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2MASS analytical study of four open cluster candidates
New Astronomy 52 (2017) 55–64
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2MASS analytical study of four open cluster candidates D. Bisht a,c,∗, R.K.S. Yadav b, A.K. Durgapal c a
Physical Research Laboratory, Ahmedabad, 380009, India Aryabhatta Research Institute of Observational Sciences, Manora Peak Nainital 263 002, India c Department of Physics, DSB Campus, Kumaun University, Nainital-263002, Uttarakhand, India b
h i g h l i g h t s • • •
The fundamental parameters of the clusters under study are derived. Luminosity and mass function have been studied for these objects. We have found mass segregation effect for these clusters and they are dynamically relaxed.
a r t i c l e
i n f o
Article history: Received 10 June 2016 Revised 18 October 2016 Accepted 25 October 2016 Available online 26 October 2016 Keywords: Star: colour-magnitude diagrams-open cluster and associations: individual: Teutsch 126 Teutsch54 Teutsch 61 and Czernik 3 Mass function Mass segregation
a b s t r a c t The astrophysical parameters of four poorly studied open star clusters namely Teutsch 126, Teutsch 54, Teutsch 61 and Czernik 3, have been estimated using the Two Micron All Sky Survey (2MASS) database. The stellar density distributions and color-magnitude diagrams are used to determine their structural parameters (cluster center, cluster radius, core radius, tidal radius, Galactocenteric coordinates and the distance from the Galactic plane). We have also derived age, color excesses, total mass, relaxation time, luminosity and mass function for each clusters. The mass function slopes for these clusters are derived as 1.59 ± 0.62, 1.31 ± 0.60, 1.22 ± 0.75 and 1.62 ± 0.56 for Teutsch 126, Teutsch 54, Teutsch 61 and Czernik 3 respectively. These values are very close with the Salpeter value (x = 1.35) within the errors. The effect of mass-segregation are observed in the clusters Teutsch 126 and Teutsch 61. Estimated values of dynamical relaxation time are less than age of the clusters under study. This concludes that these objects are dynamically relaxed. The possible reason for relaxation may be due to the dynamical evolution or imprint of star formation or both. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Open star clusters (OCs) are key objects in studying the formation and evolution of the Galactic disk. They are self gravitating stellar systems formed along the gas and dust rich Galactic plane. They contain from tens to a few thousands stars distributed in an approximately spherical structure of up to a few parsecs in radius. Gaburov and Gieles (2008) provided statistically significant samples of star clusters of known distance, age and metallicity. Estimation of astrophysical and evolutionary parameters, such as distance, age, cluster density, core radius, size of the cluster and relaxation time are very important to develop theoretical models on the Galactic structure. Our aim is to study star clusters within the disk of Galaxy, which is normally obscured by dust and gas clouds. For the present study we have used the Two Micron All Sky Survey (2MASS) ∗
Corresponding author. Fax: +91 5942 233439, +917929703573. E-mail addresses: [email protected] (D. Bisht), [email protected] (R.K.S. Yadav), [email protected] (A.K. Durgapal). http://dx.doi.org/10.1016/j.newast.2016.10.009 1384-1076/© 2016 Elsevier B.V. All rights reserved.
near-IR photometric data. Such type of data help us to solve the star formation problems and to understand the spiral structure of the Milky Way Galaxy. This survey has proven to be a powerful tool in the analysis of the structure and stellar content of open clusters (Bonatto and Bica, 2003). Recently more than thousands of open clusters have been discovered by analysing 2MASS data (Kronberger et al., 2006; Froebrich et al., 2007; Koposov et al., 2008; Glushkova et al., 2010). The basic astrophysical parameters for ∼ 1500 open clusters have been calculated by Kharchenko et al. (2013) using 2MASS JHKs and PPMXL data. Number of known open clusters in the Milky Way Galaxy are ∼ 30 0 0 (Kharchenko et al., 2013), while the expected number of open clusters are approximately 104 − 105 . Therefore, most of the open clusters are hidden in the highly obscured Galactic plane. Over this large sample of data, only few clusters are studied in detail, but most of them are unstudied or poorly studied in the literature. In the light of above discussions we aim to estimate the fundamental parameters of open star clusters Teutsch 126 (Teu 126), Teutsch 54 (Teu 54), Teutsch 61 (Teu 61) and Czernik 3 (Cz 3). To the best of our knowledge there is no detailed study available in
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the literature for these clusters. Bonatto and Bica (2010) have estimated the fundamental parameters for open clusters Teu 126 and Teu 54, using the same dataset (2MASS), but stars selection criteria is different. We have used the same procedure for cluster stars selection as given in Tadross et al. (2011). Clusters Teu 61 and Cz 3 never studied before so there is no much information in the literature about these two clusters. OCs Teu 126, Teu 54 and Cz 3 are located in the second while Teu 61 is located in the third Galactic quadrant. The two clusters Teu 126 and Cz 3 are below the Galactic plane while Teu 54 and Teu 61 are above the Galactic plane. Teu 126, Teu 54 and Cz 3 are intermediate clusters while Teu 61 is younger age open star cluster. This paper is organized as follows. Section 2 presents the description of used data set. In Section 3, we described the derivation of different fundamental parameters of the clusters. The luminosity and mass functions are presented in Section 4. Dynamical state of the clusters are described in Section 5. Finally, the conclusions are drawn in Section 6.
Table 1 Fundamental parameters of the clusters taken from Dias et al. (2002). Name Teutsch Teutsch Teutsch Czernik
126 54 61 3
α 2000
δ 2000 (deg)
l (deg)
b (deg)
d (pc)
log(age)
(deg) 333.30 341.70 113.65 15.76
55.72 59.77 −19.78 62.78
101.9 107.9 235.3 124.2
-0.6 0.6 0.1 −0.1
1740 2890 1920 1410
8.6 8.9 6.9 8.0
Table 2 Structural parameters of the clusters Teutsch 126, Teutsch 54, Teutsch 61 and Czernik 3. Background and central density are in the unit of stars per arcmin2 . rc is in arcmin while Rt (Tidal radius) is in pc. Name Teutsch Teutsch Teutsch Czernik
126 54 61 3
f0
fb
rc
Rt
δc
6.8 3.4 5.2 7.3
0.8 1.3 2.5 3.0
0.3 0.6 1.3 0.6
6.6 5.5 6.2 5.8
9.0 2.6 2.0 3.4
2. Data used 3.2. Radial density profiles The purpose of the present study is to derive the astrophysical parameters of clusters Teu 126, Teu 54, Teu 61 and Cz 3 by using 2MASS Point Source catalogue (Cutri, 2003). The 2MASS (Skrutskie et al., 2006) uses two highly automated 1.3m telescope (one at Mt. Hopkins, Arizona (AZ), USA and other at CTIO, Chile) with a 3channel camera ((256 × 256) array of HgCdTe detectors in each channel). This 2MASS photometric catalogue provides J (1.25 μm), H (1.65 μm) and Ks (2.17 μm) band photometry for millions of galaxies and nearly a half-billion stars (Carpenter, 2001). The sensitivity of 2MASS catalogue is 15.8 mag for J, 15.1 mag for H and 14.3 mag for Ks band at S/N = 10. The photometric data are taken within the radius of 20 arcmin from the cluster center. Identification maps for the clusters are taken from Leicester Database and Archive Service (LEDAS) as shown in Fig 1. The errors given in 2MASS catalogue for J, H and Ks band are plotted against J magnitudes in Fig 2. This figure shows that the mean error in J, H and Ks band is ≤ 0.05 at J ∼ 13.0 mag. The errors become ∼ 0.09 at J ∼ 15 mag. 3. Estimation of fundamental parameters 3.1. Cluster center estimation A cluster center is defined as the center of the clusters mass or the location of the maximum stellar density (the number of stars per unit area in the direction of the cluster). The centre of any cluster can be roughly estimated by eye, but to determine the central coordinates of our candidates more precisely, we applied here the star-count method to the whole area of each cluster. To estimate the cluster center, we plotted the histogram in Right Ascension (RA) and Declination (DEC) for the clusters under study. For this purpose the cluster area is divided into equal sized bin in RA and DEC. The purpose of this counting process is to estimate the maximum central density of the clusters. The histogram of the clusters in RA and DEC are shown in Fig 3. The Gaussian curve-fitting is applied to the profiles of star counts in RA and DEC respectively. The cluster center is assumed as the location of the maximum stellar density in the clusters area. In this way we found the coordinates of center for clusters as α = 333.45 ± 0.01 deg and δ = 55.72 ± 0.01 deg for Teu 126, α = 341.82 ± 0.01 deg and δ = 59.80 ± 0.01 deg for Teu 54, α = 113.65 ± 0.01 deg and δ = −19.79 ± 0.01 deg for Teu 61 and α = 15.71 ± 0.01 deg and δ = 62.81 ± 0.01 deg for Cz 3. The estimated values of the cluster centers are very close to the value listed in Table 1 for all these clusters.
To estimate the cluster extent, we established the radial density profile (RDP) of the clusters under study. The observed area of the clusters are divided into many concentric circles. To estimate the cluster extent we have used cluster center, as estimated in the previous section. The number density, Ri , in the ith zone is calcuN lated by using the formula of Ri = Ai . Where Ni is the number i
of stars and Ai is the area of the ith zone. Fig 4 represents RDPs for the clusters Teu 126, Teu 54, Teu 61 and Cz 3. The background density level with errors is also shown with dotted lines. Cluster PDPs are flatness at r ∼ 5.0, 4.0, 5.0 and 5.0 arcmin for Teu 126, Teu 54, Teu 61 and Cz 3 respectively and begin to merge with the background stellar density as seen in Fig 4. Therefor we consider 5.0, 4.0, 5.0 and 5.0 arcmin as clusters radius for all these clusters respectively. Bonatto and Bica (2010) has derived the radius as 4.5 ± 0.5 and 4.0 ± 0.5 arcmin for the clusters Teu 126 and Teu 54 respectively. These values are very close to the values derived by us within the error. A smooth continuous line represents fitted King (1962) profile:
f (r ) = f b +
f0 1 + (r/rc )2
where f0 is the central density, rc is core radius and fb is the background density. By fitting the King model to the cluster density profile we estimated the structural parameters of the clusters, which are listed in Table 2. f The density contrast parameter δc = 1 + f0 is estimated for the b
clusters under study. The estimated values of δ c are 9.0, 2.6, 2.0 and 3.4 for the clusters Teu 126, Teu 54, Teu 61 and Cz 3 respectively. These values are listed in Table 2. Present estimation of δ c is lower than the values (7 ≤ δ c ≤ 23) given for compact star clusters by Bonatto and Bica (2009) except the cluster Teu 126. This shows that the clusters Teu 54, Teu 61 and Cz 3 are sparse clusters and Teu 126 is a compact cluster. Tidal radius is the distance from the cluster core at which the gravitational influence of the Galaxy is equal to that of open cluster core. The tidal radii of open clusters depend on both combined effects of Galactic tidal fields and subsequent internal relaxation dynamical evolution of clusters (Allen and Martos, 1988). To estimate the tidal radius we used the following relation given by Jeffries et al. (2001).
Rt = 1.46 × (Mc )1/3 where Rt and Mc are the tidal radius and the total mass (see Section 4) of these clusters. Using the above relation the calculated
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Fig. 1. Identification maps of Teu 126 (upper left panel), Teu 54 (upper right panel), Teu 61 (bottom left panel) and Cz 3 (bottom right panel) taken from LEDAS.
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3.5. Age and distance to the clusters
Fig. 2. Photometric errors in J; H; and K magnitudes against J magnitude.
values of tidal radius are 6.6, 5.5, 6.2 and 5.8 pc for clusters Teu 126, Teu 54, Teu 61 and Cz 3 respectively and these are listed in Table 2.
3.3. Colour-magnitude diagrams Colour-magnitude diagram play most important role for the estimation of age and distance of open star clusters. The J, (J − H ) CMDs of the cluster and field region for the clusters Teu 126, Teu 54, Teu 61 and Cz 3 are shown in Fig 5. Stars falling within the cluster radius are considered as cluster region stars while those outside the radius are assumed as field region stars. To get the clear sequence in the CMD, we consider the stars within cluster radius. The area of the field region was kept equal to the area of the cluster region. The CMDs shown in Fig 5 exhibits a poor mainsequence (MS) extending from J ∼ 10.5 mag down to J ∼ 14 mag for Teu 126, J ∼ 12.6 mag down to J ∼ 15 mag for Teu 54, J ∼ 11 mag down to J ∼ 14 mag for Teu 61 and J ∼ 10.5 mag down to J ∼ 14 mag for Cz 3 . After that MS is merging with the field star populations and getting inseparable.
The age of a cluster is estimated by comparing the theoretical evolutionary isochrones given by Girardi et al. (20 0 0) for Z = 0.019 with the observed CMDs of the clusters as shown in Fig 7. The detailed shape and position of the different features in the CMDs depends mostly on age, reddening and also on distance. To get the clear sequence in the CMDs, we consider only those stars which lie within the cluster extent as derived in Section 3.2. The detailed description of all these clusters are given below, where the Galactocentric coordinates of the clusters are calculated adopting the distance of the Sun as 8.5 kpc to Galactic center. Teutsch 126: In Fig 7, we superimpose isochrones of different age (log(age)) = 8.40,8.45 and 8.50) with Z = 0.019 in J/(J − H ) and J/(J − K ) CMDs. The overall fit is good for log(age) = 8.45 (middle isochrone), corresponding to 290 ± 30 Myr. The estimated distance modulus ((m − Mk = 11.20 mag) provides a heliocentric distance 1.55 ± 0.1 kpc. Present estimate of age and distance of this cluster is similar to the values 400 ± 100 Myr and 1.74 ± 0.25 kpc within error derived by Bonatto and Bica (2010). The Galactocentric coordinates are X = 1.54 kpc, Y = 8.54 kpc and Z = −0.01 kpc. The Galactocentric distance of the cluster is 8.68 kpc. Teutsch 54: In Fig 7. we show the fitting of isochrones to J/(J − H ) and J/(J − K ) CMDs. The isochrones of different age (log(age) = 8.90, 8.95 and 9.0) and Z = 0.019 have been superimposed on the CMDs. We found an age of 900 ± 100 Myr. The distance modulus (m − Mk ) = 12.70 mag provide a heliocentric distance 2.60 ± 0.1 kpc. The age and distance of this cluster is very similar within error to Bonatto and Bica (2010). We estimate the Galactocentric distance as 9.19 kpc. The Galactocentric coordinates are estimated as X = 2.58 kpc, Y = 8.82 kpc and Z = 0.024 kpc. Teutsch 61: In Fig 7. we show the fitting of isochrones to J/(J − H ) and J/(J − K ) CMDs. The isochrones of different age (log(age) = 8.05, 8.10 and 8.15) and Z = 0.05 have been superimposed on the CMDs. The overall fit is good for log(age) = 8.10(middle isochrone). The best fitted isochrone provides an age of 130 ± 15 Myr. The distance modulus (m − Mk ) = 12.50 mag provide a heliocentric distance 2.55 ± 0.1 kpc. We have calculated the Galactocentric distance as 12.62 kpc for this cluster. The Galactocentric coordinates are, X = −1.34 kpc, Y = 10.66 kpc and Z = 0.004 kpc. Czernik 3: In Fig 7. we show the fitting of isochrones to J/(J − H ) and J/(J − K ) CMDs. The isochrones of different age (log(age) = 8.00, 8.05 and 8.10) and Z = 0.019 have been superimposed on the CMDs. We found and age of 115 ± 15 Myr. The distance modulus (m − Mk ) = 12.50 mag provide a heliocentric distance 1.75 ± 0.1 kpc. The Galactocentric distance is found to be 8.72 kpc. The Galactocentric coordinates are estimated as X = 1.62 kpc, Y = 9.14 kpc and Z = −0.002 kpc.
3.4. Colour-colour diagram
4. Luminosity function and mass function
Reddening is one of the very useful parameter for the reliable estimation of distance and age of the cluster. To estimate the reddening of the clusters we plot (J − H ) versus (J − K ) colourcolour diagram as shown in Fig 6 for the clusters under study. Stars plotted in this figure are taken within the cluster radius. The Zero age main sequence (ZAMS) shown by the solid line is taken from Caldwell et al. (1993). The same ZAMS shown by dotted line is shifted by E (J − H ) = 0.07 ± 0.05 mag & E (J − K ) = 0.15 ± 0.07 mag for Teu 126, E (J − H ) = 0.10 ± 0.02 mag and E (J − K ) = 0.22 ± 0.04 mag for Teu 54, E (J − H ) = 0.15 ± 0.03 mag and E (J − K ) = 0.25 ± 0.04 mag for Teu 61 and E (J − H ) = 0.16 ± 0.02 mag and E (J − K ) = 0.32 ± 0.03 mag for Cz 3. The ratio E (J − H )/E (J − K ) for all these clusters are in good agreement with the normal interstellar extinction value 0.55 suggested by Cardelli et al. (1989). However, scattering is larger due to error in JHKs data.
Luminosity function (LF) and Mass function (MF) are correlated with each other according to the well known mass-luminosity relationship. To construct the luminosity function for the clusters Teu 126, Teu 54, Teu 61 and Cz 3, we used J versus (J − Ks ) CMD. We have used the same photometric criteria described by Bisht et al. (2016) to select the cluster members. We assume that completeness factor is 100% at J = 16 mag for all these clusters. We included a reasonable number of stars in each absolute J mag bin for the best counting statistics. Before building the LFs, we converted the J magnitudes of probable member stars into the absolute magnitudes using the distance modulus of the clusters. Then we have constructed the histogram of LFs which is shown in Fig 8. This histogram shows that the luminosity function for the clusters Teu 126, Teu 54 and Cz 3 rises steadily. For the cluster Teu 61 a dip is found at MJ = 1.0 mag and steadily decreases after MJ = 2.0 mag.
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Fig. 3. Profiles of stellar counts across clusters Teu 126 (first two panels), Teu 54 (second two panels), Teu 61 (third two panels) and Cz 3 (last two panels) from top to bottom respectively. The Gaussian fits have been applied. The center of symmetry about the peaks of right ascension and declination is taken to be the position of the clusters centers.
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Fig. 4. Surface density distribution of the clusters Teu 126, Teu 54, Teu 61 and Cz 3. Errors are determined from sampling statistics (= √1N where N is the number of stars used in the density estimation at that point). The smooth line represent the fitted profile whereas dotted line shows the background density level. Long and short dash lines represent the errors in background density.
We have used the model given by Girardi et al. (20 0 0) to convert the LF into MF. The resulting mass function for these clusters Teu 126, Teu 54, Teu 61 and Cz 3 are shown in Fig. 9. The dN mass function slope can be derived by using the relation log dM = −(1 + x ) log(M ) + constant, where dN represents the number of stars in a mass bin dM with central mass M and x is mass function slope. The initial mass function for massive stars (≥ 1 M ) has been studied and well established by Salpeter (1955), where x=1.35. This form of Salpeter shows that the number of stars in each mass range decreases rapidly with increasing mass. Our derived slope of the MF x = 1.59 ± 0.62, 1.31 ± 0.6, 1.22 ± 0.75 and 1.62 ± 0.56 for the clusters Teu 126, Teu 54, Teu 61 and Cz 3 re-
spectively. The MF slope derived as 1.65 ± 0.11 and 1.04 ± 0.18 by Bonatto and Bica (2010) for the clusters Teu 126 and Teu 54 are close to our estimate within the error. It is noted that our investigated clusters have MF slopes around Salpeters value. We have also estimated the total mass considering the above mass function slope with in the mass range 0.8–3.2 M for Teu 126, 0.9–2.2 M for Teu 54, 1.1–3.2 M for Teu 61 and 0.9–2.6 M for Cz 3. Total mass was estimated as ∼ 100 M , 58M , 85M and 67M for clusters Teu 126, Teu 54, Teu 61 and Cz 3 respectively. These values are listed in Table 4.
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Fig. 5. The J, (J − H ) CMDs of open star clusters Teu 126, Teu 54, Teu 61 and Cz 3.
and 2.2 ≤
5. Dynamical state of the clusters In order to study the mass-segregation effect in the clusters Teu 126, Teu 54, Teu 61 and Cz 3, we plotted the cumulative radial stellar distribution of stars for different masses as shown in Fig. 10. We divided the main sequence stars in three mass range 3.2 ≤ MM ≤ 2.5, 2.5 ≤ MM ≤ 1.3 and 1.3 ≤ MM ≤ 0.8 for Teu 126
54, 3.2 ≤ 61, 2.6 ≤
M M ≤ 2.1, M M ≤ 3.1, M M ≤ 2.4,
M M ≤ 1.4 M ≤ M ≤ 2.0 ≤ MM ≤ 1.5
M M ≤ 0.9 for Teu ≤ MM ≤ 1.1 for Teu ≤ MM ≤ 0.9 for Cz
2.1 ≤
and 1.4 ≤
3.1
and 2.0
2.4
and 1.5
3. Fig. 10 shows the mass segregation effect for all these clusters, meaning, higher mass stars gradually sink towards the cluster center than the lower mass stars. Further, we performed KolmogrovSmirnov (K − S ) test to see the statistical significance of mass seg-
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D. Bisht et al. / New Astronomy 52 (2017) 55–64 Table 3 Derived fundamental parameters of the clusters under study. RGC is the Galactocentric distance while X , Y and Z are the Galactocentric coordinates of the clusters. The coordinate system is such that the Y-axis connects the Sun to the Galactic centre, while the X-axis is perpendicular to that. Y is positive towards the Galactic anticentre, and X is positive in the first and second Galactic quadrants (Lynga, 1982). Name Teutsch Teutsch Teutsch Czernik
126 54 61 3
Radius (arcmin)
E (J − H ) (mag)
Distance (kpc)
5.0 4.0 5.0 5.0
0.07 ± 0.05 0.10 ± 0.02 0.15 ± 0.03 0.16 ± 0.02
1.55 2.60 2.55 1.75
± ± ± ±
0.1 0.1 0.1 0.1
X (kpc)
Y (kpc)
Z (kpc)
RGC (kpc)
1.54 2.58 −1.34 1.62
8.54 8.82 10.66 9.14
−0.010 0.024 0.004 −0.002
8.68 9.19 12.62 8.72
Table 4 Structural parameters of the clusters. TEB is calculated by using the relation given by Binney and Tremanine (1987), while TES is calculated by using (Spitzer and Hart, 1971). Name Teutsch Teutsch Teutsch Czernik
126 54 61 3
Mrange (M )
MFslope
0.8–3.2 0.9–2.2 1.1–3.2 0.9–2.6
1.59 1.31 1.22 1.62
± ± ± ±
0.62 0.60 0.75 0.56
NC
MC (M )
TEB (Myr)
TES (Myr)
Age Myr
74 44 48 50
100 58 85 67
7.2 4.5 8.6 6.0
5.3 4.4 9.0 6.0
290 ± 30 900 ± 100 130 ± 15 115 ± 15
given by:
TES
√ 8.9 × 105 N × Rh 3/2 = √ m × log(0.4N )
where N is the number of cluster members, Rh is the radius with in which half of the cluster mass is contained and m is the average mass of the cluster stars (Spitzer and Hart, 1971). The value of Rh assumed to be equal to half of the cluster extent. We estimated the dynamical relaxation time as TES = 5.3 Myr for Teu 126, 4.4 Myr for Teu 54, 9.0 Myr for Teu 61 and 6.0 Myr for Cz 3. These values are listed in Table 4. To examine the results of relaxation time, we have re-calculated this value by using the method which is given by (Binney and Tremanine, 1987):
TEB =
Fig. 6. The plot of (J − H ) versus (J − K ) color-color diagram of the clusters under study. The solid line is the ZAMS taken from Caldwell et al. (1993). The dotted lines is the same ZAMS shifted by the values given in the text.
regation. This test indicates that the confidence label of masssegregation effect is 85 % for Teu 126, 80% for Teu 54, 90% for Teu 61 and 75% for Cz 3. The relatively higher confidence label for the clusters Teu 126 and Teu 61 show the mass segregation effect. No clear evidence of mass segregation is seen in the clusters Teu 54 and Cz 3. Mass-segregation effect can be due to dynamical evolution or imprint of star formation or both. In the lifetime of star clusters, encounters between its member stars gradually lead to an increased degree of energy equipartition throughout the clusters. In this process the higher mass stars gradually sink towards the cluster center and transfer their kinetic energy to the more numerous lower-mass stellar component, thus leading to mass segregation. The time scale on which a cluster will loose all traces of its initial conditions is well represented by its relaxation time TE , which is
N × tcross 8 log N
where Tcross = σD denotes the crossing time, N is the total number V of stars in the investigated region of diameter D, and σ V is the velocity dispersion, with a typical value of 3 km s−1 . The estimated values of dynamical relaxation time as TEB = 7.2 Myr for Teu 126, 4.5 Myr for Teu 54, 8.6 Myr for Teu 61 and 6.0 Myr for Cz 3, which are listed in Table 4. Our estimated values of relaxation time for all these clusters are listed in Table 4. These values are less than the clusters age. Hence we conclude that the clusters Teu 126, Teu 54, Teu 61 and Cz 3 are dynamically relaxed. 6. Conclusions We have studied the four open star clusters namely Teu 126, Teu 54, Teu 61 and Cz 3 by using 2MASS near-IR photometric data. The fundamental parameters such as galactocentric coordinates, distance, age, cluster radius, mass function slope and relaxation time are estimated more accurately for these clusters. The results are summarized in Tables 3 and 4. The main findings of our analysis are given below: •
Luminosity function for the clusters Teu 126, Teu 54 and Cz 3 rises steadily. For the cluster Teu 61, a dip is found at MJ = 1.0 mag and steadily decreases after MJ =2.0 mag. The reason for the presence of dip in the main sequence of the cluster Teu 61 is not clearly known.
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Fig. 7. Color-magnitude diagrams of the clusters under study. The curves are the isochrones of (log(age) = 8.40, 8.45 and 8.50) for the cluster Teu 126, (log(age) = 8.90, 8.95 and 9.0) for the cluster Teu 54, (log(age) = 8.05, 8.10 and 8.15) for the cluster Teu 61 and (log(age) = 8.00, 8.05 and 8.10) for the cluster Cz 3. These isochrones are taken from Girardi et al. (20 0 0).
•
•
The mass function slopes are estimated as 1.59 ± 0.62, 1.31 ± 0.60, 1.22 ± 0.75 and 1.62 ± 0.56 for Teu 126, Teu 54, Teu 61 and Cz 3 respectively. Our derived values of MF slope for these clusters are in agreement with the value 1.35 given by Salpeter (1955) for field stars in solar neighborhood. Mass segregation effect was studied for the clusters under investigation.. The K-S test indicates that the confidence label of mass-segregation effect is 85% for Teu 126, 80% for Teu 54, 90% for Teu 61 and 75% for Cz 3. The higher confidence label shows the mass segregation effect in the clusters Teu 126 and Teu 61. The dynamical relaxation time indicates that all these clusters
are dynamically relaxed. This may be due to star formation process or dynamical evolution of star clusters. Acknowledgements It is worthy to mention that, this work have been done by using WEBDA and the data products from the Two Micron All Sky Survey (2MASS), which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation (NASA).
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Fig. 8. The luminosity functions of the clusters under consideration.
Fig. 10. The cumulative radial distribution of stars in various mass range for the clusters under study.
References
Fig. 9. Mass function for Teu 126, Teu 54, Teu 61 and Cz 3 derived using Girardi et al. (20 0 0) isochrones.
Allen, C., Martos, M., 1988. RMxAA 16, 25. Binney, J., Tremanine, S., 1987. Nature 326, 219. Bisht, D., Yadav, R.K.S., Durgapal, A.K., 2016. New Astron. 42, 66–77. Bonatto, C., Bica, E., 2003. A&A 405, 525. Bonatto, C., Bica, E., 2009. MNRAS 397, 1915. Bonatto, C., Bica, E., 2010. A&A 521, A74. Caldwell, J. A. R., Cousins, A. W. J., Ahlers, C. C., van Wamelen, P., Maritz, E. J., 1993. South African Astronomical Observatory, Circ No. 15. Cardelli, J.A., Clayton, G.C., Mathis, J.S., 1989. ApJ 345, 245. Carpenter, J.M., 2001. AJ 121, 2851. Cutri, R., et al., 2003. 2MASS all-sky catalogue of point sources. CDS/ADC Electron. Catalogues 2246. Dias, W.S., Alessi, B.S., Moitinho, A., Lepine, J.R.D., 2002. A&A 389, 871. Froebrich, D., Scholz, A., Raftery, C.L., 2007. MNRAS 374, 399. Gaburov, E., Gieles, M., 2008. MNRAS 391, 190. Girardi, L., Bressan, A., Bertlli, G., Chiosi, C., 20 0 0. A&AS 141, 371. Glushkova, E.V., Koposov, S.E., Zolotukhin, I.Y., Beletsky, Y.V., Vlasov, A.D., Leonova, S.I., 2010. Astron. Lett. 36, 75. Jeffries, R.D., Thurston, M.R., Hambly, N.C., 2001. A&A 375, 863. King, I., 1962. AJ 67, 471. Koposov, S.E., Glushkova, E.V., Zolotukhin, I.Y., 2008. A&A 486, 771. Kronberger, M., Teutsch, P., Alessi, B., et al., 2006. A&A 447, 921. Lynga, G., 1982. A&A 109, 213. Salpeter, E.E., 1955. ApJ 121, 161. Skrutskie, M.F., Cutri, R.M., Stiening, R., et al., 2006. AJ 131, 1163. Spitzer, L., Hart, M., 1971. ApJ 164, 399.
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New Astronomy journal homepage: www.elsevier.com/locate/newast
2MASS analytical study of four open cluster candidates D. Bisht a,c,∗, R.K.S. Yadav b, A.K. Durgapal c a
Physical Research Laboratory, Ahmedabad, 380009, India Aryabhatta Research Institute of Observational Sciences, Manora Peak Nainital 263 002, India c Department of Physics, DSB Campus, Kumaun University, Nainital-263002, Uttarakhand, India b
h i g h l i g h t s • • •
The fundamental parameters of the clusters under study are derived. Luminosity and mass function have been studied for these objects. We have found mass segregation effect for these clusters and they are dynamically relaxed.
a r t i c l e
i n f o
Article history: Received 10 June 2016 Revised 18 October 2016 Accepted 25 October 2016 Available online 26 October 2016 Keywords: Star: colour-magnitude diagrams-open cluster and associations: individual: Teutsch 126 Teutsch54 Teutsch 61 and Czernik 3 Mass function Mass segregation
a b s t r a c t The astrophysical parameters of four poorly studied open star clusters namely Teutsch 126, Teutsch 54, Teutsch 61 and Czernik 3, have been estimated using the Two Micron All Sky Survey (2MASS) database. The stellar density distributions and color-magnitude diagrams are used to determine their structural parameters (cluster center, cluster radius, core radius, tidal radius, Galactocenteric coordinates and the distance from the Galactic plane). We have also derived age, color excesses, total mass, relaxation time, luminosity and mass function for each clusters. The mass function slopes for these clusters are derived as 1.59 ± 0.62, 1.31 ± 0.60, 1.22 ± 0.75 and 1.62 ± 0.56 for Teutsch 126, Teutsch 54, Teutsch 61 and Czernik 3 respectively. These values are very close with the Salpeter value (x = 1.35) within the errors. The effect of mass-segregation are observed in the clusters Teutsch 126 and Teutsch 61. Estimated values of dynamical relaxation time are less than age of the clusters under study. This concludes that these objects are dynamically relaxed. The possible reason for relaxation may be due to the dynamical evolution or imprint of star formation or both. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Open star clusters (OCs) are key objects in studying the formation and evolution of the Galactic disk. They are self gravitating stellar systems formed along the gas and dust rich Galactic plane. They contain from tens to a few thousands stars distributed in an approximately spherical structure of up to a few parsecs in radius. Gaburov and Gieles (2008) provided statistically significant samples of star clusters of known distance, age and metallicity. Estimation of astrophysical and evolutionary parameters, such as distance, age, cluster density, core radius, size of the cluster and relaxation time are very important to develop theoretical models on the Galactic structure. Our aim is to study star clusters within the disk of Galaxy, which is normally obscured by dust and gas clouds. For the present study we have used the Two Micron All Sky Survey (2MASS) ∗
Corresponding author. Fax: +91 5942 233439, +917929703573. E-mail addresses: [email protected] (D. Bisht), [email protected] (R.K.S. Yadav), [email protected] (A.K. Durgapal). http://dx.doi.org/10.1016/j.newast.2016.10.009 1384-1076/© 2016 Elsevier B.V. All rights reserved.
near-IR photometric data. Such type of data help us to solve the star formation problems and to understand the spiral structure of the Milky Way Galaxy. This survey has proven to be a powerful tool in the analysis of the structure and stellar content of open clusters (Bonatto and Bica, 2003). Recently more than thousands of open clusters have been discovered by analysing 2MASS data (Kronberger et al., 2006; Froebrich et al., 2007; Koposov et al., 2008; Glushkova et al., 2010). The basic astrophysical parameters for ∼ 1500 open clusters have been calculated by Kharchenko et al. (2013) using 2MASS JHKs and PPMXL data. Number of known open clusters in the Milky Way Galaxy are ∼ 30 0 0 (Kharchenko et al., 2013), while the expected number of open clusters are approximately 104 − 105 . Therefore, most of the open clusters are hidden in the highly obscured Galactic plane. Over this large sample of data, only few clusters are studied in detail, but most of them are unstudied or poorly studied in the literature. In the light of above discussions we aim to estimate the fundamental parameters of open star clusters Teutsch 126 (Teu 126), Teutsch 54 (Teu 54), Teutsch 61 (Teu 61) and Czernik 3 (Cz 3). To the best of our knowledge there is no detailed study available in
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the literature for these clusters. Bonatto and Bica (2010) have estimated the fundamental parameters for open clusters Teu 126 and Teu 54, using the same dataset (2MASS), but stars selection criteria is different. We have used the same procedure for cluster stars selection as given in Tadross et al. (2011). Clusters Teu 61 and Cz 3 never studied before so there is no much information in the literature about these two clusters. OCs Teu 126, Teu 54 and Cz 3 are located in the second while Teu 61 is located in the third Galactic quadrant. The two clusters Teu 126 and Cz 3 are below the Galactic plane while Teu 54 and Teu 61 are above the Galactic plane. Teu 126, Teu 54 and Cz 3 are intermediate clusters while Teu 61 is younger age open star cluster. This paper is organized as follows. Section 2 presents the description of used data set. In Section 3, we described the derivation of different fundamental parameters of the clusters. The luminosity and mass functions are presented in Section 4. Dynamical state of the clusters are described in Section 5. Finally, the conclusions are drawn in Section 6.
Table 1 Fundamental parameters of the clusters taken from Dias et al. (2002). Name Teutsch Teutsch Teutsch Czernik
126 54 61 3
α 2000
δ 2000 (deg)
l (deg)
b (deg)
d (pc)
log(age)
(deg) 333.30 341.70 113.65 15.76
55.72 59.77 −19.78 62.78
101.9 107.9 235.3 124.2
-0.6 0.6 0.1 −0.1
1740 2890 1920 1410
8.6 8.9 6.9 8.0
Table 2 Structural parameters of the clusters Teutsch 126, Teutsch 54, Teutsch 61 and Czernik 3. Background and central density are in the unit of stars per arcmin2 . rc is in arcmin while Rt (Tidal radius) is in pc. Name Teutsch Teutsch Teutsch Czernik
126 54 61 3
f0
fb
rc
Rt
δc
6.8 3.4 5.2 7.3
0.8 1.3 2.5 3.0
0.3 0.6 1.3 0.6
6.6 5.5 6.2 5.8
9.0 2.6 2.0 3.4
2. Data used 3.2. Radial density profiles The purpose of the present study is to derive the astrophysical parameters of clusters Teu 126, Teu 54, Teu 61 and Cz 3 by using 2MASS Point Source catalogue (Cutri, 2003). The 2MASS (Skrutskie et al., 2006) uses two highly automated 1.3m telescope (one at Mt. Hopkins, Arizona (AZ), USA and other at CTIO, Chile) with a 3channel camera ((256 × 256) array of HgCdTe detectors in each channel). This 2MASS photometric catalogue provides J (1.25 μm), H (1.65 μm) and Ks (2.17 μm) band photometry for millions of galaxies and nearly a half-billion stars (Carpenter, 2001). The sensitivity of 2MASS catalogue is 15.8 mag for J, 15.1 mag for H and 14.3 mag for Ks band at S/N = 10. The photometric data are taken within the radius of 20 arcmin from the cluster center. Identification maps for the clusters are taken from Leicester Database and Archive Service (LEDAS) as shown in Fig 1. The errors given in 2MASS catalogue for J, H and Ks band are plotted against J magnitudes in Fig 2. This figure shows that the mean error in J, H and Ks band is ≤ 0.05 at J ∼ 13.0 mag. The errors become ∼ 0.09 at J ∼ 15 mag. 3. Estimation of fundamental parameters 3.1. Cluster center estimation A cluster center is defined as the center of the clusters mass or the location of the maximum stellar density (the number of stars per unit area in the direction of the cluster). The centre of any cluster can be roughly estimated by eye, but to determine the central coordinates of our candidates more precisely, we applied here the star-count method to the whole area of each cluster. To estimate the cluster center, we plotted the histogram in Right Ascension (RA) and Declination (DEC) for the clusters under study. For this purpose the cluster area is divided into equal sized bin in RA and DEC. The purpose of this counting process is to estimate the maximum central density of the clusters. The histogram of the clusters in RA and DEC are shown in Fig 3. The Gaussian curve-fitting is applied to the profiles of star counts in RA and DEC respectively. The cluster center is assumed as the location of the maximum stellar density in the clusters area. In this way we found the coordinates of center for clusters as α = 333.45 ± 0.01 deg and δ = 55.72 ± 0.01 deg for Teu 126, α = 341.82 ± 0.01 deg and δ = 59.80 ± 0.01 deg for Teu 54, α = 113.65 ± 0.01 deg and δ = −19.79 ± 0.01 deg for Teu 61 and α = 15.71 ± 0.01 deg and δ = 62.81 ± 0.01 deg for Cz 3. The estimated values of the cluster centers are very close to the value listed in Table 1 for all these clusters.
To estimate the cluster extent, we established the radial density profile (RDP) of the clusters under study. The observed area of the clusters are divided into many concentric circles. To estimate the cluster extent we have used cluster center, as estimated in the previous section. The number density, Ri , in the ith zone is calcuN lated by using the formula of Ri = Ai . Where Ni is the number i
of stars and Ai is the area of the ith zone. Fig 4 represents RDPs for the clusters Teu 126, Teu 54, Teu 61 and Cz 3. The background density level with errors is also shown with dotted lines. Cluster PDPs are flatness at r ∼ 5.0, 4.0, 5.0 and 5.0 arcmin for Teu 126, Teu 54, Teu 61 and Cz 3 respectively and begin to merge with the background stellar density as seen in Fig 4. Therefor we consider 5.0, 4.0, 5.0 and 5.0 arcmin as clusters radius for all these clusters respectively. Bonatto and Bica (2010) has derived the radius as 4.5 ± 0.5 and 4.0 ± 0.5 arcmin for the clusters Teu 126 and Teu 54 respectively. These values are very close to the values derived by us within the error. A smooth continuous line represents fitted King (1962) profile:
f (r ) = f b +
f0 1 + (r/rc )2
where f0 is the central density, rc is core radius and fb is the background density. By fitting the King model to the cluster density profile we estimated the structural parameters of the clusters, which are listed in Table 2. f The density contrast parameter δc = 1 + f0 is estimated for the b
clusters under study. The estimated values of δ c are 9.0, 2.6, 2.0 and 3.4 for the clusters Teu 126, Teu 54, Teu 61 and Cz 3 respectively. These values are listed in Table 2. Present estimation of δ c is lower than the values (7 ≤ δ c ≤ 23) given for compact star clusters by Bonatto and Bica (2009) except the cluster Teu 126. This shows that the clusters Teu 54, Teu 61 and Cz 3 are sparse clusters and Teu 126 is a compact cluster. Tidal radius is the distance from the cluster core at which the gravitational influence of the Galaxy is equal to that of open cluster core. The tidal radii of open clusters depend on both combined effects of Galactic tidal fields and subsequent internal relaxation dynamical evolution of clusters (Allen and Martos, 1988). To estimate the tidal radius we used the following relation given by Jeffries et al. (2001).
Rt = 1.46 × (Mc )1/3 where Rt and Mc are the tidal radius and the total mass (see Section 4) of these clusters. Using the above relation the calculated
D. Bisht et al. / New Astronomy 52 (2017) 55–64
Fig. 1. Identification maps of Teu 126 (upper left panel), Teu 54 (upper right panel), Teu 61 (bottom left panel) and Cz 3 (bottom right panel) taken from LEDAS.
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3.5. Age and distance to the clusters
Fig. 2. Photometric errors in J; H; and K magnitudes against J magnitude.
values of tidal radius are 6.6, 5.5, 6.2 and 5.8 pc for clusters Teu 126, Teu 54, Teu 61 and Cz 3 respectively and these are listed in Table 2.
3.3. Colour-magnitude diagrams Colour-magnitude diagram play most important role for the estimation of age and distance of open star clusters. The J, (J − H ) CMDs of the cluster and field region for the clusters Teu 126, Teu 54, Teu 61 and Cz 3 are shown in Fig 5. Stars falling within the cluster radius are considered as cluster region stars while those outside the radius are assumed as field region stars. To get the clear sequence in the CMD, we consider the stars within cluster radius. The area of the field region was kept equal to the area of the cluster region. The CMDs shown in Fig 5 exhibits a poor mainsequence (MS) extending from J ∼ 10.5 mag down to J ∼ 14 mag for Teu 126, J ∼ 12.6 mag down to J ∼ 15 mag for Teu 54, J ∼ 11 mag down to J ∼ 14 mag for Teu 61 and J ∼ 10.5 mag down to J ∼ 14 mag for Cz 3 . After that MS is merging with the field star populations and getting inseparable.
The age of a cluster is estimated by comparing the theoretical evolutionary isochrones given by Girardi et al. (20 0 0) for Z = 0.019 with the observed CMDs of the clusters as shown in Fig 7. The detailed shape and position of the different features in the CMDs depends mostly on age, reddening and also on distance. To get the clear sequence in the CMDs, we consider only those stars which lie within the cluster extent as derived in Section 3.2. The detailed description of all these clusters are given below, where the Galactocentric coordinates of the clusters are calculated adopting the distance of the Sun as 8.5 kpc to Galactic center. Teutsch 126: In Fig 7, we superimpose isochrones of different age (log(age)) = 8.40,8.45 and 8.50) with Z = 0.019 in J/(J − H ) and J/(J − K ) CMDs. The overall fit is good for log(age) = 8.45 (middle isochrone), corresponding to 290 ± 30 Myr. The estimated distance modulus ((m − Mk = 11.20 mag) provides a heliocentric distance 1.55 ± 0.1 kpc. Present estimate of age and distance of this cluster is similar to the values 400 ± 100 Myr and 1.74 ± 0.25 kpc within error derived by Bonatto and Bica (2010). The Galactocentric coordinates are X = 1.54 kpc, Y = 8.54 kpc and Z = −0.01 kpc. The Galactocentric distance of the cluster is 8.68 kpc. Teutsch 54: In Fig 7. we show the fitting of isochrones to J/(J − H ) and J/(J − K ) CMDs. The isochrones of different age (log(age) = 8.90, 8.95 and 9.0) and Z = 0.019 have been superimposed on the CMDs. We found an age of 900 ± 100 Myr. The distance modulus (m − Mk ) = 12.70 mag provide a heliocentric distance 2.60 ± 0.1 kpc. The age and distance of this cluster is very similar within error to Bonatto and Bica (2010). We estimate the Galactocentric distance as 9.19 kpc. The Galactocentric coordinates are estimated as X = 2.58 kpc, Y = 8.82 kpc and Z = 0.024 kpc. Teutsch 61: In Fig 7. we show the fitting of isochrones to J/(J − H ) and J/(J − K ) CMDs. The isochrones of different age (log(age) = 8.05, 8.10 and 8.15) and Z = 0.05 have been superimposed on the CMDs. The overall fit is good for log(age) = 8.10(middle isochrone). The best fitted isochrone provides an age of 130 ± 15 Myr. The distance modulus (m − Mk ) = 12.50 mag provide a heliocentric distance 2.55 ± 0.1 kpc. We have calculated the Galactocentric distance as 12.62 kpc for this cluster. The Galactocentric coordinates are, X = −1.34 kpc, Y = 10.66 kpc and Z = 0.004 kpc. Czernik 3: In Fig 7. we show the fitting of isochrones to J/(J − H ) and J/(J − K ) CMDs. The isochrones of different age (log(age) = 8.00, 8.05 and 8.10) and Z = 0.019 have been superimposed on the CMDs. We found and age of 115 ± 15 Myr. The distance modulus (m − Mk ) = 12.50 mag provide a heliocentric distance 1.75 ± 0.1 kpc. The Galactocentric distance is found to be 8.72 kpc. The Galactocentric coordinates are estimated as X = 1.62 kpc, Y = 9.14 kpc and Z = −0.002 kpc.
3.4. Colour-colour diagram
4. Luminosity function and mass function
Reddening is one of the very useful parameter for the reliable estimation of distance and age of the cluster. To estimate the reddening of the clusters we plot (J − H ) versus (J − K ) colourcolour diagram as shown in Fig 6 for the clusters under study. Stars plotted in this figure are taken within the cluster radius. The Zero age main sequence (ZAMS) shown by the solid line is taken from Caldwell et al. (1993). The same ZAMS shown by dotted line is shifted by E (J − H ) = 0.07 ± 0.05 mag & E (J − K ) = 0.15 ± 0.07 mag for Teu 126, E (J − H ) = 0.10 ± 0.02 mag and E (J − K ) = 0.22 ± 0.04 mag for Teu 54, E (J − H ) = 0.15 ± 0.03 mag and E (J − K ) = 0.25 ± 0.04 mag for Teu 61 and E (J − H ) = 0.16 ± 0.02 mag and E (J − K ) = 0.32 ± 0.03 mag for Cz 3. The ratio E (J − H )/E (J − K ) for all these clusters are in good agreement with the normal interstellar extinction value 0.55 suggested by Cardelli et al. (1989). However, scattering is larger due to error in JHKs data.
Luminosity function (LF) and Mass function (MF) are correlated with each other according to the well known mass-luminosity relationship. To construct the luminosity function for the clusters Teu 126, Teu 54, Teu 61 and Cz 3, we used J versus (J − Ks ) CMD. We have used the same photometric criteria described by Bisht et al. (2016) to select the cluster members. We assume that completeness factor is 100% at J = 16 mag for all these clusters. We included a reasonable number of stars in each absolute J mag bin for the best counting statistics. Before building the LFs, we converted the J magnitudes of probable member stars into the absolute magnitudes using the distance modulus of the clusters. Then we have constructed the histogram of LFs which is shown in Fig 8. This histogram shows that the luminosity function for the clusters Teu 126, Teu 54 and Cz 3 rises steadily. For the cluster Teu 61 a dip is found at MJ = 1.0 mag and steadily decreases after MJ = 2.0 mag.
D. Bisht et al. / New Astronomy 52 (2017) 55–64
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Fig. 3. Profiles of stellar counts across clusters Teu 126 (first two panels), Teu 54 (second two panels), Teu 61 (third two panels) and Cz 3 (last two panels) from top to bottom respectively. The Gaussian fits have been applied. The center of symmetry about the peaks of right ascension and declination is taken to be the position of the clusters centers.
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Fig. 4. Surface density distribution of the clusters Teu 126, Teu 54, Teu 61 and Cz 3. Errors are determined from sampling statistics (= √1N where N is the number of stars used in the density estimation at that point). The smooth line represent the fitted profile whereas dotted line shows the background density level. Long and short dash lines represent the errors in background density.
We have used the model given by Girardi et al. (20 0 0) to convert the LF into MF. The resulting mass function for these clusters Teu 126, Teu 54, Teu 61 and Cz 3 are shown in Fig. 9. The dN mass function slope can be derived by using the relation log dM = −(1 + x ) log(M ) + constant, where dN represents the number of stars in a mass bin dM with central mass M and x is mass function slope. The initial mass function for massive stars (≥ 1 M ) has been studied and well established by Salpeter (1955), where x=1.35. This form of Salpeter shows that the number of stars in each mass range decreases rapidly with increasing mass. Our derived slope of the MF x = 1.59 ± 0.62, 1.31 ± 0.6, 1.22 ± 0.75 and 1.62 ± 0.56 for the clusters Teu 126, Teu 54, Teu 61 and Cz 3 re-
spectively. The MF slope derived as 1.65 ± 0.11 and 1.04 ± 0.18 by Bonatto and Bica (2010) for the clusters Teu 126 and Teu 54 are close to our estimate within the error. It is noted that our investigated clusters have MF slopes around Salpeters value. We have also estimated the total mass considering the above mass function slope with in the mass range 0.8–3.2 M for Teu 126, 0.9–2.2 M for Teu 54, 1.1–3.2 M for Teu 61 and 0.9–2.6 M for Cz 3. Total mass was estimated as ∼ 100 M , 58M , 85M and 67M for clusters Teu 126, Teu 54, Teu 61 and Cz 3 respectively. These values are listed in Table 4.
D. Bisht et al. / New Astronomy 52 (2017) 55–64
61
Fig. 5. The J, (J − H ) CMDs of open star clusters Teu 126, Teu 54, Teu 61 and Cz 3.
and 2.2 ≤
5. Dynamical state of the clusters In order to study the mass-segregation effect in the clusters Teu 126, Teu 54, Teu 61 and Cz 3, we plotted the cumulative radial stellar distribution of stars for different masses as shown in Fig. 10. We divided the main sequence stars in three mass range 3.2 ≤ MM ≤ 2.5, 2.5 ≤ MM ≤ 1.3 and 1.3 ≤ MM ≤ 0.8 for Teu 126
54, 3.2 ≤ 61, 2.6 ≤
M M ≤ 2.1, M M ≤ 3.1, M M ≤ 2.4,
M M ≤ 1.4 M ≤ M ≤ 2.0 ≤ MM ≤ 1.5
M M ≤ 0.9 for Teu ≤ MM ≤ 1.1 for Teu ≤ MM ≤ 0.9 for Cz
2.1 ≤
and 1.4 ≤
3.1
and 2.0
2.4
and 1.5
3. Fig. 10 shows the mass segregation effect for all these clusters, meaning, higher mass stars gradually sink towards the cluster center than the lower mass stars. Further, we performed KolmogrovSmirnov (K − S ) test to see the statistical significance of mass seg-
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D. Bisht et al. / New Astronomy 52 (2017) 55–64 Table 3 Derived fundamental parameters of the clusters under study. RGC is the Galactocentric distance while X , Y and Z are the Galactocentric coordinates of the clusters. The coordinate system is such that the Y-axis connects the Sun to the Galactic centre, while the X-axis is perpendicular to that. Y is positive towards the Galactic anticentre, and X is positive in the first and second Galactic quadrants (Lynga, 1982). Name Teutsch Teutsch Teutsch Czernik
126 54 61 3
Radius (arcmin)
E (J − H ) (mag)
Distance (kpc)
5.0 4.0 5.0 5.0
0.07 ± 0.05 0.10 ± 0.02 0.15 ± 0.03 0.16 ± 0.02
1.55 2.60 2.55 1.75
± ± ± ±
0.1 0.1 0.1 0.1
X (kpc)
Y (kpc)
Z (kpc)
RGC (kpc)
1.54 2.58 −1.34 1.62
8.54 8.82 10.66 9.14
−0.010 0.024 0.004 −0.002
8.68 9.19 12.62 8.72
Table 4 Structural parameters of the clusters. TEB is calculated by using the relation given by Binney and Tremanine (1987), while TES is calculated by using (Spitzer and Hart, 1971). Name Teutsch Teutsch Teutsch Czernik
126 54 61 3
Mrange (M )
MFslope
0.8–3.2 0.9–2.2 1.1–3.2 0.9–2.6
1.59 1.31 1.22 1.62
± ± ± ±
0.62 0.60 0.75 0.56
NC
MC (M )
TEB (Myr)
TES (Myr)
Age Myr
74 44 48 50
100 58 85 67
7.2 4.5 8.6 6.0
5.3 4.4 9.0 6.0
290 ± 30 900 ± 100 130 ± 15 115 ± 15
given by:
TES
√ 8.9 × 105 N × Rh 3/2 = √ m × log(0.4N )
where N is the number of cluster members, Rh is the radius with in which half of the cluster mass is contained and m is the average mass of the cluster stars (Spitzer and Hart, 1971). The value of Rh assumed to be equal to half of the cluster extent. We estimated the dynamical relaxation time as TES = 5.3 Myr for Teu 126, 4.4 Myr for Teu 54, 9.0 Myr for Teu 61 and 6.0 Myr for Cz 3. These values are listed in Table 4. To examine the results of relaxation time, we have re-calculated this value by using the method which is given by (Binney and Tremanine, 1987):
TEB =
Fig. 6. The plot of (J − H ) versus (J − K ) color-color diagram of the clusters under study. The solid line is the ZAMS taken from Caldwell et al. (1993). The dotted lines is the same ZAMS shifted by the values given in the text.
regation. This test indicates that the confidence label of masssegregation effect is 85 % for Teu 126, 80% for Teu 54, 90% for Teu 61 and 75% for Cz 3. The relatively higher confidence label for the clusters Teu 126 and Teu 61 show the mass segregation effect. No clear evidence of mass segregation is seen in the clusters Teu 54 and Cz 3. Mass-segregation effect can be due to dynamical evolution or imprint of star formation or both. In the lifetime of star clusters, encounters between its member stars gradually lead to an increased degree of energy equipartition throughout the clusters. In this process the higher mass stars gradually sink towards the cluster center and transfer their kinetic energy to the more numerous lower-mass stellar component, thus leading to mass segregation. The time scale on which a cluster will loose all traces of its initial conditions is well represented by its relaxation time TE , which is
N × tcross 8 log N
where Tcross = σD denotes the crossing time, N is the total number V of stars in the investigated region of diameter D, and σ V is the velocity dispersion, with a typical value of 3 km s−1 . The estimated values of dynamical relaxation time as TEB = 7.2 Myr for Teu 126, 4.5 Myr for Teu 54, 8.6 Myr for Teu 61 and 6.0 Myr for Cz 3, which are listed in Table 4. Our estimated values of relaxation time for all these clusters are listed in Table 4. These values are less than the clusters age. Hence we conclude that the clusters Teu 126, Teu 54, Teu 61 and Cz 3 are dynamically relaxed. 6. Conclusions We have studied the four open star clusters namely Teu 126, Teu 54, Teu 61 and Cz 3 by using 2MASS near-IR photometric data. The fundamental parameters such as galactocentric coordinates, distance, age, cluster radius, mass function slope and relaxation time are estimated more accurately for these clusters. The results are summarized in Tables 3 and 4. The main findings of our analysis are given below: •
Luminosity function for the clusters Teu 126, Teu 54 and Cz 3 rises steadily. For the cluster Teu 61, a dip is found at MJ = 1.0 mag and steadily decreases after MJ =2.0 mag. The reason for the presence of dip in the main sequence of the cluster Teu 61 is not clearly known.
D. Bisht et al. / New Astronomy 52 (2017) 55–64
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Fig. 7. Color-magnitude diagrams of the clusters under study. The curves are the isochrones of (log(age) = 8.40, 8.45 and 8.50) for the cluster Teu 126, (log(age) = 8.90, 8.95 and 9.0) for the cluster Teu 54, (log(age) = 8.05, 8.10 and 8.15) for the cluster Teu 61 and (log(age) = 8.00, 8.05 and 8.10) for the cluster Cz 3. These isochrones are taken from Girardi et al. (20 0 0).
•
•
The mass function slopes are estimated as 1.59 ± 0.62, 1.31 ± 0.60, 1.22 ± 0.75 and 1.62 ± 0.56 for Teu 126, Teu 54, Teu 61 and Cz 3 respectively. Our derived values of MF slope for these clusters are in agreement with the value 1.35 given by Salpeter (1955) for field stars in solar neighborhood. Mass segregation effect was studied for the clusters under investigation.. The K-S test indicates that the confidence label of mass-segregation effect is 85% for Teu 126, 80% for Teu 54, 90% for Teu 61 and 75% for Cz 3. The higher confidence label shows the mass segregation effect in the clusters Teu 126 and Teu 61. The dynamical relaxation time indicates that all these clusters
are dynamically relaxed. This may be due to star formation process or dynamical evolution of star clusters. Acknowledgements It is worthy to mention that, this work have been done by using WEBDA and the data products from the Two Micron All Sky Survey (2MASS), which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation (NASA).
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Fig. 8. The luminosity functions of the clusters under consideration.
Fig. 10. The cumulative radial distribution of stars in various mass range for the clusters under study.
References
Fig. 9. Mass function for Teu 126, Teu 54, Teu 61 and Cz 3 derived using Girardi et al. (20 0 0) isochrones.
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