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Deep CCD photometry in the globular cluster M12 Sato, Takashi 1988

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D E E P C C D P H O T O M E T R Y IN T H E G L O B U L A R C L U S T E R M12 B y T A K A S H I S A T O B . S c , T h e Un ive r s i t y of B r i t i s h C o l u m b i a , 1986 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F S C I E N C E i n T H E F A C U L T Y O F G R A D U A T E S T U D I E S Depar tmen t of Geophysics a n d A s t r o n o m y We accept th is thesis as conforming to the required s t anda rd T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A O c t o b e r 1988 © Takash i Sa to , 1988 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1 Y 3 D E - 6 ( 3 / 8 1 ) Abstract New U B V C C D photometry is presented for a single field measuring 2'.2 x 3'.5 in the galactic globular cluster M12 (NGC 6218). This field is located 3'.5 or 3 core radii from the cluster centre. The photometry reaches well down the main sequence to fainter than V = 23.5. In the colour-magnitude diagram, a possible sequence of binary stars appears separated from the upper main sequence. Excluding the possible binaries, the upper main sequence shows small intrinsic width consistent with zero spread in chemical composition and with an upper limit of A[Fe/H] < 0.2. Stars from the M12 horizontal branch and from the field found on our C C D frames have been used to derive a reddening estimate for M12 of E(B — V) = 0.23 ± 0.04. Our fiducial main sequence is compared with that defined by the subdwarfs to determine the apparent distance modulus with the result (m — M)v = 14.25 ± 0.20. The metallicity of M12 is estimated to be [Fe/H] = —1.4 using values found in the literature in conjunction with our own estimate based on 6(U — B)o.6 = —0.15 which is measured from the colour-colour diagram. Using these parameters, comparison with theoretical isochrones of VandenBerg and Bell results in a best-estimate age of 17 ± 1 Gyr, although uncertainties associated with these fundamental parameters and the oxygen abundance increase the 'true error.' A luminosity function and the corresponding mass function are also constructed using the available data. A fit to a power law mass spectrum of the form Ndm oc m ~ ( 1 + z ) d m yields x = —0.70 ± 0.16 whereas x « +1 is expected from the x - metallicity relation of McClure et al. Results obtained using multimass King models indicate that the global value for the power law index is also near —0.7 ii for M12. iii Table of Contents Abstract 1 1 Table of Contents i v List of Tables v List of Figures vi Acknowledgements v u I. Introduction 1 II. Observations and Reduction 4 III. Colour-Magnitude Diagram 17 (a) Binary Sequence 17 (b) Main Sequence Width 17 IV. Fundamental Cluster Parameters 21 (a) Reddening 21 (b) Metallicity 22 (c) Distance Modulus 24 V . Comparison with Isochrones and the Age of M12 30 V I . Luminosity Function 34 VII . Summary 4 7 Bibliography 48 iv List of Tables Table 1. Journal of Observations 5 Table 2. Photometry of M12 Stars 10 Table 3. M a i n Sequence W i d t h 19 Table 4. Summary of M12 Metallicity Estimates 23 Table 5. M12 M a i n Sequnce Fiducial 28 Table 6. Results of Completeness Experiments in M12 37 Table 7. M12 Luminosity Function 38 Table 8. M12 Mass Function 41 v List of Figures 1 Observed field in M12 6 2 Colour-magnitude diagram 16 3 Colour-colour diagram 25 4 Observed fiducial sequence and the empirical main sequence 29 5 [Fe/H] = —1.27 isochrones overlaid on M12 fiducial 32 6 V photometry errors of artificially added stars 36 7 Luminosity function for M12 39 8 Mass function for M12 42 9 Results of multimass King models 45 vi Acknowledgements It is indeed a great pleasure to thank Professor G . G . Fahlman 1 and Professor H . B . Richer 1 with whom I have enjoyed the extraordinary priviledge of having two supervi-sors. Visiting Astronomer, Canada-France-Hawaii Telescope. C F H T is operated by the National Research Council of Canada, the Centre National de la Recherche Scientifique of France, and the University of Hawaii. vii I. Introduction The study of globular clusters touches on a great variety of astrophysical problems. The ages of globular clusters give a powerful lower limit to the age of the universe and provide insight into the collapse timescale of the galactic halo. The spread in chemical composition among globulars also provides important clues about the early history of the galaxy and mechanisms of star formation. Study of individual clusters in the colour-magnitude plane serve to test many aspects of stellar evolution theory as well as the dynamics of gravitating systems. With the implementation of C C D detectors on 4m-class telescopes it is now prac-tical to undertake deep photometry programs reaching well down the main sequence. Colour-magnitude diagrams constructed from such observations are often of high enough internal precision to allow estimates of intrinsic widths of cluster main se-quences which arise from such sources as chemical inhomogeneity. The spread due to inhomogeneity tends to be very small if not zero (for example, Bolte 1987, Fahlman, Richer and VandenBerg 1985, Penny and Dickens 1986, Richer and Fahlman 1987, and Hesser et al. 1987). High precision data also allows identification of populations of binary stars. When one exists in a cluster, it reveals itself in the colour-magnitude diagram by forming a distinctly recognizable sequence above the main sequence if the stars are of equal mass (eg. E3; McClure et al. 1985). However, binary sequences are seldom observed among the large number of well studied globular clusters now in the literature. When a set of parameters including chemical composition, distance modulus and 1 interstellar reddening toward a globular cluster is well determined, the observed fiducial sequences can be compared to theoretical isochrones such as those of VandenBerg and Bell (1985). This serves as testing ground for the interior and atmospheric physics incorporated in the models in addition to yielding an age for the system. To date, ages for a large number of globular clusters determined in this way suggest all globulars are coeval at T ~ 16 ~ 18 Gyr on the scale defined by the VandenBerg and Bell (1985) isochrones which employ scaled solar abundance ratios. Variations in determined ages are of the order of the uncertainties and are not found, in a convincing manner, to correlate with any parameters such as galactocentric distance or metallicity. One possible exception may be Pal 12, for which Gratton and Ortolani (1988) as well as Stetson and Smith (1987) find an age as much as 30% younger than the rest. Due to the linearity of CCDs and the use of elaborate analysis software such as D A O P H O T (Stetson 1987), it is relatively simple to estimate completeness of the photometry even in crowded fields. This is derived by adding artificial stars to the image and determining the fraction that is recovered when the image is re-reduced using the same procedure as was employed in the program frame reductions. Corrections derived in this manner are important in constructing luminosity functions for the observed fields. This is the number of stars as a function of magnitude derived by counting the stars in magnitude bins and must be corrected for completeness and counts due to background (and foreground) objects. By comparing luminosity functions at various radial positions in the same cluster, Richer and Fahlman (1989), for example, have shown clear evidence for mass segregation in M71. In the absence of such effects of 2 dynamical evolution, it probes the initial mass function of the system, giving clues to its formation mechanism. Among the well studied globulars, McClure et al. (1986) have found that the steepness of the luminosity function of a cluster correlates with its metallicity. In this work, we study in detail the globular cluster M12 [NGC6218; I = 15°.7, 6 = 26°.3; a = 16 f c44m.6, 6 = - 01°52 ' (1950) ]. M12 does not present particular observational difficulties, in fact, its sparseness minimizes problems associated with crowding. However, it has not been a particularly well studied system. Although a modern, C C D luminosity function already exists for M12 (McClure et al. 1988), only three colour-magnitude diagrams are available in the literature. The most usefull of these is the photographic BV photometry of Racine (1971) but even this barely reaches the main-sequence turnoff. Although the turnoff is slightly better defined in Mironov et al. (1984), their analysis goes little beyond presenting an instrumental colour-magnitude diagram. In a much earlier work, Nassau and Hynek (1942), at the faint limit of their m r vs. Cr photometry, discovered signs of a horizontal branch including the R R Lyrae gap and wondered if these features might be universal to all globular clusters. 3 II. Observat ions and D a t a Reduc t ion Observations for this study were carried out at the 3.6m Canada-France-Hawaii Telescope (CFHT) over two sessions. As listed in Table 1, single 900 second exposures in each of V and B were secured in June 1984 using the R C A 1 C C D at the prime focus under non-photometric conditions. This combination of instruments yields a 2'.2 x 3'.5 field at 0".42 per pixel. The seeing was ~ 0".8 (FWHM) on both frames. These images were centred at 3'.5 toward the north-west from the cluster centre (~ 3.0 core radii) and the V frame is shown in Figure 1. In June 1985, single 120 second frames were taken for calibration purposes in V and B with the same instrument, this time under photometric conditions. A 900 second exposure in U was also secured at this time. While these frames are not identically positioned over the earlier frames, a significant portion ( 71% ) does overlap thus serving to calibrate the deeper data from 1984. Preprocessing was done using software facilities available at C F H T or the Uni-versity of British Columbia in the usual manner including corrections for bias, dark current and flat fielding. No defringing is required with this detector in the B and V bands. Relative photometry on each frame was subsequently performed using D A O P H O T (Stetson 1987). This multiple stellar profile fitting program locates and measures in-tensities for stars on a digital image relative to a model point spread function (PSF) determined from a few relatively isolated stars on the same frame. After an initial pass with FIND, an automatic star finding routine within D A O P H O T , with the user-specified detection threshold at 3.3(7 a above the sky noise and subsequent PSF fitting 4 T A B L E 1. J O U R N A L O F O B S E R V A T I O N S date band exp. seeing (FWHM) photometric? 1984 June V 900 sec 0".8 N 1984 June B 900 sec 0".8 N 1985 June V 120 sec 0".9 Y 1985 June B 120 sec 0".9 Y 1985 June U 900 sec 1".2 Y 5 0 100 200 300 Fig. 1 — Observed field in M12. This is a 900 second exposure V C C D frame centred at 3 core radii and is our deepest frame. The axes are labelled with pixel numbers which are also the coordinates for stars in the photometry list of Table 2. The scale is 0".42 per pixel. From the upper-right corner (318,0), north is approximately in the direction of (150,498) and the pixel numbers in x and y increase to the east and north, respectively. 6 (some 'bad stars' are rejected automatically during this step), the measured stars were subtracted from the image and the new image was subjected to a second pass with F IND. This procedure reveals blended stars or those hiding fainter stars in their wings which had been misidentified as a single star in the first pass. These stars were appended to those from the first list that survived the profile fitting routine and the fit was redone on the original image. It was found that a third pass with the same detec-tion threshold yields a list of stellar candidates essentially identical to that produced manually by visual inspection of the subtracted image, both consisting of objects pre-viously hidden but nonetheless stellar in appearance. For the sake of repeatability this automatic list was adopted over the manual one since this procedure is repeated many tens of times for the incompleteness experiments ( §VI) . Needless to say, an automatic detection procedure is not only less laborious but can be repeated consistently from run to run. The appended list was then put though the profile fitting procedure for ° After some experimentation, the 3.3a detection threshold was chosen for the following reasons. A detection threshold that is too low obviously results in many spurious "detections" of noise peaks. However, the results of FIND in the third pass indicated that this was not a problem at 3.3er. At the other extreme, too high a detection threshold results in a photometry list truncated at some magnitude above the real detection limit. This effect was explored by running incompleteness experiments (of the type discussed in §VI) at various thresholds. At high thresholds, completeness can drop suddenly from 100% to 0% from one bin to the next. At our adopted threshold, the completeness drops off smoothly (see Table 6). Here, the sky noise a is calculated directly from the variations in the pixel values in blank regions of the C C D image. 7 the last time. The output from D A O P H O T was transferred to the standard U B V system in the following manner. Aperture photometry with appropriate aperture corrections was performed on C C D frames containing a number of standard stars from a field in M92 and compared to photometric lists of Davis (private communication) and Stetson and Harris (1988) as well as a number of Landolt standards (Landolt 1973, 1983). The resultant counts were corrected for atmospheric extinction and exposure times to obtain instrumental magnitudes in the form v' = -2.5log(V count per sec) + 0.134X b' — v' — —2.5log(B count per sec/V count per sec) + 0.071.X" u' — b' = —2.5log(U count per sec/B count per sec) + 0.147X, where X is the airmass and the extinction coefficients are taken from a C F H T aver-age. Thus, relations calibrating instrumental magnitudes to the standard system were determined. Next, instrumental magnitudes were similarly measured for a handful of M12 stars (on the short, photometric frames) and transformed to the standard system. This provides the calibration of D A O P H O T magnitudes on the deep frames based on these same M12 stars. The final calibration relations obtained were (B — V) — 1.333(6 - v) - 0.731 ± 0.022 (tV - B) = 0.839(u - b) - 6.473 ± 0.016 V = v - 0.0418(5 - V) + 3.536 ± 0.008 where small letters refer to magnitudes output by D A O P H O T . While the values of the zero-point constants are artifacts arising from details of the reduction procedure, the associated uncertainties, which are la scatter about the zero-points assuming fixed 8 slopes, serve as a useful measure. After registering the frames, the stars in different bands were matched if their positions differed by less than 0.5 pixels and transformed using the relations above. These stars are listed in Table 2. 9 T A B L E 2. PHOTOMETRY OP M12 STARS X y V B-V U-B X y V B-V U-B 278.28 235.09 15.423 0.941 0.458 180.29 482.99 18.277 0.655 0.411 315.24 121.69 15.461 0.089 -0.106 285.87 268.33 18.280 0.637 0.051 236.67 39.41 15.478 0.941 0.456 195.30 217.11 18.294 0.656 0.065 272.61 333.40 15.908 0.039 -0.127 254.37 21.99 18.308 0.648 239.48 42.01 16.096 1.219 0.176 240.22 194.25 18.348 0.661 0.039 241.34 30.09 16.500 0.915 296.72 392.31 18.360 0.655 0.074 144.08 146.61 16.549 0.732 0.122 191.28 134.42 18.361 0.695 0.048 139.97 434.79 16.602 0.832 0.490 256.90 11.47 18.365 0.669 232.27 58.35 16.655 0.915 0.490 293.77 204.99 18.375 0.657 0.009 142.17 273.57 16.753 1.047 0.674 293.67 241.78 18.384 0.625 0.019 192.27 212.89 16.838 0.912 0.310 309.15 22.08 18.389 0.651 261.55 381.34 16.852 0.873 0.439 145.95 341.94 18.406 0.629 0.068 96.89 343.94 17.039 0.872 0.282 298.85 101.90 18.411 0.664 0.024 109.13 283.56 17.116 0.887 0.269 253.48 285.59 18.411 0.648 0.041 87.50 442.12 17.218 0.832 299.92 183.63 18.414 0.639 0.051 251.83 19.77 17.309 0.567 222.45 233.93 18.422 0.679 0.218 305.69 380.07 17.317 0.849 0.319 146.98 45.24 18.426 0.547 167.16 137.16 17.385 0.863 0.249 91.39 139.18 18.432 3.516 142.00 11.55 17.431 0.912 198.58 294.32 18.445 0.644 0.012 162.48 93.31 17.520 0.543 0.113 282.19 405.88 18.446 0.656 0.060 280.44 23.96 17.548 0.867 251.86 47.80 18.447 0.836 0.261 273.41 352.49 17.551 0.855 0.196 258.81 380.62 18.452 0.568 0.074 269.40 87.12 17.599 0.824 0.175 98.93 148.41 18.466 0.680 246.12 159.87 17.613 0.748 0.198 202.46 89.32 18.468 0.720 0.019 210.98 75.42 17.685 0.803 0.174 240.45 171.28 18.481 0.664 0.028 196.32 41.73 17.735 0.765 83.68 268.16 18.483 0.697 0.020 162.26 457.17 17.748 0.780 0.204 213.86 166.57 18.489 0.668 0.039 202.37 147.42 17.759 0.773 0.103 305.78 103.96 18.492 0.644 -0.028 156.54 9.20 17.789 2.668 49.90 220.13 18.499 0.663 153.46 10.68 17.813 0.709 277.75 30.99 18.499 0.689 207.46 457.60 17.922 0.748 0.274 160.30 237.88 .. - 18.499 0.667 0.159 176.48 188.84 17.938 0.701 0.124 111.42 418.25 18.499 0.971 0.640 221.34 153.83 17.940 0.704 0.024 279.55 100.51 18.504 0.173 0.135 248.69 383.51 17.958 0.663 0.127 279.25 122.59 18.513 0.660 0.052 170.42 161.53 17.960 0.704 0.108 279.82 150.00 18.529 0.672 0.007 240.83 214.74 17.962 0.697 0.052 34.29 488.98 18.534 0.729 83.42 275.37 17.964 0.719 0.102 149.49 290.48 18.539 0.663 0.058 279.04 37.06 18.009 0.676 124.76 60.30 18.539 0.528 108.35 21.22 18.067 0.685 154.81 421.51 18.540 0.667 0.052 4.98 302.66 18.086 0.573 97.61 150.01 18.541 0.693 207.66 53.38 18.100 0.685 0.059 289.07 28.20 18.576 0.664 150.86 135.50 18.107 0.659 0.087 298.28 91.44 18.590 0.685 0.103 298.16 62.96 18.124 0.648 0.060 155.46 2.53 18.596 0.723 295.54 175.18 18.133 0.644 0.068 230.40 134.27 18.596 0.665 -0.020 159.38 71.02 18.147 0.655 0.095 203.51 469.16 18.597 0.645 0.162 157.23 177.95 18.167 0.676 0.043 107.74 308.58 18.603 0.673 0.028 65.21 362.92 18.212 0.661 0.056 91.93 207.04 18.608 0.647 181.64 372.97 18.244 0.565 0.120 260.42 190.14 18.615 0.668 -0.022 220.36 47.10 18.250 0.659 0.097 200.13 268.74 18.634 0.659 0.140 49.66 408.37 18.256 0.653 0.104 206.33 259.32 18.650 0.684 0.014 10 T A B L E 2. - continued X y V B-V U-B X y V B-V U-B 204.48 43.92 18.703 0.701 0.022 303.26 78.32 19.109 0.751 0.068 89.67 184.13 18.707 0.728 63.56 166.50 19.121 0.771 193.94 158.34 18.707 0.680 0.043 150.35 179.56 19.124 0.701 0.113 177.44 393.80 18.708 0.663 0.042 146.00 212.97 19.132 0.687 0.060 80.37 302.13 18.713 0.703 0.006 189.79 224.29 19.144 0.684 -0.050 292.50 83.71 18.716 0.652 0.000 283.58 90.25 19.168 1.941 169.93 51.95 18.717 0.676 0.215 183.83 127.42 19.168 0.740 0.012 253.39 26.06 18.720 0.693 200.44 433.69 19.168 0.880 0.276 239.70 279.27 18.734 0.672 0.166 161.64 47.59 19.169 0.887 0.125 131.52 456.53 18.739 1.653 -0.447 268.10 88.75 19.171 0.713 0.077 181.10 260.22 18.764 0.671 0.121 245.87 227.93 19.172 0.716 -0.002 239.77 403.48 18.770 0.680 0.074 204.03 319.57 19.177 0.725 0.025 205.44 220.21 18.775 0.669 0.045 69.83 323.37 19.178 0.683 152.94 68.95 18.789 0.611 0.075 261.76 264.46 19.192 0.709 0.134 123.08 433.92 18.790 0.732 0.315 188.49 43.48 19.214 0.755 0.049 117.54 180.45 18.802 0.693 0.027 300.29 331.12 19.232 0.696 0.003 157.47 82.43 18.822 1.092 0.061 209.97 230.67 19.234 0.747 -0.059 249.42 304.20 18.848 0.688 0.095 173.78 69.50 19.235 0.721 0.118 152.87 288.33 18.848 0.647 0.026 173.59 64.25 19.243 0.731 0.056 217.14 257.93 18.852 0.695 0.042 28.45 476.25 19.263 0.685 130.77 98.64 18.854 0.665 291.71 14.25 19.268 0.779 276.54 365.45 18.854 0.657 0.351 293.10 79.18 19.271 0.219 0.144 273.60 50.81 18.855 0.701 -0.010 16.23 292.13 19.284 0.719 196.63 153.01 18.858 0.696 -0.034 283.81 199.49 19.285 0.743 0.322 120.29 269.76 18.860 0.635 0.074 136.86 255.23 19.291 0.732 -0.004 186.66 250.73 18.860 0.691 0.007 252.15 148.85 19.301 0.727 86.19 125.73 18.867 0.677 50.74 328.88 19.312 0.719 230.51 312.16 18.869 0.648 0.087 283.99 15.85 19.315 0.759 285.82 105.93 18.917 0.685 0.035 112.05 139.35 19.330 0.740 238.77 126.85 18.920 0.693 0.040 261.42 322.60 19.341 0.720 0.036 73.63 296.63 18.922 1.007 0.427 106.75 463.51 19.342 0.735 0.101 191.41 381.24 18.927 0.727 0.047 270.82 250.22 19.362 0.740 0.097 251.81 421.80 18.930 0.676 0.113 310.72 458.82 19.373 0.799 0.301 73.68 323.80 18.934 0.673 225.50 308.51 19.384 0.732 147.10 131.95 18.942 0.645 0.276 298.20 173.49 19.384 0.720 -0.002 225.13 215.01 18.944 1.103 -0.302 270.80 43.85 19.391 0.740 198.73 450.01 18.950 0.680 0.135 260.23 420.78 19.394 0.728 250.63 233.23 18.968 1.104 -0.222 297.89 310.50 19.399 0.723 0.061 312.85 189.48 18.969 0.569 -0.003 149.14 411.59 19.404 0.735 0.171 163.49 32.42 18.975 0.707 245.38 130.35 19.415 0.752 -0.024 176.42 92.60 18.982 0.748 0.001 104.12 230.12 19.419 0.824 -0.065 257.91 103.26 18.983 0.709 0.063 239.67 58.59 19.424 0.735 0.093 226.11 72.98 19.004 0.699 0.006 92.59 107.24 19.431 0.815 266.55 418.55 19.036 0.663 0.121 186.80 32.43 19.435 0.752 0.115 199.31 289.44 19.050 0.707 -0.002 106.96 191.74 19.439 0.352 -0.116 216.73 184.25 19.058 0.751 0.116 199.24 226.62 19.448 0.735 0.003 33.29 315.35 19.058 0.743 209.45 145.78 19.450 0.719 0.059 138.57 131.68 19.087 0.712 0.204 296.99 194.54 19.457 0.728 0.056 269.99 12.91 19.105 0.645 212.71 338.33 19.476 0.764 0.041 102.56 277.61 19.109 0.709 0.080 171.82 183.29 19.483 0.765 0.088 11 T A B L E 2. — continued X y V B-V U-B X y V B-V U-B 229.67 393.08 19.486 0.732 0.310 182.62 208.91 19.795 0.777 0.077 173.90 257.55 19.499 0.744 0.126 52.54 250.61 19.807 0.779 288.68 139.33 19.503 0.773 0.063 252.82 129.58 19.827 0.800 165.64 152.64 19.513 0.769 0.053 307.70 334.49 19.833 0.787 0.139 229.60 238.47 19.531 0.769 0.115 295.59 290.46 19.835 0.808 0.300 303.47 83.56 19.537 0:806 0.057 135.29 82.13 19.835 0.795 212.25 218.23 19.538 ' 0:772 0.056 306.86 8.58 19.835 0.751 108.30 165.11 19.540 0.761 144.54 126.36 19.842 1.479 310.57 393.09 19.549 1.191 199.27 111.04 19.846 0.825 -0.086 236.80 139.11 19.549 0.789 0.027 208.81 392.94 19.850 0.833 0.045 273.16 114.33 19.551 0.703 0.147 124.77 94.75 19.854 0.744 288.74 128.48 19.555 0.731 0.094 246.01 408.18 19.860 0.820 0.154 64.53 228.86 19.563 0.741 272.50 19.88 19.863 0.803 293.91 122.05 19.564 0.751 0.044 300.45 351.17 19.877 0.823 212.70 408.09 19.572 0.743 0.249 204.77 136.19 19.880 0.871 0.209 270.14 463.15 19.576 0.744 231.30 436.99 19.892 0.808 0.113 116.48 425.83 19.579 0.721 0.144 126.75 73.40 19.900 0.797 306.98 284.14 19.604 0.729 0.267 230.18 481.42 19.903 0.860 101.68 284.37 19.618 0.797 -0.056 61.12 146.71 19.908 0.781 192.50 59.93 19.621 0.776 237.89 363.51 19.914 0.629 0.123 272.27 434.94 19.631 0.717 78.14 342.09 19.914 0.803 0.232 108.40 202.53 19.643 0.837 0.030 292.84 202.80 19.917 0.681 0.160 265.60 389.06 19.644 0.789 0.111 179.32 190.57 19.928 0.811 0.222 140.22 14.32 19.644 0.792 210.41 109.36 19.943 0.860 -0.002 30.16 491.90 19.645 0.755 287.36 182.38 19.947 0.871 0.180 235.36 79.91 19.650 0.820 210.29 97.34 19.948 0.845 294.58 318.89 19.676 0.800 229.60 361.91 19.952 0.809 156.41 119.92 19.683 0.761 0.197 220.49 85.35 19.956 0.812 0.254 274.97 45.28 19.686 0.833 242.87 36.72 19.964 0.817 286.65 395.92 19.691 1.435 258.10 9.19 19.970 0.780 252.75 104.10 19.692 0.728 0.238 249.19 17.75 19.972 0.695 205.87 231.29 19.694 0.829 0.065 212.09 134.24 19.975 0.885 0.355 253.67 217.85 19.699 0.815 154.97 74.05 19.977 0.804 0.337 298.34 270.55 19.700 0.759 0.319 231.15 144.39 19.983 0.844 0.079 159.03 54.90 19.710 0.775 0.155 241.19 74.37 19.986 0.845 0.078 197.82 100.74 19.713 0.856 0.108 136.13 16.96 19.997 0.880 188.69 228.50 19.715 0.771 0.107 236.01 112.77 20.008 0.832 0.060 12.76 472.09 19.727 0.815 247.20 394.75 20.018 0.883 0.204 185.06 132.61 19.733 0.748 0.234 305.07 378.04 20.029 0.585 -0.082 271.08 59.82 19.759 0.875 -0.052 223.75 395.12 20.047 0.781 0.240 206.12 169.12 19.761 0.787 -0.070 113.16 152.45 20.048 0.892 288.46 23.53 19.762 0.725 196.87 69.59 20.051 0.809 143.69 452.91 19.765 0.813 0.115 210.31 252.60 20.054 0.891 0.108 255.40 143.19 19.765 0.805 302.60 278.82 20.055 0.951 0.066 39.23 324.97 19.770 0.776 303.47 64.76 20.057 0.871 56.94 257.78 19.774 0.781 281.79 211.55 20.057 0.876 224.89 85.70 19.782 0.967 0.297 296.24 223.29 20.058 0.855 96.89 320.00 19.785 0.788 0.108 209.65 26.82 20.059 0.844 307.79 271.08 19.790 0.859 0.185 185.82 38.25 20.071 0.847 0.114 250.27 325.53 19.792 0.852 0.068 128.59 196.73 20.072 0.852 0.123 12 TABLE 2. — continued X y V B-V U-B X y V B-V U-B 191.01 74.33 20.080 0.857 0.231 287.97 158.79 20.316 0.965 254.61 84.52 20.082 0.855 0.071 280.94 135.94 20.318 0.925 0.045 231.32 341.55 20.086 0.849 106.50 324.79 20.320 0.884 0.013 160.96 276.21 20.091 0.872 0.203 243.29 24.12 20.326 1.005 196.74 127.07 20.096 0.684 149.92 48.97 20.329 0.868 207.00 376.41 20.108 0.896 0.022 278.18 150.87 20.335 0.701 167.10 392.47 20.109 0.881 0.458 301.75 55.45 20.342 0.868 291.87 285.81 20.119 0.752 0.307 133.59 141.72 20.345 0.792 0.231 285.73 43.59 20.123 0.939 287.04 301.32 20.348 0.881 85.24 437.80 20.124 0.793 155.27 485.09 20.348 0.904 0.652 181.59 396.35 20.129 0.837 211.88 44.51 20.359 1.124 122.56 282.28 20.153 0.851 291.26 89.94 20.362 1.079 0.077 38.82 411.94 20.155 0.841 0.244 266.93 313.07 20.381 0.863 264.87 104.60 20.157 0.881 0.148 151.19 154.53 20.385 0.985 -0.065 154.92 337.77 20.159 0.883 0.129 286.55 169.16 20.389 0.965 168.39 123.78 20.168 0.903 0.347 163.91 234.04 20.402 0.787 0.284 286.49 64.09 20.172 0.891 -0.206 169.91 156.89 20.402 0.771 258.51 198.95 20.173 0.899 0.034 283.88 89.31 20.404 -0.524 -0.231 260.05 30.19 20.185 0.901 264.52 19.19 20.413 0.981 106.39 47.77 20.188 0.860 197.46 210.48 20.428 0.877 52.71 332.64 20.189 1.328 306.32 85.95 20.438 1.003 187.61 30.59 20.203 0.927 133.29 223.63 20.443 0.896 311.37 31.47 20.212 0.883 220.70 7.98 20.447 1.035 314.71 175.77 20.216 0.909 186.55 229.27 20.449 0.968 0.050 200.16 166.97 20.219 0.880 -0.014 281.11 118.77 20.467 0.816 215.07 420.02 20.220 0.920 0.453 167.08 371.38 20.480 0.899 0.319 198.26 378.93 20.220 0.927 205.52 202.91 20.481 0.901 105.60 487.28 20.224 0.833 59.62 232.30 20.484 0.887 305.48 216.46 20.234 0.768 -0.014 279.65 45.10 20.491 0.940 262.35 274.63 20.238 0.904 126.43 263.35 20.502 0.925 279.31 71.48 20.240 0.885 218.94 314.77 20.510 1.013 0.061 218.82 411.24 20.241 0.953 0.104 135.35 351.83 20.517 0.952 0.379 250.32 175.03 20.248 0.879 102.19 463.69 20.531 1.005 0.322 196.11 125.87 20.255 1.091 -0.378 203.59 119.72 20.539 0.957 110.68 143.97 20.266 0.928 302.33 309.88 20.545 0.888 164.94 141.27 20.272 0.907 0.175 94.30 310.92 20.550 0.861 283.01 383.14 20.274 1.515 174.56 384.68 20.558 1.032 163.45 61.00 20.282 0.947 231.62 308.52 20.560 0.799 0.354 307.86 156.94 20.284 0.880 0.077 205.33 347.05 20.578 0.971 192.50 317.88 20.286 0.848 0.328 137.32 280.30 20.586 0.992 277.15 225.48 20.286 0.799 0.590 176.76 254.14 20.587 0.969 161.36 64.36 20.291 0.955 0.091 142.92 162.76 20.599 0.888 246.23 - 87.08 20.295 0.924 211.09 7.27 20.616 1.103 309.68 217.04 20.295 0.945 245.12 209.66 20.621 0.987 0.379 298.08 446.70 20.297 0.972 0.181 132.49 63.95 20.623 1.061 107.50 191.77 20.298 1.612 185.05 97.36 20.626 0.915 276.02 178.37 20.308 0.852 0.374 293.97 270.53 20.627 0.944 0.600 293.27 303.59 20.309 0.833 0.047 149.80 377.21 20.628 0.985 306.92 68.17 20.312 0.952 149.94 43.73 20.635 0.900 192.17 413.31 20.312 0.835 288.83 388.06 20.637 1.043 13 TABLE 2. — continued 251.78 250.23 199.14 292.56 239.16 264.90 173.51 259.35 216.52 296.77 122.67 39.85 167.23 311.34 175.66" 217.18 142.82 249.48 83.34 149.16 181.66 270.74 145.68 303.73 244.44 261.03 217.98 254.82 149.02 244.78 179.64 144.71 271.39 166.89 297.35 118.60 104.23 256.57 132.62 157.46 125.26 192.28 306.32 190.20 304.73 149.18 173.05 310.89 170.93 88.22 267.59 480.71 232.50 320.67 114.89 158.41 341.36 127.31 29.73 160.27 301.91 382.12 174.14 36.17 -52.96 94.31 94.11 462.10 166.52 236.34 123.99 289.98 338.56 210.48 228.67 329.98 473.81 219.35 272.90 41.40 346.23 382.44 422.41 463.75 82.72 250.75 284.41 345.51 57.56 480.28 276.86 228.03 250.30 377.44 18.55 33.35 140.99 59.07 220.39 274.54 20.637 20.642 20.647 20.653 20.657 20.665 20.667 20.673 20.676 20.680 20.688 20.693 20.693 20.695 20.696 20.696 20.700 20.701 20.714 20.726 20.740 20.740 20.743 20.748 20.758 20.761 20.778 20.778 20.785 20.788 20.805 20.814 20.817 20.835 20.835 20.848 20.851 20.853 20.864 20.871 20.877 20.883 20.886 20.890 20.907 20.907 20.918 20.929 20.931 20.955 B-V 0.947 1.040 0.828 0.964 0.908 0.952 0.872 0.968 0.919 0.903 0.975 0.983 0.905 0.965 0.740 0.972 1.001 1.004 0.977 1.145 1.021 0.907 0.975 0.932 0.847 0.875 1.121 0.727 0.764 0.719 0.903 0.992 0.876 1.011 1.025 1.004 0.921 0.847 0.953 1.377 1.012 1.035 1.193 0.971 1.127 0.899 1.031 1.045 0.867 1.069 U-B 0.207 0.592 -0.173 0.406 0.342 0.516 0.291 0.347 0.364 • • • •• • 0.047 215.99 300.73 274.99 305.99 112.64 278.94 184.42 310.56 180.26 198.91 279.97 153.02 259.71 288.37 268.88 296.78 193.33 260.46 111.90 192.66 228.25 302.21 27.45 251.78 243.29 70.63 124.97 194.54 149.11 226.22 189.13 193.30 285.70 270.69 284.64 307.47 183.43 288.13 270.09 25.65 40.89 294.08 159.70 247.59 263.66 230.93 46.38 192.50 296.61 294.43 115.94 254.84 213.40 346.32 351.28 345.29 163.71 143.38 442.89 211.87 167.66 233.82 303.52 66.17 157.92 299.69 172.32 136.14 416.33 170.65 321.72 71.99 395.86 8.21 245.97 449.47 426.23 142.46 402.16 335.10 131.15 209.15 478.33 399.30 144.35 183.74 164.84 20.36 366.57 323.13 462.47 296.93 152.41 284.55 338.91 174.76 446.68 338.83 35.40 277.25 20.965 20.968 20.972 20.976 20.978 20.980 20.999 21.012 21.012 21.027 21.033 21.037 21.039 21.044 21.046 21.047 21.050 21.055 21.065 .21.065 21.080 21.098 21.109 21.112 21.129 21.134 21.139 21.142 21.148 21.149 21.150 21.152 21.166 21.174 21.184 21.185 21.212 21.223 21.223 21.229 21.229 21.244 21.247 21.249 21.272 21.285 21.291 21.301 21.308 21.311 B-V 1.069 0.955 1.041 1.097 1.027 1.068 1.913 0.957 1.004 0.725 1.108 0.648 1.011 1.001 0.911 1.016 0.628 1.199 1.433 1.772 1.047 1.167 1.083 1.000 1.099 1.053 1.216 1.121 0.977 1.055 0.976 1.163 1.076 1.133 1.172 0.937 0.788 1.005 1.131 1.003 1.031 1.153 1.063 1.052 0.883 1.092 1.133 1.075 1.340 1.087. U-B 14 T A B L E 2. — continued X y V B-V U-B X y V B-V U-B 202.79 176.71 21.311 1.179 189.26 161.94 21.789 1.159 56.43 261.35 21.314 1.009 171.41 350.16 21.810 1.117 179.87 132.79 21.319 1.304 302.29 240.80 21.811 1.705 271.27 107.03 21.325 1.079 37.66 86.96 21.816 1.244 33.56 373.21 21.330 1.168 7.93 55.99 21.820 0.231 227.38 33.58 21.349 1.280 223.15 12.77 21.826 1.331 182.53 353.20 21.357 1.224 249.25 86.76 21.842 1.245 203.63 297.43 21.364 1.152 0.206 123.49 25.23 21.856 1.283 164.98 41.68 21.366 1.129 285.00 67.08 21.864 0.952 -0.504 132.16 190.81 21.370 0.991 270.14 410.30 21.897 1.001 299.98 127.36 21.378 1.279 255.67 258.00 21.905 0.813 242.51 242.05 21.399 0.871 225.39 41.68 21.919 0.811 68.66 451.76 21.413 1.029 260.15 461.68 21.936 1.124 233.08 88.93 21.426 1.255 223.99 169.64 21.947 1.000 284.08 246.99 21.432 0.933 292.40 281.76 21.962 1.305 34.28 382.39 21.434 1.040 262.02 120.34 21.966 1.281 8.90 478.84 21.437 1.091 174.32 44.64 21.973 1.355 290.02 90.57 21.443 0.975 , , 148.52 63.37 21.978 1.445 120.79 419.34 21.446 0.912 220.05 268.99 21.979 0.940 -0.474 215.11 288.93 21.460 0.936 107.53 213.87 21.981 1.095 150.71 224.77 21.463 0.887 40.40 307.87 21.987 0.869 213.62 250.46 21.470 1.072 57.52 96.95 22.014 1.241 255.53 109.09 21.478 1.059 174.09 343.76 22.017 0.727 43.99 392.09 21.486 0.940 258.63 34.66 22.038 1.180 115.43 325.92 21.500 0.999 309.64 138.58 22.058 0.984 207.82 483.69 21.517 1.167 112.54 382.29 22.071 0.923 160.91 34.83 21.525 1.032 67.72 33.99 22.110 0.924 217.56 206.15 21.526 1.159 268.30 59.67 22.115 0.907 218.23 204.77 21.568 0.909 240.00 150.64 22.182 1.323 305.07 43.68 21.583 1.169 261.65 230.36 22.182 1.477 253.91 358.46 21.597 1.281 115.99 108.49 22.198 1.169 214.28 150.25 21.602 1.105 191.60 485.22 22.340 0.732 83.17 154.29 21.603 1.192 16.45 320.39 22.994 0.244 270.79 48.31 21.606 1.104 108.56 52.03 21.613 0.852 279.39 40.65 21.620 1.196 .... 177.61 277.37 21.628 1.175 72.29 466.38 21.641 1.079 188.61 285.21 21.642 1.323 172.88 248.73 21.647 1.187 276.44 215.95 21.649 0.955 204.05 352.68 21.649 1.296 229.20 22.21 21.657 1.352 262.74 473.56 21.667 0.973 248.46 206.36 21.682 1.305 220.64 23.55 21.684 1.381 , , 212.80 186.40 21.706 1.583 201.19 256.32 21.744 1.153 101.30 177.42 21.778 1.223 240.42 240.70 21.786 1.304 15 14 - l l l l 1 l 1 l l | l i l l I l l l l | l l l l l 1 l 1 l | l 1 1 1 i 1 1 1 1 15 — 16 t — 17 • — 18 * 19 • . — 20 21 — • • — 22 _ • _ • • • • • • — 23 — — 24 - i i i i i i i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I I I I i I i r 0 .5 . 1 1.5 2 ( B - V ) Fig. 2 — Colour-magnitude diagram. All stars detected in both V and B as described in the text (and listed in Table 2) are shown. An apparent sequence of binary stars can be seen parallel to the upper main sequence. 16 III. Colour-Magnitude Diagram (a) Binary Stars Figure 2 is the colour-magnitude diagram (CMD) constructed from data in Table 2. Casual inspection of the C M D calls attention to an apparent sequence of binary stars. This is the series of points seen near the turn-off displaced ~ 0.75 mag (as for equal mass systems) above the upper part of the main sequence. Despite the growing number of C C D C M D ' s of galactic globular cluster main sequences, binary sequences are seldom seen, even though most of these C M D ' s are of high enough internal precision to reveal binary sequences if they are present. Indeed, the list of globular clusters with an observed binary sequence in the literature (E3, McClure et al. 1985, and perhaps M68 and M92, McClure et al. 1987, Stetson and Harris 1988, respectively) is a short one. A n examination of the photometry list shows that 11 out of 129 or 9% of the entries in this region (18.3 < V < 19.5) appear to be associated with the binary population. Unfortunately, with the small numbers available, statistical tests designed to prove that an excess of stars exist to the red side of the main sequence turn out to be inconclusive. (b) Main Sequence Width The combination of a 4m class telescope, good seeing, a C C D detector, and analysis software such as D A O P H O T yields precision photometry for a large number of stars allowing fruitful attempts at determining the intrinsic width of the main sequence. Studies of this sort performed on other globular clusters (see, for example, references 17 in §1) tend to show small, if any, intrinsic spread in colour. This implies that within each cluster there are no mechanisms operating which would give rise to non-zero main sequence widths. These include inhomogeneities in chemical composition (helium, iron and C N O abundances, etc.), differential reddening across the field, etc. (That is, unless these factors are somehow intricately related thus conspiring to form a narrow main sequence.) This is also the case for M12 as is evident in the following. Table 3 lists observed widths o-O08 of the main sequence in various V magnitude bins determined by fitting a Gaussian to the colour distribution of the stars in that bin. This is done by first rejecting all stars that fall outside 2a of the mean based on stars from Table 2 and performing the fit on the remaining stars. This process rejects field stars, stars with large photometric errors or those otherwise not "belonging" to the main sequence, in particular, the binary candidates. Inspection of the residuals indicates that the slope of the main sequence is not important with this small bin size. These widths can be compared to uncertainties in the photometry for V and B which are combined in quadrature to give a e z p . Here, ay is determined by artificially adding stars of known magnitudes to the C C D image and re-reducing the new image using the same procedure as the original one. Thus the differences between input and recovered magnitudes can be used to calculate ay. These are the same experiments performed to measure the completeness on the V frame and is discussed further in §VI. The errors for B magnitudes are determined using similar experiments. We note that according to these results, the uncertainties returned by D A O P H O T are too small at the faint end. This effect has also been reported by Bolte 18 T A B L E 3. MAIN SSEQUENCE WIDTH V Range Oy 0~exp °~obs Vint 18.2-18.4 0.004 0.010 0.011 0.008 18.4-18.6 0.007 0.006 0.009 0.028 0.026 18.6-18.8 0.008 0.010 0.013 0.014 0.005 18.8-19.0 0.012 0.010 0.016 0.031 0.027 19.0-19.2 0.013 0.011 0.017 0.023 0.014 19.2-19.4 0.014 0.011 0.018 0.014 19.4-19.6 0.016 0.013 0.021 0.023 0.009 19.6-19.8 0.023 0.020 0.031 0.049 0.038 19.8-20.0 0.023 0.025 0.034 0.046 0.031 20.0-20.2 0.022 0.029 0.036 0.041 0.020 20.2-20.4 0.027 0.022 0.035 0.052 0.039 20.4-20.6 0.030 0.057 0.064 0.069 0.026 20.6-20.8 0.047 0.045 0.065 0.064 20.8-21.0 0.048 0.069 0.079 0.084 0.029 21.0-21.2 0.056 0.077 0.095 0.147 0.112 21.2-21.4 0.039 0.071 0.081 0.117 0.084 21.4-21.6 0.048 0.068 0.083 0.105 0.064 21.6-21.8 0.065 0.097 0.117 0.118 0.017 19 (1987) who compared D A O P H O T magnitudes of stars which appear on two or more different C C D frames. The intrinsic width can then be estimated as o^nt = cr^bs — o-^xp. It can be seen that the colour widths in the first seven bins are consistent with a zero intrinsic width. Alternatively, we calculate an average width, < o}nt >!/ 2 = 0.016. At the metallicity of M12 (see §IVb), the VandenBerg and Bell (1985) isochrones give colour change due to metallicity variation of A(JB — V) /A\Fe/H] c± 0.07mag/dex. Thus A[Fe/H] < 0.2 dex. This is given as an upper limit since effects other than metallicity variations could also be operating and since Oint may indeed be zero given current observational limitations. 20 I V . Fundamenta l Clus te r Parameters In the next section, our photometry is compared to the theoretical isochrones of VandenBerg and Bell (1985). Before proceeding, we wish to predetermine as many of the relevant cluster parameters as possible so as to restrict the choice of isochrones for comparison. This includes adopting values for the reddening, metallicity, and distance modulus associated with M12. By comparing our C M D only to a restricted set of isochrones, we hope to improve the precision with which parameters determined directly from the isochrones are evaluated, in particular, the age of M12. Another approach is that of Janes and Demarque (1983) who compare several quantitative indices measured from both the observed C M D and a comprehensive set of isochrones to determine the age and metallicity simultaneously. While this method may yield internally consistent results among a sample of globular clusters, it can be vulnerable to systematic errors. The approach adopted here attempts to minimize this problem by utilizing available observational data. (a) Reddening Interstellar reddening in the direction of M12 (/ = 15° b = +26°) has been es-timated in a number of studies. From measurements of integrated light, Zinn (1980) derives E(B - V) = 0.17 and van den Bergh (1967) adopts 0.25 for his study. The compilation of Harris and Racine (1979) lists a value of 0.19 ±0 .04 for M12. Crawford and Barnes (1975) have obtained uvby photometry for stars in the cluster foreground with the result E(b - v) = 0.15 [or E(B - V) = E(b - v)/0.7 = 0.21]. The reddening 21 map of Burstein and Heiles (1982) based on HI column densities indicates a much lower value of E(B - V) ~ 0.12. In this study, a small number of field stars in the cluster foreground and two blue stars from the horizontal branch are used to derive an independent estimate for the reddening. The field stars are identified on our C C D frames as outliers from the M12 principal sequences in the V, (B — V) and/or V, (U — B) diagrams. Five (and possibly two more) such stars were found above V = 19.0 where 6.6 are predicted from the galaxy model tabulated in Ratnatunga and Bahcall (1985). The photometry of these stars have been dereddened in the (U — B) vs. (B — V) colour-colour diagram along trajectories appropriate for their colours; E(U — B) = 0.8 E(B — V) for the (red) field stars, E(U - B) = 0.73 E(B - V) for the (blue) H B stars. This yields a best estimate of E{B — V) = 0.23 ± 0.04 which is adopted for the remainder of this work. (b) Metallicity The compilation of Harris and Racine (1979) lists [Fe/H] = -1.64 ± 0.2 for M12. Other values in the literature include —1.56 ± 0 . 0 5 (Zinn 1980, integrated light) and -1.61 ±0 .12 (Zinn and West 1984, AV1A & Q3g ) although Smith (1984, Q39 ) derives [Fe/H] — —1.16±0.14 (see Table 4 for a summary). We note that none of these metal-licity estimates are derived from direct high dispersion spectroscopic studies of M12 stars. They are based on empirical indices whose calibrations are often controversial perhaps giving rise to large errors, systematic and otherwise. In any event, one should be cautioned that the use of a mean metal abundance tagged to iron may be inadequate (Pilachowski, Sneden and Wallerstein, 1983). 22 T A B L E 4. S U M M A R Y O F M12 M E T A L L I C I T Y E S T I M A T E S source method [Fe/H] Smith (1984) Q39 -1.16 ±0 .12 Zinn (1980) integrated light -1.56 ± 0 . 0 5 Zinn & West (1984) A V 1 . 4 , Q39 -1.61 ±0 .12 Harris & Racine (1979) -1 .64(±0.2) this work 6{U - B)o.6 -1.1 ± 0 . 5 adopted -1.4 23 In this work, the metallicity of M12 is determined independently from the available data by measuring the ultraviolet excess of the main sequence stars defined as 6(U — 5)o.6 = {U- B)0 - { U - B ) o.Hyadesj where 0.6 indicates that 6 is measured at (or corrected to) (B — V) = 0.6. Figure 3 is the (U - B)0 vs. (B - V)0 colour-colour diagram plotted from the colours listed in Table 2 and dereddened by E(B — V) = 0.23 and E(U — B) = 0.8 E(B — V). The average [U — B)Q colour of the main sequence stars between (B — V)0 — 0.45 and 0.50 is then determined and we derive 6(U — B)0.475 = 0.13. After correcting for the guillotine by a factor of 1.15 (Sandage 1969) we obtain 6(U—73)o.6 = 0.15±0.07. Using the 6 - metallicity calibration for globulars (Richer and Fahlman 1984,1986), we finally arrive at the metallicity estimate, [Fe/H] = —1.1±0.5. However, given the large uncertainty (due chiefly to photometric errors in U), and that the 8{U — B) - [Fe/H] relation for globulars is somewhat ill-defined (see, for eg., Richer and Fahlman, 1986, Figure 3), this is not inconsistant with [Fe/H] = —1.2 1.6, as indicated by the sources listed above. Taking the arithmetical average of all five sources, we adopt [Fe/H] = —1.4 for subsequent analysis. (c) Distance Modulus There are very few independent determinations of the distance to M12. Most values cited in the literature are traceable to Racine (1971). He derived (m — M ) y = 14.3±0.2 based on his photographic C M D where he estimated VUB — 14.9 and assumed MV{HB) = 0.6. Harris and Racine (1979) also list ( m - M ) y = 14.3 for M12. Although the horizontal branch is not well delineated in our C M D , V(HB) = 14.9 is not in obvious conflict with our results. However, when using the observed horizontal branch 24 PQ I D - 1 L l I I I I I M I I I I l I I I I I I I I I I I I I I I l I I I I I I I 1 I 0 .5 "i i i i i i i i i l i i i i i i - . 5 0 i I i i 11 r 1.5 F i g . 3 — C o l o u r - c o l o u r d i a g r a m . T h e M12 s ta rs are p l o t t e d w i t h r e d d e n i n g co r rec t ions w h i c h are E(B - V) = 0.23 a n d E(U - B) = 0.8E(B - V). T h e lower c u r v e s h o w n is the H y a d e s sequence a n d the u p p e r cu rve is t he 'zero m e t a l l i n e ' f r o m S a n d a g e (1969). 25 magnitude to derive a distance, one must beware that My (HB) may well be a function of metallicity. Accordingly, My(HB) as faint as 0.9 may be more appropriate for M12 (Sandage 1982). A recent determination of My(RR) from the statistical parallax of field R R Lyrae stars yields an average absolute magnitude of 0.76 ±0.14 (Hawley et al. 1986). In either of these cases, (m — M)y for M12 will have a value as small as 14.0 ~ 14.1. In many studies of globulars, the distance modulus is independently determined by comparing the main sequence fiducial with a group of subdwarfs with well determined parallaxes. There are only six such stars. The most recent sample uses the photometry of Carney (1979) and/or Carney and Aaronson (1979) in conjunction with parallax data from the new Yale Parallax Catalogue (in preparation by van Altena). Also in-cluded are the associated (new, revised) Lutz-Kelker corrections from Lutz, Hanson and van Altena (1987). Lutz-Kelker corrections (Lutz and Kelker, 1973) correct for the observational bias in the parallaxes used in computing absolute magnitudes. Their appropriateness in this type of study has been the topic of some concern (see, for ex-ample, Fahlman, Richer and VandenBerg 1985) and distance moduli have often been derived with and without Lutz-Kelker corrections. These new corrections, which are approximately one half the magnitude of the original values appear to be more suc-cessful (Hesser, et al., 1987, Richer et al., 1988). Once My is determined for each star, the colour for each star is shifted to correct for the difference between metallicities of that star and of the cluster. These differential colour corrections are derived using VandenBerg and Bell (1985) isochrones of different metallicities near the cluster value. 26 More recently, Lutz, Hanson and van Altena (1988) have derived an empirical main sequence using the same technique of correcting w for statistical bias but using a much larger number (50) of stars. The result is expressed in the form My = 1.41 4-5 . 1 7 ( £ - V) -0.94[Fe/H] with standard deviation of 0.04 magnitudes. This is slightly (~ 0.15 mag) brighter than the sequence loosely defined by the six subdwarfs but agreement with the VandenBerg and Bell isochrones is much better. Table 5 lists the observed main sequence fiducial for M12. These are the mean colours in 0.3 mag bins in V determined by fitting Gaussians to the colour distribution and result from the same calculations used to find the main sequence widths already discussed. Here, note that the bins have been allowed to overlap. The dereddened main sequence fiducial shifted by (m — M ) y = 14.25 magnitudes superposed with the Lutz et al. (1988) line for [Fe/H] = —1.4 is shown in Figure 4. This is the best match obtained by sliding one over the other vertically. This method, as simple as it is, achieves more than sufficient precision since the total uncertainty, estimated at 0.2 mag is dominated by errors inherent in the photometry and the Lutz et al. line. At my(HB) = 14.9, this puts the absolute magnitude of the horizontal branch at 0.65 magnitudes. The difference between the V magnitudes of the horizontal branch (from Racine 1971) and the turnoff is ~ 3.45, quite typical for globular clusters (Sandage 1982, Richer et al. 1988) although the magnitude of the turnoff is difficult to evaluate precisely due to its near vertical morphology. In the next and subsequent sections, (m — M)y = 14.25 ± 0.20 mag is adopted as the apparent distance modulus to M12. 27 T A B L E 5. M 1 2 MAIN SEQUENCE FIDUCIAL V B-V V B-V 18.4 0.655 20.2 0.883 18.5 0.658 20.3 0.900 18.6 0.670 20.4 0.912 18.8 0.673 20.5 0.944 18.9 0.672 20.6 0.952 19.0 0.678 20.7 0.958 19.1 0.706 20.8 0.963 19.2 0.717 20.9 0.977 19.3 0.728 21.0 1.032 19.4 0.743 21.1 1.043 19.5 0.753 21.2 1.107 19.6 0.767 21.3 1.089 19.7 0.785 21.4 1.076 19.8 0.804 21.5 1.085 19.9 0.815 21.6 1.116 20.0 0.836 21.7 1.190 20.1 0.864 21.8 1.168 28 .5 1 ( B - V ) „ F i g . 4 — O b s e r v e d f i d u c i a l sequence a n d the e m p i r i c a l m a i n sequence. T h e M 1 2 m a i n sequence f i d u c i a l is ove r l ayed w i t h the L u t z et al. (1988) l ine for [Fe/H] = —1.4. T h e obse rved f i d u c i a l is c o r r e c t e d for a r e d d e n i n g o f E(B — V) = 0 .23. T h e d i s t ance m o d u l u s d e r i v e d i n t h i s m a n n e r is ( m — M)v = 14.25 ± 0 . 2 0 . 29 V . Comparison with Isochrones and the Age of M12 In addition to the parameters discussed above, we need to know the helium abun-dance Y and the mixing length parameter a in order to describe the isochrones fully. Here, we adopt canonical values Y = 0.2 and a = 1.6. A parameter of recent debate is the oxygen abundance in globular clusters. Oxygen constitutes half of all metals by mass even at solar abundance ratios and together with carbon and nitrogen it is an important source of opacity in stellar interiors. As well, C N O elements are both reactants and products of nuclear reactions occuring within main sequence stars. As such, they (and in particular, oxygen) have strong effects on isochrone morphology (McClure et al. 1987). Pilachowski, Sneden, and Wallerstein (1983) have measured oxygen abundances in a number of globular cluster giants spectroscopically and have found, in general, that [O/Fe] values are above solar by ~ 0.25 dex, suggesting perhaps this is a universal characteristic among all globulars. Gratton (1987) also finds a similar result ([O/Fe] — 0.4 ±0.1) . Furthermore, isochrones with [O/Fe] > 0 have been employed successfully in recent C M D studies of other globular clusters (Richer, Fahlman and VandenBerg 1988, Hesser, et al. 1987). Unfortunately, direct determination of the oxygen abundance in M12 stars is not available in the literature. Thus we cannot directly constrain, a priori, the selection of isochrones with regard to this parameter. In any event, a recent study of C N O abundances in globular cluster stars by Pilachowski (1988) indicates that we cannot reliably determine oxygen abundances in metal poor giants without knowing carbon and nitrogen abundances and constructing precise model atmospheres because star-30 to-star variations in C N abundance cause changes in the upper atmosphere, affecting the strengths of lines formed in that region. Taken at face value, this makes all pre-viuous determinations of oxygen abundances in cluster and field giants suspect. In light of this problem (and since a comprehensive set of oxygen enhanced VandenBerg and Bell-type isochrones are not generally available), we will use [O/Fe] = 0 for the present. A comprehensive set of isochrones based on scaled solar abundances is avail-able from VandenBerg and Bell (1985). However, we note that an age decrease of 1 ~ 2 Gyr is expected from experience with other globulars 6 should the canonical oxygen enhancement prove appropriate. A good fit can be obtained using VandenBerg and Bell isochrones with [Fe/H] = —1.27 as displayed in Figure 5. This diagram utilizes a distance modulus of 14.25 mag and the isochrones are shifted in colour by 6(B—V) = 0.04 in addition to the reddening, E(B — V) = 0.23. A small magnitude shift is also necessary to bring the isochrones into agreement with the Lutz et al. main sequence especially after applying a colour shift. At 6~(B — V) = 0.04, this shift applied to the isochrones is approximately —0.05 mag in M y . Thus, the effective distance modulus for M12 with respect to the isochrones is 14.20 mag. Of course, the need for the color shift itself is not completely understood but in studies of this nature it is customary to apply to the VandenBerg and Bell isochrones some 0.02 ~ 0.04 mag shift toward the red. Presumably, the reason for this b Wi th oxygen enhancement, we see approximately, 1 Gyr age decrease per 0.3 dex increase in [O/Fe] (McClure et al. 1987). For typical values of [O/Fe], resulting ages would be lower by 1 ~ 2 Gyr than those implied by models with scaled solar abundance ratios. 31 8 I i i i i i 1 i i i i i i i i i I i i i .5 1 ( B - V ) Q F i g . 5 — [Fe/H] = —1.27 i sochrones o v e r l a i d o n M 1 2 f i d u c i a l . I sochrones f r o m V a n -d e n B e r g a n d B e l l (1985) for 14, 16 a n d 18 G y r , Y = 0 .2, a = 1.6 a n d [Fe/H] = - 1 . 2 7 are o v e r l a i d o n the m a i n sequence fiducial (dots) a n d i n d i v i d u a l d a t a (crosses) for b r i g h t e r s ta r s . I n o r d e r to achieve the m o s t r easonab le fit, a v e r t i c a l shif t c o r r e s p o n d -i n g to ( m — M)v = 14.20 a n d a c o l o u r shif t o f 6{B — V) = 0.04 i n a d d i t i o n to the r e d d e n i n g o f E(B — V) = 0.23 were a p p l i e d . 32 is the difficulty in predicting (B — V) from the model temperature, (eg. Gratton and Ortolani 1988 and references therein). Observational errors, especially in the reddening and the calibration, may also be responsible although it is more difficult to explain in this way why the isochrones are systematically too blue and never too red. With this set of parameters, Figure 5 suggests an age for M12 of 17 ± 1 Gyr. The uncertainty here refers to a possible range in age taking Figure 5 at face value. That is, it does not account for the sometimes large uncertainties associated with parameters used in constructing Figure 5. Uncertainties in the reddening, metallicity and distance modulus lead to age uncertainties which are not all independent. When combined, the effective uncertainty is estimated at —2, +5 Gyr. Further, if the canonical oxygen enhancement is adopted, we expect the age scale to decrease such that the 'true' age may indeed be closer to 15 or 16 Gyr. 33 V I . Luminosity Function The luminosity function (LF) is simply the number of stars in some magnitude interval as a function of magnitude. It is constructed for M12 in the following way. (l) Since the V frame is our deepest one, we count the number of stars in the V photom-etry list in 0.5 magnitude bins. (2) Corrections for incompleteness are determined by artificially adding stars of known magnitude to the C C D frame and rereducing it in an identical manner to see what fraction is recovered and with what error. (3) For each bin, corrections for non-cluster stars are determined using model predictions. The last step is accomplished using the tables of Ratnatunga and Bahcall (1985) which list the number of field stars expected in directions of galactic globular clus-ters predicted using the Bahcall and Soneira (1980) model of the Galaxy. As already noted (§IVa.), at magnitudes where field stars are readily distinguished from the clus-ter members, the observed field star count closely matches model predictions. To the limiting magnitude of our data, background galaxies are expected to make insignificant contribution to the total count (Drukier et al. 1988, equation 1). The incompleteness corrections have been computed as a function of V magni-tude by adding a total of 2148 stars to the V frame over 50 separate tests, using the A D D S T A R facility within D A O P H O T . Typically, 40 stars per run were added. The inverse of the recovered fraction is applied as the correction factor. The recovered magnitudes were investigated for effects of 'bin-jumping' (Drukier et al. 1988). It was found that the matrix approach used in that study is not neccesary here since the only stars that jump from one bin to another are those inserted at magnitudes very close 34 to bin boundaries such that they are recovered in adjacent bins due only to small and nominal errors. This leads to a symmetric distribution of errors to the useful complete-ness limit of our data when combined with our luminosity function which, as we shall see soon, is more or less fiat. These photometry errors are shown in Figure 6 in the form Vadded — Vrecovered vs- Vadded- This is also the basis of c r e i p discussed earlier in §IIIb. Instead, we use the customary one dimensional correction as listed in Table 6. Combining these steps, the luminosity function can be written as N = Nc x I — Nt where Nc is the number of stars counted in a particular bin, I is the correction for incompleteness for that bin derived as A/R, the numbers of stars added over that recovered, and Nb is the background count obtained from Ratnatunga and Bahcall. For the bin size, we have chosen 0.5 mag as a compromise between resolution and Poisson noise. However, simple experimentation showed no dramatic changes in the resulting LF when the size of the bin is altered. The luminosity function thus constructed is listed in Table 7 and plotted in Figure 7. Since colour information is not available for many of the stars, particularly at the faint end where the B data reaches the detection limit before the data in 7, a colourless calibration for the V magnitude is used assuming a mean colour of (B — V) = 0.9. We thus use V = v + 3.498 mag. This results in an error of at most 0.01 mag in an extreme case since the colour coefficient in the calibration is very small. For example, for A ( B - V ) = 0.25, | A V | = | - 0.0418 X 0.25| = 0.01. The last column in Table 7 is the final, corrected luminosity function and the quoted uncertainty represents Poisson noise in the raw count and the incompleteness tests and also include a 25% uncertainty 35 -2 I — ' ' 1 ' i ' I ' 1 ' ' i I i i i 1 16 18 20 22 24 V m a g n i t u d e ( a d d e d ) Fig. 6 — Photometry errors of artificially added stars. Artificial stars recovered in the incompleteness experiments are also used to estimate errors for magnitudes determined using D A O P H O T . Here, A V = VreCoVered — Vradded is plotted against Vadded-36 T A B L E 6. R E S U L T S O F C O M P L E T E N E S S E X P E R I M E N T S I N M12 V Magnitude Number Found Number Input Completeness 16.0-16.5 2 2 1.00 16.5-17.0 6 6 1.00 17.0-17.5 9 9 1.00 17.5-18.0 11 12 0.92 18.0-18.5 44 46 0.96 18.5-19.0 79 82 0.96 19.0-19.5 85 91 0.93 19.5-20.0 119 132 0.90 20.0-20.5 134 148 0.91 20.5-21.0 147 162 0.91 21.0-21.5 130 137 0.95 21.5-22.0 146 166 0.88 22.0-22.5 118 139 0.85 22.5-23.0 90 112 0.80 23.0-23.5 98 145 0.68 23.5-24.0 54 169 0.32 24.0-24.5 14 138 0.10 24.5-25.0 5 162 0.03 37 T A B L E 7. M 1 2 L U M I N O S I T Y F U N C T I O N V magnitude ( ± 0.25) observed count completeness corrected count background count member count 16.25 2 1.00 2 0.20 2 ± 2 16.75 7 1.00 7 0.20 7 ± 4 17.25 7 1.00 7 0.75 6 ± 3 17.75 19 0.92 21 0.75 20 ± 7 18.25 45 0.96 47 0.75 46 ± 9 18.75 74 0.96 77 0.75 76 ± 12 19.25 73 0.93 78 2.2 76 ± 12 19.75 101 0.90 112 2.2 110 ± 14 20.25 115 0.91 127 2.2 125 ± 15 20.75 101 0.91 111 2.2 109 ± 13 21.25 103 0.95 109 9.8 99 ± 14 21.75 98 0.88 111 9.8 102 ± 13 22.25 119 0.85 140 9.8 130 ± 16 22.75 127 0.80 158 9.8 148 ± 18 23.25 71 0.68 105 15. 90 ± 14 38 2.5 ;> o 1.5 1 h-.5 — 0 18 20 22 V Magnitude 24 F i g . 7 — L u m i n o s i t y f u n c t i o n for M 1 2 . T h e o r d i n a t e is the l og o f the n u m b e r o f s tars b e l o n g i n g to each b i n as l i s t e d i n T a b l e 7. 39 quoted by Ratnatunga and Bahcall as an upper limit of errors in their background corrections. That is, (6N)2 = (SNE x I)2 + (NC x 61)2 + (6Nb)2 where 6NC = y/Ne, 61 = S/R/A and. 6N\, = 0.25iVfc. A very interesting feature of this luminosity function is that it is flat. Often, luminosity functions of globular clusters are described (although to varying goodnesses of fit) in terms of a power-law mass spectrum of the form N(m)dm cc m - ( i + i ) ^ m Values of x ranging from —0.5 to 1.5 are found and these appear to correlate with cluster metallicity in the sense that x is larger for metal poor globulars (McClure et al. 1986, but see Fahlman et al. 1985 for M15). Figure 8 displays the mass function (MF) for M12 tabulated in Table 8. The mass function is derived from the luminosity function via the isochrones already discussed which provide a relation between mass and luminosity. For the lower main sequence, the M - L relation from Table IV of Drukier et al. (1988) is adopted. This is an extension of the VandenBerg and Bell isochrones below m = 0 . 6 M Q . It is easily seen that a power-law mass spectrum with x « — 1 provides a good description of the M F . A least-squares fit to the curve, excluding the last point, formally gives x = —0.70 ± 0 . 1 6 . In contrast, if we were to expect these clusters to follow the correlation between metallicity and the power law index x, then based on their metallicities we would expect to see values in the range x = 1 ~ 1.5 for M12 and Pal 5. Values near —1 would be expected for globular clusters more metal rich than 47 Tuc. Here, it should be noted that the luminosity and mass functions have been derived completely ingoring the fact that some of the entries in our photometry list may be 40 T A B L E 8. M12 M A S S F U N C T I O N V magnitude member m Am count ±0.25 count M 0 M © per MQ 17.25 6 0.8448 0.0024 2604 17.75 20 0.8398 0.0090 2220 18.25 46 0.8269 0.0174 2661 18.75 76 0.8045 0.0266 2859 19.25 76 0.7747 0.0332 2289 19.75 110 0.7423 0.0385 2854 20.25 125 0.6987 0.0400 3121 20.75 109 0.6590 0.0391 2791 21.25 99 0.6205 0.0376 2627 21.75 102 0.5831 0.0379 2683 22.25 130 0.5442 0.0424 3076 22.75 148 0.4990 0.0507 2925 23.25 90 0.4418 0.0618 1457 Here m is the mass corresponding to the V magnitude listed in column 1. The size of the mass bin A m is the difference between the masses corresponding to the V magnitudes at the bin boundaries. Member count and the count per M Q are shown to the nearest integer. 41 0 - . 1 -.2 - .3 log mass - . 4 F i g . 8 — M a s s f u n c t i o n for M 1 2 . I n t h i s p l o t , the o r d i n a t e is the l o g a r i t h m o f the n u m b e r o f s tars p e r u n i t mass t a k e n f r o m T a b l e 8. T h e s ta igh t l ine d r a w n t h r o u g h the d a t a is t he least squares fit t o a p o w e r - l a w mass s p e c t r u m (see t ex t ) . A l s o d i s p l a y e d are l ines w i t h s lopes c o r r e s p o n d i n g to p o w e r - l a w ind ices o f x = + 1 , 0 a n d —1. 42 binaries. However, simple corrections indicate that the shapes of L F amd M F are not significantly affected. Based on qualitative ideas about the dynamics of gravitating systems, the flatness of the mass function, that is, the unsually small number of low mass stars, suggests a history of dynamical evolution in M12. At 3 core radii, our field is relatively close to the centre of the cluster such that mass segregation effects might be expected to drive low mass stars further outward. It may be of interest to explore the possible binary population in connection with the luminosity function. First, we expect to see binary systems concentrated toward the core of a dynamically relaxed cluster simply because binaries are twice as massive as similar, but single, stars. Thus mass segregation may indeed be responsible for the suspected binary sequence being observed in our field (at 3 core radii) as well as the lack of an observed binary sequence in a typical modern globular cluster C M D whose fields are located much further from centre (typically, ten to few tens of core radii). This also implies a higher binary frequency in the core. Although the small number of binary candidates preclude unambiguous conclusions regarding a binary density gradient across our single field, a multiradius set of observations can provide good evidence one way or the other. In addition, since hard binaries become harder with encounters, single stars encountering these systems will be imparted kinetic energy corresponding to this change in binding energy. Thus low mass stars can be ejected from the vicinity of the core or perhaps from the cluster altogether. The other possibility is that the observed mass function is a reflection of the initial 43 mass function (IMF) or at least that it represents the present global M F . This can be explored using the available data with the help of multimass King models. These have been used to address the question: given x ~ —0.7 in our field, what is the global value? Figure 9 shows the results from models based on input M F s with various global values of x. It shows the apparent slopes of the M F s as functions of radius as a conse-quence of mass segregation. The low mass cut-off is set at 0 . 1 M Q in all cases. White dwarfs are also included by extrapolating the mass function toward higher masses. This implies the presence of a large number of white dwarfs. We see that at 3 core radii, the observed slope of the M F ts the global slope to a good approximation. In fact, one could not have chosen a better single field with which to determine the global value for x. Thus we conclude that the global mass function of M12 has a slope near x = —0.7 and that we are not observing an effect of mass segregation. This result is, of course, dependent on the applicability of King models to this problem. However, experience with M71 (Richer and Fahlman 1989), for instance, has shown that simple multimass King models go a long way toward explaining the observed M F variation with radius for that cluster and that the general idea of dynamical relaxation acting on a global mass function to produce the radial dependence in local mass functions seems basically correct. Thus, a global slope near x = 1.0, as would be predicted from McClure et al. (1986), is clearly inconsistent with the data. We note that the above results are in alarming conflict with that of McClure et al. (1988) who derived x = +0.5 for M12 based on an independent luminosity function. 44 - 2 -1 0 1 log (r/r c ) 2 F i g . 9 — R e s u l t s o f m u l t i m a s s K i n g m o d e l s . A p p a r e n t s lopes o f mass func t ions have b e e n c o m p u t e d u s i n g m u l t i m a s s K i n g m o d e l s w i t h i n p u t g l o b a l mass func t ions whose s lopes are as i n d i c a t e d a n d t r u n c a t e d at O . 1 M 0 . F o r each m o d e l d i s p l a y e d , the concen -t r a t i o n p a r a m e t e r is 1.21 i n a c c o r d w i t h t he obse rva t ions ( W e b b i n k 1985) . T h e filled c i r c l e s h o w n is f r o m the obse rva t ions o f M c C l u r e et al. (1988) a n d the d a t a f r o m the present s t u d y are s h o w n w i t h t he e r ro r ba r s . 45 Although this still represents a natter M F than expected based on the McClure et al. (1986) or similar relations, it is much too steep to be consistent with our value. This is difficult to reconcile since their L F is similar to our own. Their field is at 5.0 core radii which is close enough to our 3.0 core radii such that the difference cannot be attributed simply to a radial effect. They adopt a somewhat lower metallicity, which leads to a small difference in x via differences in the corresponding mass-luminosity functions. However, this effect works in the wrong direction. That is, using the M - L relation for [Fe/H] = —1.77 with our L F , we derive a mass function well described by x = —1.0. Also, our methods differ in that McClure et al. use only two bins in computing x; they use the ratio of the numbers of stars with M y = 4.25 — 5.75 and M y = 5.75 — 8.25. Again, this procedure applied to our own data yields a lower value of x = —0.8. A satisfactory explanation for our difference thus remains elusive. 46 VII. Summary We have presented new U B V C C D photometry of a single field in M12 reaching below V — 23.5 mag. The main results of this study are as follows. (1) . A sequence of binary stars appears to exist in our C M D . In the upper main sequence, the binary frequency may be as high as 9% . (2) . When the presence of the possible binaries are accounted for, the main sequence shows very small intrinsic width. Thus we conclude that M12 is chemically homoge-neous to A[Fe/H\ < 0.2 dex. (3) . The fundamental cluster parameters for M12 derived from our data are E(B—V) = 0.23 ± 0.04 and (m — M)v — 14.25 ± 0.20. The metallicity of M12 is estimated from the several values found in the literature in conjunction with the ultraviolet excess 8(U — B)o.6 measured from our photmetry. The goodness of fit with the VandenBerg and Bell (1985) isochrones gives support to our choice of [Fe/H] — —1.4. (4) . A n overlay of the isochrones and our C M D yields a best-estimate age of 17 Gyr (-2, +5 Gyr). This is expected to decrease by 1 ~ 2 Gyr if the canonical oxygen enhancement of about 0.5 dex is assumed. (5) . The luminosity function in our field is well described by a power law mass spectrum of index x = —0.7. Results obtained through multimass King models indicate that the global value of x is also near —0.7 for M12. 47 Bibliography Bahcall, J .N . and Soneira, R . M . 1980, Ap. J. Suppl., 44, 73. Bolte, M . 1987, Ap. J., 319, 760. Burstein, D., and Heiles, C. 1982, A.J., 87, 1165. Carney, B . W . 1979, Ap. J., 233, 211. Carney, B . W . and Aaronson, M . 1979, A.J., 84, 867. Crawford, D .L . , and Barnes, J . V . 1975, Pub. A.S.P., 87, 65. Davis, L . , private communication. Drukier, G .A. , Fahlman, G . G . , Richer, H .B . , and VandenBerg, D .A. 1988, A.J., 95, 1415. Fahlman, G .G . , Richer, H.B. , and VandenBerg, D . A . 1985, Ap. J. Suppl., 58, 225. Gratton, R . G . 1987, Astr. Ap., 177, 177. Gratton, R . G . and Ortolani, S. 1988, Astr. Ap. Suppl., 73, 137. Harris, W.E . , and Racine, R. 1979, Ann. Rev. Astr. Ap., 17, 241. Hawley, S.L., Jeffreys, W.H. , Barnes, T . G . , Lai , W. 1986, Ap. J., 302, 626. Hesser, J .E . , Harris, W.E . , VandenBerg, D .A . , Allwright, J .W., Shott, P., and Stet-son, P .B. 1987, Pub. A.S.P., 99, 739. Janes, K . and Demarque, P. 1983, Ap. J., 264, 206. Landolt, A . U . 1973, A.J., 78, 959. Landolt, A . U . 1983, A.J., 88, 439. Lutz, T .E . , Hanson, R . B . , and van Altena, W . F . 1987, Bull. AAS, 19, 675. 48 Lutz, T .E . , Hanson, R . B . , and van Altena, W . F . 1988, private communication. Lutz, T . E . and Kelker, D . H . 1973, Pub. A.S.P., 85, 573. McClure, R .D. , Hesser, J .E. , Stetson, P.B. , and Stryker, L . L . 1985, Pub. A.S.P., 97, 665. McClure, R .D. , Stetson, P.B. , Hesser, J .E. , Smith, G .H. , Harris, W.E . , and Vanden-Berg, D . A . 1988, The Harlow-Shapley Symposium on Globular Cluster Systems in Galaxies, I A U Symp. 126, ed. J .E . Grindlay and A . G . Davis Philip (Dordrecht: Kluwer), p485. McClure, R .D. , VandenBerg, D . A . , Bell, R . A . , Hesser, J .E . , and Stetson, P .B. 1987, A.J., 93, 1144. McClure, R .D. , VandenBerg, D .A . , Smith, G .H. , Fahlman, G .G . , Richer, H .B . , Hesser, J .E . , Harris, W . E . , Stetson, P.B. , and Bell , R . A . 1986, Ap. J., 307, L49. Mironov, A . V . , Samus', N . N . , Shugarov, S.Yu., and Yuferov, A . O . 1984, Astronomicheskij Tsirkulyar, No. 1313, 1. Nassau, J . J . and Hynek, J .A . 1942, Ap. J., 96, 37. Penny, A . J . and Dickens, R . J . 1986, M.N.R.A.S., 220, 845. Pilachowski, C A . 1988, presented at Commision 37 meeting, The Abundance Spread Within Globular Clusters, at the 20th General Assembly of the I A U , 2 - 1 1 Aug., 1988; Baltimore, U.S.A. Pilachowski, C . A . , Sneden, C , and Wallerstein, G . 1983 Ap. J. Suppl, 52, 241. Racine, R. 1971, A.J., 76, 331. Ratnatunga, K . U . and Bahcall, J .N . 1985, Ap. J. Suppl., 59, 63. 49 Richer, H .B . and Fahlman, G . G . 1984, Ap. J., 277, 227. Richer, H .B . and Fahlman, G . G . 1986, Ap. J., 304, 273. Richer, H .B . and Fahlman, G . G . 1987, Ap. J., 316, 189. Richer, H .B . and Fahlman, G : G . 1989, in press, to appear in Ap. J., Apr i l 1, 1988. Richer, H .B . , Fahlman, G .G . , and VandenBerg, D . A . 1988, Ap. J., 329, 187. Sandage, A . 1969, Ap. J., 158, 1115. Sandage, A . 1982, Ap. J., 252, 553. Smith, H . A . 1984, Ap. J., 281, 148. Stetson, R B . 1987, Pub. A.S.P, 99, 191. Stetson, P .B. , and Harris, W . E . 1988, preprint. Stetson, P .B. , and Smith, G . H . 1987, ESO Workshop on Stellar Evolution and Dy-namics in the Outer Halo of the Galaxy, M . Azzopardi and F . Matteucci, eds. (Garching: ESO) , p387. van den Bergh, S. 1967, A.J, 72, 70. VandenBerg, D . A . and Bell , R . A . 1985, Ap. J. Suppl., 58, 561. Zinn, R. 1980, Ap. J. Suppl., 42, 19. Zinn, R. and West, M . J . , 1984, Ap. J. Suppl., 55, 45. 50 

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