A spectroscopic and dynamical study of binary and other Cepheids |||||||||||||||||||| A thesis submitted in partial fulfillment of the requirements for the Degree of Doctor of Philosophy in Astronomy in the University of Canterbury by Orlon K. L. Petterson |||||||||{ University of Canterbury 2002 Abstract High resolution observations have been made of a number of southern Cepheids to make an observational and theoretical study of Cepheid variables using radial velocities. The stars studied were part of a long term programme to observe southern variable stars, from which a valuable database of radial velocities gathered over a long period were available. Sixteen ´echelle spectrograph orders in the wavelength region 5400{8600A˚ were used, which included a number of absorption lines covering a range of species and excitation potentials. The line bisector technique was used to measure stellar and telluric lines and to obtain radial velocities. To improve the precision of the radial velocities we used telluric lines to calibrate the observations to a common reference frame. 1 The radial velocities have a precision of 300ms− allowing the detection of velocity 1 ∼ differences of 1 km s− with confidence. The radial velocity data obtained at Mount ∼ John University Observatory (MJUO) was combined with data from various sources to determine the orbits of any Cepheids exhibiting orbital motion. The various orbital parameters were determined for a number of systems and where radial velocities for the companions exist, some estimate of the mass was made. The precision of the radial velocities obtained from MJUO also allowed us to search for line level effects for a number of species among the Cepheid spectra. A number of IAU standard stars were observed to calibrate the radial velocities obtained at MJUO to the IAU standard scale. The radial velocities from MJUO were found not to differ significantly from the IAU values. Binary Cepheids are particularly useful in the determination of Cepheid masses, which are still an active topic for astronomical research. The value of the MJUO data was that it provided a consistent set of data against which other sources of data could be compared. For 8 of the Cepheids new or improved orbital solutions were found. They are Y Car, YZ Car, AX Cir, BP Cir, S Mus, V636 Sco, V350 Sgr, W Sgr and T Mon. Of these 8 systems, 3 had radial velocities for their respective companions which allowed the determination of the mass of the Cepheids. Masses were determined for the 9 day Cepheid S Mus (6.0 0.4 M ), the double mode Cepheid Y Car (4.5 1.8 M ) and the 5 day Cepheid V350 Sgr (6.0 0.9 M ). New results presented here include the first orbital solution for the binary Cepheid AX Cir, a completely revised orbital solution for the binary Cepheid YZ Car which established its eccentricity, and orbital motion. The binary Cepheid BP Cir however was found to require a new pulsation period of 2.39819d to fit the observed pulsational velocities. Observations of the suspected binary Y Oph show it to be an unusual Cepheid with no 1 evidence of binarity ( 0.5 km s− ) in our data. Finally, the 5 day Cepheid W Sgr was ∼ observed to have the lowest orbital amplitude measured. We discussed the line level effects found in our observations, where a number of spectral lines were observed to show departures from the Fei velocity curve. Line level effects were observed in Hα, Caii, Baii, Feii, Sii and Siii. Most of the Cepheids were observed to show the same progression of line level effects, with the best example being the bright Cepheid β Dor. The Siii velocities indicate that these lines have the lowest velocity amplitude and form deeper in the atmosphere than the Fei, where as the Caii and Hα lines were all observed to have much greater velocity amplitudes with the peak of these velocity curves occurring later, in pulsational phase. These observations are consistent with the lines forming at different depths as a density wave propagates through the atmosphere. X Sgr is peculiar due to its interesting spectra which at certain phases show line doubling and at most other phases the lines were asymmetric. These observations are interpreted to support the idea that X Sgr has strong shock waves present and that X Sgr has greater atmospheric transparency in the spectral region near 6000A.˚ We also present the results of dynamical modelling of a pulsating Cepheid. Using a non-linear radiative hydrodynamic code developed by A. Fokin, we have modelled two Cepheids, AX Cir and YZ Car. These models have then been compared with the observa- tions obtained here. After extensive modelling using the latest OP opacities, it has been determined that the Cepheid AX Cir can be modelled using parameters L = 2050 L , M = 4.8 M and Teff = 5900K. The model reproduced the observed stellar characteris- tics, such as the photometric amplitude and pulsational period. Comparison between the observations and the model for the selected spectral lines, Fei 5576A,˚ Siii 6347A,˚ Baii 5853A˚ and Caii 8542A˚ show good agreement with similar amplitudes and velocity curves. With no strong shock waves being produced by the model, the observed line level effects can be explained by a density wave. The 18 day Cepheid YZ Car was chosen to explore the capabilities of the radiative hydrodynamic code for a long period Cepheid. The best model developed that reproduced the observed stellar characteristics had parameters L = 9350 L , M = 7.7 M and Teff = 5590K. The period was 18.314 days and the bolometric light curve agreed well with the observed visual light curve. Comparison of the theoretical and observed radial velocities showed good agreement. Ab uno disce omnes. From a single instance learn the nature of the whole vi Contents Figures xiv Tables xvi 1 Introduction 1 1.1 A brief history 1 1.2 Cepheid light and velocity curves 3 1.3 Cepheid Evolution 7 1.3.1 Binary evolution 10 1.4 Masses of Cepheids 10 1.5 Spectroscopic observations 13 1.5.1 Line asymmetries 15 1.5.2 Line splitting 16 1.5.3 Line level effects 16 1.6 Thesis outline 17 2 Observations 19 2.1 Cepheid radial velocity programme 19 2.1.1 Observing 20 2.1.2 Standard stars 21 2.1.3 Telluric absorption 21 2.2 The telescope 22 2.3 The ´echelle spectrograph 22 2.4 Detectors 24 2.4.1 The PM3000 CCD system 26 2.4.2 The Series 200 CCD system 26 2.4.3 Features of the Series 200 camera 30 2.5 Observing Procedure 30 2.5.1 Nightly observations 34 3 Reduction 39 3.1 FIGARO 40 3.2 ECHOMOP 40 3.3 MIDAS 40 3.4 Ec´ helle spectra 41 3.5 PM3000 CCD reduction procedure 44 vii viii Contents 3.6 Series 200 CCD reduction procedure 46 3.6.1 Calibration 47 3.6.2 Order trace template 47 3.6.3 Wavelength template file 51 3.6.4 Wavelength calibration 53 3.6.5 Overall procedure 54 3.6.6 2-D wavelength fitting 55 3.6.7 Order extraction and standardisation 56 4 Analysis 59 4.1 Radial velocity determination 59 4.1.1 Line bisector method 60 4.1.2 Cross-correlation 61 4.2 Telluric line velocities 62 4.3 Stellar radial velocities 67 4.4 Radial velocities 72 4.5 Orbital motion amongst binary Cepheids 72 4.6 Searching for line level effects 77 5 Radial velocity standards 81 5.1 β Aquarii 82 5.2 β Ceti 85 5.3 β Corvi 89 5.4 β Leporis 92 5.5 α Trianguli Australis 95 5.6 HR 6970 98 5.7 Discussion 101 6 The Binary Cepheids 103 6.1 S Muscae 104 6.1.1 Historical background 104 6.1.2 Current analysis 107 6.2 Y Carinae 111 6.2.1 Historical background 111 6.2.2 Current analysis 113 6.3 YZ Carinae 116 6.3.1 Historical background 116 6.3.2 Current analysis 117 6.4 AX Circini 122 6.4.1 Historical background 122 Contents ix 6.4.2 Current analysis 124 6.5 BP Circini 127 6.5.1 Historical background 127 6.5.2 Current analysis 130 6.6 T Monocerotis 131 6.6.1 Historical background 131 6.6.2 Current analysis 134 6.7 Y Ophiuchi 137 6.7.1 Historical background 138 6.7.2 Current analysis 140 6.8 V636 Scorpii 141 6.8.1 Historical background 141 6.8.2 Current analysis 143 6.9 V350 Sagittarii 146 6.9.1 Historical background 147 6.9.2 Current analysis 148 6.10 W Sagittarii 151 6.10.1 Historical background 151 6.10.2 Current analysis 153 6.11 Discussion 157 7 Line level effects and the solitary Cepheids 161 7.1 Observational results 162 7.1.1 General characteristics 162 7.1.2 Binaries 164 7.1.3 Y Oph and BP Cir 171 7.2 The solitary Cepheids 173 7.2.1 TT Aquilae 173 7.2.2 l Carinae 177 7.2.3 β Doradus 180 7.2.4 X Puppis 183 7.2.5 SW Velorum 185 7.2.6 X Sagittarii - a peculiar Cepheid 187 7.3 Discussion 192 8 Models 193 8.1 Model Atmospheres 194 8.2 Modelling codes 196 8.2.1 A nonlinear model: The initial static model 200 8.2.2 The radiative hydrodynamic model 201 8.3 Modelling spectral lines 205 8.4 The AX Circini models 207 8.5 The YZ Carinae models 215 8.5.1 Linear Non-Adiabatic model 215 8.5.2 Non-linear analysis 217 9 Conclusion 223 9.1 Future work 226 10 Acknowledgements 229 References 231 A Reduction and analysis programs 241 A.1 Programs 241 A.1.1 Iprep 241 A.1.2 Clean 243 A.1.3 Makedark 244 A.1.4 Makeflat 245 A.1.5 maketrace 246 A.1.6 Makewave 247 A.1.7 Dospec2 248 A.1.8 Reducing 250 A.1.9 Checkwave 252 A.1.10 Fit2dwave 253 A.1.11 NDF2wave 254 A.1.12 2dwave.m 254 A.1.13 Wave2NDF 259 B Reduction techniques, a comparative analysis 261 B.1 Echomop - optimal verses profile extraction 261 B.2 Optimal and profile extraction with quadratic fit 268 C Radial velocity data 273 x Figures 1.1 Light curves in different colours for a Cepheid 5 1.2 Bolometric light and radial velocity curves of a Cepheid 6 1.3 Evolutionary tracks for Cepheids 8 2.1 Thorium-Argon wavelength reference spectrum 24 2.2