Conclusion

CCD photometry of three Magellanic Cloud fields near young clusters has been obtained and analysed, resulting in the discovery of many new variable stars, chiefly Cepheids and Long-Period Variables. The detailed results from each of the fields are described below in Sections 6.1-6.3. The discovery, and subsequent JK photometry, of a number of low-amplitude LPVs in the LMC fields has also resulted a possible new method for determination of the mode of pulsation of LPVs. This is summarised in Section 6.4.

Some of the results presented here are not totally conclusive, and would benefit greatly from further research. There exists a substantial amount of data for other MC fields that is not yet analysed, and when combined with (suitably chosen) new observations, should go a long way towards resolving these issues beyond doubt. Various possibilities for future work are outlined in Section 6.5.

NGC 330

V and I band CCD photometry of the SMC cluster NGC 330 has been obtained over an interval of 4 years with the aim of identifying variable stars in and around this rich, young cluster. The search has revealed 22 Cepheid variables, of which 14 are newly discovered. All of these variables appear to belong to the SMC field population rather than being true cluster members. Twenty Long-Period Variables and nine other variables were identified, including two eclipsing variables (one newly discovered), and four close binary stars, two of which show emission lines in their spectra. Analysis of the Cepheids indicates that only small to moderate amounts of convective core overshoot ( Λ$\raisebox{-0.6ex}{$ \stackrel {\raisebox{-.2ex}{$\textstyle <$}}{\sim} $}$0.5) occur during the main-sequence phases for stars of mass 2 - 3M_$\odot$. The Cepheid PLC relation obtained from VI photometry, when compared to the theoretical relation of Chiosi, Wood and Capitanio (1993), yields a distance modulus for these short period Cepheids of 18.92, if no overshoot is assumed, or 18.72 if moderate overshoot ( Λ = 0.5) is adopted. Only two modes of pulsation are present in this group of Cepheids, most likely they are the fundamental and first overtone modes.

NGC 1850

V and I band CCD imaging of the rich LMC cluster NGC 1850 spanning more than five years has been analysed. In a 10^′×10^′ field surrounding the cluster, more than 30 variable stars have been identified, including seven classical Cepheids, one anomalous Cepheid, two RR-Lyrae variables, nineteen long period variables (LPVs), one blue eclipsing binary, one possible pair of eclipsing giants, and several peculiar variables. Of the two variables (both Cepheids) located near the cluster core, one is a likely cluster member and the other is a probable field star.

Isochrone fitting to the cluster CMD yields an age of 80 Myr if an LMC distance modulus of 18.5 is adopted. A comparison of pulsation and evolution masses for the Cepheids still yields a ratio of evolution to pulsation mass of ∼1.2 for evolution models computed with core overshoot parameter Λ=0.5 (d_ov/H_P=0.25). An overshoot parameter Λ∼ 1.0 would be required to bring the evolution and pulsation masses into agreement. One of the Cepheids in the field is a bump Cepheid, and a calculation of the bump mass yields a value in reasonable agreement with the pulsation mass. It is shown that detailed modelling of individual bump Cepheids is capable of providing very tight constraints on the LMC distance modulus. The distance derived for this object is 18.51±0.03. The Cepheid period-luminosity-colour relation compared to the theoretical relation yields a LMC distance modulus of 18.60. Finally, arguments are presented which suggest that the LPVs are a mixture of fundamental mode pulsators and small-amplitude overtone pulsators.

NGC 2058-65

V and I band CCD photometry of the field around the little-studied young LMC clusters NGC 2058 and NGC 2065 is presented. The region has been monitored for more than three years. The region appears to be composed of at least two distinct stellar populations: the old LMC field population, and a much younger population of age ∼1.4×10⁸ years. The clusters in the field appear to be members of the latter population. The region is found to be very rich in Cepheid variables, with 50 being identified in this 10^′×10^′ field, of which 34 are newly discovered. One eclipsing binary and 43 LPVs were also detected, all of which are newly discovered. A substantial fraction of the Cepheids appear to be associated with several of the clusters in this field. The Cepheids consist of approximately equal numbers of first overtone and fundamental-mode pulsators. Cepheid evolution masses obtained from moderate convective core overshoot models are compared with pulsation masses and it is found that the evolutionary masses are ∼15 - 20% higher than the pulsation masses. A large degree of convective core overshoot ( Λ$\raisebox{-0.6ex}{$\,\stackrel {\raisebox{-.2ex}{$\textstyle >$}}{\sim}\,$}$0.5) would be required to bring the evolution and pulsation masses into agreement, and evolutionary models without convective core overshoot appear to be ruled out. These results are similar to those obtained for NGC 1850.

The LMC distance modulus is derived by comparing the theoretical and observational Cepheid P-L-C relation, and a value of 18.52±0.03 is obtained. VI photometry of Cepheids from NGC 1850, NGC 1866, NGC 2058-65 and a sample of long-period Cepheids from Martin et al. (1979), are used to derive the observational LMC Cepheid P-L relation down to short periods. The fitted P-L relation, which includes Cepheids with periods ranging from 1.8 days to 130 days, is V₀ = - 2.63 logP   +  17.06. The Cepheid P-L relation appears to be linear throughout this wide range of periods.

Mira Pulsation Modes

New IR observations of LPVs in the LMC are presented, which show that the LPVs lie on two (K,logP) sequences, one sequence being the well-known Mira sequence and the other being a sequence parallel to the Mira sequence but separated from it by ΔlogP ∼ 0.35. The LPVs on the Mira sequence have a wide range of amplitudes (0.1<ΔI<3) while those on the second sequence have relatively small amplitudes (ΔI< 0.5). The previously known LPVs of large amplitude (ΔI> 0.5) in the LMC lie almost always on the Mira sequence.

Recent angular diameter measurements for Mira variables suggest that the radii of these stars are very large and consistent with pulsation in the first overtone mode rather than the fundamental mode (Haniff et al. 1995). On the other hand, nonlinear pulsation models of Mira variables suggest that the observed pulsation velocity amplitudes can only be achieved during fundamental mode pulsation, at least for stellar masses $\raisebox{-0.6ex}{$ \stackrel {\raisebox{-.2ex}{$\textstyle <$}}{\sim} $}$2.0M_$\odot$.

Theoretical models of LPVs predict a ratio of fundamental to first or second overtone period of ΔlogP ∼0.3-0.4, and overtone pulsators are expected to have smaller limiting amplitudes than fundamental mode pulsators. Hence, the observations presented here may be easily understood if the LPVs on the Mira sequence are fundamental mode pulsators while the lower-amplitude LPVs on the second sequence are overtone pulsators. A second test of the pulsation mode is obtained by computing pulsation periods for model stars on the LMC old giant branch and comparing these periods with those of observed Mira variables. Once again, the fundamental mode pulsators have periods consistent with those seen in the LMC Miras while the overtone periods are too short. These results suggest that Mira variables are fundamental mode pulsators.

Further Work

There is much work required to be done in order to investigate more completely the problem of the Cepheid Mass Discrepancy. A re-analysis of the data presented here using a more uniform set of evolutionary models would aid in the interpretation of the results.

A large amount of VI data on a number of other Magellanic Cloud clusters exists. Analysis of a number of these clusters which lie in differing environments may allow investigation of any possible environmental dependence on the Cepheid mass discrepancy problem. The results of the two LMC fields studied are similar (namely, large amounts of overshoot required in the evolutionary models), but the SMC field indicates only low to moderate overshoot is necessary. The population of Cepheids between the LMC and SMC are quite different, the SMC objects being much lower mass. It would be helpful to study another SMC cluster to confirm the results of the NGC 330 analysis. Also, selection of clusters with low (and uniform) reddening are required (in contrast to the NGC 2058-65 field), as the derived pulsation masses are sensitive to the assumed reddening.

Further work on the determination of masses of bump Cepheids will allow the effects of metallicity to investigated. There are already a relatively large number of LMC bump Cepheids known. Through the choice of an appropriate sample of bump Cepheids, the effects of period, amplitude, and colour may be investigated. High resolution spectroscopy of these objects is needed to quantify the metallicity.

A much larger sample of LPVs is desirable in order to strengthen the case for Mira variables pulsating in the fundamental mode. The major difficulty lies in the identification of low-amplitude variables which have fairly regular pulsation. As the amplitudes get lower, the fraction of stars which pulsate regularly also appears to get lower. The stars must be monitored for a number of cycles in order to confirm their regular variability. CCD photometry is the best way to detect such stars, as the amplitudes are much too low to be detected using wide-field historical photographic surveys.

The wide-field microlensing searches (MACHO, EROS, OGLE) will eventually provide a very large sample of red variables in the Magellanic Clouds. These catalogs will be ideal for LPV candidate selection, as the data will be high-quality, well-sampled, long time-series CCD photometry. Once candidate objects are identified, infrared photometry in the J and K bands is required.

Further investigation on the mechanism for variability of LPVs could also be done. How the variability of these objects depends upon spectral type is poorly known. Spectroscopy of a suitably chosen sample would provide insights into this problem.