LUMINOSITY FUNCTIONS FOR OLD STELLAR SYSTEMS by Peter Anthony Bergbusch L> ^ B.Sc., University of Saskatchewan, 1974 rACULTY 0 f GRADUATE STotd - M.Sc., University of Regina, 1984 „JL Dissertation submitted in partial fulfillment flr ' ^ DEAN of the requirements for the degree of P DOCTOR OF PHILOSOPHY in the Department of Physics and Astronomy We accept this dissertation as conforming to the required standard Dr. D.A. VandenBerg, Supervisor (Department of P’.ysics and Astronomy) Dr. F.D.A, Hartwick, Departmental Member (Dept, of Physics and Astronomy) Th'. O.J. Pritchet, Departmental Member (Department of Physics and Astronomy) Dr. R.D. McClure, Outside Member (Dominion Astrophysical Observatory) Dr. F.P. Robinsojv-Qutside Member (Department of Chemistry) Dr. II. Srivastava, Outside Member (Department of Mathematics) “ " / ■ —y — • r ----------------------- Dr. ( i.Ci . Fahlman, External Examiner (University of British Columbia) ©PETER ANTHONY BERGBUSCH, 1992 University of Victoria September 1992 All rights reserved. This dissertation may not be reproduced, in whole or in part, by mimeograph or other means, without the permission of the author. 11 Supervisor: Professor Don A, VandenBerg ABSTRACT The potential for luminosity functions (LFs) of post-turnoff stars to constrain basic cluster parameters such as age, metallicity, and helium abundance is examined in this di, sertation. A review of the published LFs for the globular cluster (GC) M92 suggests that the morphology of the transition from the main sequence to the red giant branch (ltGB) is sensitive to these parameters. In particular, a small bump in this region may provide an important age discriminant for GCs. A significant deficiency in the number of stars over a 2 mag interval, just below the turnoff, remains unexplained. A method of interpolating isochrones and LFs accurately from evolutionary se­ quences, from the lower main sequence to the RGB tip, i j discussed. The interpolation schf me is based on primary interpolation points which are identified by the behaviour of the derivative d(logTe#)/d(log t) along an evolutionary sequence. New BV CCD observations, calibrated with Landolt and Graham standard stars, for the old open cluster NGC 2243 and for the bright stars in the GCs NGC 288 and NGC 7099 are presented. The colour magnitude diagram (CMD) of NGC 2243 contains a strong binary star component. Comparisons with the fiducial sequences of the GC 47 Tuc (Hesser et al. 1987) indicate that t! two clusters have similar abundances, while comparisons with the new oxygen-enhanced isochrones (Bergbusch & VandeuBerg 1992) suggest that NGC 2243 has an age of 4-5 Gyr, and a metallicity [Fe/H] - 0.65. The morphology of both the CMD and the LF through the turnoff region cannot be attributed to the merging of the binary and single star sequences, but convective overshooting works m the correct sense to account for the differences between the isochrones and the CMD. For NGC 288 and NGC 7099, excellent overall consistency among the Zero Age Horizontal Branch, isochrone, and LF fits is obtained for cluster ages of 14-16 Gyr. The manifestation of the transition bump in NGC 288’s LF provides a particularly Ill strong constraint 011 the age, since this feature becomes more prominent as the metal licity increases, /t'-method helium abundance estimates give V ~ 0.23 for NGC 288 and F w 0.31 for NGC 7099. The 2nd param eter problem is discussed in light of these results. The RGB bump, present in canonical LFs, is only weakly identified in the cumulative LF (C’LF) of NGC 288, and may not be present at all in NGC 7099’s CLF. However, the brightest RGB stars in both clusters are found within as 0.2 mag of the RGB tip predicted by the oxygen-enhanced models. Examiners: Dr. D.A. VandenBere Dr. F.D.A. Hartwick Dk C.J~Pritchet Dr. R.D. McClure Dr. F.P. Robinson Dr. H. Srivastava / Dr. G.6 . Fahlmafi iv Table of Contents A bstract ii Table of Contents iv List of Tables viii List of Figures ix Acknowledgements xvii C hapter 1 Introduction 1 1.1 The Relevance of Luminosity Functions 1 1.2 The Helium Abundance 9 1.3 M92: An Illustration 13 1.3.1 The Age Luminosity Relations 14 1.3.2 The Luminosity Function Near the Turnoff 17 1.3.3 The Giant Branch Luminosity Function 22 1.3 4 Discussion 23 1.3.5 Conclusions 28 1.4 Scope of the Work 30 C hapter 2 The Construction of Model LFs and Isochrones 31 2.1 Introduction 31 2.2 The Mathematical Formalism 32 2.3 Equivalent Evolutionary Phases (EEPs) 36 2.3.1 The Zero-Age Main-Sequence (ZAMS) 37 2.3.2 Core Hydrogen Exhaustion (CHE) ?8 V 2.3.3 The Blue Hook (BH) 40 2.3.4 Post-Main-Sequence EEPs 41 2.4 Joining the Giant Branch to the Main Sequence Track 45 2.4.1 Idealized Upper Giant Branches 47 2.5 Tests of Interpolation Accuracy 48 C hapter 3 Data Acquisition and Reduction 55 3.1 Observations 55 3.2 Standard Svars 56 3.2.1 Cluster Photoelectric Sequences 64 3.3 Profile-Fitting Photometry of Cluster Fields 67 3.4 Artificial Star Tests 70 3.5 Rectification of the LF 71 C hapter 4 The Old Open Cluster NGC 2243 77 4.1 Introduction 77 4.2 Cluster and Background Fields 79 4.3 Artificial Star Tests 83 4.4 Cluster Members: The Location of the Giant Branch 94 4.5 The Color-Magnitude Diagram 95 4.5.1 Comparison with 47 Tuc 98 4.5.2 Comparison with Isochrones 101 4.6 The Luminosity Function 104 4.7 Discussion 111 vi 4.8 Summary 114 C hapter 5 The Globular Cluster NGC 288 116 5.1 (’luster parameters 116 5.2 Observations 119 5.2.1 Comparison with Other Cluster Photom etry 123 5.3 Artificial Star Tests 125 5.4 Analysis of the CMD 133 5.5 The Luminosity Function 142 5.6 The Helium Abundance 157 5.7 Discussion 159 C hapter 6 The Globular Cluster NGC 7099 162 6.1 Cluster Parameters 162 6.2 Observations 164 6.2.1 Comparisons with Other Cluster Photometry 167 6.3 Artificial Star Tests 171 6.4 Analysis of the CMD 179 6.5 The Luminosity Function 185 6.6 The Helium Abundance 193 6.7 Discussion 197 C hapter 7 Conclusions and Ftature Work 198 References 203 Appendices 210 VH A. NGC 2243 211 B. NGC 288 216 C. NGC 7099 263 vm List of Tables Table 1-1 Apparent Distance Moduli for Various Ages and Compositions 15 Table 3-1(a) Temporal Coefficients 61 Table 3-1 (b) Zero-Points and Zenith Extinctions 61 Table 3-2 NGC 2243 Photoelectric Sequences 66 Table 3-3 NGC288 Photoelectric Sequence 66 Table 3-4 NGC 7099 Photoelectric Sequence 66 Table 4-1 Observing Log (NGC 2243) 81 Table 4-2 Artificial Star Photometric Accuracy (NGC 2243) 89 Table 4-3 Artificial Star Completeness Fractions (NGC 2243) 108 Tabic 4-4 Rectified Luminosity Function (NGC 2243) 108 Table 5-1 Observing Log for NGC 288 120 Table 5-2 Fiducial Sequences for NGC 288 127 Table 5-3 Artificial Star Photometric Accuracy (NGC 288) 131 Table 5-4 Artificicl Star Completeness Fractions (NGC 288) 147 Table 5-5 Rectified Luminosity Function (NGC 288) 149 Table 6-1 Observing Log for NGC 7099 164 Table 6-2 Fiducial Sequences for NGC 7099 174 Table 6-3 Artificial Star Photometric Accuracy (NGC 7099) 176 Table 6-4 Artificial star Completeness Fractions (NGC 7099) 190 Table 6-5 Rectified Luminosity Function (NGC 7099) 192 List of Figures Figure 1-1 The effects of age, helium abundance, and metallicity on model LFs through the turnoff region. Figure 1-2 The effects of age, helium abundance, ;.nd metallicity on RGB LFs. Figure 1-3 The effects of age, helium abundance, and metallicity on RGB CLFs. Figure 1-4 V-magnitude as a function of metallicity for the brightest RGB stars in 33 globular clusters. Figure 1-5 Age-luminosity relations at the turnoff for selected metal-poor LFs. Figure 1-6 A composite LF for the turnoff region of M92, based on data from the literature. Figure 1-7 Theoretical LFs through the turnoff region, normalized at Afy = 2. Figure 1-8 Theoretical LFs through the turnoff region, superimposed on the composite LF for M92. Figure 1-9 Theoretical RGB LFs superimposed on Hai vick’s observed LF for M92. Figure 1-10 Theoretical CLFs superimposed on M92:s RGB CLF. Figure 2-1 The functional relation L — L (M ,t) in the L-M.-1 coordinate frame. Figure 2-2{a) The identification of primary EEPs on the temperature and luminosity derivatives. Figure 2-2(b) Evolutionary sequences with the primary EEPs, as identified in Fig. 2-2(a), indicated. Figure 2-3 The interpolation scheme, based on the primary EEPs identified in Fig. 2-2. Figure 2-4 Comparisons between idealized RGBs and the original sequences computed with the Eggleton code. Figure 2-5 Isochrones interpolated from evolutionary sequences separated by 0.3A4q, compared with those interpolated from the 0.1 M® grid to illustrate the linearity of the interpolation scheme. Figure 2-6(a) Evolutionary sequences and isochrones with approximately the same spacing in the L — Teg plane. Figure 2-6(b) Evolutionary sequences, recovered from the isochrones in 2-6(a) a,’e compared with the original sequences through the turnoff region. Figure 3-1 Correlation between the temporal coefficients «3 and 64 in the photometric transformation equations. Figure 3-2(a) Differences between the observed and standard magnitudes and colours as a function of time.