THE ARAUCARIA PROJECT. OGLE-LMC-CEP-1718: AN EXOTIC ECLIPSING BINARY SYSTEM COMPOSED OF TWO CLASSICAL OVERTONE CEPHEIDS IN A 413 DAY ORBIT^*

Classical Cepheids are distance indicators par excellence and a fundamental rung on the cosmic distance ladder, connecting our Milky Way galaxy to galaxies in the Local Group and beyond (Freedman et al. 2001; Gieren et al. 2005a, 2006; Pietrzyński et al. 2006; Riess et al. 2011). In order to render Cepheids even more robust and reliable distance indicators, it is imperative to understand their physical and evolutionary properties with the highest possible accuracy. In that context, it has been a breakthrough to find classical Cepheids in detached, double-lined eclipsing binary systems, which permit a determination of their basic physical parameters much more accurately than what is possible for any single Cepheid star. In particular, the analysis of the OGLE-LMC-CEP-0227 system located in the Large Magellanic Cloud (LMC), containing a classical Cepheid pulsating with a period of 3.8 days together with a stable red giant in a 310 day orbit, has yielded for the first time a Cepheid mass and radius determination accurate to 1% and valuable independent insight on the p factor needed for Baade–Wesselink-type analyses (Pietrzyński et al. 2010; Pilecki et al. 2013). A second eclipsing binary system in the LMC containing an even shorter-period classical Cepheid, OGLE-LMC-CEP-1812, was analyzed by Pietrzyński et al. (2011) and again yielded a very accurate measurement of the dynamical mass of the Cepheid. These two Cepheid mass determinations have gone a long way to solve the famous Cepheid mass discrepancy problem, leading to improved predictions of Cepheid masses from stellar pulsation and evolution theories (Marconi et al. 2013; Prada Moroni et al. 2012).

Here we report on the confirmation of an even more exotic, and so far unique, eclipsing binary system in the LMC consisting of a pair of classical Cepheids in a 413 day orbit. The system, herein named OGLE-LMC-CEP-1718, was discovered and identified as a double Cepheid by Alcock et al. (1995). Later, Soszyński et al. (2008) found that it also exhibits eclipsing variability, but it was not yet clear if the two Cepheids were indeed gravitationally bound. Our spectroscopic observations of this double-lined system over the past years clearly show that the two Cepheids orbit each other, with the additional radial velocity variability of the Cepheids due to their pulsations superimposed on their orbital radial velocity curves. Evidently, the analysis of this system and the characterization of the physical properties of its coeval Cepheids holds great promise for deepening our understanding of Cepheid physics and evolution.

In this paper, we present spectroscopic observations of OGLE-LMC-CEP-1718 and extract the orbital radial velocity curves of the two components of the system and the individual pulsational radial velocity curves of the Cepheids. We add new photometric data from the OGLE III and OGLE IV surveys to that presented by Soszyński et al. (2008) to the radial velocity data to obtain the orbital solution as well as a determination of several physical parameters of the Cepheids, particularly their masses and pulsation modes.

Using the MIKE spectrograph at the 6.5 m Clay Telescope at Las Campanas Observatory and the HARPS spectrograph attached to the 3.6 m telescope at the ESO La Silla Observatory, we obtained 38 high-resolution spectra of OGLE-LMC-CEP-1718 (mean magnitudes I = 14.511, V = 15.190; Soszyński et al. 2008) between 2011 September 29 and 2013 December 12. Radial velocity determinations from these spectra were made using the Broadening Function Method (Rucinski 1992, 1999) implemented in the RaveSpan code (Pilecki et al. 2012). We analyzed the spectra in the range of 4125–6800 Å using the theoretical spectra taken from the library of Coelho et al. (2005) as templates. The radial velocities determined in this way were typically accurate to 0.3 km s⁻¹ and we have never seen any systematic difference between data obtained with the MIKE and HARPS spectrographs. The measured radial velocities of both components are presented in Table 1.

In addition to these radial velocity data, we were able to use 1535 I-band measurements of the system collected by the OGLE Project (Udalski 2003) over many years, including data from the most recent OGLE III and IV surveys. The previous photometric analysis performed by Soszyński et al. (2008) had detected three periods—one describing the orbital motion of the two stars, and two additional magnitude variations due to the pulsations of two Cepheids with periods of 1.96 and 2.48 days. This was a promising indication that the Cepheids might be gravitationally bound, but it could also be a blend.

The analysis of the radial velocity data set confirms the genuine spectroscopic binary nature of the system, with orbital motion of the two stars superimposed on the intrinsic radial velocity variations due to their pulsations. Knowing the pulsation periods from the photometry, we were able to fit a complex model of orbital motion together with a pulsation variability for each object (see also Pilecki et al. 2013). This analysis clearly shows that the orbital period of the system is only half of the one originally assumed by Soszyński et al. (2008). This is a consequence of the fact that with the inclination and orbit orientation of the system, presented in Table 2 along with other orbital parameters derived in our orbital solution, only the primary eclipse is visible in the photometry whereas a possible secondary eclipse remains elusive and cannot be detected in the data. The absence of a secondary eclipse is fully consistent with the eccentricity and the other orbital parameters obtained in our analysis.

We were able to determine the four individual radial velocity curves that are superimposed in the data—the orbital radial velocities of the components of the system, and the pulsational radial velocity curves of the primary (P = 1.96 days) and secondary (P = 2.48 days) Cepheid components in the system. The orbital radial velocity curve of OGLE-LMC-CEP-1718 and the pulsational radial velocity curves of its two Cepheids are shown in Figures 1–3. The disentangling of the four different radial velocity curves is not yet perfect, but the small residuals from the fitted curves that are only slightly larger than the typical precision of the individual radial measurements demonstrate that the disentangling has been achieved with a high degree of accuracy with our code.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

The pulsational radial velocity curves are both low amplitude and approximately sinusoidal, as are the corresponding I-band light curves of the Cepheids that are shown in Figures 4 and 5. In Figure 6, we show the orbital I-band light curve based on the full data set, folded on the orbital period of 412.807 days.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

From our orbital solution, we find that the masses of the Cepheids are 3.3 and 3.28 M_☉, respectively, individually determined with an accuracy of 3% (see Table 3). Because the high-eccentricity error does not contribute to the evaluation of the mass ratio, it is determined with a much better accuracy. The analysis indicates that the two Cepheids in the OGLE-LMC-CEP-1718 system have equal masses to within ±1.5%.

Table 3. Properties of CEP-1718

Parameter	Primary	Secondary
Pulsation period (days)	1.9636625	2.480917
Pulsation mode	FO	FO
Mass (M☉)	3.3 ± 0.11	3.28 ± 0.11
Radius a (R☉)	24.0 ± 1.2	$28.5_{-1.1}^{+2.9}$
Orbital period (days)	412.807 ± 0.008
Tpri (days)	2455050.5 ± 0.1
Semimajor axis (R☉)	454.9 ± 3.6
Inclination (deg)	$84.5_{-0.4}^{+0.15}$

Note. ^aThe values were calculated using the sum of the radii from our light curve analysis, and the ratio obtained from the period–radius relation for first-overtone Cepheids from Sachkov (2002). The errors were estimated independently.

Download table as:  ASCIITypeset image

The very short pulsation periods suggest pulsation in non-fundamental modes. In Figure 7, we have plotted the positions of the two Cepheids on the I-band light curve Fourier decomposition diagrams of Soszyński et al. (2008). The loci of both stars on these diagrams, particularly on the R₂₁ − log P diagram, strongly suggest that both Cepheids in OGLE-LMC-CEP-1718 are pulsating in the first overtone mode.

Zoom In Zoom Out Reset image size

This result can be checked in a different way. Since we cannot observe the secondary eclipse in the light curve, we cannot determine the individual radii of the Cepheids. However, the analysis of the light curve does return the sum of the radii, in this case 52.5 ± 1.5 R_☉. Assuming first overtone pulsation for the two Cepheids in OGLE-LMC-CEP-1718, we can calculate their expected radii from a period–radius relation calibrated for first overtone Cepheids. Using the observational relation given by Sachkov (2002), we obtain radii of R = (26.1 ± 2.5) R_☉ for the primary and R = (31.0 ± 2.6) R_☉ for the secondary (longer-period) Cepheid, with the radii ratio of 1.19. These predictions are in excellent agreement with the predictions from the theoretical period–radius relation for first overtone Galactic Cepheids of Bono et al. (2001; 27 and 32 R_☉, respectively). As the ratio is much better constrained than the radii themselves, we have used it to calculate the individual radii of the Cepheids (using the known sum), obtaining R₁ = 24 R_☉ and R₂ = 28.5 R_☉, which is clearly consistent with the values from the given relation. If we assume fundamental mode pulsation for both Cepheids and use the fundamental mode Cepheid period–radius relation from Sachkov (2002), which is very similar to other calibrations of that relation, e.g., Gieren et al. (1998), the expected sum of the radii is 44.0 ± 0.3 R_☉, indicating that fundamental mode pulsation is much more unlikely. We have to note, however, that in this case the calculations are based on the extrapolation as the periods of our stars are shorter than the shortest one among the stars used to obtain the relation.

Yet another argument supporting the first overtone pulsation hypothesis comes from the observed brightness of OGLE-LMC-CEP-1718. Using the fitted PL relations for first overtone Cepheids in the LMC from the OGLE project (Soszyński et al. 2008), the expected apparent magnitudes for the primary Cepheid are 15.439 and 16.110 in I and V bands, respectively, whereas for the secondary Cepheid, the corresponding values are 15.104 and 15.786. This leads to expected total apparent magnitudes of both components of I_tot = 14.506 and V_tot = 15.183, respectively. The observed apparent magnitudes of the system are I_obs = 14.511 and V_obs = 15.190, in excellent agreement with the expected magnitudes if both Cepheids pulsate in the first overtone mode.

One possibility to reconcile the fact that both Cepheids in the system have the same masses but different pulsation periods would be the assumption that the primary, shorter-period Cepheid is actually pulsating in the second overtone mode. The observed period ratio of 1.96/2.48 = 0.79 would be consistent with the hypothesis that the primary Cepheid is pulsating in the second overtone while the secondary Cepheid is a first-overtone pulsator—a period ratio of about 0.8 is indeed commonly observed for double-mode 1O/2O Cepheids. However, in the OGLE database of Cepheids in the Magellanic Clouds (Soszyński et al. 2008), which contains the largest samples of Cepheids, among others approximately 100 single-mode second-overtone Cepheids and approximately 420 double-mode 1O/2O Cepheids, the largest-known period of a second-overtone Cepheid is 1.32 days (in the double-mode Cepheid OGLE-SMC-CEP-0305 in the Small Magellanic Cloud). This is very much shorter than the period of 1.96 days observed for the primary Cepheid in our OGLE-LMC-CEP-1718 system.

The largest-known amplitude of the I-band light curve of a second-overtone Cepheid is 0.138 mag (in the single-mode Cepheid OGLE-SMC-CEP-3509). Our object has a smaller amplitude of 0.097 mag (see Figure 4), but the amplitude is decreased by the light from the secondary component through blending. Transforming the magnitudes to fluxes, removing the contribution of the secondary Cepheid, and transforming the flux back to magnitudes now yields an I-band amplitude of 0.231 mag for the short-period primary Cepheid in the OGLE-LMC-CEP-1718 system. This is much larger than any known amplitude of a second-overtone oscillation.

The shapes of the light curves cannot be directly compared because there are no second-overtone Cepheids with periods of around two days. However, it can be stated that all second-overtone Cepheid light curves are more symmetrical than the one of the primary in our system—indeed, they are nearly sinusoidal. Finally, the total luminosity of the OGLE-LMC-CEP-1718 system perfectly agrees with the assumption that the system consists of two first-overtone Cepheids, as already mentioned above. In conclusion, if the 1.96 day Cepheid in our system would indeed be a second-overtone pulsator, it would be the longest-period and the largest-amplitude second-overtone Cepheid known in any galaxy. Given the large number of second-overtone Cepheids known to date, it seems extremely unlikely that we found such an extreme object in the only eclipsing binary system consisting of two classical Cepheids that has been discovered so far.

Our conclusion then is that we have found a system composed of two classical Cepheids that have, within a 1.5% uncertainty, identical masses. Both stars are almost certainly pulsating in the first-overtone mode, presumably have the same ages, but have substantially different periods and luminosities. It will be challenging for stellar evolutionary theory to explain the observed properties of these Cepheids, which will be the topic of a forthcoming study of our group.

We have presented the first confirmed eclipsing binary system with both components identified as classical Cepheids. These two variables orbit each other in an eccentric orbit with a period of 413 days. Strong evidence is presented that both variables are pulsating in the first-overtone mode. The dynamical masses of both Cepheids are identical to within 2% and the absolute masses are determined with an accuracy of 3%. Both orbital light and radial velocity curves of the system and the pulsational light and radial velocity curves of the two Cepheids are very well determined from our data, although improvement is possible and desirable.

The OGLE-LMC-CEP-1718 system, as the first confirmed eclipsing binary system containing two classical Cepheids, might well turn out to be a Rosetta Stone for our deeper understanding of the pulsational and evolutionary properties of Cepheids. In response to this opportunity and the challenges presented by the system, we plan to improve the existing radial velocity data and obtain observations of near- and mid-IR photometry, which should help to better understand the physics of these variables. In particular, near-infrared light curves for the two Cepheids in the system will provide a unique opportunity to test the basic assumptions made in the near-infrared surface brightness technique (Fouqué & Gieren 1997; Gieren et al. 2005b; Storm et al. 2011) of the distance determination to Cepheids by taking advantage of the knowledge that both Cepheids are at the same distance.

We gratefully acknowledge financial support for this work from the BASAL Centro de Astrofisica y Tecnologias Afines (CATA) PFB-06/2007, and from the Millenium Institute of Astrophysics (MAS) of the Iniciativa Cientifica Milenio del Ministerio de Economia, Fomento y Turismo de Chile, project IC120009. Support from the Polish National Science Center grant MAESTRO 2012/06/A/ST9/00269 and the TEAM subsidy of the Foundation for Polish Science (FNP) is also acknowledged. The OGLE project has received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013) and ERC grant agreement no. 246678 to A.U. A.G. acknowledges support from FONDECYT grant No. 3130361. We greatly appreciate the expert support of the staff members at the Las Campanas and ESO La Silla Observatories, where the data for this project were obtained. The research in this paper was partially supported by the Polish Ministry of Science and Higher Education through the program Ideas Plus award No. Id P2012000162. We also thank the referee, Laszlo Szabados, for constructive remarks that helped to improve this paper.