View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server The MACHO Pro ject SMC Variable Star Inventory. I. The Second-overtone Mo de of Cepheid Pulsation From First/Second Overtone (1H/2H) Beat Cepheids 1;2 3 1;4 5 6 1;2;7 C. Alco ck , R.A. Allsman , D. Alves , T.S. Axelro d , A.C. Becker , D.P. Bennett , 1;2 5 2;8 2;8 1;2 K.H. Co ok , K.C. Freeman ,K. Griest , M.J. Lehner , S.L. Marshall , 5 10 5 12 11 B.A. Peterson , P.J. Quinn , A.W. Ro dgers , A. Rorab eck ,W. Sutherland , 6 2;8 A. Tomaney , T. Vandehei (The MACHO Collab oration) { 2{ Received ; accepted 1 Lawrence Livermore National Lab oratory, Livermore, CA 94550 E-mail: alcock, alves, dminniti, kcook, [email protected] 2 Center for Particle Astrophysics, University of California, Berkeley, CA 94720 3 Sup ercomputing Facility, Australian National University, Canb erra, ACT 0200, Australia E-mail: [email protected] 4 DepartmentofPhysics, University of California, Davis, CA 95616 5 Mt. Stromlo and Siding Spring Observatories, Australian National University, Weston Creek, ACT 2611, Australia E-mail: tsa, kcf,peterson, [email protected] 6 Departments of Astronomy and Physics, University of Washington, Seattle, WA 98195 E-mail: austin, becker, [email protected] 7 Physics Department, University of Notre Dame, Notre Dame, IN 46556 E-mail: [email protected] du 8 DepartmentofPhysics, University of California, San Diego, La Jolla, CA 92093 E-mail: kgriest, tvandehei, [email protected] 9 DepartmentofPhysics, University of California, Santa Barbara, CA 93106 10 Europ ean Southern Observatory, Karl-Schwarzchild Str. 2, D-85748, Garching, Germany E-mail: [email protected] 11 Department of Physics, University of Oxford, Oxford OX1 3RH, U.K. E-mail: [email protected] c.uk 12 Dept. of Physics & Astronomy, McMaster University, Hamilton, Ontario, L8S 4M1 Canada E-mail: welch, [email protected] .ca { 3{ ABSTRACT We rep ort the discovery of 20 1H/2H and 7 F/1H b eat Cepheids in the SMC by the MACHO Pro ject. We utilize the 20 1H/2H stars to determine lightcurve shap e for the SMC second-overtone (2H) mo de of Cepheid pulsation. We predict, similar to the ndings of Alco ck et al. [1997, ApJ, submitted], that 2H Cepheids will have nearly or purely sinusoidal lightvariations; that the P {L relation for 2H Cepheids will not be distinguishable from the P {L relation for 1H Cepheids within photometric accuracy; and that 2H stars may b e discernable from F and 1H stars using the amplitude-p erio d diagram and Fourier parameter progressions for p erio ds P < 0:7days, our current sample 2H p erio d limit. Subject headings: Cepheids | Magellanic Clouds | stars: fundamental parameters | stars: oscillations { 4{ 1. Intro duction The second-overtone (2H) mo de of Cepheid pulsation has b een predicted to exist theoretically since Stobie (1969a, 1969b)'s pioneering investigations. Yet, since then, we have found only scant evidence for 2H mo de excitation in our Galaxy. CO Aur was recognized as a rst-overtone/second-overtone (1H/2H) b eat Cepheid by Mantegazza (1983), and later con rmed as such by various studies (e.g.,Antonello & Mantegazza 1984; Bab el & Burki 1987). On the other hand, HR 7308 is a prop osed singly-p erio dic 2H Cepheid whose mo dal status remains uncertain, despite many investigations (Burki et al. 1986; Fabregat, Suso, & Reglero 1990; Simon 1985; Bersier 1996; Bersier & Burki 1996). This paucity of Galactic 2H Cepheids is not unexp ected. From a theoretical standp oint, Galactic 2H Cepheids should havelow masses and luminosities (Chiosi, Wo o d & Capitano 1993). As well, they are exp ected to be the shortest-p erio d Cepheids at a given luminosity (Chiosi et al. 1993), so that they should app ear in greater frequency in lower metallicityenvironments than our own (see e.g., the p erio d frequency distributions of Cepheids in Lipunova 1992). Observationally,inour own galaxy, CO Aur's semi-amplitude of pulsation for its 2H mo de is only 0:043 0:002 mag (Pardo & Poretti 1996)|so that, even if we observe these faint stars, we might not detect their variability. The advent of large-scale astronomical surveys has improved our chances of observing 2H Cepheids. As by-pro ducts of gravitational microlensing searches in the Galactic bulge and Magellanic Clouds, the MACHO and EROS Collab orations have found 45 1H/2H and at least 37 F/1H b eat Cepheids in the LMC (Alco ck et al. 1995, 1997; Beaulieu et al. 1997), and 27 1H/2H and 10 F/1H b eats (counting this work and Beaulieu et al. 1997) in the SMC to date. Concurrent analyses of these, and other ndings, has allowed investigations of the 2H mo de of Cepheid pulsation. Pardo & Poretti (1996) re-analyzed the comp osite lightcurve of CO Aur, the sole 1H/2H b eat Cepheid in the Galaxy, and noted that its 2H { 5{ mo de app eared as a purely sinusoidal light variation. Alco ck et al. (1997) analyzed 45 rst-overtone/second-overtone b eat Cepheids in the LMC, showing (1) that the 2H mo de 1 < 0:2) lightcurves ; (2) that LMC resulted in sinusoidal, or nearly sinusoidal (0 R 21 2H Cepheids could be distinguished from LMC 1H and F Cepheids in Fourier space for P < 1:4 days; (3) that 2H Cepheids should overlap the short-p erio d edge of the 1H P {L sequence; and (4) that the lo cation of 2H pulsators in the log L{log T plane dep ended e signi cantly on the adopted M {L relation, and would have to come from observation. Finally,Antonello & Kanbur (1997) haveinvestigated the 2H mo de of Cepheid pulsation by non-linear pulsation mo dels appropriate to the LMC (Z 0:01). They con rmed that 2H Cepheids should be more numerous for lower metallicities, and pro duced theoretical R {P 21 sequences which agreed qualitatively with the sequences for LMC 1H/2H b eat Cepheids in Welch et al. (1997). They also predicted a resonance of the R {P and {P sequences 21 21 near P =1 day. With the recent reduction of SMC photometry by the MACHO pro ject, we are in a p osition to add to our knowledge of the 2H mo de. We rep ort the discovery of 20 1H/2H b eat Cepheids in the SMC (distinct from the stars in Beaulieu et al. 1997), and their implications for the 2H mo de of Cepheid pulsation. We compare our ndings to the 2H mo de characterizations in the LMC and Galaxy to date, and provide guidance on how to discern 2H from F and 1H Cepheids. 1 R = V =V is the relative amplitude of the rst harmonic and `base' frequency mo del k 1 k 1 P O amplitudes in a truncated Fourier series V (t) = V + V cos(2k t + ), while the 0 k k k =1 phase di erence = k . For b eat Cepheids, R and are calculated for each k 1 k 1 21 21 mo de of pulsation. { 6{ 2. Observations and Analysis We refer the reader to Alco ck et al. (1995) for a description of our two-bandpass photometry (the MACHO V and R bands) and b eat Cepheid identi cation pro cess. The b eat Cepheids rep orted in this pap er were selected by our alert system software and not by a full analysis run. Therefore, the total number of b eat Cepheids in these elds is likely to be 4-5 greater than rep orted here. To be identi ed as an alert, a star must be 7 sigma brighter than the template and have increased in brightness by at least 0.35 mag. SMC observations of these Cepheids span 3years; lightcurves consist of anywhere from 163{1306 observations, which are free of p ossible cosmic ray events, bad or missing pixels, or data su ering from p o or image quality. This pap er utilizes MACHO V -band photometry for all results. We sub jected each star to our co ding of the CLEANest algorithm (Foster 1995, 1996a, 1996b) for joint frequency analysis and lightcurve mo delling. This metho d avoids having to cho ose a truncated Fourier series order a priori, as discussed in Pardo & Poretti (1997) and Alco ck et al. (1997). Brie y, CLEANest uses the date-comp ensated discrete Fourier transform (DCDFT) of Ferraz-Mello (1981) on a time series to pro duce a power sp ectrum 1 1 for test frequencies from = (2T ) to = (2 min(t)) in steps of (the res span max res frequency resolution), where T is the total timespan of the observations for a star, span and t the time separation between successive observations. If any of the frequencies in the power sp ectrum are adopted as signi cant, they are mo deled by cos(2 t) and sin(2 t) terms (plus a constant) as in Foster (1995). The resultant mo del is subtracted from the data, these residuals are sub jected to another DCDFT, and the pro cess is iterated until no signi cant frequencies remain. Each time a DCDFT of the data or residuals has b een p erformed, CLEANest seeks to nd the n-tuple of frequencies which gives the b est description of the data. Op erationally, frequency space is searched for frequencies in the { 7{ neighb ourho o d of the currently adopted ones for a maximum of Foster (1996a, 1996b)'s mo del amplitude.