In this paper we study some van den Bergh open clusters combining photometry and astrometry. A model which analyses the proper motion distribution and the stellar density is applied to find the kinematic parameters and stellar membership in the region of the open clusters vdB92, vdB146 (NGC 7129) and vdB150. The astrometric data are obtained from UCAC4 catalogue. The centre coordinates, the components of mean proper motion, the angular diameter and the astrometric members are reported, taking the following values: for vdB92: α=105.97281°±0.13113°, δ=−11.57814°±0.10575°, μ<sub>α</sub>cosδ=−3.46±0.19mas/yr, μ<sub>δ</sub>=1.27±0.19mas/yr, 34', 60 members; for vdB146: α=325.78423°±0.15297°, δ=66.13575°±0.02907°, μ<sub>α</sub>cosδ=−2.71±0.25mas/yr, μ<sub>δ</sub>=−3.32±0.25mas/yr, 9', 5 members; and for vdB150: α=332.22519°±0.06074°, δ=73.40232°±0.0.07789°, μ<sub>α</sub>cosδ=3.07±0.90mas/yr, μ<sub>δ</sub>=4.65±0.90mas/yr, 15', 7 members. The incidence of the proper motion errors in the determination of the cluster parameters and of the stellar membership is analysed and it is found that they do not significantly change. We finally compare the astrometric members with the photometric ones given in the literature.
The study of embedded clusters can provide the key to a better understanding of a number of fundamental problems in astrophysics, e.g. distances, masses, ages, Metalicity. Moreover, the analysis of the complex gravitational interactions of their individual members contributes to the study of stellar dynamics.
Several of these clusters have been investigated using only photometric techniques to determine the members. As open cluster members share similar photometric and kinematic properties, it is useful to complete the study of the stars of the cluster region by employing astrometric methods. Recently, Corti and Orellana [
In this work we improve the membership probability of the stars in the regions of van den Bergh open clusters vdB92, vdB146 and vdB150.
Open cluster vdB92: has equatorial coordinates α J 2000 = 7 h 03 m 56.4 s and δ J 2000 = − 11 ∘ 34 ' 57.7 ' ' ( l = 224 .66 ∘ , b = − 2.52 ∘ ) (Bonatto and Bica [
Open cluster vdB146: is situated in Cepheus and its coordinates are α J 2000.0 = 21 h 42 m 59 s and δ J 2000.0 = 66 ∘ 06 ' 48 ' ' ( l = 105.4044 ∘ , b = 9.8852 ∘ ) (Dias et al. [
More recently, an important investigation of vdB146 and the dust cloud where it is embedded is made by Straižys et al. [
Open cluster vdB150: discovered in 1966 by van den Bergh, it is placed in Cepheus and its coordinates are α J 2000.0 = 22 h 12 m 48 s and δ J 2000.0 = 73 ∘ 20 ' 00 ' ' ( l = 112.0625 ∘ , b = 13.9057 ∘ ) (Dias et al. [
The images of the optical environments of the three open clusters are taken from the Digital Sky Survey (DSS) (
We perform our investigation taken the stellar position and proper motions from the UCAC4 Catalogue, which has 113 million stars and 105 million of them with proper motions. The catalogue is complete to about magnitude R = 16 having an average density over 2000 stars/(')2.
Positional errors are about 15 to 20 mas for stars in the 10 to 14 mag range. Errors in proper motions of the bright stars (to R ~ 12 ) run from about 1 to 3 mas/yr, typical errors of the fainter stars using SPM and NPM data are at the level of 2 to 6 mas/yr.
These data are supplemented by 2MASS photometric data for about 110 million stars and 5-band (B, V, g, r, i) photometry from the APASS (AAVSO Photometric All-Sky Survey) for over 50 million stars. A detailed description of the construction of UCAC4 catalogue can be found in Zacharias et al. [
Data extraction has been performed using the Vizier1.
Astrometrically, the existence of an open cluster is pointed out by an overdensity in the sky as well as in the Vector Point Diagram (VPD). The identification of members of the cluster with respect to field stars is done by evaluating both overdensities simultaneously.
The projected stellar density of each cluster is analysed in a region whose size and magnitude limit depend on local characteristics. We consider the faintest magnitude up to which an overdensity can be distinguished. Up to the 14 magnitude, we examine a region sized of 30 ' × 30 ' for vdB92. Up to the 15 magnitude, we examine another of 24 ' × 24 ' for vdB146. A region of 15 ' × 15 ' is chosen for vdB150 analysis up to magnitude 13.
The observed local density is evaluated at the nodes of a grid of a given size by adding the stars within a circle whose radius s 0 is weighted by a smoothing parameter following Stock and Abad’s rule (Stock and Abad [
The analysis is continued by adopting the proper motion distribution of Vasilevskis-Sanders (Vasilevskis et al. [
The proper motion distribution for the i-th star takes the form:
grid’s size | s 0 | α 0 [˚] | δ 0 [˚] | |
---|---|---|---|---|
vdB92 | 0.5 ' × 0.5 ' | 2.2' | 105.97917 ± 0.01248 | −11.56889 ± 0.01222 |
vdB146 | 0.5 ' × 0.5 ' | 2.2' | 325.71247 ± 0.03016 | 66.09753 ± 0.01222 |
vdB150 | 0.5 ' × 0.5 ' | 2.2' | 332.41250 ± 0.04279 | 73.404167 ± 0.01222 |
Φ i ( μ x i , μ y i , r i ) = ρ 0 exp ( − r i / r 0 ) 2 π σ c 2 × exp [ − ( μ x i − μ x c ) 2 + ( μ y i − μ y c ) 2 2 σ c 2 ] + ρ f 2 π σ x f σ y f × exp [ − ( μ x i − μ x f ) 2 2 σ x f 2 − ( μ y i − μ y f ) 2 2 σ y f 2 ] (1)
where μ x i , μ y i , r i are components of proper motion in x and y and the distance from the approximate cluster’s centre for the i-th star, ρ 0 is the central cluster stellar density, r 0 is the characteristic radius, ρ f is the constant areal stellar density for field stars, μ x f , μ y f are the field mean proper motion; σ x f , σ y f the elliptical dispersions for field stars, μ x c , μ y c the cluster mean proper motion, and σ c its circular dispersion for cluster stars. These parameters are obtained after applying the method of maximum likelihood to Equation (1).
The probability for the i-th star is calculated as
P c i ( μ x i , μ y i , r i ) = ρ 0 exp ( − r i / r 0 ) 2 π σ c 2 × exp [ − ( μ x i − μ x c ) 2 + ( μ y i − μ y c ) 2 2 σ c 2 ] Φ i ( μ x i , μ y i , r i ) (2)
A cluster member is found when P c i ≥ 0.5 .
Open cluster vdB92:
We choose the stars in a circular region of radius 30' centered at the ( α 0 , δ 0 ) given in
The parameters ρ 0 = 0.640 ± 0.066 stars / ( ' ) 2 , r 0 = 4.102 ' ± 0.820 ' and ρ f = 0.169 ± 0.024 stars / ( ' ) 2 adjust the function ρ ( r i ) to the radial stellar density profile.
After Equation (1) is resolved, the cluster parameters are μ α cos δ c = − 3.46 ± 0.19 mas / yr , μ δ c = 1.27 ± 0.19 mas / yr , σ c = 1.44 ± 0.13 mas / yr and the field parameters μ α cos δ f = − 1.56 ± 0.33 mas / yr , μ δ f = 1.01 ± 0.24 mas / yr , σ μ α cos δ f = 7.03 ± 0.23 mas / yr and σ μ δ f = 5.26 ± 0.17 mas / yr .
60 stars are found to be astrometric members of the cluster. Their coordinates lead to calculate the equatorial coordinates of the centre of the cluster α c = 105.97281 ∘ ± 0.13113 ∘ , δ c = − 11.57814 ∘ ± 0.10575 ∘ and an amount of 17.11' for the radius, in good agreement with Bonatto and Bica’s value.
The location of the members in the spatial distribution and in the VPD is shown with black circles in
No. | UCAC4 | α [˚] | ϵ α [mas] | δ [˚] | ϵ δ [mas] | μ α cos δ | ϵ μ α cos δ | μ δ | ϵ μ δ | P c i |
---|---|---|---|---|---|---|---|---|---|---|
[mas/yr] | [mas/yr] | |||||||||
1 | 393-021227 | 105.9809748 | 17 | −11.5727017 | 17 | −3.9 | 2.7 | 0.4 | 2.6 | 0.98 |
2 | 393-021223 | 105.9785765 | 13 | −11.5761306 | 13 | −4.7 | 2.1 | 2.1 | 1.8 | 0.98 |
3 | 393-021222 | 105.9785174 | 15 | −11.5614681 | 20 | −5.0 | 1.3 | 2.4 | 1.8 | 0.97 |
6 | 393-021237 | 105.9868448 | 16 | −11.5782645 | 16 | −4.3 | 1.6 | 0.1 | 1.6 | 0.98 |
9 | 393-021212 | 105.9687412 | 25 | −11.5810700 | 41 | −4.7 | 1.4 | 2.2 | 1.6 | 0.97 |
10 | 393-021207 | 105.9646874 | 16 | −11.5821648 | 16 | −4.5 | 1.6 | 0.7 | 1.6 | 0.98 |
14 | 393-021229 | 105.9818480 | 23 | −11.5463681 | 17 | −1.3 | 1.6 | 3.2 | 1.6 | 0.87 |
16 | 393-021252 | 105.9950262 | 17 | −11.5919895 | 23 | −3.8 | 1.6 | −1.0 | 2.2 | 0.94 |
27 | 393-021276 | 106.0118339 | 16 | −11.5376506 | 16 | −5.2 | 1.6 | 2.7 | 1.6 | 0.93 |
33 | 393-021175 | 105.9298500 | 3 | −11.5517245 | 3 | −5.2 | 1.4 | 3.5 | 1.6 | 0.85 |
44 | 393-021278 | 106.0127642 | 33 | −11.5219553 | 16 | −5.9 | 3.2 | -0.2 | 1.5 | 0.85 |
56 | 393-021313 | 106.0408306 | 33 | −11.5482892 | 23 | −4.1 | 2.9 | −1.1 | 2.5 | 0.88 |
70 | 393-021163 | 105.9150692 | 15 | −11.5312978 | 16 | −2.2 | 1.4 | −1.7 | 1.5 | 0.68 |
90 | 393-021335 | 106.0592459 | 16 | −11.5895948 | 17 | −3.5 | 2.0 | 1.0 | 2.2 | 0.96 |
127 | 393-021221 | 105.9767768 | 13 | −11.4748273 | 20 | −4.2 | 1.3 | 1.9 | 1.8 | 0.94 |
131 | 393-021156 | 105.8952642 | 18 | −11.5221453 | 19 | −1.6 | 3.1 | 0.5 | 3.7 | 0.86 |
135 | 393-021292 | 106.0225950 | 14 | −11.4822689 | 15 | −5.8 | 1.2 | 1.5 | 1.3 | 0.85 |
179 | 393-021348 | 106.0677624 | 45 | −11.4999575 | 17 | −2.7 | 5.2 | -0.5 | 2.0 | 0.85 |
182 | 392-020650 | 106.0514348 | 16 | −11.6563784 | 17 | −2.4 | 1.4 | 4.1 | 1.6 | 0.62 |
191 | 393-021393 | 106.0970439 | 18 | −11.5571039 | 19 | −2.6 | 1.5 | 2.6 | 1.6 | 0.87 |
217 | 392-020512 | 105.8942362 | 17 | −11.6575553 | 18 | −1.7 | 2.1 | -0.3 | 2.4 | 0.75 |
237 | 393-021409 | 106.1058277 | 17 | −11.5471642 | 17 | −3.8 | 6.6 | 2.4 | 6.7 | 0.89 |
250 | 392-020551 | 105.9635974 | 18 | −11.6968653 | 18 | −1.6 | 2.2 | 3.2 | 2.2 | 0.66 |
254 | 392-020688 | 106.0825609 | 53 | −11.6506845 | 188 | −4.1 | 5.2 | -0.9 | 19.5 | 0.78 |
259 | 393-021418 | 106.1100442 | 17 | −11.5392295 | 17 | −3.6 | 1.5 | 0.9 | 1.5 | 0.91 |
265 | 393-021155 | 105.8945630 | 16 | −11.4648164 | 37 | −1.3 | 1.4 | 2.4 | 3.5 | 0.70 |
287 | 393-021286 | 106.0164024 | 17 | −11.4360525 | 17 | −4.3 | 1.3 | 3.3 | 1.5 | 0.76 |
289 | 392-020697 | 106.0921245 | 27 | −11.6519084 | 28 | −1.8 | 1.6 | 0.7 | 1.6 | 0.81 |
300 | 393-021330 | 106.0568768 | 17 | −11.4501334 | 16 | −4.9 | 1.9 | -0.8 | 2.1 | 0.71 |
301 | 393-021299 | 106.0279209 | 16 | −11.4356939 | 18 | -0.9 | 1.5 | 0.5 | 2.3 | 0.61 |
328 | 393-021447 | 106.1290406 | 16 | −11.5650778 | 29 | −2.5 | 1.5 | −1.1 | 2.8 | 0.64 |
---|---|---|---|---|---|---|---|---|---|---|
342 | 393-021406 | 106.1041883 | 16 | −11.4835395 | 16 | −3.4 | 1.6 | -0.1 | 1.5 | 0.84 |
362 | 392-020527 | 105.9301680 | 17 | −11.7145245 | 17 | −1.5 | 1.4 | 0.8 | 1.5 | 0.73 |
378 | 392-020519 | 105.9179180 | 28 | −11.7136909 | 23 | −1.8 | 2.8 | 3.2 | 2.2 | 0.6 |
391 | 392-020759 | 106.1285603 | 24 | −11.6316039 | 17 | −2.6 | 2.1 | 1.9 | 1.6 | 0.84 |
401 | 393-021466 | 106.1429036 | 40 | −11.5667806 | 51 | −4.8 | 4.7 | -0.8 | 4.1 | 0.66 |
421 | 393-021260 | 106.0029971 | 17 | −11.4062206 | 16 | −4.8 | 2.3 | 0.3 | 2.1 | 0.79 |
432 | 392-020556 | 105.9666474 | 20 | −11.7345720 | 21 | −1.7 | 1.9 | 0.7 | 2.0 | 0.72 |
456 | 394-020286 | 105.9729062 | 27 | −11.3974145 | 29 | −5.3 | 3.2 | 2.4 | 3.6 | 0.68 |
457 | 393-021421 | 106.1122303 | 15 | −11.4573417 | 16 | −3.7 | 1.5 | 0.2 | 1.5 | 0.82 |
480 | 393-021405 | 106.1035562 | 18 | −11.4436020 | 17 | −2.5 | 2.6 | 3.5 | 1.5 | 0.58 |
535 | 393-021497 | 106.1595942 | 100 | −11.5240609 | 100 | −2.8 | 8.0 | 2.8 | 8.0 | 0.72 |
537 | 393-021500 | 106.1603709 | 30 | −11.5253356 | 30 | −2.8 | 2.5 | 2.8 | 2.5 | 0.71 |
544 | 392-020478 | 105.8189924 | 19 | −11.6645889 | 17 | −2.2 | 2.0 | -0.1 | 1.8 | 0.67 |
557 | 394-020263 | 105.9193250 | 27 | −11.3920539 | 31 | −3.9 | 2.6 | 0.4 | 3.0 | 0.79 |
559 | 393-021504 | 106.1649495 | 17 | −11.5283389 | 108 | −5.0 | 2.2 | 0.2 | 10.2 | 0.70 |
568 | 393-021345 | 106.0661868 | 17 | −11.4015603 | 38 | −4.5 | 1.4 | 1.3 | 3.2 | 0.79 |
636 | 393-021093 | 105.7886430 | 16 | −11.4965078 | 12 | −2.6 | 2.1 | 0.5 | 1.5 | 0.73 |
728 | 393-021503 | 106.1640180 | 15 | −11.4527612 | 24 | −3.3 | 1.5 | 1.4 | 2.3 | 0.75 |
731 | 392-020848 | 106.1893774 | 16 | −11.6331556 | 24 | −4.1 | 1.7 | 1.0 | 2.3 | 0.74 |
778 | 394-020364 | 106.0915403 | 24 | −11.3749025 | 16 | −3.5 | 2.7 | 2.2 | 1.5 | 0.69 |
781 | 392-020854 | 106.1961348 | 16 | −11.6389848 | 16 | −3.9 | 2.6 | 1.0 | 3.4 | 0.72 |
793 | 392-020451 | 105.7608103 | 32 | −11.6379198 | 17 | −2.5 | 3.8 | 1.5 | 1.6 | 0.67 |
806 | 393-021119 | 105.8177209 | 17 | −11.4058306 | 16 | −2.3 | 4.6 | 0.1 | 5.2 | 0.56 |
836 | 393-021540 | 106.1919289 | 18 | −11.4683867 | 19 | −3.9 | 2.0 | 1.8 | 2.2 | 0.69 |
844 | 393-021084 | 105.7723095 | 22 | −11.4539595 | 19 | −4.5 | 3.7 | 2.6 | 4.0 | 0.56 |
903 | 391-021627 | 105.9887286 | 16 | −11.8123475 | 16 | −4.8 | 6.0 | 2.1 | 6.0 | 0.55 |
957 | 393-021586 | 106.2271024 | 14 | −11.5058823 | 24 | −4.9 | 2.2 | 1.4 | 2.5 | 0.55 |
987 | 393-021075 | 105.7460736 | 15 | −11.4571648 | 15 | −3.9 | 1.5 | 1.4 | 1.5 | 0.62 |
1095 | 394-020201 | 105.8297924 | 18 | −11.3439367 | 19 | −3.3 | 6.1 | 1.6 | 7.4 | 0.57 |
Dias et al. [
Open cluster vdB146:
We take 63 stars in a circular region of radius 10' centered at α 0 = 325.71247 ∘ ± 0.03016 ∘ , δ 0 = 66.09753 ∘ ± 0.01222 ∘ . The elliptical subregion of the VPD contains 59 stars.
The parameters ρ 0 = 2.681 ± 0.184 stars / ( ' ) 2 , r 0 = 0.841 ' ± 0.045 ' and ρ f = 0.128 ± 0.007 stars / ( ' ) 2 fit the radial stellar density profile.
The cluster parameters take the values μ α cos δ c = − 2.71 ± 0.25 mas / yr , μ δ c = − 3.32 ± 0.25 mas / yr , σ c = 0.56 ± 0.18 mas / yr and the field parameters μ α cos δ f = − 0.49 ± 1.47 mas / yr , μ δ f = − 0.83 ± 0.71 mas / yr , σ μ α cos δ f = 10.79 ± 1.04 mas / yr and σ μ δ f = 5.21 ± 0.50 mas / yr .
We find five astrometric cluster members and then calculate the equatorial coordinates of the centre of the cluster α c = 325.78423 ∘ ± 0.15297 ∘ , δ c = 66.13575 ∘ ± 0.02907 ∘ and the value of 4.31' for the radius. The location of the members in the spatial distribution and in the VPD is shown with black circles in
Open cluster vdB150:
The model is applied in a circular region of radius 30' and centered at α 0 = 332.412 ∘ ± 0.043 ∘ , δ 0 = 73 .404 ∘ ± 0.012 ∘ with 84 stars. The elliptical subregion of the VPD contains 77 stars.
The parameters ρ 0 = 0.409 ± 0.0163 stars / ( ' ) 2 , r 0 = 2.421 ' ± 0.124 ' and ρ f = 0.024 ± 0.002 stars / ( ' ) 2 adjust the radial stellar density profile.
The cluster parameters take the values μ α cos δ c = 3.07 ± 0.90 mas / yr , μ δ c = 4.65 ± 0.90 mas / yr , σ c = 2.39 ± 0.64 mas / yr and the field parameters μ α cos δ f = − 0.69 ± 1.83 mas / yr , μ δ f = 1.09 ± 1.23 mas / yr , σ μ α cos δ f = 15.32 ± 1.29 mas / yr and σ μ δ f = 10.29 ± 0.87 mas / yr .
Seven stars are found to be the astrometric members of the cluster, three of them are fainter than 13 mag. Therefore, the equatorial coordinates of the centre of the cluster and radius take the values α c = 332.22519 ∘ ± 0.06074 ∘ , δ c = 73.40232 ∘ ± 0.07789 ∘ and 7.25' respectively.
The location of the members in the spatial distribution and in the VPD is shown with black circles in
In summary, the centre coordinates and components of the mean proper motion of each cluster are shown in
We analyse the incidence of stellar proper motions errors in the determination of the cluster parameters and stellar membership. We follow the method proposed
No. | UCAC4 | α [˚] | ϵ α [mas] | δ [˚] | ϵ δ [mas] | μ α cos δ | ϵ μ α cos δ | μ δ | ϵ μ δ | P c i |
---|---|---|---|---|---|---|---|---|---|---|
[mas/yr] | [mas/yr] | |||||||||
4 | 781-037984 | 325.7090821 | 14 | 66.1097712 | 12 | −3.6 | 0.6 | −4.0 | 0.7 | 1.00 |
6 | 781-037989 | 325.7441039 | 24 | 66.1029014 | 23 | −2.1 | 1.0 | −3.1 | 0.9 | 1.00 |
12 | 781-037993 | 325.7783568 | 28 | 66.1150281 | 27 | −1.9 | 1.0 | −2.8 | 2.4 | 0.99 |
23 | 781-037976 | 325.6679480 | 22 | 66.1686000 | 36 | −3.1 | 1.3 | −3.4 | 2.0 | 0.94 |
65 | 781-038012 | 325.9598056 | 24 | 66.1465675 | 14 | −3.0 | 0.9 | −3.3 | 1.1 | 0.55 |
No. | UCAC4 | α [˚] | ϵ α [mas] | δ [˚] | ϵ δ [mas] | μ α cos δ | ϵ μ α cos δ | μ δ | ϵ μ δ | P c i |
---|---|---|---|---|---|---|---|---|---|---|
[mas/yr] | [mas/yr] | |||||||||
1 | 817-026634 | 332.4172003 | 3 | 73.3909014 | 3 | 5.7 | 1.2 | 4.0 | 1.4 | 1.00 |
18 | 817-026638 | 332.5618659 | 23 | 73.3626687 | 38 | 2.4 | 1.6 | 4.5 | 3.5 | 0.99 |
22 | 817-026624 | 332.2750918 | 76 | 73.3474664 | 71 | 4.6 | 5.0 | 1.6 | 5.2 | 0.97 |
24 | 818-027029 | 332.2982621 | 22 | 73.4727898 | 21 | 0.8 | 5.0 | 4.0 | 6.9 | 0.98 |
33 | 817-026636 | 332.5407018 | 135 | 73.3221962 | 80 | 1.0 | 5.2 | 7.7 | 4.7 | 0.95 |
54 | 817-026629 | 332.3280112 | 111 | 73.3015528 | 110 | 2.2 | 5.2 | 1.3 | 5.5 | 0.93 |
67 | 818-027020 | 332.1690986 | 88 | 73.5030850 | 93 | 2.5 | 12.1 | 8.2 | 6.2 | 0.90 |
Cluster | α c [˚] | δ c [˚] | μ α cos δ [mas/yr] | μ δ [mas/yr] | N | D ['] |
---|---|---|---|---|---|---|
vdB92 | 105.97281 ± 0.13113 | −11.57814 ± 0.10575 | −3.46 ± 0.19 | 1.27 ± 0.19 | 60 | 34 |
vdB146 | 325.78423 ± 0.15297 | 66.13575 ± 0.02907 | −2.71 ± 0.25 | −3.32 ± 0.25 | 5 | 9 |
vdB150 | 332.22519 ± 0.06074 | 73.40232 ± 0.07789 | 3.07 ± 0.90 | 4.65 ± 0.90 | 7 | 15 |
by Chen et al. [
Comparing these results to those obtained in Subsection 3.2 (see
In addition, the effect of the proper motion errors on the determination of cluster members for each cluster is examined. Therefore, we count the number
μ α cos δ [mas/yr] | μ δ [mas/yr] | N | |
---|---|---|---|
vdB92 | −3.41 ± 0.04 | 1.26 ± 0.04 | 57 ± 1 |
vdB146 | −2.60 ± 0.04 | −3.39 ± 0.07 | 4 ± 1 |
vdB150 | 3.37 ± 0.30 | 4.40 ± 0.21 | 7 ± 1 |
of times in which a cluster member obtained in Subsection 3.2 keeps its membership condition throughout the 25 simulations.
It is easy to see that between 80% and 90% of the members maintain their condition, despite the proper motion errors.
We compare the stellar astrometric membership condition in the regions of vdB92, vdB146 and vdB150 with the photometric one given in the literature.
Open cluster vdB92:
In 2010, Bonatto and Bica made an infrared photometric analysis using 2MASS data and derived fundamental parameters. We take these parameters to plot the CMD of the 60 astrometric members (
In their investigation, Bonatto and Bica [
Open cluster vdB146:
We analyse the astrometric membership condition of the nine cluster members obtained by Aveni and Hunter [
Taking into account that cluster members must share similar kinematic features, the VPD of the photometric members (
Straižys et al. [
While comparing our results with these six cluster members, it can be seen that only star No. 105 (UCAC4 781-037982) does not fulfil the astrometric membership condition due to its proper motion. These results are shown in
Open cluster vdB150:
Aveni and Hunter [
Even if the Aveni and Hunter’s stellar membership criterion of the sampling indicates an uncertainty for all the 18 stars, our study shows that four of these stars are astrometic members, 10 do not fulfil this condition due to the values of their proper motions, two are excluded of the analysis as they have no proper motion and two are located further than 30' of the adopted centre. These results are shown in
Aveni and Hunter’s number | UCAC4 | V [mag] | B − V [mag] | μ α cos δ [mas/yr] | μ δ [mas/yr] | astrometric member |
---|---|---|---|---|---|---|
1 | 781-037989 | 10.26 | 0.44 | −2.1 | −3.1 | yes |
2 | 781-037993 | 12.19v? | 0.88 | −1.9 | −2.8 | yes |
3 | 781-037991 | 13.26 | 0.72 | - | - | - |
4 | 781-037984 | 10.09 | 0.39 | −3.6 | −4.0 | yes |
7 | 781-038012 | 12.35 | 0.61 | −3.0 | −3.3 | yes |
9 | 781-037982 | 13.25 | 0.45 | −4.5 | 3.5 | no |
10 | 781-037976 | 12.38 | 0.57 | −3.1 | −3.4 | yes |
23 | 782-037014 | 10.62 | 1.26 | −6.7 | −13.6 | no |
24 | 780-039381 | 10.66 | 0.31 | −4.1 | −8.6 | no |
catalogue (HIP 109389). This distance is in good agreement with the location of the cluster at 316.2 pc determined by Aveni and Hunter [
Taking profit that open cluster members share similar photometric and kinematic properties, astrometric and photometric results are combined in this work to reduce the uncertainty introduced by each technique individually.
We report that vdB92 has μ α cos δ c = − 3.46 ± 0.19 mas / yr , μ δ c = 1.27 ± 0.19 mas / yr , σ c = 1.44 ± 0.13 mas / yr , 60 astrometric members, α c = 105.97281 ∘ ± 0.13113 ∘ , δ c = − 11.57814 ∘ ± 0.10575 ∘ and a value of 34' for the diameter. In the case of vdB146, the obtained values of these parameters are μ α cos δ c = − 2.71 ± 0.25 mas / yr , μ δ c = − 3.32 ± 0.25 mas / yr , σ c = 0.56 ± 0.18 mas / yr , 5 members, equatorial centre coordinates α c = 325.78423 ∘ ± 0.15297 ∘ , δ c = 66.13575 ∘ ± 0.02907 ∘ and a diameter of 9'. In the case of vdB150, the obtained values of these parameters are μ α cos δ c = 3.07 ± 0.90 mas / yr , μ δ c = 4.65 ± 0.90 mas / yr , σ c = 2.39 ± 0.64 mas / yr , 7 members, equatorial centre coordinates α c = 332.22519 ∘ ± 0.06074 ∘ , δ c = 73.40232 ∘ ± 0.07789 ∘ and a diameter of 15'. It is worthy to mention that the astrometric parameters of vdB146 and vdB150 are determined for the first time using UCAC4 data.
The incidence of proper motion errors in the determination of the cluster parameters and of the stellar membership is evaluated by applying the model to 25 simulated samples of each cluster. We conclude that the observational errors do
Aveni and Hunter’s number | UCAC4 | V [mag] | B − V [mag] | μ α cos δ [mas/yr] | μ δ [mas/yr] | astrometric member |
---|---|---|---|---|---|---|
1 | 817-026634 | 8.38 | 0.09 | 5.7 | 4.0 | yes |
2 | 815-027770 | 8.11 | 1.18 | −5.0 | 11.4 | no |
3 | 817-026679 | 5.96v? | 1.00 | 21.5 | 20.6 | no |
4 | 817-026677 | 8.49 | 0.16 | 20.2 | 23.8 | no |
5 | 819-026990 | 8.12 | 0.43 | 40.8 | 37.1 | no |
6 | 814-028129 | 6.95 | 1.93 | −11.0 | −9.0 | no |
8 | 816-027561 | 12.09 | 0.98 | −0.8 | 6.1 | no |
9 | 816-027570 | 11.13 | 0.62 | −10.5 | −6.2 | no |
10 | 816-027578 | 11.42 | 0.62 | −9.2 | −12.2 | no |
11 | 817-026638 | 11.51 | 0.91 | 2.4 | 4.5 | yes |
12 | 817-026648 | 10.02 | 1.67 | 9.4 | 7.2 | no |
13 | 818-027034 | 9.23 | 0.28 | −4.4 | −15.1 | no |
14 | 818-027020 | 10.61 | 0.59 | 2.5 | 8.2 | yes |
15 | 818-027055 | 12.12 | 1.70 | - | - | - |
16 | 818-027029 | 12.41 | 0.79 | 0.8 | 4.0 | yes |
17 | 818-027035 | 12.47 | 0.81 | 23.4 | 37.0 | no |
18 | 818-027036 | 12.46 | 1.20 | - | - | - |
19 | 818-027043 | 12.48 | 1.36 | 3.0 | 36.3 | no |
not significantly change the mean proper motion and the number of members of the examined clusters.
Finally, we compare our membership results and the photometric ones given in the literature to lead to a successful membership determination. In the case of vdB92, we take Bonatto and Bica [
This work was supported by Consejo Nacional de Investigaciones Cientficas y Técnicas (CONICET), Argentina, and by Universidad Nacional de La Plata (UNLP) under grant no. 11/G114.
Orellana, R.B., De Biasi, M.S. and Paiz, L.G. (2017) Membership Determination of van den Bergh Open Clusters vdB92, vdB146 (NGC 7129) and vdB150. International Journal of Astronomy and Astrophysics, 7, 273-290. https://doi.org/10.4236/ijaa.2017.74023