06 ±0.00 0.55 ±0.09 0.42 ±0.05 0.26 ±0.05 0.65 ±0.05 0.71 ±0.07 0.35 ±0.05 1.10 ±0.05 0.67 ±0.05 0.18 ±0.05 0.91 ±0.05 1.06 ±0.11 0.66 ±0.05 0.12 ±0.03 0.80 ±0.05 0.80 ±0.05 0.83 ±0.06 0.55 ±0.02

1630±75 2205±100 2530±115 2235±100 1575±70 1210±55 2090±95 2175±100 1155±55 2580±120 2120±95 1980±90 1200±55 2275±105 1730±80 1910±90 1340±60 2585±120 3450±160 2530±115 960±45 1220±55 2530±115 1220±55 900±40 820±35 1140±50 2330±100 2330±100 1670±75 2545±115 1300±60 1845±85 2160±100 1983±90 1850±85 1450±65 930±40 1735±80 820±35 1390±60 1140±50 866±40 950±44 1127±52 1320±60

9.6 10.1 10.3 10.1 9.7 9.4 10.2 10.3 9.5 10.7 10.3 10.4 9.5 10.2 6.77 7.1 7.5 9.6 10.4 9.9 9.4 9.7 11.0 9.7 8.1 8.1 7.6 7.1 7.6 8.3 8.4 9.3 9.7 9.9 9.9 6.74 7.06 7.57 6.89 7.68 7.12 7.41 8.4 8.4 8.4 9.8

1007 1432 1656 1469 1120 868 1550 1688 945 2132 1673 1824 984 1566 1728 1521 1046 761 1398 1150 710 1159 2525 1217 316 297 802 1392 1091 384 522 685 1095 1276 1300 1764 1445 926 1631 820 1384 1092 152 190 204 1229

1281 28 4 1677 23 4 1912 47 4 1684 20 4 1107 6 4 842 12 4 1392 173 4 1371 35 4 659 80 4 1447 134 4 1281 228 4 748 181 4 673 136 4 1642 165 4 67 19 1 1152 88 4 836 38 4 2470 52 4 3154 27 4 2251 102 4 278 584 4 251 286 4 30 v156 4 30 73 4 567 624 4 549 531 4 589 555 4 1494 1123 4 1752 845 4 1620 135 4 2480 232 4 1090 185 9 1482 93 8 1742 78 9 1492 103 9 520 201 1 123 23 1 86 9 1 590 41 1 18 16 1 125 13 1 323 62 1 852 35 5 931 19 5 1108 37 5 332 349 5 (continued on next page)

Astrophysical behavior of open clusters

Czernik Czernik Czernik Czernik Czernik Czernik Czernik Czernik Czernik Czernik Czernik Czernik Czernik Czernik Czernik Czernik Czernik Czernik Czernik Czernik Dol-Dzim Dol-Dzim Dol-Dzim Dol-Dzim Dol-Dzim Dol-Dzim Dol-Dzim Dol-Dzim Dol-Dzim Dol-Dzim Dol-Dzim Ruprecht Ruprecht Ruprecht Ruprecht Ruprecht Ruprecht Ruprecht Ruprecht Ruprecht Ruprecht Ruprecht Dolidze Dolidze Dolidze Dolidze

93

(continued) a

21 26 27 37 39 41 2 3 4 6 7 8 2 6 7 8 11 17 18 23 26 47 60 218 52401 52205 52508 1434 2156 4291 15 53 1 12 4 15 1 2 11 144 351 89 1

Rlim:

Rc

Age

EBV

R

Rgc

X

Y

Z

00

0

0

Gyr

mag

pc

kpc

pc

pc

pc

00 00 00 00 00 00 24 14 30 59 48 54 27 58 12 30 18 00 00 06 02 13 38 04 39 50 35 40 30 45 19 39 00 00 25 04 15 48 59 36 09 45 54

6.0 11.0 14.0 4.0 4.0 5.0 5.5 8.0 3.2 3.0 5.0 5.0 3.8 1.3 13.0 5.0 8.2 2.8 2.4 3.6 2.2 7.7 2.1 2.8 3.0 2.2 3.0 3.5 2.0 2.8 6.0 6.4 1.6 5.0 2.2 2.5 1.5 2.5 3.0 5.0 4.2 3.5 4.0

0.65 0.80 0.78 0.40 0.06 0.25 0.41 0.88 0.04 0.28 0.22 0.12 0.87 0.11 0.32 0.34 0.45 0.16 0.16 0.37 0.24 0.27 0.09 0.06 0.30 0.23 0.26 0.27 0.07 0.09 0.12 0.13 0.04 0.36 0.13 0.08 0.10 0.30 0.26 0.30 0.19 0.07 0.10

0.20±0.08 0.10±0.01 0.05±0.00 0.30±0.08 0.25±0.06 0.40±0.05 0.79±0.02 1.41±0.11 1.26±0.09 0.60±0.02 2.00±0.10 2.24±0.10 0.10±0.01 0.08±0.01 0.08±0.01 5.00±0.30 0.40±0.03 0.79±0.03 0.35±0.03 0.89±0.04 0.44±0.02 0.80±0.05 0.40±0.01 0.40±0.01 3.20±0.14 3.20±0.14 1.00±0.05 0.32±0.02 0.25±0.02 0.80±0.04 0.45±0.03 0.50±0.04 0.40±0.03 0.30±0.02 0.05±0.05 0.50±0.03 0.25±0.01 0.90±0.06 0.50±0.04 0.80±0.08 0.16±0.02 1.60±0.13 0.40±0.03

0.55 ±0.03 0.44 ±0.04 0.75 ±0.07 0.48 ±0.05 0.44 ±0.05 0.53 ±0.03 0.61 ±0.11 0.64 ±0.11 0.60 ±0.10 0.91 ±0.07 0.42 ±0.04 0.30 ±0.05 0.36 ±0.04 1.32 ±0.13 1.39 ±0.15 1.16 ±0.12 1.13 ±0.10 0.73 ±0.12 0.52 ±0.07 0.16 ±0.05 1.27 ±0.15 0.73 ±0.05 0.67 ±0.05 0.88 ±0.06 0.30±0.03 1.82±0.15 0.36±0.04 0.66±0.05 0.67±0.05 0.61 ±0.05 0.91 ±0.07 0.61 ±0.05 1.36 ±0.10 0.91 ±0.07 0.91 ±0.07 1.33 ±0.10 0.57 ±0.04 0.18 ±0.05 0.70 ±0.05 0.73 ±0.05 0.70±0.05 0.21 ±0.02 0.79 ±0.05

1447±65 1907±88 1015±45 1490±70 872±40 1763±80 2835±130 4650±215 2150±100 1580±70 2540±115 2220±100 1190±55 3250±145 1800±80 2160±100 1905±85 2960±135 1860±85 3113±140 2600±120 2465±110 1325±60 1215±55 2800±130 660±30 1640±75 3035±140 2100±95 1790±82 2509±116 2360±109 2286±105 3016±139 1993±92 1925±89 3150±145 2125±100 3443±159 1704±79 1310±60 2646±122 2890±133

9.9 10.2 7.5 8.2 8.3 8.2 11.2 12.3 7.3 7.03 7.5 7.3 7.34 8.0 7.3 7.8 8.3 11.4 9.2 11.2 7.1 6.03 7.17 7.28 5.75 7.84 6.93 9.5 10.6 7.53 10.74 10.72 7.16 10.47 9.95 7.36 5.35 6.37 11.83 8.75 7.19 8.62 8.00

1339 1657 914 411 218 435 2570 3423 1347 1488 1334 1404 1163 278 251 30 30 2887 567 2513 1656 145 38 1188 2694 654 1505 523 2087 1107 2161 2184 1538 1658 1339 1278 3005 2032 3280 81 1310 288 974

399 826 122 1429 844 1708 1142 3147 1675 530 2158 1693 250 3071 1238 1933 1850 650 1770 1795 2003 2456 1324 254 430 80 407 2986 230 1406 1273 894 1691 2510 1475 1437 937 621 1044 1702 14 2588 2719

377 458 424 93 22 31 358 28 28 28 109 302 27 18 104 64 142 38 33 390 61 154 16 14 629 35 507 143 47 10 48 27 40 217 43 82 115 5 39 14 16 465 87

d

h

m

s



0

05 07 16 20 20 20 06 07 13 18 19 19 18 10 14 19 20 05 22 07 19 08 09 17 18 18 19 22 06 13 06 06 19 07 02 19 06 04 06 21 17 19 20

27 30 36 03 16 18 09 10 43 30 49 52 17 59 32 45 43 08 52 21 29 42 15 16 56 12 27 10 04 36 43 29 22 20 07 11 14 58 25 21 49 59 01

24 06 30 00 24 49 09 28 40 30 22 07 11 01 33 16 24 24 06 47 01 33 53 12 37 53 16 34 51 56 04 24 32 57 23 09 47 14 24 44 00 33 18

07 11 08 37 37 37 04 08 63 12 21 11 18 59 56 27 35 39 58 00 14 48 50 39 26 24 23 52 24 62 01 09 12 22 60 14 12 43 13 50 28 49 33

04 54 57 41 52 45 35 26 01 18 09 37 49 29 53 50 35 05 17 59 52 05 00 24 57 21 34 49 09 05 40 10 40 52 15 50 52 00 51 36 44 18 36

Ref.

5 5 5 5 5 5 3 3 3 1 3 3 1 4 4 4 4 3 3 3 3 1 1 1 1 1 1 3 3 1 7 7 7 7 7 7 1 1 7 7 1 7 7

A.L. Tadross

Dolidze Dolidze Dolidze Dolidze Dolidze Dolidze Dias Dias Dias Dias Dias Dias Turner Turner Turner Turner Turner King King King King BH BH BH ESO ESO ESO IC IC IC Alessi Alessi Juchert Juchert Riddle Riddle Skiff Skiff Teutsch Teutsch Collinder Patchick Toepler

94

Table 1 Cluster

Astrophysical behavior of open clusters Table 2

95

References of studied clusters.

Number

Reference

1 2 3 4 5 6 7 8 9

Tadross Tadross Tadross Tadross Tadross Tadross Tadross Tadross Tadross

(2008a) (2008b) (2009a) (2009b) and Nasser (2010) (2011) et al. (2012) (2012a) (2012b)

open clusters in the Galaxy based on the 2MASS database. Froebrich (2010) studied 269 open clusters; ages, core radii, reddening, Galactocentric distances and the scale-heights were determined. Similar to this kind of study, Schilbach (2006) derived the linear sizes of some 600 clusters and investigated the effect of the mass segregation of stars in open clusters. Bica et al. (2003) researched 346 open clusters, based on the 2MASS database; they studied the linear diameters and spatial distribution of open clusters in the Galaxy. Tadross (2001, 2002) studied 160 open clusters used UBV-CCD observations and derived the relationships projected onto the Galactic plane in morphological way. Dutra and Bica (2001) studied 42 new infrared star clusters, stellar groups and candidates towards the Cyngus X region. Dutra and Bica (2000) have studied 103 Galactic open clusters and compared the reddening values obtained from far infrared IRAS and COBE observations with those obtained from visible observations. Dambis (1999) determined the main parameters of 203 open clusters based on the published photoelectric and CCD data. Malysheva (1997) published a Catalogue of parameters for 73 open clusters determined from uvbyb photometry; his values are in good agreement with those of Loktin and Matkin (1994). Loktin (1997) published their improved version Catalogue, which contained the updated parameters of homogeneously estimated excesses, distances, and ages for 367 open clusters. Friel (1995) and Janes and Phelps (1994) based on a sample of some 70 objects investigated how the extinction and age depend on the position in the Galaxy. Also, a comparison between the age and position in the Galaxy was studied by Lynga˚ (1980), Lynga˚ (1982). In addition an old study of Janes (1979) used UBV photometry to study the reddening and metallicity of 41 open clusters. 3. Data analysis The current study depended mainly on the correlations between the astrophysical parameters of 263 open star clusters of different names listed as follows: 124 clusters of NGC; 24 objects of Berkeley; 23 of Kronberger; 23 of Czernik; 11 of Dol-Dzim; 11 of Ruprecht; 10 of Dolidze; 6 of Dias; 5 of Turner; 4 of King; 3 of BH; 3 of Eso; 3 of IC; 2 of Alessi; 2 of Juchert; 2 of Riddle; 2 of Skiff; 2 of Teutsch; 1 of Collinder; 1 of Patchick; and 1 cluster of Toepler. This sample contains clusters with ages in the range from 5 Myr to 5 Gyr. They are located at distances up to 4.7 kpc from the Sun (R ), up to 12.5 kpc from the Galactic Centre (Rgc ), and less than ±2 kpc from the Galactic Plane (Z). They range from 0.25 to 16.5 arcmin in limiting radii (Rlim: ), and up

to 1 arcmin in core radii (Rc ); with noticing that the estimated Rlim: and Rc in parsecs depending mainly on the distance of the clusters individually. Data extraction has been performed for each cluster using the known tool of VizieR for 2MASS.1 Point Source Catalogue database of Skrutskie (2006). The investigated clusters have been selected from WEBDA and DIAS databases under some conditions mentioned in our last series papers. It is noticed that most clusters’ sizes seem to be greater in the infrared band (2MASS observations) than in the optical band; because this system can detect the very faint stars, even those behind the curtains of interstellar matter. The real spatial distribution of open clusters along the Milky Way Galaxy refers to some paucity of the clusters at G. longitudes range from 140 to 200. The lack of objects in that direction is noticed also in earlier studies and confirmed for open clusters by Benjamin (2008), and Bukowiecki (2011). Older clusters seem to be more dispersed than younger ones of the Hyades, as shown in the left panel of Fig. 1. The relationships between the astrophysical parameters of open clusters are presented here with respect to their ages and places, so then the astrophysical behaviour of open clusters along the Milky Way Galaxy can be investigated. 4. Limiting and core radii One of the main tasks in this work was the determination of the radial density profile (RDP) for each cluster, i.e. the observed stellar density q that was plotted as a function of the angular radial distance from the cluster centre, King (1966): qðrÞ ¼ fbg þ

f0 1 þ ðRlim =Rc Þ2

where Rc ; f0 , and fbg are the core radius, the central density, and the background density, respectively. The core radius was derived as a distance where the stellar density drops to half of f0 . The parameters were derived with the least-square method. The cluster’s limiting radius, Rlim , was defined by comparing qðrÞ with the background density level qbg , (cf. Bukowiecki, 2011). From both Rc and Rlim , one can estimate the concentration parameter c ¼ logðRlim =Rc Þ, Peterson and King (1975). This parameter can be added as a new item to characterize the structure of clusters along the Galaxy. In the present work, the concentration parameters are ranging from 0.39 to 2.5. In this context, Nilakshi (2002) concluded that the angular size of the coronal region is about 6 times the core radius, while Maciejewski and Niedzielski (2007) reported that Rlim may vary for individual clusters from 2Rc to 7Rc . In our case, for the whole sample, the average values of limiting radius, core radius, and concentration parameter are 4.6 arcmin, 0.3 arcmin, and 1.2, respectively. We concluded that Rlim ¼ 6:85Rc ; for the clusters up to Rc = 0.5 arcmin, and Rlim ¼ 2:88Rc ; for the clusters up to Rc ¼ 1:0 arcmin. i.e, our conclusion is almost in agreement with Maciejewski and Niedzielski (2007). 5. Main photometric parameters Depending on the 2MASS data, deep stellar analyses of the candidate clusters have been presented. The photometric data 1

http://vizier.u-strasbg.fr/viz-bin/VizieR?-source=2MASS.

96

A.L. Tadross

Fig. 1 Left panel represents the clusters’ distribution according to their Galactic longitudes and latitudes, the dark area refers to the paucity of the clusters at G. longitudes ranging from 140o to 200o . Right panel represents the clusters’ distribution according their distances from the Galactic centre, Rgc , and Galactic plane, Z, assuming that Z ¼ 33 pc, and Rgc ¼ 8:5 kpc for the Sun. Both panels plotted for two ranges of clusters’ ages, younger and older than Hyades.

of 2MASS not only allow us to construct relatively well defined CM diagrams of the clusters, but also permit a more reliable determination of astrophysical parameters. In this paper, we used extraction areas having a radius of 20 arcmin, which are larger than the estimated limiting radius of the clusters. Because of the weak contrast between the cluster and the background field density, some inaccurate statistical results may be produced beyond the real limit of cluster borders (Tadross, 2005). The main astrophysical parameters of the clusters, e.g. age, reddening, distance modulus, can be determined by fitting the isochrones to the cluster CMDs. To do this, we applied several fittings on the CMDs of the clusters by using the stellar evolution models of Marigo (2008) of Padova isochrones on the solar metallicity. It is worth mentioning that the assumptions of solar metallicity are quite adequate for young and intermediate age open clusters, which are closer to the Galactic disc. So, Near-Infrared surveys are very useful for the investigation of such clusters. It is relatively less affected by high reddening from the Galactic plane. However, for specific age isochrones, the fit should be obtained at the same distance modulus for both diagrams [J–(J–H) & Ks –(J–Ks )], and the colour excesses should obey Fiorucci and Munari’s (2003) relations for normal interstellar medium. We note that, it is difficult to obtain some accurate determinations of the astrophysical parameters due to the weak contrast between clusters and field stars. Reddening determination is one of the major steps in the cluster compilation. Therefore, we used Schlegel (1998) as a guide for estimating reddening. In this context, for colour excess transformations, we used the coefficient ratios AJ ¼ 0:276 and AAHV ¼ 0:176, which were derived from AV absorption ratios in Schlegel (1998), while the ratio AKs ¼ 0:118 was derived from Dutra (2002). Applying the calAV culations of Fiorucci and Munari (2003) for the colour excess of 2MASS photometric system; we ended up with the followJH s ¼ 0:309  0:130, EEJK ¼ 0:485  0:150, where ing results: EEBV BV

6. Ages and locations The distribution of our sample according to the distances from the Galactic centre, Rgc, and the height from the Galactic plane, Z, is presented in the right panel of Fig. 1. We can see that the clusters with ages younger than Hyades, i.e. less than ð7  108 yrÞ are strongly concentrated to the Galactic plane. While the clusters which are older than Hyades are more dispersed from the Galactic plane (cf. Friel, 1995). However, the correlations of the clusters’ ages and locations with the other properties along the Milky Way Galaxy are presented in the following sections. 7. Reddening distribution In fact reddening affects the distance determination via the main sequence fitting, actually it affected all the clusters’ dimensions and positions on the Galaxy (cf. Tadross, 2002). The distribution of the reddening of our sample versus the Galactic latitudes confirms that the higher values of reddening are concentrated on and near the Galactic plane as shown in Fig. 2. Along the Galactic longitude bins of 20 the distribution of the mean reddening at each bin shows that the higher values are concentrated around the longitude range from 345 to 130, i.e. in the directions of the Galactic centre and Sagittarius arm, as shown in Fig. 3. The general trend of reddening with age shows that reddening decreases with ages

V ¼ 3:1. Also, we can de-redden the distance modulus RV ¼ EABV Ks J ¼ 0:887, EABV ¼ 0:322. Then the disusing these formulae: EABV tance of each cluster from the Sun, R , can be calculated. Consequently, the distance from the Galactic plane (Z ), and the projected distances in the Galactic plane from the Sun (X &Y ) can be determined, see Table 3. For more details about the distance calculations, see Tadross (2011).

Fig. 2 The distribution of the reddening versus the Galactic latitudes.

Astrophysical behavior of open clusters

Fig. 3 The distribution of the mean reddening along the Galactic longitude bins of 20 for each.

97

Fig. 5 The relation between the reddening and distance from the Galactic centre Rgc . The vertical line represents the galactocentric radius of the Sun, assuming that Rgc ¼ 8:5 kpc.

Fig. 4 The relation between the clusters’ ages and reddening. Left and right panels represent the very young and old clusters respectively.

where younger clusters tend to be more reddened than older ones, see Fig. 4. On the other hand, the relation between reddening and Rgc reveals that the clusters inside the galactocentric radius of the Sun (Rgc ¼ 8:5 kpc) have higher values of reddening than that of outside ones, as shown in Fig. 5. This confirms to some extent that the Sun’s vicinity clusters are young and medium ones than those outside clusters.

Fig. 6 The relation between the diameters and the absolute values of the height from the Galactic plane, jZj.

8. Diameters’ relations The linear diameters have been plotted versus the absolute values of the height from the Galactic plane jZj, and the distance from the Galactic centre Rgc as shown in Figs. 6 and 7, respectively. We can see that most clusters with typical diameters (D < 10 pc) are concentrated near the Galactic plane, especially those inside the galactocentric radius of the Sun Rgc 6 8:5 kpc. The general trend of this relation appears that large, old clusters are found far from Rgc – it is confirmed by Bukowiecki (2011) – and also at large height Z (Tadross, 2002). Some young clusters with larger diameters are belonging to the Galactic plane are founded loose and unbound objects. The relation between the diameters and the galactocentric radii has been examined to be: Diam: ¼ 0:53Rgc  0:19 The standard error of this relation 3.0 Burki and Maeder (1976) found a correlation between these quantities only for the very young clusters, but we have found such correlation for intermediate and older clusters as well.

Fig. 7 The relation between the galactocentric radii, Rgc , and linear diameters of the clusters, assuming that Rgc ¼ 8:5 kpc for the Sun. The standard error  3.0.

Fig. 8 represents the relation between ages and linear diameters of our sample. It can be expressed as follows: Diam: ¼ 3:18LogðageÞ  18:53 The standard error of this relation 3.2 We can see that, to some extent, there is a correlation between diameters and ages, whereas clusters of large sizes

98

A.L. Tadross

Fig. 8 The relation between ages and linear diameters of the studied clusters. The standard error  3.2.

belong to older ages, which have also large heights from Z. Youngest clusters with large sizes are supposed to be some groups of OB associations and probably they are not bound systems (Lynga˚, 1982; Janes et al., 1988). Massive clusters with small sizes will be dissolved due to encounters among their members, while those of very large sizes with the same mass will be unstable in the Galactic tidal field, and they may take a very long time to have stability and relaxation (Theis, 2001). Small clusters with typical diameters less than 10 pc show a concentration to the Galactic plane (Wielen, 1971, 1975) in the range of jZj < 100 pc, see Fig. 6, but larger clusters have both intermediate and old ages. 9. Ages’ relations The clusters’ ages have been plotted versus Z, as shown in Fig. 9. Most clusters with ages t  108:9 yr are lying around jZj  200 PC, while older ones are lying higher than such heights. It indicated that the thickness of the Galactic disc has not changed on the time scale of about 109:0 yr and the clusters can be formed everywhere inside this layer (cf. Tadross, 2002). Lynga˚ and Palous (1987) have found that old clusters are much thicker distributed in the outer parts of the Galaxy than in the inner parts, Bukowiecki (2011). Also in our study the thickness of the Galactic disc increases for older clusters as well. Old clusters not only spend their time in the outer disc away from the disruptive effects of giant

Fig. 10 The distribution of our sample on the Galactic plane. The three circles refer to the three famous arms of the Galaxy: Perseus (P), Sagittarius (S), and Carina (C).

molecular clouds, but also, they spend their time at large distances from the Galactic plane, further enhancing their survivability (Friel, 1995). On the other hand, the relation between ages and Rgc of the clusters implies that there is a lack of old clusters in the inner parts of the Galactic disc, and the anti-centre clusters survive longer than such clusters. In the inner parts of the Galaxy they have never gotten the relaxation state in the fluctuating gravitational field of that part (Lynga˚, 1980; McClure, 1981; Vanden Bergh, 1985). The general trend reveals that, lifetime increases outwards the Milky Way Galaxy, where clusters live longer than those in the inner parts of it. 10. Galactic spiral arms To show the shape of the spiral arms of the Galaxy, several studies have been carried out in the last five decades. The positions of the clusters on the Galactic plane have been used to trace the spiral arms of the Milky Way Galaxy. Centred on the Sun at (X ¼ Y ¼ 0) the distribution of the clusters on the Galactic plane has been plotted, as shown in Fig. 10. Within a radius of 4 kpc from the Sun (cf. Janes et al., 1988) the distribution of the studied clusters defines three concentration features which are related to the spiral structure of the Galaxy, i.e. Perseus, Sagittarius and Carina. It is assumed that there are more than three arms of the Galaxy but because of the patchy cloud and absorption effects we cannot detect them all! 11. Galactic warp

Fig. 9 The relation between ages and the heights from the Galactic plane, assuming that Z ¼ 33 pc for the Sun.

The effect of the Galactic warp may be declared from the distribution of the open clusters of our sample using the Galactic coordinates X and Y versus the height Z within ±2 kpc from the Galactic plane, as shown in Fig. 11. The directions of the

Astrophysical behavior of open clusters

99

Fig. 11 The distribution of our sample according to their Galactic coordinates X and Y versus the height from the Galactic plane Z. The Sun’s position is at X ¼ Y ¼ 0.

G. X and G. Y were defined to be positive in the direction of the Galactic radial centre and towards the direction of Galactic rotation respectively (Janes et al., 1988; Camero´n, 1999; Piatti, 2003). No strong indication to the warp has been detected on the G. X direction, but, to some extent, it can be detected on the G. Y direction. This may refer to the leak of the studied clusters, especially those that have large distances from the Sun’s vicinity (Tadross, 2002). 12. Conclusion The results of our studied clusters in the last five years using near-infrared JHKS photometric system are obtained here, and the correlations between the astrophysical parameters along the Milky Way Galaxy are achieved. It is obvious that (JHKS ) 2MASS system affected the magnitude limit of the clusters, which detects many faint members located away from the cluster’s core, so then the cluster seems to be larger than in optical bands. Detecting stars located in the lower parts of CMDs, makes the fitting with standard zero age main sequence much easier. This, of course, has contributed to the evaluation of the cluster parameters, i.e. distances, diameters, ages, reddening, etc. From our reduction, we concluded that Rlim ¼ 6:85Rc ; for the clusters up to Rc ¼ 0:5 arcmin, and Rlim ¼ 2:88Rc ; for the clusters up to Rc ¼ 1:0 arcmin, which are in agreement with Maciejewski and Niedzielski (2007). We also noticed that the linear size of open clusters increases with ages. The reddening decreases outward the Galactic plane, Z and the Galactic Center, Rgc , as well. This is noticed also for clusters located near the Sun vicinity and further than 8.5 kpc from the Galactic centre, i.e. the density of dust and gas decreases, too. From our analysis, we noticed that the number of clusters decreases with Z; more than half of the studied clusters (52%) have aged less than 500 mega years and located at average jZj ¼ 75 pc. Hence, the older ones are located at average jZj ¼ 275 pc, which is in agreement with Bukowiecki (2011). We can show that the difference between younger and older clusters can be declared in locations and sizes as the following relation: Diam: ¼ 0:53Rgc  0:19 ¼ 3:18LogðageÞ  18:53 We found that the number of older clusters increases with Rgc and younger ones are obtained at an average Rgc ¼ 8:8 kpc, which is confirmed by Tadross (2002), Froebrich (2010), and Bukowiecki (2011). The paucity of the clusters at

G. longitudes ranging from 140o to 200o is noticeable by Tadross (2002), Benjamin (2008), Froebrich (2010), and Bukowiecki (2011). It may reflect the real spatial structure of the Milky Way Galaxy in that direction near the feature region of the Perseus arm (the external youngest arm of the Galaxy). Acknowledgements This publication makes use of data products from the Naval Observatory Merged Astrometric Dataset (NOMAD) and the Two Micron All Sky Survey 2MASS, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Centre/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. Catalogues from CDS/ SIMBAD (Strasbourg), and Digitized Sky Survey DSS images from the Space Telescope Science Institute have been employed. References Benjamin, R.A., 2008. BAAS 40, 266. Bica, E., Bonatto, Ch., Dutra, C.M., 2003. A&A 405, 991. Bukowiecki, L. et al, 2011. Acta Astronom. 61, 231. Burki, G., Maeder, A., 1976. A&A 51, 247. Camero´n, F., 1999. A&A 351, 506. Dambis, A.K., 1999. Astron. Lett. 25, 7. Dutra, C., Bica, E., 2000. A&A 359, 347. Dutra, C., Bica, E., 2001. A&A 376, 434. Dutra, C. et al, 2002. A&A 381, 219. Fiorucci, M., Munari, U., 2003. A&A 401, 781. Friel, E.D., 1995. Annu. Rev. Astron. Astrophys. 33, 381. Froebrich, D. et al, 2010. MNRAS 409, 1281. Janes, K.A., 1979. Astrophys. J. Suppl. 39, 135. Janes, K., Tilley, C., Lynga˚, G., 1988. Astron. J. 95, 771. Janes, K.A., Phelps, R.L., 1994. AJ 108, 1773. King, I., 1966. AJ 71, 64. Loktin, A.V., Matkin, N., 1994. Astron. Astrophys. Trans. 4, 153. Loktin, A.V. et al, 1997. Baltic Astron. 6, 316. Lynga˚, G., 1980. In: Hesser, J.E. (Ed.), IAU Symposium, 85, 13, Reidel, Dordrecht. Lynga˚, G., 1982. Astro. Astrophys. 109, 213. Lynga˚, G., Palous, J., 1987. Astro. Astrophys. 188, 35. Maciejewski, G., Niedzielski, A., 2007. A&A 467, 1065. Malysheva, L., 1997. Astron. Lett. 23, 585. Marigo, P. et al, 2008. A&A 482, 883. McClure, R. et al, 1981. Astrophys. J. 243, 841.

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