Galactic clusters with associated Cepheid variables – VII. Berkeley 58 and CG Cassiopeiae
D. G. Turner,1†,‡,§ D. Forbes,2†D. English,2‡P. J. T. Leonard,3 J. N. Scrimger,4 A. W. Wehlau,5 R. L. Phelps,6†L. N. Berdnikov7§ and E. N. Pastukhova8
1Department of Astronomy and Physics, Saint Mary’s University, Halifax, Nova Scotia B3H 3C3, Canada
2Department of Physics, Sir Wilfred Grenfell College, Memorial University of Newfoundland, Corner Brook, NF A2H 6P9, Canada
3ADNET Systems, Inc., 7515 Mission Dr, Suite A1C1, Lanham, Maryland 20706, USA
4Faculty of Computer Science, Dalhousie University, Halifax, Nova Scotia B3H 1W5, Canada
5Department of Physics and Astronomy, The University of Western Ontario, London, Ontario N6A 3K7, Canada
6Office of Integrative Activities, National Science Foundation, Division of Astronomical Sciences, 4201 Wilson Blvd, Arlington, Virginia 22230, USA
7Sternberg Astronomical Institute, 13 Universitetskij prosp., Moscow 119992, Russia
8Institute of Astronomy, Russian Academy of Sciences, 48 Pyatnitskaya ul, Moscow 109017, Russia
Accepted 2008 May 1. Received 2008 May 1; in original form 2008 March 31
A B S T R A C T
Photoelectric, photographic and CCDUBVphotometry, spectroscopic observations and star counts are presented for the open cluster Berkeley 58 to examine a possible association with the 4.37 d Cepheid CG Cas. The cluster is difficult to separate from the early-type stars belonging to the Perseus spiral arm, in which it is located, but has reasonably well-defined parameters:
an evolutionary age of∼108yr, a mean reddening ofE(B−V) (B0)=0.70±0.03 s.e. and a distance of 3.03±0.17 kpc (V0−MV =12.40±0.12 s.d.). CG Cas is a likely cluster coronal member on the basis of radial velocity, and its period increase of+0.170±0.014 s yr−1 and large light amplitude describe a Cepheid in the third crossing of the instability strip lying slightly blueward of strip centre. Its inferred reddening and luminosity areE(B−V)= 0.64±0.02 s.e. andMV = −3.06±0.12. A possible K supergiant may also be a cluster member.
Key words: stars: evolution – Cepheids – open clusters and associations: individual:
Berkeley 58.
1 I N T R O D U C T I O N
After the rediscovery in the early 1950s of spatial coincidences be- tween Cepheids and open clusters by Irwin (1955, 1958), Eggen (see Sandage 1958) and Kholopov (1956), a number of searches for additional coincidences were made by Kraft (1957), van den Bergh (1957) and Tifft (1959), among others. Tifft’s search resulted in the discovery of a near-spatial coincidence between the 4.37 d Cepheid CG Cassiopeiae and an anonymous open cluster, subsequently cat- alogued as Berkeley 58 (Setteducati & Weaver 1962), which lies
E-mail: turner@ap.smu.ca
†Visiting Astronomer, Kitt Peak National Observatory, National Optical As- tronomy Observatories, which is operated by the Association of Universities for Research in Astronomy, Inc. (AURA) under cooperative agreement with the National Science Foundation.
‡Visiting Astronomer, Dominion Astrophysical Observatory, Herzberg In- stitute of Astrophysics, National Research Council of Canada.
§Visiting Astronomer, Harvard College Observatory Photographic Plate Stacks.
less than one cluster diameter to the west. The field is coincident with a portion of the Perseus spiral arm that is relatively rich in open clusters, and the cluster NGC 7790 with its three Cepheid members lies in close proximity. The possibility that CG Cas might be an outlying member of NGC 7790 was raised at one time by Efre- mov (1964a,b), and found some support in a star count analysis by Kovalenko (1968). More detailed star counts in the field (Turner 1985) indicate otherwise, as do the available proper motion data (Frolov 1974, 1977). The Cepheid does lie in the corona of Berkeley 58 (Turner 1985), although Frolov has argued that it is not a probable cluster member.
Given a probable distance of 3 kpc to both CG Cas and Berkeley 58 (e.g. Frolov 1979; Phelps & Janes 1994), it is not clear that existing proper motion data are precise enough to provide conclusive evidence pertaining to the cluster membership of CG Cas. The present study was therefore initiated in order to examine the case in more detail. As demonstrated here, there is strong ev- idence that CG Cas is a likely member of Berkeley 58 and that it can serve as a calibrator for the Cepheid period–luminosity (PL) relation.
Table 1. PhotoelectricUBVdata for stars in Berkeley 58.
Star RA(2000) Dec.(2000) V B−V U−B n Notes
CG Cas 00 00 59.24 60 57 32.5 11.20 1.30 +1.00 15 F5-G1 I
1 00 01 21.61 60 50 21.2 7.28 0.14 −0.39 4
2 00 00 47.68 60 48 49.8 9.80 0.27 −0.10 4
3 00 00 46.10 60 58 46.5 9.85 1.35 +1.20 4
4 00 00 42.77 61 03 26.1 10.02 0.58 +0.02 4
5 00 00 32.75 60 54 11.8 10.79 2.04 +2.44 2 (K II)?
6 00 00 20.63 60 59 43.1 10.95 0.50 −0.12 4 B3-5 Va
7 00 00 48.46 61 02 49.5 11.49 0.46 −0.44 4 B3-5 Vnn
8 00 00 10.99 61 01 53.6 12.04 0.59 +0.26 1
9 23 59 45.42 60 56 28.1 12.11 0.57 +0.48 3
10 00 00 52.47 60 56 14.1 12.16 2.25 +2.51 3
11 00 00 40.07 61 03 21.9 12.35 0.50 −0.25 4 B2.5 V
12 00 00 48.77 60 59 17.2 12.55 1.41 +1.10 1
13 00 00 33.91 60 57 58.7 12.78 0.62 +0.09 4
14 00 00 13.07 60 56 25.4 12.82 0.57 +0.04 4
15 00 00 25.25 61 00 29.8 13.12 1.59 +1.50 3
16 00 00 22.63 60 59 20.7 13.22 0.52 +0.21 5
17 00 00 25.83 60 57 58.2 13.30 0.83 +0.55 4
18 00 00 15.03 60 57 05.0 13.35 0.57 +0.03 4 B6 Vn
19 00 00 09.46 60 57 47.6 13.36 0.72 +0.44 2
20 00 00 06.89 60 57 37.6 13.41 0.60 +0.11 2
21 00 00 36.95 61 02 55.7 13.41 0.66 +0.49 3
22 00 00 19.09 60 57 29.8 13.54 1.55 +1.39 4
23 00 00 16.44 60 57 08.8 13.60 0.56 +0.00 4 B5:: Vnn
23 00 00 03.17 60 55 57.1 13.69 0.57 +0.10 4 B7 V
25 00 00 56.70 61 01 12.0 13.71 1.43 +1.23 2
26 00 00 38.39 60 58 26.2 14.11 0.73 +0.59 4
27 00 00 57.31 60 58 54.9 14.14 0.84 +0.26 4
28 00 00 22.18 60 56 39.7 14.20 0.62 +0.19 5
29 00 00 15.73 60 56 08.6 14.70 0.57 +0.18 4
30 00 00 16.73 60 55 55.6 14.71 0.72 +0.35 5 double
.. . . . . . . 15.46 0.76 . . . CCD
31 00 00 10.33 60 56 25.4 14.74 1.57 . . . 2
32 00 00 19.10 60 57 44.5 14.75 0.62 +0.44 3
33 00 00 09.64 60 57 10.1 14.91 1.02 +0.54 1
34 00 00 11.54 60 55 19.5 15.06 1.09 . . . 2
.. . . . . . . 14.88 0.66 +0.13 CCD
35 00 00 18.88 60 56 24.1 15.09 0.61 +0.25 4
37 00 00 14.44 60 55 43.3 15.16 1.17 . . . 1
37 00 00 23.28 60 57 27.8 15.63 0.81 +0.79 3
aV654 Cas (Berdnikov 1993).
2 O B S E RVAT I O N A L DATA
A variety of observations were obtained for the present investi- gation. Table 1 presents photoelectricUBVphotometry for bright members of Berkeley 58, obtained during observing runs at Kitt Peak National Observatory in 1981 September, 1982 August and 1984 August. The data, acquired using 1P21 photomultipliers and standardUBVfilter sets used in conjunction with pulse-counting photometers on the No. 4 0.4-m, No. 2 0.9-m, and 1.3-m telescopes at Kitt Peak, have associated uncertainties typical of our previous investigations of Cepheid clusters (Turner 1992; Turner, Forbes &
Pedreros 1992; Turner, Mandushev & Forbes 1994), namely stan- dard internal errors for a single observation of±0.01 in V and B−V, and±0.02 inU−B, for stars brighter thanV=13. The estimated external errors for all but the faintest stars are similar in magnitude. The stars are identified by their numbering in Fig. 1, as well as by their 2000 coordinates in the Two Micron All-Sky Survey (2MASS) (Cutri et al. 2003); the number of individual observations for each star is given in Column 7 of Table 1.
Star 6 is the eclipsing system V654 Cas, for which Berdnikov (1993) cites photoelectric values ofVandB−Voutside of eclipse that are close to the values given here. Star 30 is a close opti- cal double with components of nearly identical brightness. The photoelectric values apply to the combined light from both stars, whereas CCD observations provide uncontaminated data for the south-western star of the pair, as established by its CCD magni- tude being 0.75 mag fainter. By contrast, the CCDVmagnitude for star 35 is 0.21 mag brighter, which suggests possible variability in the object. Individual photoelectric observations for CG Cas are presented in Table 2.
Photographic UBV photometry was also obtained for stars in the nuclear and coronal regions of Berkeley 58 from photographic plates of the cluster field obtained in 1984 September using the 1.2-m Elginfield telescope of the University of Western Ontario. The star images were measured using theIRISdiaphragm photometer at Saint Mary’s University, and were reduced to theUBVsystem and calibrated with reference to the photoelectric standards identified in Table 1 using the techniques discussed by Turner & Welch (1989).
Figure 1. A finder chart for the field of Berkeley 58 from the red image of the Palomar Observatory Sky Survey. The field of view measures 20 arcmin
×20 arcmin and is centred at 2000 coordinates: RA=00h00m12.s9,Dec.= +60◦5607. The top image depicts the location of CG Cas relative to the cluster core, the lower image identifies photoelectrically observed stars.
[The National Geographic Society-Palomar Observatory Sky Atlas (POSS- I) was made by the California Institute of Technology with grants from the National Geographic Society.]
The resulting data are presented in Table 3 in similar format to the data of Table 1, and the stars are identified by their 2000 coordinates.
The photographic values for cluster stars in common with the CCD survey (Phelps & Janes 1994) agree very closely with the CCD values, when the latter are adjusted to the present system. However, earlier photographic UBVphotometry of cluster stars by Frolov (1979) displays systematic differences relative to the present data.
Since the present survey samples a much larger number of cluster
Table 2.Photoelectric UBV observations for CG Cas- siopeiae.
HJD V B−V U−B
244 4849.8938 11.37 1.28 . . .
244 4854.8655 11.53 1.36 . . .
244 4856.8539 11.22 1.14 . . .
244 4857.8358 11.08 1.14 . . .
244 4857.8689 11.09 1.16 . . .
244 5197.9177 10.92 1.04 0.74
244 5205.9366 11.45 1.25 0.84
244 5206.8851 11.04 1.10 0.76
244 5933.8457 11.73 1.40 1.04
244 5935.8748 10.99 1.08 0.85
244 5937.8601 11.59 1.37 0.96
244 5938.8420 11.74 1.38 1.02
244 5939.8315 10.85 0.99 0.72
244 5941.8773 11.55 1.35 0.93
244 5942.7724 11.76 1.42 1.04
stars, no attempt was made to combine Frolov’s data with the present photometry.
CCDUBVphotometry for stars in the nuclear region of Berkeley 58 was published previously by Phelps & Janes (1994), but for this study was recalibrated using the Table 1 stars as standards. The revised photometry for cluster stars is presented in Table 4, where the star numbers correspond to the scheme adopted by Phelps &
Janes (1994), incremented by 1000. The stars are also identified by their 2000 coordinates. Since theU-band measurements have a much brighter limit than theBandVmeasures, the CCD photometry is less useful for studying the reddening in the field. But it is valuable for identifying the faint portion of the cluster main sequence.
Spectroscopic imaging of bright stars in Berkeley 58 was made in 1984 July and 1985 September using the Cassegrain spectrograph on the 1.8-m Plaskett telescope of the Dominion Astrophysical Observatory. The observations, at a dispersion of 15 Å mm−1 and centred in the blue spectral region, were recorded photographically and later scanned for radial velocity measurement with the PDS microdensitometer at the David Dunlap Observatory of the University of Toronto (see Turner & Drilling 1984). It was also possible to estimate spectral types for the stars from the photographic spectra, with results presented in Table 1.
The field of the Cepheid CG Cas was also examined on archival images in the collections of Harvard College Observatory and Sternberg Astronomical Institute in order to obtain brightness esti- mates for the star and to construct seasonal light curves for com- parison with a standard light curve constructed from photoelectric observations (Berdnikov 2007). The resulting data were used to estimate times of light maximum for the Cepheid and to track its O−C changes, the differences between observed (O) and computed (C) times of light maximum. Rate of period change, in conjunction with light amplitude, is an excellent diagnostic of the location of individual Cepheids in the instability strip (Turner, Abdel-Sabour Abdel-Latif & Berdnikov 2006a), such information providing an excellent parameter for comparison with what can be gleaned from information on the age of the surrounding stars provided by the cluster Hertzsprung–Russell diagram.
3 S TA R C O U N T S
The first step in studying Berkeley 58 involved star counts made using a photographic enlargement from a glass copy of the Palomar
Table 3. PhotographicUBVData for stars in Berkeley 58.
Star RA(2000) Dec.(2000) V B−V U−B Star RA(2000) Dec.(2000) V B−V U−B
101 23 59 36.09 +60 49 01.9 9.48 0.52 −0.05 179 00 01 21.27 +60 53 30.5 14.01 0.60 +0.47
102 00 00 13.86 +61 04 47.4 9.76 0.33 +0.15 180 23 59 56.23 +60 56 25.0 14.03 0.58 +0.08
103 00 01 16.38 +60 49 18.1 9.82 0.36 −0.28 181 23 58 53.10 +60 57 05.6 14.05 0.98 +0.93
104 23 59 24.28 +60 48 18.3 10.12 1.82 +0.74 182 23 59 10.64 +60 51 55.7 14.06 0.90 +0.25
105 23 59 35.71 +60 47 49.6 10.26 1.48 +0.84 183 23 59 17.01 +60 51 12.5 14.07 1.03 +0.19
106 00 00 03.42 +60 50 36.1 11.10 0.71 −0.05 184 23 59 47.40 +60 48 27.0 14.07 0.92 +0.30
107 23 59 36.15 +60 47 33.1 11.59 0.73 +0.13 185 23 59 50.39 +60 58 39.3 14.09 1.64 . . .
108 23 59 42.73 +60 47 16.1 11.60 2.12 +2.67 186 00 00 49.32 +60 48 06.5 14.10 0.91 +0.08
109 23 59 07.11 +60 55 06.8 11.67 1.51 +1.09 187 00 00 24.36 +60 55 35.8 14.11 0.63 +0.09
110 00 01 05.72 +60 51 17.7 11.83 1.10 +0.67 188 23 59 49.10 +60 50 32.7 14.13 1.07 +0.35
111 00 00 11.91 +60 50 28.6 11.85 0.53 +0.17 189 23 58 57.51 +60 58 24.8 14.14 1.31 +0.85
112 00 01 20.84 +60 52 34.9 11.92 1.31 +0.95 190 23 59 22.80 +60 57 04.3 14.14 0.52 −0.12
113 00 01 21.00 +61 00 48.4 12.08 0.47 +0.31 191 23 59 05.78 +61 01 43.6 14.15 0.79 +0.70
114 00 01 10.16 +61 03 50.0 12.17 0.88 +0.34 192 23 59 46.99 +61 03 27.0 14.16 0.58 +0.38
115 00 01 20.63 +60 55 32.1 12.37 0.56 +0.12 193 00 00 55.95 +61 03 02.4 14.16 0.55 +0.19
116 00 00 07.17 +60 48 48.4 12.39 0.80 +0.52 194 00 00 04.13 +60 51 51.7 14.17 0.86 +0.54
117 23 58 53.91 +60 56 37.2 12.40 0.78 +0.52 195 00 00 37.31 +60 46 36.1 14.17 1.09 +0.43
118 23 59 10.07 +60 55 48.6 12.41 0.78 +0.52 196 23 59 37.23 +61 01 47.2 14.19 0.71 −0.04
119 23 59 40.81 +60 51 12.4 12.41 1.35 +1.05 197 00 01 14.97 +60 54 01.9 14.20 0.87 +0.26
120 00 00 24.15 +61 05 54.4 12.51 1.65 +1.73 198 23 59 07.54 +60 59 40.0 14.21 0.80 −0.01
121 00 00 16.78 +60 52 39.3 12.54 0.71 +0.22 199 23 59 49.51 +60 59 23.1 14.25 0.97 +0.85
122 00 01 05.00 +60 50 58.3 12.58 0.30 −0.02 200 00 00 26.46 +60 50 28.7 14.30 0.66 +0.52
123 23 59 11.61 +61 02 04.7 12.59 1.64 +0.71 201 00 00 51.81 +60 46 54.6 14.30 0.86 +0.22
124 23 59 43.07 +61 03 17.7 12.63 0.52 +0.20 202 00 00 23.33 +60 51 42.1 14.31 0.81 +0.21
125 23 59 06.63 +60 53 17.9 12.78 0.60 +0.33 203 23 59 34.32 +60 59 24.9 14.32 0.97 +0.31
126 00 01 05.84 +60 59 50.1 12.82 0.47 −0.01 204 23 59 17.67 +60 54 45.5 14.34 1.06 +0.33
127 00 01 33.08 +60 53 08.0 12.90 0.53 +0.41 205 00 00 11.83 +61 05 55.5 14.34 0.97 +0.41
128 00 00 57.98 +61 04 02.5 12.97 0.56 −0.20 206 23 59 41.42 +60 51 28.7 14.40 0.58 +0.40
129 00 00 25.44 +60 59 52.4 13.05 1.66 +1.57 207 00 00 25.66 +60 50 43.7 14.43 0.76 +0.18
130 23 59 03.83 +60 51 31.8 13.08 0.97 +0.23 208 23 59 42.89 +61 02 29.1 14.46 0.54 +0.03
131 23 58 54.24 +60 54 15.1 13.11 1.46 +1.48 209 00 00 58.82 +60 55 01.6 14.47 0.96 +0.59
132 00 00 26.72 +60 59 55.4 13.12 0.69 +0.29 210 00 00 00.99 +61 00 51.4 14.48 0.97 +0.78
133 23 59 19.28 +60 50 11.7 13.20 0.56 −0.04 211 00 01 25.15 +61 02 11.0 14.51 0.79 +0.56
134 23 59 24.57 +60 55 27.9 13.30 0.65 +0.40 212 23 59 23.62 +60 59 41.4 14.52 0.77 +0.36
135 23 59 59.65 +61 04 09.7 13.32 1.32 +1.21 213 00 00 26.84 +60 49 40.7 14.55 1.00 +0.51
136 00 00 27.04 +60 46 43.8 13.32 1.10 +0.22 214 00 01 21.95 +61 02 29.5 14.55 0.94 +0.62
137 00 00 28.97 +60 47 58.6 13.39 0.89 +0.24 215 00 00 25.83 +60 55 38.0 14.57 0.65 +0.28
138 00 00 21.24 +60 51 10.6 13.40 0.49 +0.20 216 23 59 06.22 +60 53 57.6 14.58 1.10 +0.46
139 00 01 16.05 +61 02 45.5 13.44 0.83 +0.55 217 00 01 18.21 +61 01 23.9 14.59 1.08 +0.49
140 23 59 41.35 +61 05 46.4 13.45 0.69 +0.25 218 00 00 16.19 +60 53 17.5 14.59 2.38 . . .
141 23 58 50.90 +60 54 37.2 13.46 1.14 +0.16 219 23 59 22.49 +60 52 00.0 14.60 1.28 +0.28
142 00 00 15.19 +60 59 41.4 13.50 0.55 +0.08 220 00 00 01.21 +60 57 39.2 14.60 0.73 +0.47
143 00 01 38.02 +60 57 11.3 13.51 0.90 +0.24 221 00 00 28.99 +60 52 57.1 14.61 0.85 +0.31
144 00 00 19.83 +60 49 11.5 13.52 0.94 +0.48 222 00 00 53.50 +60 55 22.0 14.65 0.38 +0.08
145 23 59 48.55 +60 46 45.3 13.56 1.29 +0.38 223 00 00 28.35 +61 05 20.9 14.70 0.66 −0.01
146 00 00 24.12 +60 58 43.8 13.58 1.17 +0.83 224 23 59 58.59 +60 54 09.2 14.73 1.01 +0.71
147 00 01 14.18 +60 56 32.2 13.59 0.46 +0.03 225 00 01 16.76 +60 54 30.9 14.74 0.45 −0.17
148 23 59 24.83 +60 59 52.9 13.64 1.18 . . . 226 00 00 18.03 +60 51 36.5 14.75 0.76 +0.37
149 00 00 07.41 +61 00 24.1 13.64 0.61 +0.23 227 23 59 32.73 +60 59 21.3 14.79 0.79 +0.48
150 00 00 01.78 +60 48 57.5 13.68 0.61 +0.30 228 00 00 10.51 +60 58 01.8 14.79 0.77 +0.43
151 23 58 55.65 +60 52 55.3 13.70 0.75 +0.27 229 23 59 40.12 +60 57 06.2 14.81 0.96 +0.33
152 23 59 09.72 +60 55 33.4 13.71 0.93 +0.31 230 00 00 20.17 +60 55 54.3 14.86 0.68 +0.28
153 23 59 52.24 +60 56 50.2 13.72 0.56 +0.13 231 00 00 02.48 +60 54 42.4 14.88 0.45 +0.20
154 00 00 49.48 +61 03 45.2 13.72 1.44 +0.78 232 23 59 49.71 +60 53 31.9 14.90 0.76 +0.39
155 00 01 38.95 +60 57 40.8 13.73 0.53 −0.01 233 00 00 04.01 +60 54 47.8 14.93 0.61 +0.19
156 00 00 27.09 +61 05 48.8 13.74 1.06 +0.32 234 00 00 33.02 +60 55 51.9 14.96 1.05 +0.44
157 23 59 34.31 +60 49 44.5 13.75 1.14 +0.47 235 00 00 09.83 +60 54 30.1 15.00 0.69 +0.21
158 00 00 44.24 +60 46 52.3 13.75 0.65 +0.08 236 00 00 44.08 +61 05 04.7 15.00 0.48 +0.49
159 00 00 31.53 +60 46 32.0 13.76 0.84 +0.34 237 00 00 09.76 +61 05 34.5 15.12 0.38 +0.26
160 00 00 38.87 +60 53 10.0 13.77 0.53 +0.09 238 23 59 42.48 +60 56 18.8 15.14 0.59 +0.36
161 23 59 26.17 +60 49 45.8 13.78 1.45 +1.09 239 00 00 04.71 +60 57 45.6 15.15 0.67 +0.44
162 23 59 41.19 +61 04 51.7 13.79 0.54 +0.27 240 23 59 19.79 +61 00 25.5 15.16 0.70 +0.13
Table 3 – continued
Star RA(2000) Dec.(2000) V B−V U−B Star RA(2000) Dec.(2000) V B−V U−B
163 00 01 38.40 +60 56 46.7 13.79 0.45 +0.29 241 23 59 39.28 +60 57 14.7 15.17 0.64 +0.31
164 00 01 13.36 +61 01 33.3 13.81 0.67 +0.05 242 00 00 22.59 +60 57 40.8 15.17 0.63 +0.09
165 23 59 20.85 +61 02 22.0 13.86 0.98 +0.61 243 23 59 53.74 +60 57 08.8 15.20 1.04 +0.39
166 00 00 05.82 +60 50 35.8 13.86 0.42 +0.00 244 00 00 04.46 +61 00 44.7 15.21 0.72 +0.28
167 00 00 02.37 +60 46 38.7 13.86 1.07 +0.04 245 00 00 06.29 +60 54 44.8 15.21 0.66 +0.29
168 23 59 04.31 +61 01 44.6 13.90 0.93 +0.84 246 00 00 38.77 +60 56 31.4 15.21 0.82 +0.49
169 00 00 00.15 +60 55 14.2 13.90 0.56 +0.06 247 23 59 50.61 +60 55 25.6 15.23 0.71 . . .
170 23 59 03.70 +61 01 50.1 13.91 0.88 +0.87 248 23 59 57.24 +60 55 02.8 15.24 0.69 +0.29
171 00 01 09.90 +60 52 54.7 13.93 0.94 +0.43 249 23 59 55.11 +60 53 44.8 15.26 0.71 +0.31
172 00 01 08.86 +60 58 34.1 13.94 1.04 +0.66 250 00 00 08.27 +60 56 42.6 15.35 0.94 +0.61
173 23 59 27.78 +60 55 30.8 13.97 0.67 +0.49 251 00 00 14.46 +60 57 47.6 15.42 0.77 +0.39
174 00 00 13.79 +61 01 04.7 13.98 0.98 +0.48 252 00 00 15.30 +60 54 57.0 15.42 0.72 . . .
175 00 00 26.02 +60 55 07.4 13.98 0.64 +0.20 253 00 00 31.15 +61 04 07.7 15.59 0.85 . . .
176 00 01 10.45 +60 58 30.7 13.99 0.68 +0.42 254 00 00 10.69 +60 55 58.4 15.62 0.79 . . .
177 00 00 11.44 +60 51 41.8 14.01 0.56 +0.12 255 00 00 06.19 +60 56 32.6 15.79 0.56 +0.23
178 00 01 16.45 +60 58 25.5 14.01 1.05 +0.21
Observatory Sky Survey (POSS) E plate for the field. Strip counts in several different orientations delineated the cluster centre, followed by ring counts illustrated in Fig. 2; the centre of symmetry is located at RA = 00h00m12.s9, Dec. = +60◦5607 (2000). The upper portion of Fig. 2 illustrates ring counts for stars detected on the 2MASS survey (Cutri et al. 2003) to the survey limit, whereas the lower portion shows star counts from the POSS-E plate to two different magnitude limits.
The counts from the 2MASS survey were made without regard for overlap with the star cluster NGC 7790, which lies 23 arcmin to the north-west of Berkeley 58, whereas the counts from the POSS-E plate were restricted beyond 11 arcmin from the cluster centre to sectors that avoided overlap with the outlying regions of NGC 7790.
The effect of contamination from the coronal region of NGC 7790 is detectable in the 2MASS star counts beyond roughly 12 arcmin from the cluster centre, but because of restrictions imposed by the location of Berkeley 58 on the POSS, we were unable to establish uncontaminated star counts from the POSS-E plate beyond about 15 arcmin from the cluster centre. Nevertheless, the two sets of counts appear to yield similar parameters for the inner regions of the cluster. Berkeley 58 is estimated to have a nuclear radius ofrn 4.5 arcmin (4.0 pc) in the notation of Kholopov (1969), whereas the coronal (or tidal) radius is estimated to beRc11 arcmin (9.7 pc) from the trends in the 2MASS star densities as well as the apparent flattening of the POSS-E star densities in the outermost rings.
Star counts predict a total of 197± 27 members brighter than the limit of the 2MASS survey lying within 5 arcmin of the cluster centre, 487±82 members within 11 arcmin of the cluster centre, field stars within the same regions being 715 and 4835, respectively.
Field stars clearly outnumber cluster members in both regions. CG Cas is located 5.8 arcmin from the centre of Berkeley 58, in the clus- ter coronal region just beyond its nuclear boundaries. Although not projected on the core of Berkeley 58, CG Cas is spatially coincident with the cluster, which occupies most of the field of Fig. 1.
4 B E R K E L E Y 5 8
Fig. 3 is aUBVcolour–colour diagram for the field of Berkeley 58 surveyed in this study, as constructed from the data of Tables 1, 3 and 4. The phase-averaged data for CG Cas are from Berdnikov (2007). A reddened sequence of B- and A-type cluster members
can be detected in the data, but a cluster reddening ofE(B−V) 0.7 places them in a section of the colour–colour diagram where they can be confused photometrically with unreddened, foreground, G-type stars. For that reason, it becomes essential to make the process of photometric identification of likely spectral classes for individual stars as reliable as possible, through the use of a well- established interstellar extinction relation. The spectral types ob- tained for six of the B-type, photoelectrically observed, cluster stars imply a reddening law for Berkeley 58 described byE(U−B)/
E(B−V)=0.75, along with a small curvature term (Turner 1989), identical to the reddening slope found previously for star clusters spatially adjacent to Berkeley 58 (Turner 1976b). Berkeley 58 stars were therefore dereddened with such a relationship, except for late- type stars where a steeper relationship was adopted, dependent upon the likely intrinsic colours of the stars.
Fig. 3 data indicate an absence of any unreddened O-, B- or A-type stars in the observed sample. That feature is confirmed by available 2MASS data for the observed stars (Cutri et al. 2003), which are depicted in theJHKcolour–colour diagram of Fig. 4.
An intrinsic relation for main-sequence stars in the 2MASS system was constructed from 2MASS observations of unreddened standard stars and stars in open clusters of uniform reddening (e.g. Turner 1996b), adjusted with a reddening slopeE(H−K)/E(J− H)= 0.55, as derived from reddened stars of known spectral type. The number of cluster stars withU-band observations is a small fraction of the total sample, so Fig. 4 contains many more stars than Fig. 3.
The selection of 2MASS data was also not restricted according to the magnitude of cited uncertainties in the data, so several points in Fig. 4 display unusually large scatter. It seems clear, however, that the sample of cluster stars surveyed consists mainly of stars reddened byE(J−H)≥0.1, which corresponds toE(B−V)≥ 0.36.
The correlation of reddening with distance towards Berkeley 58 was established from the availableUBVphotometry by deredden- ing the colours for individual stars in conjunction with a copy of the POSS field on which derived colour excessesE(B−V) were recorded as they were obtained, with multiple solutions resolved by reference to the reddenings for spatially adjacent stars as well as by the reddenings derived for the stars from their 2MASS colours (Fig. 4). In most cases, the smallerJHKreddening of stars rela- tive to those obtained fromUBVcolours was sufficient to resolve
