First PPMXL photometric analysis of open cluster Ruprecht 15

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/51937590 First PPMXL photometric analysis of open cluster Article in Research in Astronomy and Astrophysics · September 2011 DOI: 10.1088/1674-4527/12/2/004 · Source: arXiv CITATIONS READS 3 40 1 author: Ashraf Latif Tadross National Research Institute of Astronomy and Geophysics 46 PUBLICATIONS 190 CITATIONS SEE PROFILE All content following this page was uploaded by Ashraf Latif Tadross on 26 November 2016. The user has requested enhancement of the downloaded file. Research in Astronomy and Astrophysics manuscript no. (LATEX: Ruprecht˙15.tex; printed on November 4, 2011; 9:25) First PPMXL photometric analysis of open cluster ”Ruprecht 15”. Tadross, A. L. National Research Institute of Astronomy & Geophysics, 11421-Helwan, Cairo, Egypt. altadross@yahoo.com Abstract The first series in studying the astrophysical parameters of open clusters using PPMXL⋆ database is presented here, applied to ”Ruprecht 15”. The astrophysical parameters of Ruprecht 15 have been estimated here for the first time. Key words: open clusters and associations – individual: Ruprecht 15 – astrometry – Stars – astronomical databases: catalogues. 1 INTRODUCTION This paper is a part of our continuation series whose goal is to obtain the main astrophysical properties of previously unstudied OCs using modern databases. The most important thing for using PPMXL database lies in containing the positions, proper motions of USNO-B1.01 and the Near Infrared (NIR) photometry of the Two Micron All Sky Survey (2MASS)2 , which let it be the powerful detection of the star clusters behind the hydrogen thick clouds those concentrate on the Galactic plane. The only available information about Ruprecht 15 (hereafter Ru 15) are the coordinates and the optical apparent diameter, which were obtained from WEBDA3 site and the last updated version of DIAS4 collection (version 3.0, 2010 April 30). This cluster is situated in the Southern Milky Way at J2000.0 coordinates ′ ′′ α = 07h 19m 34s , δ = −19◦ 37 30 , ℓ = 233.54◦ , b = −2.896◦ , and its diameter is about 2.0 arcmin. Fig. 1 represents the blue image of Ru 15 as taken from Digitized Sky Survey (left panel), while the right panel represents J-image of the cluster as taken from Interactive 2MASS Image Service5 . This paper is organized as follows. PPMXL data extraction is presented in Section 2, while the data analysis and reductions for estimating parameters are described in Sections 3. Finally, the conclusion is devoted to Section 4. ⋆ http://vizier.cfa.harvard.edu/viz-bin/VizieR?-source=I/317 1 http://vizier.cfa.harvard.edu/viz-bin/VizieR?-source=I/284 2 http://vizier.cfa.harvard.edu/viz-bin/VizieR?-source=II/246 3 http://obswww.unige.ch/webda 4 http://www.astro.iag.usp.br/∼wilton/ 5 http://irsa.ipac.caltech.edu/applications/2MASS/IM/interactive.html 2 Tadross, A. L. 2 PPMXL DATA EXTRACTION The current PPMXL Catalogue of Roeser et al. (2010) is combining the proper motion of USNO-B1.0 and NIR JHKs pass-band of 2MASS databases. USNO-B1.0 of Monet et al. (2003) is a spatially unlimited catalogue that presents positions, proper motions, and magnitudes in various optical pass-bands. The data were obtained from scans of Schmidt plates taken for the various sky surveys during the last 50 years. USNO-B is believed to provide all-sky coverage, completeness down to V = 21 mag. It is noted that, based on the proper motion measurements, stars with large proper motions are likely to be foreground stars instead of cluster members. Background stars cannot readily be distinguished from members by proper motions. Nonetheless, identifying foreground stars is useful in cleaning up the colour-magnitude diagrams and determining the field star contamination. So, USNO-B is a very useful catalogue, which gives us an opportunity to distinguish between the members and background/field stars. On the other hand, the NIR 2MASS photometry provides some direct answers to questions on the large scale structure of the Milky Way Galaxy and the local Universe. It provides J, H, and Ks band photometry for millions of galaxies and nearly a half-billion stars (Carpenter, 2001). 2MASS observations are obtained using two highly automated 1.3-m telescopes, one at Mount Hopkins in Arizona (Northern Survey) and the other at Cerro Tololo in Chile (Southern Survey). Each telescope was equipped with three-channel camera, each channel consisting of 256 x 256 array HgCdTe detectors. It is uniformly scanning the entire sky in the three NIR bands J (1.25µm), H (1.65µm) and Ks (2.17µm). This survey has proven to be a powerful tool in the analysis of the structure and stellar content of open clusters (Bica et al. 2003, Bonatto & Bica 2003). The photometric uncertainty of the 2MASS data is less than 0.155 at Ks ∼ 16.5 magnitude which is the photometric completeness for stars with |b| > 25o , Skrutskie et al. (2006). Ru 15 is located near the Galactic plane (|b| < 3◦ ), therefore we expect significant foreground and background field contamination. The apparent diameter is less than 5 arcmin, hence the downloaded data has been extended to reach the field background stars, whereas the cluster dissolved there, so that we extracted the data to a radius of about 20 arcmin. Every star has 3-colour photometric values J, H, Ks mag; and proper motion (pm) values in right ascension (α) and declination (δ), i.e. (pm α cos δ & pm δ) mas yr−1 . According to Roeser et al. (2010), the stars with proper motion uncertainties ≥ 4.0 mas yr−1 have been removed. In this context, to get a net worksheet data for Ru 15, the photometric completeness limit has been applied on the photometric passband 2MASS data to avoid the over-sampling at the lower parts of the cluster’s CMDs (cf. Bonatto et al. 2004). The stars with observational uncertainties ≥ 0.20 mag have been removed (Claria & Lapasset 1986). Pm vector point diagram (VPD) with distribution histogram of 2 mas yr−1 bins for (pm α cos δ) and (pm δ) have been constructed as shown in Fig. 2. To purify the inner region VPD, the outer region, where field stars dominates, should be excluded. The radius of the inner region is in agreement with the cluster limited radius. The Gaussian function fit to the central bins provides the mean pm in both directions. All data lie at that mean ±1 σ (where σ is the standard deviation of the mean) can be considered as astrometric probable members. In addition, the stellar photometric membership criteria are adopted based on the location of the stars within ±0.1 mag around the ZAMS curve in the colour magnitude diagrams (CMDs). First PPMXL photometric analysis of open cluster ”Ruprecht 15”. 3 3 DATA ANALYSIS AND REDUCTIONS 3.1 Cluster’s Center and Radial Density Profile The star-count method to the whole area of Ru 15 has been applied, and the 20 arcmin data that obtained around the adopted center are dividing into equal sized bins in α and δ. The cluster center is define as the location of maximum stellar density of the cluster’s area. The Gaussian curve-fitting is applied to the profiles of star counts in α & δ respectively as shown in Fig. 3. The differences between our estimated center and the obtained one of Webda are shown in the figure. To establish the radial density profile (RDP) of Ru 15, we counted the stars within concentric shells in equal incremental steps (r ≤ 1) arcmin from the cluster center. We repeated this process for 1 < r ≤ 2 up to r ≤ 10 arcmin, i.e. the stellar density is derived out to the preliminary radius of the cluster. The star counts of the next steps should be subtracted from the previous ones, so that we obtained only the amount of the stars within the relevant shell’s area, not a cumulative count. Finally, we divided the star counts in each shell to the area of that shell those stars belong to. The density uncertainties in each shell was calculated using Poisson noise statistics. Fig. 4 shows the RDP from the new center of Ru 15 to the maximum angular separation of 5 arcmin where the stability of density has been reached. To determine the structural parameters of the cluster more precisely, we applied the empirical King model (1966). The King model parameterizes the density function ρ(r) as: ρ(r) = fbg + f0 1 + (r/rc )2 (1) where fbg , f0 and rc are background, central star density and the core radius of the cluster respectively. From the concentration parameter c, defined as c = (Rlim /Rcore ), Nilakshi et al. (2002) concluded that the angular size of the coronal region is about 6 times the core radius. Maciejewski & Niedzielski (2007) reported that Rlim may vary for individual clusters between about 2Rcore and 7Rcore . In our case, we can see that Rlim =6.9Rcore , i.e. it lies within the previous vales. The clusters limiting radius can be defined at that radius which covers the entire cluster area and reaches enough stability with the background density, i.e. the difference between the observed density profile and the background one is almost equal zero. It is noted that the determination of a cluster radius is made by the spatial coverage and uniformity of PPMXL photometry which allows one to obtain reliable data on the projected distribution of stars for large extensions to the clusters’ halos. On the other hand, the concentration parameter seems to be related to cluster age, i.e. for clusters younger than about 1 Gyr, it tends to increase with cluster age. Nilakshi et al. (2002) notes that the halos’ sizes are smaller for older systems. Finally, we can infer that open clusters appear to be somewhat larger in the near-infrared than in the optical data, Sharma et al. (2006). Knowing the cluster’s total mass (Sec. 3.3), the tidal radius can be given by applying the equation of Jeffries et al. (2001): Rt = 1.46 (Mc )1/3 = 10.7 pc where Rt and Mc are the tidal radius and total mass of the cluster respectively. (2) 4 Tadross, A. L. 3.2 Colour-Magnitude Diagrams Using the 2MASS ZAMS solar metallicity isochrones of Marigo et al. (2008); downloaded from Padova isochrones6 ; the photometrical parameters age, reddening and distance can be obtained applying several isochrones of different ages to both CMDs (J, J-H & Ks , J-Ks ) of Ru 15. These fits should be obtained at the same distance modulus for both diagrams, and the colour excesses should be obeyed Fiorucci & Munari (2003)’s relations for normal interstellar medium as shown in Fig. 5. The observed data has been corrected for interstellar reddening using the coefficients ratios AH AV and AKs AV AJ AV = 0.276 = 0.176, which were derived from absorption rations in Schlegel et al. (1998), while the ratio = 0.118 was derived from Dutra et al. (2002). Fiorucci & Munari (2003) calculated the colour excess values for 2MASS photometric system. We ended up with the following results: AV EB−V EJ−H EB−V = 0.309 ± 0.130, EJ−Ks EB−V = 0.485 ± 0.150, where RV = = 3.1. Also, we can de-redden the distance modulus using these formulae: AJ EB−V = 0.887, AKs EB−V = 0.322, then the distance of the cluster from the Sun (R⊙ ) can be calculated. Therefore, (m-M)J =11.90 ± 0.10 mag (∼ 1845 ± 85 pc), E(J-H) = 0.20 ± 0.05 mag, and (J-Ks ) = 0.31 ± 0.07 mag. After estimating the cluster’s distance R⊙ , the distance from the galactic center (Rg ) and the projected distances on the galactic plane from the Sun (X⊙ & Y⊙ ) and the distance from galactic plane (Z⊙ ) can be determined, see Table 1. For more details about the distances calculations, see Tadross (2011). 3.3 Luminosity, Mass Functions and the total mass It is difficult to determine the membership of the cluster using only the stellar RDP. The stellar membership is found more precise for those stars are close to the cluster’s center and in the same time very near to the main-sequence (MS) in CMDs. These MS stars are very important in determining the luminosity, mass functions and the total mass of the investigated cluster. The number of stars per luminosity interval, or in other words, the number of stars in each magnitude bin, gives us what so-called the luminosity function (LF) of the cluster. In order to estimate the LF of Ru 15 we count the observed stars in terms of absolute magnitude after applying the distance modulus as shown in Fig. 6. The magnitude bin intervals are selected to include a reasonable number of stars in each bin and for the best possible statistics of the luminosity and mass functions. In this context, the total luminosity is found to be ∼ −4.1 mag. The LF and the mass function (MF) are correlated to each other according the known Mass-luminosity relation. The accurate determination of both of them (LF & MF) suffers from some problems e.g. the field contamination of the cluster members; the observed incompleteness at low-luminosity (or low-mass) stars; and mass segregation, which may affect even poorly populated, relatively young clusters (Scalo 1998). On the other hand, the properties and evolution of a star are closely related to its mass, so the determination of the initial mass function (IMF) is needed, that is an important diagnostic tool for studying large quantities of star clusters. IMF is an empirical relation that describes the mass distribution (a histogram of stellar masses) of a population of stars in terms of their theoretical initial mass (the mass they were formed with). The IMF is defined in terms of a power law as following: 6 http://stev.oapd.inaf.it/cgi-bin/cmd First PPMXL photometric analysis of open cluster ”Ruprecht 15”. dN ∝ M −α dM where dN dM 5 (3) is the number of stars of mass interval (M:M+dM), and α is a dimensionless exponent. The IMF for massive stars (> 1 M⊙ ) has been studied and well established by Salpeter (1955), where α = 2.35. This form of Salpeter shows that the number of stars in each mass range decreases rapidly with increasing mass. It is noted that our investigated cluster Ru 15 has MF slope ranging around Salpeter’s value as shown in Fig. 7. To estimate the total mass of Ru 15, the mass of each star has been estimated from a polynomial equation developed from the data of the solar metallicity isochrones (absolute magnitudes vs. actual masses) at the age of the cluster (500 Myr). The summation of multiplying the number of stars in each bin by the mean mass of that bin yields the total mass of the cluster, which is about 390 M⊙ . 3.4 Dynamical state and relaxation time The time in which the cluster needs from the very beginning to build itself and reach the stability state against the contraction and destruction forces is known as the relaxation time (Trelax ) of the cluster. Trelax is depending mainly on the number of members and the cluster diameter. To describe the dynamical state of the cluster, the relaxation time can be calculated in the form: Trelax = N Tcross , 8 ln N (4) where Tcross = D/σV denotes the crossing time, N is the total number of stars in the investigated region of diameter D, and σV is the velocity dispersion (Binney & Tremaine 1998) with a typical value of 3 km s−1 (Binney & Merrifield 1987). Using the above formula we can estimate the dynamical relaxation time for R 15, and then the dynamical-evolution parameter τ can be calculate for the cluster by: τ= age , trelax (5) If the cluster’s age is found greater than its relaxation time, i.e. τ ≫ 1.0, then the cluster was dynamically relaxed, and vice versa. In our case, Ru 15 is indeed dynamically relaxed, where τ > 100. 4 CONCLUSIONS The astrophysical parameters of yet unstudied open cluster ”Ruprecht 15” have been estimated using the PPMXL database. This cluster is found to have a real stellar density profile, its stellar members are lying at the same absolute distance modulus, reddening range, its IMF slope is in agreement with Salpeter’s (1955) value, and its age is greater than its relaxation time, which infers that this cluster is indeed dynamically relaxed. All the astrophysical parameters of ”Ruprecht 15” are listed in Table 1. Acknowledgements It is worthy to mention that, this publication made use of WEBDA, DIAS catalogues, and the data products from PPMXL database of Roeser et al. (2010). 6 Tadross, A. L. Fig. 1 Left panel represents the blue image of Ru 15 as taken from Digitized Sky Surveys, while the right panel represents J-image of the cluster as taken from Interactive 2MASS Image Service, the small open circle indicates the cluster’s central part. North is up, east on the left. References Bica, E., Bonatto, Ch., Dutra, C.M. 2003, A&A, 405, 991 Binney, J., & Tremaine, S. 1987, in Galactic Dynamics, Princeton series in astrophysics, Princeton University Press Binney, J., & Merrifield, M. 1998, in Galactic Astronomy, Princeton series in astrophysics, Princeton University Press Bonatto, Ch., Bica, E. 2003, A&A, 405, 525 Bonatto, Ch., Bica, E., Girardi, L. 2004, A&A, 415, 571 Carpenter, J. M. 2001, AJ, 121, 2851 Clariá, J.J., & Lapasset, E. 1986, AJ, 91, 326 Dutra, C., Santiago, B., Bica, E. 2002, A&A, 381, 219 Fiorucci, M., Munari, U. 2003, A&A, 401, 781 Jeffries, R.D., Thurston, M.R., Hambly, N.C. 2001, A&A, 375, 863 King, I. 1966, AJ, 71, 64 Maciejewski, G. & Niedzielski, A. 2007, A&A, 467, 1065 Marigo, P., Girardi, L., Bressan, A., Groenewegen, M., Silva, L., Granato, G. L. 2008, A&A, 482, 883 Monet, D. et al. 2003, Astron. J., 125, 984 Nilakshi et al. 2002, A&A, 383, 153 Roeser, S., Demleitner, M., Schilbach, E. 2010, AJ, 139, 2440 Salpeter, E. 1955, ApJ, 121, 161 Scalo, J. 1998, ASPC, 142, 201 Sharma et al. 2006, AJ, 2006, 132, 1669 Skrutskie, M., et al. 2006, AJ, 131, 1163 Schlegel, D., Finkbeiner, D., Davis, M. 1998, ApJ, 500, 525 Tadross, A. L. 2011, JKAS, 44, 1 This manuscript was prepared with the RAA LATEX macro v1.2. First PPMXL photometric analysis of open cluster ”Ruprecht 15”. Fig. 2 Proper motion vector point diagram VPD of Ru 15 after avoiding all data with pm errors ≥ 4 mas yr−1 . Histograms of 2 mas yr−1 bins in both directions are drawn. The Gaussian function fit to the central bins provides the mean pm α cos δ = –0.84 ± 0.1 mas yr−1 and pm δ = 6.7 ± 0.09 mas yr−1 . Fig. 3 Estimating the cluster center coordinates of Ru 15. The Gaussian fit provides the coordinates of ′ ′′ highest density areas in α & δ as 07h 19m 38s & − 19◦ 37 35 respectively. The differences between our ′′ estimated center and the obtained one of Webda are 4s in α and 5 in δ. 7 8 Tadross, A. L. Fig. 4 The radial density distribution for stars in the field of Ru 15. The density shows a maximum at the center ρ = 63 stars/arcmin2 and then decreases down to ρ = 3 stars/arcmin2 at 2.2 arcmin, where the decrease becomes asymptotical at that point. The curved solid line represents the fitting of King (1966) √ model. Errors bars are determined from sampling statistics (1/ N where N is the number of stars used in the density estimation at that point). The dashed line represents the background field density, where fbg = 3.0 stars per arcmin2 . The core radius rc = 0.32 arc min. Fig. 5 The net NIR CMDs of Ru 15 for stars lying closely to the fitted isochrones and after removing all contaminated field stars. Age = 500 Myr, distance modulus = 11.9 mag (∼ 1845 pc), E(J-H) = 0.20 mag, and (J-Ks ) = 0.31 mag. First PPMXL photometric analysis of open cluster ”Ruprecht 15”. Fig. 6 The luminosity function of Ru 15 in terms of the absolute magnitude MJ . The colour and magnitude filters cutoffs have been applied to the cluster (dark area) and the field (white area) respectively. Fig. 7 The mass function of Ru 15. The slope of the initial mass function IMF is found to be Γ = −2.37 ± 0.20; with correlation coefficient of 0.82. 9 10 Tadross, A. L. Table 1 The present results of Ruprecht 15. Parameter The present result Center α = 07h 19m 38s ′ δ = −19◦ 37 35 ′′ c 6.9 (see Sec. 3.1) pm α cos δ −0.84 ± 0.10 mas yr−1 pm δ Age 6.7 ± 0.09 mas yr−1 500 ± 60 Myr. Metal abundance 0.019 E(J − H) 0.20 ± 0.05 mag. E(J − Ks ) E(B − V ) 0.31 ± 0.07 mag. 0.65 ± 0.05 mag. RV 3.1 (see Sec. 3.2) Distance Modulus 11.90 ± 0.10 mag. Distance Rlim 1845 ± 85 pc. ′ 2.2 (1.20 pc.) Membership 265 stars fo 63 ± 2 stars/arcmin2 fbg 3 stars/arcmin2 Rc 0.32 ± 0.04 (0.20 pc) ′ Rt 10.7 pc. Rg 9.7 kpc. X⊙ 1095 kpc. Y⊙ −1482 kpc. Z⊙ τ Total Luminosity IMF slope Total mass Relaxation time −93 pc. > 100 (see Sec. 3.4) ∼ −4.1 mag. Γ = −2.37 ± 0.20 ∼ 390 M⊙ 2.7 Myr