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University of Northern Iowa UNI ScholarWorks Faculty Publications Faculty Work 8-2000 Masses for Galactic Beat Cepheids Noella L. D'Cruz University of Washington Siobahn M. Morgan University of Northern Iowa See next page for additional authors Let us know how access to this document benefits ouy Copyright ©2000 the American Astonomical Society Follow this and additional works at: https://scholarworks.uni.edu/ear_facpub Part of the Earth Sciences Commons Recommended Citation D'Cruz, Noella L.; Morgan, Siobahn M.; and Böhm-Vitense, Erika, "Masses for Galactic Beat Cepheids" (2000). Faculty Publications. 1. https://scholarworks.uni.edu/ear_facpub/1 This Article is brought to you for free and open access by the Faculty Work at UNI ScholarWorks. It has been accepted for inclusion in Faculty Publications by an authorized administrator of UNI ScholarWorks. For more information, please contact [email protected]. Authors Noella L. D'Cruz, Siobahn M. Morgan, and Erika Böhm-Vitense This article is available at UNI ScholarWorks: https://scholarworks.uni.edu/ear_facpub/1 THE ASTRONOMICAL JOURNAL, 120:990È997, 2000 August ( 2000. The American Astronomical Society. All rights reserved. Printed in U.S.A. MASSES FOR GALACTIC BEAT CEPHEIDS NOELLA L. DÏCRUZ1 Department of Astronomy, University of Washington, Box 351580, Seattle WA 98195-1580; noella=physics.usyd.edu.au SIOBAHN M. MORGAN Department of Earth Science, University of Northern Iowa, Cedar Falls, IA 50614-0335; morgans=uni.edu AND ERIKA BO HM-VITENSE Department of Astronomy, University of Washington, Box 351580, Seattle WA 98195-1580; erica=astro.washington.edu Received 1999 October 18; accepted 2000 April 24 ABSTRACT Accurate mass determinations for Cepheids may be used to determine the degree of excess mixing in the interiors of their main-sequence progenitors: the larger the excess mixing, the larger the luminosity of the Cepheid of a given mass, or the smaller the mass of a Cepheid with given luminosity. Dynamical masses determined recently for a few Cepheid binaries indicate excess mixing somewhat stronger than that corresponding to the convective overshoot models by Schaller et al. Beat Cepheids can be used similarly to test main-sequence mixing in stellar interiors. The period ratios for beat Cepheids depend on luminosity,Teff, heavy element abundance, and mass. By comparing pulsational models and the obser- vationally derived luminosity,Teff, metallicities, and period ratios it is possible to obtain masses for these stars, the so-called beat masses. With the old opacities masses much smaller than the evolutionary masses were obtained. With the new OPAL opacities a beat mass close to the dynamical mass was obtained for the binary beat Cepheid Y Carinae, showing that it is now possible to obtain reliable beat masses. In this paper, we determine beat masses for seven Galactic beat Cepheids for which photometric ^ and spectroscopic data are available. We Ðnd an average mass around 4.2 0.3M_ for these stars, though the actual error limits for each star may be larger mainly because of uncertainties in E(B[V ) and the heavy element abundances. (As derived spectroscopically, beat Cepheids are in general metal- poor, with[0.4 [ [Fe/H] [ 0.0). The relation between the derived beat masses and the luminosities again indicates excess mixing that is somewhat larger than that corresponding to the models by Schaller et al. Key words: Cepheids Hertzsprung-Russell (HR diagram) È stars: abundances È stars: evolution È stars: fundamental parameters È stars: interiors 1. INTRODUCTION called evolutionary masses, derived from the comparison of observed luminosities and those obtained from stellar evo- Cepheid variables have been used for many years as lution theory. For many years, there was a discrepancy astronomical tools to measure distances. They form an between the beat masses (1È3M ) and the evolutionary important step in the extragalactic distance ladder (see _ masses (D4È7M_). Simon (1982) suggested that this Feast & Walker 1987 and Feast 1999 for reviews). They also problem could be resolved if, for temperatures around 105 play an important role in furthering our understanding of K, stellar opacities for the heavy elements were increased by stellar evolution and pulsations (e.g., for instance Bo hm- a factor of 2È3 over the Cox & Tabor (1976) opacities. Vitense 1992). Andreasen (1988) conÐrmed SimonÏs result. New opacities, Most Cepheids pulsate in a single modeÈthe fundamen- the OPAL opacities derived by Iglesias & Rogers (1996), are tal modeÈwhich can yield information about their mean indeed higher by the required amount. For stellar models P 1@2 density via the Ritter relation, i.e., period o . However, calculated with these new opacities, beat Cepheid masses some Cepheids pulsate in more than one mode. These are agree approximately with evolutionary masses (Moskalik, called double-mode or beat Cepheids. Their period ratios Buchler, & Marom 1992). It therefore appears that the can be measured very accurately and depend on their new beat masses are indeed the correct masses for these masses, luminosities,Teff, and the abundances of the heavy Cepheids. This conclusion is supported by the study of elements. With the luminosities known from the period- Bo hm-Vitense et al. (1997), who determined the dynamical [ luminosity relation,Teff derived from(B V )0 colors, and mass for the binary beat Cepheid Y Car and found agree- element abundances known from spectrum analysis, the so- ment with its beat mass. called beat masses can be determined from the period The luminosity for a Cepheid with a given mass depends ratios. These beat masses can be compared with the so- on the degree of mixing in the interior of its main-sequence progenitor: the larger the degree of mixing, the larger the luminosity. This means that for a given luminosity, as deter- ÈÈÈÈÈÈÈÈÈÈÈÈÈÈÈ 1 Current address: Chatterton Department of Astronomy and Depart- mined from the period-luminosity relation, a Cepheid has a ment of Astrophysics, School of Physics, University of Sydney, NSW 2006 smaller mass for a larger degree of mixing in its main- Australia. sequence progenitor. The empirical determination of the 990 MASSES FOR GALACTIC BEAT CEPHEIDS 991 Cepheid masses therefore o†ers the opportunity to deter- mined using the Petersen diagram (Petersen 1973), in which, mine the degree of mixing in massive main-sequence stars. for a given luminosity, the period ratiosP1/P0 for the 1H/F For a few Cepheid binaries with blue main-sequence mode pulsators are plotted as a function oflog P0 for stars companions, dynamical masses of Cepheids can be deter- with di†erentTeff and di†erent stellar masses. Theoretical mined (see, for instance,Bo hm-Vitense et al. 1998 and refer- periods and period ratios have been calculated, for instance, ences therein). The beat Cepheids now o†er another by Christensen-Dalsgaard & Petersen (1995) and most possibility to determine additional empirical Cepheid recently by Morgan & Welch (1997), who calculated masses and thereby get additional information about the periods and period ratios for di†erent heavy element abun- degree of interior mixing for main-sequence stars of di†er- dances and di†erent stellar masses using OPAL opacities. ent masses. Here we make extensive use of calculations by one of us In this paper, we are concerned only with beat Cepheids (S. M.). Di†erent models are well separated in the Petersen within our Galaxy for which heavy element abundances diagram. The luminosities of the beat Cepheids are known andTeff have been determined. D. Welch has compiled a list from the period-luminosity relation. WithTeff and heavy of 17 Milky Way beat Cepheids.2 Two additional stars may element abundances known from photometry and spectro- be beat Cepheids as well. It is likely that more of these stars scopic analyses and with the observed period ratios of the exist but have not yet been discovered. These stars typically beat Cepheids, we look in the Petersen diagrams for the pulsate in the fundamental (F) and Ðrst-overtone (1H) best-Ðtting beat masses. modes with periodsP0 andP1, respectively. There is only The Galactic beat Cepheids appear to have a range in one Galactic beat Cepheid, CO Aur, that pulsates in the metallicity that may extend from about solar to [Fe/H] D Ðrst- and second-overtone modes (Pardo & Poretti 1997; [0.4, hence we also explore the metallicity parameter space Poretti & Pardo 1997). We study seven of the Galactic beat when searching for the best-Ðtting model. As beat Cepheids Cepheids whose photometry is available in the literature. are among the lowest-period Cepheids, their masses are The Large Magellanic Cloud contains a large number of expected to be near the low end of the Cepheid mass range, beat Cepheids. The MACHO microlensing collaboration i.e., around 4È6 M_. (Alcock et al. 1995; Welch et al. 1997) reported the dis- The Petersen diagram has been successfully used to covery of 76 beat Cepheids. These contain a much larger obtain the mass of the solar metallicity binary beat Cepheid fraction of 1H/2H pulsators compared with the Milky Way. Y Car(Bo hm-Vitense et al. 1997). Its dynamical mass was ^ The EROS microlensing survey (Beaulieu et al. 1997) has found to be 3.8 1M_, which agrees well with its beat discovered 11 beat Cepheids in the Small Magellanic Cloud mass of 3.8 M_. so far, of which seven are pulsating in the 1H/2H mode, while four pulsate in the F/1H mode. These stars have, 3. EFFECTIVE TEMPERATURES, LUMINOSITIES, AND however, lower than solar heavy element abundances that METALLICITIES are not well known at present. TheirT s are also not yet eff In this paper, we have studied seven Galactic beat well known, mainly because of uncertain interstellar Cepheids for which sufficient data are available in the litera- reddening corrections. We therefore restrict our studies here ture with respect to photometry, reddenings, and metalli- to the Galactic Cepheids.

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