THE CoRoT DISCOVERY OF A UNIQUE TRIPLE-MODE CEPHEID IN THE GALAXY

Double-mode Cepheids are a powerful tool to test the stellar models of supergiants since the simultaneous excitation of two pulsation modes tightly constrains the physical parameters. In the 1990s, the introduction of the new OPAL opacities (Rogers & Iglesias 1994) solved the discrepancy between the beat and pulsation masses (Moskalik et al. 1992), also reconciling the evolutionary ones (Christensen-Dalsgaard & Petersen 1995). Nowadays, the period ratio is used to investigate the metallic content of stellar systems hosting double-mode Cepheids. Sziládi et al. (2007) obtained observational evidence of the relation between the period ratios and the metal abundances by means of high-resolution spectroscopy of galactic double-mode Cepheids. The metallicity of the Large (LMC) and Small (SMC) Magellanic Clouds has been investigated by using the period ratios of hundreds of double-mode Cepheids in the framework of large-scale surveys: MACHO (e.g., Alcock et al. 1999), EROS-2 (e.g., Marquette et al. 2009), OGLE-III (e.g., Soszyński et al. 2008a, 2008b)

The involved radial modes are the fundamental (F) and the first (1O), second (2O), and third (3O) overtones. Typical period ratios are 1O/F = 0.71, 2O/1O = 0.80, 3O/1O = 0.68. However, the large-scale surveys revealed other particular subclasses (for a review, see Moskalik 2014): stars with a nonradial mode in close proximity to the dominant 1O mode and double-mode pulsators with a period ratio of 0.60–0.64.

On the other hand, triple-mode Cepheids are extremely rare. The current statistics (Moskalik 2014) report six cases of 1O/2O/3O stars (three in the LMC, one in the SMC, and two in the galactic bulge) and four cases of F/1O/2O stars (two in the LMC, two in the SMC). The two triple-mode Cepheids in the galactic bulge have extremely short periods: the 1O periods are 0.295 day and 0.230 day, corresponding to F periods shorter than 0.4 day. The modeling of three periods and the evolutionary calculations are expected to place strong constraints both on Cepheid mass–luminosity relations and on the internal physics.

The variability of GSC 0746-01186 was discovered in the ASAS survey (ASAS 064135+0756.6; Pojmanski 2002). The star was classified as a Cepheid with P = 1.28859 days, with an amplitude of 0.41 mag and 〈V〉 = 12.48. Later, Khruslov (2009) identified it as a double-mode Cepheid with periods P₁ = 1.28861 days and P₂ = 1.03153 days. These periods were confirmed by the analysis of the NSVS data (Woźniak et al. 2004). The ratio of 0.8005 suggested a pulsation in the 1O and 2O modes. GSC 0746-01186 ≡ ASAS 064135+0756.6 ≡ SRa01b.16229 was re-observed during the BEST II survey (Berliner Exoplanet Search Telescope; Klagivik et al. 2013). The double-mode pulsation and the period ratio were both confirmed. The space mission CoRoT (Baglin et al. 2006) monitored the star in a serendipitous mode since it is located in a field contiguous to that of the open cluster NGC 2264, the main target of the first short run in the anticenter direction (SRa01). We definitely cross-identify CoRoT 0223989566 ≡ GSC 0746-01186 ≡ ASAS 064135+0756.6 ≡ 2MASS 06413457+0756396 when searching for Cepheids in the CoRoT database (E. Poretti et al., in preparation).

CoRoT 0223989566 was observed continuously for 23.4 days from 2008 March 7 to March 31. The EXODAT catalog (Deleuil et al. 2009) reports a spectral type of A5 III, an E_{B − V} = 1.1 mag (both from spectral energy distribution analysis) and a very low contamination level due to close stars, i.e., 0.004 in a range from 0 to 1. The "CoRoT Variability Classifier" (CVC) automated supervised method (Debosscher et al. 2009) correctly suggests a classical or a double-mode Cepheid. The measurements of CoRoT 0223989566 were performed in the 512 s mode from JD 2454533.4120 to 2454536.008 and then in the 32 s mode until the end of the observations at JD 2454556.795.

All the CoRoT measurements were taken into account for the initial frequency analysis. The outliers were removed by means of a cross-check between the flags provided by the reduction pipeline and a visual inspection of the light curve. Outliers are for most measurements that suffer from hot pixels during the passage through the South Atlantic Anomaly. The final time series is composed of 52,148 measurements: they were obtained in the chromatic mode, but here we discuss the white measurements only since we are interested in a detailed frequency analysis requiring a high signal-to-noise ratio (S/N). The high-precision, high duty-cycle CoRoT photometry provides us with an excellent representation of the beating between two commensurable periods (Figure 1, top panel). The light curve is a succession of two "bright" maxima followed by two "faint" ones. The four maxima span the short beating period of 5.16 days = 4P₁ = 5P₂.

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The frequency analysis was performed by means of the iterative sine-wave, least-squares fitting method (Vaniĉek 1971). It was applied to both the original CoRoT time series composed of 32 s and 512 s exposures and to a new data set obtained by grouping 16 consecutive 32 s measurements into a single 512 s point. The frequency values were refined by the MTRAP algorithm (Carpino et al. 1987), allowing us to search for the best fit by keeping the values of the harmonics and the combination terms locked to the independent frequencies. The analysis of the CoRoT data identified the two frequencies corresponding to the periods already known (Figure 2; the power spectra from the original time series are shown). The peak at f₁ = 0.776 day⁻¹ is by far the highest in the power spectrum, but 2f₁ and f₂ = 0.970 day⁻¹ are also immediately noticeable (panel (a)). The f₂ peak and the combination terms f₁ + f₂ and f₂ − f₁ were detected after prewhitening the data with f₁ and its harmonics (panel (b)). The four terms f₁, f₂, f₁ + f₂, and f₂ − f₁ are the most common in the solutions of the light curves of double-mode Cepheids obtained from ground-based data (Pardo & Poretti 1996). We expected that the subsequent analysis of the CoRoT time series would disclose the rich ensemble of combination terms between the harmonics of f₁ and f₂. Therefore, it was a great surprise to detect a new independent term f₃ = 0.529 day⁻¹, at the next step (panel (c)). The presence of the f₁ + f₃ peak was particularly important since it immediately ruled out that f₃ was due to the variability of a close, unresolved star in the CoRoT mask or to a binary companion. After this, the combination terms between the harmonics of f₁, f₂, and f₃ were detected step-by-step, as shown in panel (d) for a subset of nine of them. The final solution of the CoRoT light curve was provided by the independent terms f₁ = 0.776006 ± 0.000002 day⁻¹, f₂ = 0.969787 ± 0.000016 day⁻¹, and f₃ = 0.529632 ± 0.000143 day⁻¹, their harmonics (up to 7f₁, 2f₂, and 2f₃) and a set of 23 other combination terms, for a total of 34 components. Table 1 lists the ordered structure of the combination terms and the least-squares solution obtained from the time series composed of the 512 s and 32 s measurements, which leaves a residual rms of 0.0010 mag. The error bars on the amplitudes σ(A) = 6 × 10⁻⁶ mag and on the phases σ(ϕ_i) = σ(A)/A_i can be immediately derived following Montgomery & O'Donoghue (1999).

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The discovery of f₃ opened the possibility that other modes were excited and we performed an additional analysis to find them. The power spectra of the entire data set show some peaks close to f₁ and, much less relevant, to f₂. The highest one was at f = 0.728 day⁻¹ with an amplitude 0.008 times that of f₁. The nature of these peaks is ambiguous. They could have a stellar origin and be due to a long-term modulation of the main oscillations observed in some 1O/2O Cepheids (Moskalik 2014). However, we cannot rule out the possibility that this long-term effect is actually due to satellite drift and/or detector aging. The analysis of the light curve of the residuals helped us to clarify this point. After the prewhitening with 34 components, the data show residual oscillations up to ±2 mmag (Figure 1, middle panel). The amplitudes of the peaks found in the frequency analysis of the residuals are smaller than 0.1 mmag. An erratic nature could be more plausible, but not fully convincing. Therefore, we calculated a new set of residuals by subdividing the 23.4 days time baseline into six contiguous subsets spanning 3.9 days each. The frequency values were kept fixed, but the amplitudes and phases were recalculated for each subset. Then, the residuals obtained from these subsets were merged. The residual light curve thus obtained is almost flat and the erratic oscillations have completely disappeared (Figure 1, bottom panel). We can infer that the erratic oscillations are due to instrumental effects that are affecting the CoRoT photometry in such a way that the usual technique of prewhitening was not able to clean (see also the case of CoRoT 101155310; Poretti et al. 2011). The frequency analysis of the residuals after subtracting the 34 components from the six subsets (Figure 2, panel (e)) did not detect any peak below 1.0 day⁻¹, where we expected the independent modes we were looking for.

Therefore, we can conclude that after f₃ no other independent mode is detectable in the light curve of CoRoT 0223989566. The noise level of the power spectrum of the residuals (Figure 2, (panel (e)) is around 0.004 mmag in the 0–3 day⁻¹ region and increases to 0.012 mmag in the 5.0–7.0 day⁻¹ region. Some of the peaks visible in the 5.0–7.0 day⁻¹ region are close to combination terms (e.g., 6f₁ + f₃ = 5.18 day⁻¹, 7f₁ = 5.43 day⁻¹, 7f₁ + f₂ = 6.40 day⁻¹, 6f₁ + 2f₂ = 6.59 day⁻¹), but their amplitudes (0.028, 0.040, 0.028, and 0.030 mmag, respectively) are below the heuristically accepted threshold of S/N = 3.5 (Breger et al. 1993).

For the sake of completeness, we successfully verified that the f₃ component was also detectable in the CoRoT data before removing the outliers and that the solution of the time series composed of the grouped 512 s points supplies the same combination terms of the solution listed in Table 1.

The analysis of the data of CoRoT 0223989566 returned three independent periods: P₁ = 1.2886 days, P₂ = 1.031140 days, and P₃ = 1.888538 days. This triplet is completely new among galactic Cepheids. The period ratios are P₁/P₂ = 0.8002, P₂/P₃ = 0.546, and P₁/P₃ = 0.682.

3.1. The Petersen Diagram

Figure 3 shows the Petersen diagram of the galactic double-mode Cepheids. There is little doubt that P₁ and P₂ can be typified with the 1O and 2O modes, as is done in the galactic, LMC, and SMC double-mode Cepheids. P₃ is giving us more trouble. The ratio 0.68 has been observed in two double-mode LMC Cepheids (Soszyński et al. 2008a) and in six triple-mode Cepheids (1O/2O/3O) in both the Magellanic Clouds (Moskalik 2014). The related periods were identified with those of the 3O and 1O modes. However, this is not the case for CoRoT 0223989566: since P₃ is longer than P₁, it should be the 1O mode and P₁ the 3O one, contradicting the previous robust identification of P₁ as the 1O mode.

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The fact that P₃ is much longer than P₁ and P₂ naturally suggests its identification with the F radial mode. However, the corresponding ratio 1O/F = 0.682 is lower than the usual one (0.694–0.746; Moskalik 2014). Moreover, Figure 3 shows how the 1O/F ratio is expected to increase toward short F-periods, thus making the 0.682 ratio of CoRoT 0223989566 still more peculiar. There is only one example of a ratio of 0.68 typified as a 1O/F one, i.e., J045917-691418 (P₀ = 3.08 days and P₁ = 2.10 days) in the LMC (it is the apparently lowest outlier in Figure 3 of Marquette et al. 2009). The unusual ratio is explained in terms of an high-metallicity of Z = 0.030 (see also Figure 3 in Buchler & Szabó 2007), while the mean metallicity of LMC double-mode Cepheids is 0.004.⁴ The fundamental period of CoRoT 0223989566 is shorter than that of J045917-691418 and a still higher metallicity is necessary to include the (log P, P₁/P₀) location of CoRoT 0223989566 between the limits where F and 1O are both unstable (Buchler & Szabó 2007).

Therefore, if P₃ is actually the F mode, CoRoT 0223989566 is a very particular star: not only a unique F/1O/2O Cepheid in the Galaxy but also one with an unusual 1O/F ratio. In any case, CoRoT 0223989566 is the triple-mode Cepheid showing the longest periods, both in the Galaxy and in the Magellanic Clouds. In the context of the galactic Cepheids, it should be noted that P = 1.8 days seems to be the shortest F period among the 1O/F double-mode stars and the longest 1O period among the 2O/1O ones (Figure 3).

3.2. The Analysis of the Fourier Parameters

3.3. The Location of CoRoT 0223989566 in the Milky Way

The intensive CoRoT monitoring of CoRoT 0223989566 discovered a unique case among triple-mode galactic Cepheids. The 0.682 ratio between the two longest periods is quite unusual. If interpreted as a 1O/F ratio, the fact that CoRoT 0223989566 belongs to a metal-rich environment like the "outer arm" of the Milky Way could explain the value. We also note that the periods of CoRoT 0223989566 are much longer than those of the triple-mode Cepheids detected in the galactic bulge. If not a radial mode, the excitation of an isolated nonradial mode with a period much longer than that of the 1O mode is also unusual for high-amplitude pulsators. As expected (e.g., Moskalik & Dziembovski 2005; Moskalik 2014), the discovery of a new member of the rare class of triple-mode Cepheids set new observational constraints on the stellar parameters of these variables and, in a wider context, on their evolutionary models.

The CoRoT space mission has been developed and operated by CNES, with contributions from Austria, Belgium, Brazil, ESA (RSSD and Science Program), Germany, and Spain. This research has made use of the ExoDat Database, operated at LAM-OAMP, Marseille, France, on behalf of the CoRoT/Exoplanet program. The present study has used the SIMBAD database operated at the Centre de Données Astronomiques (Strasbourg, France).