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Cepheid variable stars have long been used as distance indicators due to their strong period-luminosity relation. However, the period of a Cepheid is affected by its metallicity so any difference in metal-content between calibration Cepheids and Cepheids being used for distance measure would lead to a systematic error in the distance calculated. Metallicity measurements are traditionally achieved by spectroscopic analysis but this can lead to considerable uncertainties. Therefore, the first part of this thesis looks at using double-mode, or beat, Cepheids to measure metallicity. Specifically, to measure the metallicity gradient across the Triangulum galaxy, M33. Beat Cepheids can be used to trace metallicity because their period ratio is sensitive to metal abundance which is well described by pulsation models. To find variable stars, image subtraction techniques are applied to observations of two separate datasets of M33. PSF fitting photometry is carried out on the data to produce calibrated light curves. The is also done to cross-calibrate the two datasets but an amplitude discrepancy arises in many of the Cepheid light curves. This amplitude problem is not caused by mismatching of the stars between the datasets, via either pixel matching or WCS coordinate transform. Nor is there any correlation with the Cepheid position in M33. Further investigation, beyond the scope of this thesis, into this issue is required. The amplitudes are corrected using a scaling factor so that an Analysis of Variance routine can be applied on the light curves to find Cepheid periods. Cepheids are only kept if the ratio between their two strongest periods lies within an appropriate range. 3 beat Cepheids are found, on top of another 5 already known beat Cepheids, in M33. The metallicities of the beat Cepheids are determined by comparing the period ratios with beat Cepheids of known metallicity in the Milky Way and Magellanic Clouds. The galactocentric distances of the stars are determined by deprojecting their celestial coordinates with M33's inclination and position angles along with the distance. Therefore, the metallicity of M33 as a function of radius can be immediately obtained, yielding the metallicity gradient across the galaxy. Using this method the metallicity gradient of M33 is found to be steeper than measurements made by recent spectroscopic analysis of HII regions. This is more in line with what is expected from recent work deriving the Cepheid Period-Luminosity relation for M33. There exists a period-age relation for Cepheid variable stars. The second part of the thesis aims to derive this empirically using observations of 6 stellar clusters in the Large Magellanic Cloud. The age for each cluster is taken from literature and were determined by Isochrone fitting. The same image subtraction techniques as used on the M33 data are used to find Cepheids and their periods in the LMC clusters. Cepheids are only considered to be cluster members if they fall within the half-light radius of the cluster and have proper motions matching their host cluster. The mean periods of the Cepheids in each cluster along with the cluster ages is then used to derive the period-age relation. The period-age relation derived here shows a steeper gradient than those produced by models or previous empirical derivations. There is a large spread in periods of the Cepheids in any given cluster that increases inversely with cluster age. This effect cannot be replicated if the cluster's population is recreated with a single stellar model. However, the period spread can be described using stellar models of multiple initial rotation rates. |
