CSIRO PUBLISHING Publications of the Astronomical Society of Australia, 2012, 29, 509–522 http://dx.doi.org/10.1071/AS12003 Absolute-Magnitude Calibration for Red Giants Based on Colour–Magnitude Diagrams of Galactic Clusters: I. Calibration in V and B–V S. KaraaliA-,B, S. BilirA, and E. Yaz Gok€ ceA AIstanbul University, Faculty of Sciences, Department of Astronomy and Space Sciences, 34119, Istanbul, Turkey BCorresponding author. Email: [email protected] Abstract: We present an absolute-magnitude calibration for red giants using the colour–magnitude diagrams of six Galactic clusters with different metallicities: M92, M13, M5, 47 Tuc, M67 and NGC 6791. The combination of the absolute magnitude offset from the fiducial of giant sequence of the cluster M5 with the corresponding metallicity offset provides a calibration estimation for the absolute magnitude of red giants for a given (B À V)0 colour. The calibration is defined in the colour interval 0.75 # (B À V)0 # 1.50 mag and it covers the metallicity interval À2.15 , [Fe/H] # þ0.37 dex. 91% of the absolute magnitude residuals obtained by the application of the procedure to another set of Galactic clusters lie in the interval À0.40 , DM # þ0.40 mag. The mean and the standard deviation of the residuals are 0.05 and 0.19 mag, respectively. We fitted the absolute magnitude also to metallicity and age for a limited sub-sample of (B À V)0 colour, just to test the effect of age in absolute-magnitude calibration. Comparison of the mean and the standard deviation of the residuals evaluated by this procedure with the corresponding ones provided by the procedure where the absolute magnitude fitted to a third degree polynomial of metallicity show that the age parameter may be omitted in absolute magnitude estimation of red giants. The derived relations are applicable to stars older than 4 Gyr, the age of the youngest calibrating cluster. Keywords: stars: distances — globular clusters: individual (M92, M13, M5, 47 Tuc) — open clusters: individual (M67, NGC 6791) Received 2012 January 9, accepted 2012 April 17, published online 2012 May 31 1 Introduction adopted as the mean metal abundance for a Galactic Stellar kinematics and metallicity are two primary means population, such as thin, thick discs and halo. The studies to deduce the history of our Galaxy. However, such goals of Phleps et al. (2000) and Chen et al. (2001) can be given can not be achieved without stellar distances. The dis- as examples. A slightly different approach is that of Siegel tance to a star can be evaluated by trigonometric or pho- et al. (2002) where two relations, one for stars with solar- tometric parallaxes. Trigonometric parallaxes are only like abundances and another one for metal-poor stars were available for nearby stars where Hipparcos (Perryman derived between MR and the colour index R À I, where MR et al. 1997) is the main supplier of data. For stars at large is the absolute magnitude in the R filter of Johnson distances, the use of photometric parallaxes is unavoid- system. For a star of given metallicity and colour, the able. The study of the Galactic structure is strictly tied to absolute magnitude can be estimated by linear interpola- precise determination of absolute magnitudes. tion of two ridgelines and by means of linear extrapola- Different methods can be used for absolute magnitude tion beyond the metal-poor ridgeline. determination where most of them are devoted to dwarfs. The most recent procedure used for absolute magni- The method used in the Stromgren’s€ uvby 2 b (Nissen & tude determination consists of finding the most likely Schuster 1991) and in the UBV (Laird, Carney & Latham values of the stellar parameters, given the measured 1988) photometries depends on the absolute-magnitude atmospheric ones, and the time spent by a star in each offset from a standard main-sequence. In recent years the region of the H-R diagram. In practice, researchers select derivation of absolute magnitudes has been carried out by the subset of isochrones with [M/H] Æ D[M/H],whereD[M/H] means of colour–absolute magnitude diagrams of some is the estimated error on the metallicity, for each set of specific clusters whose metal abundances are generally derived Teff, log g and [M/H]. Then a Gaussian weight is associated to each point of the selected isochrones, which y Retired. depends on the measured atmospheric parameters and the Journal compilation Ó Astronomical Society of Australia 2012 www.publish.csiro.au/journals/pasa Downloaded from https://www.cambridge.org/core. IP address: 170.106.202.226, on 29 Sep 2021 at 01:12:04, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1071/AS12003 510 S. Karaali et al. Table 1. Data for the clusters used in our work Cluster V À MV E(B À V)(V À MV)0 [Fe/H][a/Fe] Reference (mag) (mag) (mag) (dex) M92 14.80 0.025 14.72 À2.15 0.33 (1), (2), (3) M13 14.44 0.020 14.38 À1.41 0.22 (1), (3) M5 14.50 0.020 14.44 À1.17 0.24 (4) 47 Tuc 13.37 0.040 13.25 À0.80 0.27 (5), (6) M67 9.65 0.038 9.53 À0.04 – (7) NGC 6791 13.25 0.100 12.94 0.37 – (7) (1) Sandage (1970), (2) Stetson & Harris (1988), (3) Gratton et al. (1997), (4) Sandquist et al. (1996), (5) Hesser et al. (1987), (6) Percival et al. (2002), (7) Sandage, Lubin & VandenBerg (2003). considered errors. This criterion allows the algorithm to 47 Tuc. The V and B À V data were taken from the first select only the points whose values are closed by the reference, but the second one refers to their V À MV dis- pipeline. For details of this procedure we cite the works of tance modulus, E(B À V) colour-excess and [Fe/H] Breddels et al. (2010) and Zwitter et al. (2010). This metallicity. The reason of this selection is to obtain the procedure is based on many parameters. Hence it provides best fitting of the colour–magnitude diagrams to the iso- absolute magnitudes with high accuracy. Also it can be chrones (see Section 3). Thus, in the case of more than one applied to both dwarf and giant stars simultaneously. reference in Table 1, the last one refers to the distance In Karaali et al. (2003), we presented a procedure for modulus, colour excess, and metallicity. The original V the photometric parallax estimation of dwarf stars which and B À V data refer to the fiducial sequence, i.e. giants, depends on the absolute magnitude offset from the main- sub-giants, and main-sequence stars of the clusters. We sequence of the Hyades cluster. In this study, we will use a plotted these sequences on a diagram for each cluster and similar procedure for the absolute magnitude estimation identified red giants by means of their positions in the of red giants by using the apparent magnitude-colour diagram. The (V, B À V) points in Table 2 consist of the diagrams of Galactic clusters with different metallicities. fiducial sequence of the referred cluster. Hence, they In Section 2 we present the data. The procedure used for represent the cluster in question quite well. However, they calibration is given in Section 3, and Section 4 is devoted are not error free. The errors for these couples may be a bit to summary and discussion. larger for the photographic magnitude and colours of the clusters M92 and M13 than the CCD ones of the other clusters. As noted above the bright magnitudes and the 2 Data corresponding colours of the cluster M92, and all mag- Six clusters with different metallicities, i.e. M92, M13, nitude and colours of the cluster M13 which were taken M5, 47 Tuc, M67, and NGC 6791, were selected for our from Sandage (1970) are photographic data. We will see program. The range of the metallicity given in iron in Section 3 that the data of these clusters are in good À # # þ À abundance is 2.15 [Fe/H] 0.37 dex. The V MV agreement with the data of the other clusters investigated À apparent distance modulus, (V MV)0 true distance by using CCD technic. We, then fitted the fiducial modulus, E(B À V) colour excess, and [Fe/H] iron abun- sequence of the red giants to a sixth degree polynomial for dance are given in Table 1, whereas the V and B À V data all clusters, except M92 for which a seventh degree ¼ À ¼ are presented in Table 2. We adopted R AV/E(B V) polynomial was necessary for a good correlation coeffi- 3.1 to convert between colour excess and extinction. cient. The calibration of V0 is as follows: Although different numerical values appeared in the lit- erature for specific regions of our Galaxy, a single value is X7 V ¼ a ðB À VÞi ð1Þ applicable everywhere. Different distance moduli and 0 i 0 i¼1 interstellar extinctions were cited in the literature for the clusters. The data in Table 1 and Table 2 are taken from The numerical values of the coefficients a (i ¼ 0, 1, 2, 3, the authors cited in the reference list of Table 1. The V and i 4, 5, 6, 7) are given in Table 3, and the corresponding B À V data of M92 were taken from two sources, diagrams are presented in Figure 1.