A Study on the Fundamental Properties of Open Cluster NGC 6791 Based on the SDSS-DR8 and 2MASS Data

ELSEVIER

CHINESE ASTRONOMY AND ASTROPHYSICS Chinese Astronomy and Astrophysics 36 (2012) 1–11

A Study on the Fundamental Properties of Open Cluster NGC 6791 Based on the SDSS-DR8 and 2MASS Data†  GAO Xin-hua1 CHEN Li

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School Of Information Science and Engineering, Changzhou University, Changzhou 213164 2 Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030 1

Abstract The stellar spectroscopic data of SDSS-DR8 (The Eighth Data Release of Sloan Digital Sky Survey) and the near-infrared photometric data of 2MASS (Two Micron All Sky Survey) point sources are used to analyze the fundamental parameters of the open cluster NGC 6791. Using the radial velocities of 274 stars in the region of the cluster, we calculate the membership probability for each star with the maximum likelihood method. Based on the stars with high membership probabilities, we have derived the radial velocity and metal abundance of the cluster to be respectively Vr =-46.4±0.2 km·s−1 and [F e/H] =0.32±0.11 dex, in good agreement with the results obtained by other authors on the basis of high-resolution spectroscopy. Using red clump giants in the cluster as “standard candle”, we have derived the absolute distance modulus of the cluster to be (m − M )0 =13.02±0.08 mag or 4.02±0.15 kpc in distance, consistent with the values obtained from main-sequence fittings by some authors. And our main conclusions are: (1) NGC 6791 is extremely metal-rich; (2) Within the spectral resolution of SDSS, the discriminated 87 cluster members have no evident difference in matallicity; (3) The obtained distance modulus is insensitive to the age, metallicity and dust distinction, so it is a kind of reliable indirect measurement. Key words: open clusters and associations: individual, NGC 6791—stars: metal abundance —stars: distance—stars: radial velocity †

Supported by National Natural Science Foundation Received 2010–02–24; revised version 2010–03–23  A translation of Acta Astron. Sin. Vol. 52, No. 4, pp. 265–274, 2011 � [email protected]; [email protected]

0275-1062/11/$-see front matter 2012 Elsevier All rights reserved. c 2012B.V. 0275-1062/01/$-see front © matter  Elsevier Science B. V. All rights reserved. doi:10.1016/j.chinastron.2011.12.003 PII:

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1. INTRODUCTION The open cluster is a relatively loose stellar system in which stars are bound together purely by the gravitational force, its member stars have approximately similar ages, metal abundances, and spatial velocities. Relative to the field stars, the age, distance, metallicity, reddening, and some other important parameters of an open cluster are more easy to be precisely determined. Hence, for a long time, open clusters are considered by astronomers as the tracer objects in the structure and evolution studies of the Galactic disk[1−2] . As the cluster’s member stars have the characteristics of simple age, broad mass distribution, and uniform chemical composition, astronomers often take an open cluster as the important laboratory to study the star formation and evolution. For example, initially, the red clump giants, as an important evolutionary stage of low-mass stars, were discovered occasionally by Cannon[3] in the study of old open clusters. NGC 6791 (αJ2000 = 19h 20m 53s ; δJ2000 = +37◦ 46� 18�� ) is normally considered to be an open cluster yet to date, but it differs obviously from other known open clusters. It is a kind of rather compact rich cluster with more member stars, easy to be mistaken for a spherical cluster by its shape[4] . Not long ago, Platais et al.[5] estimated its total mass being about 5000 M� , bigger than any common open cluster. Based on high-resolution spectroscopy, several authors have given a rather coincident metallicity of [F e/H] ∼+0.4 dex[6−9] , much higher than those of common open clusters. Based on the high-quality photometric data, several authors have plotted its color-magnitude diagram (CMD) and estimated its age to be in the range of 8∼10 Gyr[4−5,9−10] , so NGC 6791 belongs to the oldest type of open clusters, and its age is similar to that of a rather young spherical cluster. Not long ago, some authors revealed the double-peaked structure in the white dwarf luminosity function (WDLF) of NGC 6791, and the evident difference between the age determined from the WDLF and that determined by the main-sequence turnoff (MS-TO) of stars[11−13] . Recently, some authors indicated further that between the stars in the inner and outer regions of NGC 6791 exists an 1 Gyr age difference, and that the stars in the inner region are even older in average[14]. If it is true, this means that the star formation process in NGC 6791 may differ from that of common clusters, namely, NGC 6791 has probably undergone two times of star formation processes, and therefore it is not an open cluster of traditional meaning. In 2006, Carraro et al.[6] suggested that NGC 6791 is probably the nuclear part of a bigger stellar system disrupted by the Galactic tidal force, and that this stellar system has been very effective to the metal-enrichment process. In 2009, Boesgard et al.[9] also pointed out that the orbit of motion of NGC 6791 indicates that it may originate from the metal-rich central region of the Galactic system, and its present position is caused by strong disturbances. The large mass, extreme metal-richness, extreme oldness, peculiar WDLF, 1 Gyr age difference between the stars in the inner and outer regions, these unusual characteristics of NGC 6791 make it become the object being closely concerned about by astronomers constantly. The in-depth study on NGC 6791 will help us with a better understanding on the formation and evolution of stars, as well as the formation and evolution of the Galactic system.



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2. DATA 2.1 SDSS-DR8 The instruments used for the Sloan Digital Sky Survey (SDSS)[15] include a telescope with the 2.5 m aperture and 7 square degree field of view (the angular diameter of viewing field is 3◦ ), and a pair of multi-object fiber spectrographs with the spectral resolution of R =1800[16], which can obtain 640 spectra of objects by observing only once. The data that we used are the data of the Eighth Data Release of SDSS (SDSS-DR8)[17] . Since the second period of the observation program (SDSS-II), SDSS begins to take the study on the Galactic system as one of its major projects. As one of 3 research projects of SDSS-II, the Sloan Extension for Galactic Understanding and Exploration (SEGUE or SEGUE-1, in brief)[18] is an observation project particularly aiming at the Galactic system, the purpose is to make the imaging and spectroscopic observations on a large number of stars in the Galactic disk and halo, and finally to obtain their spatial distribution, radial velocities, chemical compositions, ages, and other important information, and thereby to study the structure and evolution of the Galactic system. The observed data of SEGUE-1 are released with the 7th Data Release (DR7) of SDSS[19] . SEGUE-1 has used a set of programs called as SEGUE Stellar Parameter Pipeline (SSPP, in brief)[20−21] for automatic processing of stellar spectra, which can provide 3 important parameters including the metal abundance of the stellar atmosphere, the equivalent temperature, and the surface gravitational acceleration. The third period of SDSS (SDSS-III)[22] has also arranged the Galactic study as the one (SEGUE-2) of its 4 projects, and as the first data release of SDSS-III, the Eighth Data Release (DR8) of SDSS includes the fundamental atmospheric parameters of 118,000 stars observed in the period of SEGUE-2, in addition to those observed before, the total number of stars with the fundamental atmospheric parameters released in DR8 reaches about 500,000. Besides, DR8 has used an improved SSPP program to recalculate the fundamental atmospheric parameters of all 500,000 stars[17] , so the obtained stellar atmospheric parameters are even more reliable[23] . Now, the up-to-date version of SSPP gives the accuracies of the radial velocity and metal abundance to be 4 km·s−1 and 0.21 dex, respectively[22] . 2.2 2MASS The Two Micron All Sky Survey (2MASS) program is equipped with two highly-automatic 1.3 m diameter telescopes, on which the observations at the J (1.25 μm), H (1.65 μm), and Ks (2.16 μm) 3 near-infrared wavebands can be made simultaneously, the purpose is to make the near-infrared survey on the whole sky. The 2MASS Point Source Catalogue (PSC, in brief) includes the photometric and astrometric data of 470,992,970 sources, in which, most sources are stars in the Galaxy, and each is provided with the position, magnitude, magnitude error, photometric quality, and other information. PSC covers the 99.99% area of all sky, in case of no interference source, its complete limiting magnitudes are J ≤15.8 mag, H ≤15.1 mag, and Ks ≤14.3 mag[24] , respectively. 3. RADIAL VELOCITY AND METAL ABUNDANCE In order to study the fundamental properties of an open cluster, we have to first separate effectively the cluster stars from the field stars, this step is called the “member judgement”.

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The common methods to judge cluster members are of two kinds, namely the photometric method (H-R diagram) and kinematic method (proper motion or radial velocity). The kinematic method is generally believed to be more effective, because that the kinematic method can be set up on the basis of a rather strict mathematical model, and that the model parameters and membership probability can be easily calculated[25] . The theoretical basis of the kinematic method is that the cluster members have consistent velocities of motion in space, the initiative works made by Vasilevskis[26] and Sanders[27] have laid a foundation for judging the membership probability by proper motions, and Zhao et al.[28] and Girard et al.[29] have improved this method to make it suit the case of proper motions of unequal accuracies. Considered the rather high accuracy of radial velocity, we will adopt the radial velocity as the basis of the member judgement of NGC 6791, especially the radial velocities provided by SDSS-DR8 are accurate enough to meet our requirements[23] . Assuming that the radial velocities of the field stars and cluster stars satisfy respectively two Gaussian distributions, considered the unequal accuracies of radial velocities, the distribution functions of radial velocities for the field stars and cluster stars can be expressed as follows: Φ(vi ) = Φf i + Φci , 1 − nc Φf i = 2 + �2 ) αi , 2π(σf0 i nc Φci = 2 + � 2 ) βi , 2π(σc0 i   1 (vi − vf )2 , αi = exp − 2 + �2 2 σf0 i    1 (vi − vc )2 . βi = exp − 2 + �2 2 σc0 i

(1) (2) (3) (4) (5)

Here, vi is the radial velocity of the i-th star, �i is the observational error of vi , nc is the normalized number of cluster stars, Φf i and Φci are respectively the distribution functions of radial velocities for the field stars and cluster stars, vf and vc are respectively the mean radial velocities of the field stars and cluster stars, and σf 0 and σc0 are respectively the intrinsic dispersions of radial velocities for the field stars and cluster stars, the total number of the parameters to be determined is 5. For N stars, we have the the following likelihood functions: L(θj ; j = 1, 5) = ln

N  1

Φ(vi ) =

N 

ln(Φ(vi )) ,

(6)

1

N ∂L ∂  = Φi (θ1 , θ2 ...θ5 ) . ∂θj ∂θj 1

(7)

After the equations of Eq.(7) are solved according to the maximum likelihood principle, the optimum estimates of the 5 parameters of the distribution function of NGC 6791 are obtained as shown in Table 1, and the membership probability of the i-th star can be expressed as Pi =

Φci Φci = . Φ Φci + Φf i

(8)

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Table 1 nc 0.4

55

Distribution parameters of NGC 6791

vf (km·s−1 ) -24.0

vc (km·s−1 ) -46.3

σf0 (km·s−1 ) 33.6

σc0 (km·s−1 ) 2.3

Fig.1 shows the histogram of radial velocities for the 274 sample stars selected in the region of NGC 6791 (1◦ × 1◦ , centered at the cluster’s center), from this figure we can find that the radial velocities of numerous stars are concentrated around -50 km·s−1 . 150

100 N



50

0 −200

Fig. 1

−150

−100

−50 0 Vr / (km�s−1)

50

100

Distribution of radial velocities for the 274 stars in the region of NGC 6791

From the histogram of membership probabilities (Fig.2) and the spatial distribution of stars (Fig.3), we can find that our membership judgment is effective. In order to remove as possible the field-star pollution, we select artificially 95 stars with a membership probability P >0.7 as the cluster members to participate in the calculations of cluster’s mean radial velocity and metal abundance. Using the 95 cluster member stars, we have calculated the cluster’s mean radial velocity and its uncertainty to be Vr =-46.4±0.2 km·s−1 . The pollution of field stars can not be removed completely by only radial velocities, in fact, as shown in Fig.3, a few sample stars far apart the cluster center are still very possible to be the field stars, although their membership probabilities are greater than 0.7. This situation exists even in the region around the cluster center. Hence, in the calculation of cluster’s mean metallicity, we have deleted first the 5 stars lying beyond the tidal radius but with P >0.7 (refer to Fig.3), the tidal radius adopts rtidal =10 arcmin[5] . Besides, it is necessary to delete those sample stars inside the tidal radius, although whose membership probabilities are greater than 0.7, but whose metal abundances are very different from others. If the number of this kind of stars is extremely small, and the difference of metal abundance is significant, then we suppose that they are very possible to be the field-star pollution. If the number of these stars is rather large and their metal abundances are relatively consistent, then we suppose that a certain difference of metal abundance exists among the member stars of NGC 6791. Consequently,

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200

150

N

100

50

0 0.0

0.2

0.4

P

0.6

0.8

1.0

Fig. 2 Distribution of membership probabilities for the 274 stars in the region of NGC 6791

38.2

Dec / o

38.0 37.8 37.6 37.4 37.2 289.6 289.8 290.0

290.2 290.4 290.6 290.8 RA / o

Fig. 3 The spatial distribution of the 274 stars with different membership probabilities. Crosses indicate the stars with P >0.7, dots indicate the stars with P <0.7, and “⊕” indicates the star lying beyond the tidal radius but with P >0.7

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we have deleted 3 sample stars whose metal abundances are greater than the 3 times of the rms error of the mean metal abundance, these deleted sample stars of high membership probability have obviously different metal abundances (see Fig.4). Finally, 87 member stars are used for calculating the mean metal abundance, the calculated mean metal abundance and its uncertainty are [F e/H] =0.32±0.11 dex. Considered the spectral resolution of SDSS spectra (R �1800), the metallicity spread of the 87 member stars is not apparent (see Fig.4). And the obtained mean radial velocity and metal abundance are coincident very well with the results obtained by other authors on the basis of high-resolution spectroscopy[6−9]. It is noteworthy that the DR7-SSPP may underestimate significantly the metal abundance [F e/H] for the stars exceeding the solar abundance, for such a metal-rich cluster NGC 6791, it is underestimated for about 0.3 dex, this point has been discussed in our previous paper[30] , but the improved DR8-SSPP has successfully solved this problem. 80

60

60

40

40

20

20

N

80

0 −4 80

−3

−2

−1

0

1

60

40

40

20

20

0 −4

Fig. 4

0 −4 80

60 N



−3

−2 −1 [Fe/H] / dex

0

1

0 −4

−3

−2

−1

−3

−2 −1 [Fe/H] / dex

0

1

0

1

Upper left: Distribution of [F e/H] for 274 stars; Upper right: Distribution of [F e/H] for the 95

stars with P >0.7; Lower left: Distribution of [F e/H] for the 90 stars lying inside the tidal radius and with P >0.7; Lower right: Distribution of [F e/H] for the 87 stars lying inside the tidal radius and with P >0.7, after a 3σ deletion

4. ABSOLUTE DISTANCE MODULUS BASED ON RED CLUMP GIANTS Red clump giants are small-mass stars at the stage of helium core burning, in the H-R diagram they are obviously clustered, in addition to the very small luminosity dispersion, hence very easy to be discriminated. Theoretical and observational studies indicate that the red clump giants have approximately the identical luminosity, and the luminosity at

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some wavebands is almost independent to the metal abundance and age, so they are a kind of perfect “standard candle”[31−36] . In 2007, using the 2MASS data, van Helshoecht et al.[35] analyzed the absolute magnitudes of the red clump giants in a sample of 24 open clusters, as well as the relationships of the absolute magnitude with the age and metal abundance. This 24 open clusters cover wide ranges in both age and matallicity, for them, the distance modulus has been obtained previously by main-sequence fitting, according to the distance modulus and referring to the apparent magnitudes of red clump giants, the absolute magnitudes of red clump giants can be obtained. van Helshoecht et al.[35] concluded that the absolute magnitude of red clump giants is Mk = −1.57±0.05 mag, and that in the ranges of age and metallicity of the cluster sample, this value is less affected by the age and metallicity, so it can be used as an idea “standard candle”. This work is an indirect measurement on the absolute magnitude of red clump giants, the premise is that the cluster sample has reliable values of distance, metallicity, and age. In 2008, with the revised Hipparcos astrometric data, Groenewegen[36] remeasured the absolute magnitude for a group of sample red clump giants around the sun, which have highly accurate triangular parallaxes and high-quality spectroscopic metallicity values, and obtained the absolute magnitude to be MKs =-1.54±0.04 mag, correlated very weakly with the metallicity. Groenewegen’s work[36] is a direct measurement on the Ks-band absolute magnitude of red clump giants. Using the J-band and Ks-band photometric data provided by the PSC of 2MASS, we have plotted the color-magnitude diagram (CMD) (see Fig.5) for the stars in the region of NGC 6791 (within 5 arcmin from the cluster center, in consistence with the size given by the Dias’s open cluster catalogue[37] ). From this CMD, we can find that NGC6791 is very old in deed, most stars in it have left the main sequence. And from the CMD we can find easily a certain amount of red clump giants exist truly in NGC 6791. Judging by eyes, we have marked the region of red clump giants with a rectangular frame in the CMD (see Fig.5). The range of colors covered by the rectangular frame is: 0.7≤ J − Ks ≤0.8 mag, the range of magnitudes is: 11.3≤ Ks ≤11.7 mag, and this region contains 19 red clump giants. In order to reduce as possible the error caused by infiltrated field stars, we adopt the median value mKs =11.52 mag of the Ks magnitudes of 19 red clump giants as the mean apparent magnitude, its dispersion is 0.07 mag. Thus, we obtain the mean apparent magnitude of red clump giants to be mKs =11.52±0.07 mag. Considered that the error of Ks magnitude at 11.52 mag is less than 0.025 (refer to Fig.5), we have neglected the effect of the observational error of Ks magnitudes of red clump giants on the calculation of distance modulus. By the following formula, we can obtain the absolute distance modulus of NGC 6791: (m − M )0 = mKs − MKs − AKs ,

(9)

in which (m − M )0 is the cluster’s absolute distance modulus, AKs is the value of dust distinction at the Ks waveband. We adopt the distinction relation AKs /Av =0.118[38], the value of reddening E(B − V ) adopts 0.117 mag[37] , and the Ks-band absolute magnitude of red clump giants adopts the value (-1.54±0.04 mag) obtained by Groenewegen[36] in 2008 on the basis of revised Hipparcos data. Finally, we obtain the absolute distance modulus of NGC 6791 to be (m−M )0 =13.02± 0.08 mag, or (4.02±0.15) kpc in distance. This result agrees well with the results obtained by fitting isochrones in Refs.[4,6,10]. Compared with the traditional method of isochrone fitting, the major advantage of our method is that only the directly observed values are

GAO Xin-hua and CHEN Astronomy andand Astrophysics 36 (2012) 1–11 GAO Xin-hua et Li al./ /Chinese Chinese Astronomy Astrophysics 36 (2012) 1–11

9

8

8

9

9

10

10

Ks / mag

Ks / mag

used (refer to Eq.(9)), we need not to refer to the information about the age and metallicity of the cluster, and that the effect of the distinction value is much less than that of the optical waveband. In 2005, with the observed data obtained from the 4m telescope at Kitt Peak and the IRIM infrared camera, Carney et al.[39] measured the distance of NBGC 6791, and also by using the red clump giants as “standard candle”, they obtained the absolute distance modulus to be (m−M )0 =13.07±0.04 mag. This value is a little larger than ours, it is mainly because that for the red clump giants, the absolute magnitude Mk =-1.61±0.03 mag given by Alves[33] was used by them, which is about 0.07 mag brighter than the value obtained by Groenewegen in 2008.

11 12 13

11 12 13

14

−0.5

0.0

0.5 1.0 J−Ks / mag

14

1.5

0.20

0.20

0.15

0.15

0.10 0.05 0.00

6

8

10

12 14 J / mag

0

20

40

60

80

100

12

14

16

N

Ks error / mag

J error / mag



16

18

0.10 0.05 0.00

6

8

10

Ks / mag

Fig. 5 Upper left: Color-magnitude diagram for stars lying within 5 arcmin from the center of NGC 6791. The rectangle indicates the region of red clump giants; Upper right: Distribution of Ks-band magnitudes, corresponding to the CMD; Lower left: J-band magnitude versus magnitude error. The vertical line indicates the complete limiting magnitude (15.8 mag); Lower right: Ks-band magnitude versus magnitude error. The vertical line indicates the complete limiting magnitude (14.3 mag)

5. CONCLUSIONS Using the stellar spectroscopic data of SDSS-DR8 and the near-infrared photometric data of 2MASS, we have analyzed the radial velocity, metal abundance and absolute distance

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modulus of the famous stellar cluster NGC 6791. The obtained radial velocity and metal abundance are coincident very well with the results obtained by several other authors on the basis of high-resolution spectroscopy, but the samples adopted by these authors are relatively small, including only rather bright giants. Our sample includes 274 stars, there are 95 stars judged as high-probability member stars, in which the 5 high-probability stars positioned beyond the tidal radius of NGC 6791, in addition to the other 3 stars with metal abundances deviated obviously from the others, are deleted in the calculation of the mean metal abundance of the cluster. Within the spectral resolution of SDSS, no apparent metallicity difference has been found among the 87 member stars. We believe that this is more likely caused by the relatively consistent metal abundances of the member stars in NGC 6791, rather than by the selection effect of our sample, even though some one suggested recently that an 1 Gyr age difference probably exists among the stars in NGC 6791[14], but it can hardly cause a significant metallicity difference. Besides, using the red clump giants as the “standard candle”, we have obtained the absolute distance modulus of NGC 6791, and it agrees very well with the results obtained by other authors using the isochrone fitting method. Because of the very weak correlations of the near-infrared absolute Ks magnitude of red clump giants with the metal abundance and age, the distance modulus given by us is insensitive to the age and metal abundance of the cluster, furthermore, the photometric data at the near-infrared Ks waveband are used, the effect of the uncertainty of dust distinction is also very small. ACKNOWLEDGEMENT This study has used the data of Sloan Digital Sky Survey and the data of the Point Source Catalogue of 2MASS. We thank the Referee for valuable suggestion. References 1

Friel E. D., ARA&A, 1995, 33, 381

2

Chen L., Hou J. L., Wang J. J., AJ, 2003, 125, 1397

3

Cannon R. D., MNRAS, 1970, 150, 111

4

King I. R., Bedin L. R., Piotto G., et al., AJ, 2005, 130, 626

5

Platais I., Cudworth K. M., Kozhurina-Platais V., et al., ApJ, 2011, 733, L1

6

Carraro G., Villanova S., Demarque P., et al., ApJ, 2006, 643, 1151

7

Origlia L., Valenti E., Rich R. M., et al., ApJ, 2006, 646, 499

8

Gratton R., Bragaglia A., Carretta E., et al., ApJ, 2006, 642, 462

9

Boesgaard A. M., Jensen E. E. C., Deliyannis C. P., AJ, 2009, 137, 4949

10

Chaboyer B., Green E. M., Liebert J., AJ, 1999, 117, 1360

11

Bedin L. R., Salaris M., Piotto G., et al., ApJ, 2005, 624, L45

12

Bedin L. R., King I. R., Anderson J., et al., ApJ. 2008, 678, 1279

13

Bedin L. R., Salaris M., Piotto G., et al., ApJ, 2008, 679, L29

14

Twarog B. A., Carraro G., Anthony-Twarog B. J., ApJ, 2011, 727, L7

15

York D. G., Adelman J., Anderson J. E. Jr., et al., AJ, 2000, 120, 1579

16

Gunn J. E., Siegmund W. A., Mannery E. J., et al., AJ, 2006, 131, 2332

17

Aihara H., Allende Prieto C., An D., et al., ApJS, 2011, 193, 29

18

Yanny B., Rockosi C., Newberg H. J., et al., AJ, 2009, 137, 4377

19

Abazajian K. N., Adelman-McCarthy J. K., Agueros M. A., et al., ApJS, 2009, 182, 543



GAO Xin-hua and CHEN Li / Chinese Astronomy and Astrophysics 36 (2012) 1–11 GAO Xin-hua et al. / Chinese Astronomy and Astrophysics 36 (2012) 1–11

20

Lee Y. S., Beers T. C., Sivarani T., et al., AJ, 2008, 136, 2022

21

Lee Y. S., Beers T. C., Sivarani T., et al., AJ, 2008, 136, 2050

22

Eisenstein D. G., Weinberg D. H., Agol E., et al., arXiv: 1101.1529

23

Smolinski J. P., Lee Y. S., Beers T. C., et al., AJ, 2011, 141, 89

24

Skrutskie M. F., Cutri R. M., Stiening R., et al., AJ, 2006, 131, 1163

25

Shi Huo-ming, Zhao Jun-liang, Progress of Astronomy, 1992, 10, 22

26

Vasilevskis S., AJ, 1962, 67, 699

27

Sanders W. L., A&A, 1971, 14, 226

28

Zhao J. L., He Y. P., A&A, 1990, 237, 54

29

Girard T. M., Grundy W. M., Lopez C. E., et al., AJ, 1989, 98, 227

30

Gao X. H., Chen L., RAA, 2010, 10, 761

31

Paczynski B., Stanek K. Z., ApJ, 1998, 494, L219

32

Sarajedini A., AJ, 1999, 118, 2321

33

Alves D. R., ApJ, 2000, 539, 732

34

Grocholski A. J., Sarajedini A., AJ, 2002, 123, 1603

35

van Helshoecht V., Groenewegen M. A. T., A&A, 2007, 463, 559

36

Groenewegen M. A. T., A&A, 2008, 488, 935

37

Dias W. S., Alessi B. S., Moitinho A., et al., A&A, 2002, 389, 871

38

Dutra C. M., Santiago B. X., Bica E., A&A, 2002, 381, 219

39

Carney B. W., Lee J. W., Dodson B., AJ, 2005, 129, 656

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