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The Effect of the Metallicity on the Cepheid Period-Luminosity Relation

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The Effect of the Metallicity on the Cepheid Period-Luminosity Relation Gauging the Universe: the Effect of the Metallicity on the Cepheid Period-Luminosity Relation Dissertation der Fakult¨atf¨urPhysik der Ludwig-Maximilians-Universit¨atM¨unchen vorgelegt von Marta Mottini aus Magenta, Italien M¨unchen, den 19-06-2006 Datum der mündlichen Prüfung: 19. Juni 2006 1. Gutachter: Priv. Doz. Dr. Achim Weiss 2. Gutachter: Prof. Dr. Adalbert W.A. Pauldrach Summary The aim of this thesis is to assess the effect of the metallicity on the Cepheid Period-Luminosity (PL) relation. The novelty of the approach adopted in this project consists in the homogeneous analysis of a large sample of Cepheids (72) observed in three galaxies (the Milky Way, the Large Magellanic Cloud and the Small Magellanic Cloud), spanning a factor of ten in metallicity. This allows us to explore the effect of the metallicity on the PL relation in a wide range and to study the gas enrichment histories of three different galaxies. To fulfil this goal, firstly, we have selected a sample of Cepheids for which distances and accurate photometry are available in the literature and we have collected high-resolution, high signal-to-noise spectra of these stars, using the highly advanced facilities of the European Southern Observatory in Chile. Secondly, we have directly measured iron and α-elements (O, Na, Mg, Al, Si, Ca, Ti) abundances of our sample from these spectra. We have compared our iron abundances with studies on Galactic and Magellanic Cepheids and found a good agreement for the average values and for the individual stars in common. We have then made a broader comparison with results for the Magellanic Clouds from the analysis of F and K non-variable supergiants (they have ages and temperatures similar to Cepheid stars) and of B stars, which are progenitors of Cepheids, and found a good agreement. Cepheids do not show any peculiar differences with these two other population of stars, this indicate that, during this evolutionary stage, there are no changes of the original iron content of the gas from which they were formed. We have then studied the trends of the individual α elements abundance ratios relative to iron as a function of the iron content of our programme star. We can draw some preliminary conclusion considering oxygen, silicon and calcium as the most reliable indicators among the α elements we have analysed. The trends of the abundance ratios of O, Si and Ca are in fairly good agreement with observational studies on Cepheids and on different kinds of stellar populations in the Galaxy and the Magellanic Clouds. The elemental abundances we have determined were used to investigate the effect of metallicity on the PL relation in the V and K bands, in order to check if there is a change of the effect as wavelength increases. We note different behaviours in the two bands. The metallicity has an effect in the V band in the sense that metal-rich Cepheids are fainter than metal-poor ones, while it does not have any effects in the K band. Thus, to safely measure the distances of galaxies, one can use the PL relation in the infrared bands (namely K), so as to minimise the effect of the metallicity. Using the K band has the additional advantage of reducing the effects of the interstellar extinction to the level of other systematic and random errors. Contents 1 Introduction 1 1.1 Cepheids: a brief history .................................. 1 1.2 Cepheids: characteristics .................................. 4 1.3 Cepheids: evolution .................................... 8 1.3.1 Binary evolution .................................. 11 1.4 PL and PLC relations ................................... 11 1.4.1 PL relation ..................................... 11 1.4.2 PL-Color relation .................................. 13 1.4.3 Uncertainties .................................... 16 1.5 The distance scale ..................................... 18 1.6 The metallicity problem .................................. 19 1.7 This thesis project ..................................... 23 2 Observations 25 2.1 Selection criteria and characteristics of the data-set ................... 25 2.2 Data reduction ....................................... 26 2.3 The Galactic sample .................................... 27 2.4 The Magellanic sample ................................... 32 2.5 Telescopes and instruments ................................ 32 2.5.1 The ESO-1.5 m telescope and FEROS ...................... 35 2.5.2 The VLT and UVES ................................ 35 3 Methodology 43 3.1 Overview of the analysis of stellar spectra ........................ 43 3.2 Line lists ........................................... 50 3.3 Equivalent widths ..................................... 51 3.4 Stellar parameters ..................................... 56 3.5 Model atmospheres ..................................... 59 i Contents 3.6 Spectrum synthesis ..................................... 60 4 Results: iron abundances 63 4.1 Abundances and their uncertainties ............................ 63 4.1.1 Tests on dependencies on period and stellar parameters . 64 4.1.2 Uncertainties .................................... 70 4.2 Comparison with previous studies on Cepheids ..................... 74 4.2.1 Galactic Cepheids ................................. 75 4.2.2 Magellanic Cepheids ................................ 75 4.3 A broader comparison from different stellar population in the Magellanic Clouds . 77 5 Preliminary results: α elements 81 5.1 Abundance analysis .................................... 83 5.1.1 Oxygen abundances ................................ 84 5.2 Results and comparison with previous works ....................... 87 5.2.1 Individual trends of the abundance ratios .................... 88 5.2.2 Preliminary conclusions .............................. 97 6 The effect of the metallicity on the PL relation 99 6.1 The adopted standard PL relations ............................101 6.2 Results ............................................102 6.2.1 The effect of iron content .............................102 6.2.2 The effect of the estimated total metallicity . 103 6.3 Uncertainties ........................................106 6.4 Comparison with previous results .............................110 6.5 LMC distance: “short” vs “long” scale . 112 6.6 Future steps .........................................114 Conclusions 115 A Spectroscopy: basic principles 119 A.1 Dispersion ..........................................119 A.1.1 Dispersing element .................................120 A.2 Resolution ..........................................123 B Line lists 125 Bibliography 139 Acknowledgements 147 ii Chapter 1 Introduction Cepheids variables have played an important role in astronomy since it was recognised that they could be used to determine distances through their Period-Luminosity relation. Most derived characteristics of a star or any other astrophysical object, such as mass, age, energy output and size, depend significantly on how well one is able to determine its distance. Therefore measuring distances is a capital element at the core of astrophysical research. For over eighty years Cepheids have served as an effective tool for studying the universe. Cepheids provide one of the best means of determining the distances to nearby galaxies and they are used to calibrate secondary distance indicators, thus they play a crucial role to establish the extragalactic distance scale, being the first rung of the distance ladder. Furthermore the measure- ment of the Hubble constant (H0), which sets the scale of the Universe in space and time, depends heavily on accurate extragalactic distance measurements. Cepheids are also useful objects for investigating the structure of our Galaxy, the plausibility of physical assumptions adopted to compute evolutionary models of the late evolutionary stages of massive stars and the gas enrichment history that led to the formation of young stellar population. 1.1 Cepheids: a brief history The first two Cepheids were discovered by two pioneers in the systematic observation of variable stars, E. Pigott and J. Goodricke, in 1784. These were η Aquilae and δ Cephei, the latter supplied the name now used for this class of stars. In 1894 A.A. Belopol’skii detected periodic variations in the radial velocitiesa of Cepheids and, in 1899, K. Schwarzschild found the amplitude of a Cepheid’s luminosity variation to be considerably higher in photographic light than in visual light. This pointed to a variability of the temperature, as well as of the luminosity. These facts found their natural explanation in the hypothesis of Cepheid pulsations, first proposed by Ritter in 1879 and later by Umov, Plummer and Shapley (see H. aThe radial velocity of a star is the velocity in the direction of the line of sight. This can be measured from a star’s spectrum using the Doppler effect. 1 1 Introduction Shapley 1914). The case for the pulsation hypothesis grew to be accepted due to new measurements which confirmed that the surface temperature of Cepheids changed over the pulsational cycle. In addition, theoretical work of Sir Arthur Eddington put this hypothesis on a firmer basis (A. Eddington 1927, 1941, 1942). He showed that Cepheids are single stars that undergo radial pulsations, because they can be shown to have characteristics which can be described like those of a heat engine. Later work by S. A. Zhevakin (1963), R. F. Christy (1966), J. P. Cox (1980) and others provided a deeper understanding of the mechanism behind Cepheid pulsations. The driving mechanism, known as k-mechanism, behind ”self-excited”
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