Peremennye Zvezdy (Variable Stars) 44, No. 3, 2024 Received 28 April; accepted 24 May.	Article in PDF
	DOI: 10.24412/2221-0474-2024-44-28-41

Search for Evolutionary Period Changes in the Double-mode Cepheid V367 Sct

L. N. Berdnikov^[1], A. A. Belinskii^[1], A. K. Dambis ^[1], E. N. Pastukhova^[2], M. A. Burlak^[1], N. P. Ikonnikova^[1], E. O. Mishin^[1], N. I. Shatskii^[1]

1. Sternberg Astronomical Institute, Moscow State University, Universitetskij pr. 13, Moscow 119992, Russia; leonid.berdnikov@gmail.com

2. Institute of Astronomy, Russian Academy of Sciences, ul. Pyatnitskaya 48, Moscow, 119017, Russia

It follows from the computations performed by Eggenberger et al. (2021), Nguyen et al. (2022), and Yusof et al. (2022) that the evolutionary tracks of short-period Cepheids with periods shorter than 5 days (masses less than ) either have no blue loop after the first crossing of the instability strip or this loop does not reach the instability strip, which means that the second and third crossings do not occur. This means that all short-period Cepheids are observed at the first crossing.

According to the theory, the periods of Cepheids during the first crossing increase so rapidly that the O-C diagrams should be parabolas with steep upward branches. However, no steep parabolas, i.e. rapid evolutionary period changes, have been found in the O-C diagrams for 41 short-period Cepheids (hereafter referred to simply as Cepheids) studied over a time interval of more than a hundred years (Csoernyei et al., 2022). The O-C diagrams of such Cepheids look like small-amplitude semi-regular oscillations, which are sometimes superimposed onto a slight trend; if this trend is interpreted as a result of evolutionary period changes, then the rate of these changes formally corresponds to the second or third crossing of the instability strip (Turner et al., 2006).

As of now, rapid evolutionary period changes have been found only for three Cepheids. These are two normal Cepheids, V1033 Cyg and OGLE-LMC-CEP-2132 with the periods of and , respectively (Berdnikov et al., 2019, 2023) and one bimodal Cepheid, V371 Per, pulsating both in the fundamental tone and first overtone with the periods of and , respectively (Berdnikov et al., 2023). In order to understand how these three Cepheids differ from the others, first of all, it is necessary to increase the sample size, that is, to investigate period changes in unexplored Cepheids.

One of such objects is the bimodal Cepheid V367 Sct, and the aim of this study is to search for evolutionary changes of its pulsation periods.

1. LIGHT CURVES FOR BOTH OSCILLATIONS OF V367 Sct

From July 16 to October 10, 2021, we acquired 379 -band CCD frames for the bimodal Cepheid V367 Sct with the 60-cm telescope of the Caucasian Mountain Observatory of Sternberg Astronomical Institute of M.V.Lomonosov Moscow State University (Berdnikov et al., 2021). The method of constructing light curves (Fig. 1) for the fundamental mode ( ) and the first overtone ( ) is described by Berdnikov et al. (2021).

Table 1 lists the -band light-curve parameters for both oscillations of V367 Sct: magnitude at maximum light, amplitude, and intensity-mean magnitude. Table 2 lists the Fourier coefficients (for the cosine expansion). The Fourier coefficients for fall within the domains of classical (DCEP) Cepheids and those for , within the domain of low-amplitude Cepheids (DCEPS), which pulsate in the first overtone (Udalski et al., 2018).

2. TECHNIQUE OF STUDYING PERIOD CHANGES AND OBSERVATIONAL DATA USED

We investigate changes in Cepheid pulsation periods using the standard technique of the analysis of O-C diagram. The O-C residuals can be most accurately determined using the Hertzsprung method (Hertzsprung, 1919) whose computer implementation is described by Berdnikov (1992f). We use the method described by Lombard & Koen (1993) to confirm the reality of the period changes found.

To study the periods of V367 Sct, we compiled published photographic, photoelectric, CCD observations. We supplemented these data with our own eye estimates of the star's magnitudes on photographic plates of the Sternberg Astronomical Institute plate archive and with ASAS-3 (Pojmanski, 2002) and ASAS-SN (Jayasinghe et al., 2019) survey photometry.

Table 3 summarizes information about the number of observations used. These observations span a 113-year time interval.

3. RESULTS AND DISCUSSION

We use the method described by Berdnikov et al. (2021) to extract the light curves corresponding to the fundamental mode and first overtone from observations of V367 Sct (Fig. 1). We computed seasonal light curves based on the data obtained; Table 4 summarizes the results of their analysis performed using the Hertzsprung method. The first and second columns of this table give the times of maximum light and their errors; the third column gives the type of observations; the fourth and fifth columns present the epoch number and the O-C residual, respectively; the sixth and seventh columns are the number of observations and the source of data, respectively. The data from Table 4 are shown in the O-C diagrams (Figs. 2 and 3 for the fundamental mode and first overtone, respectively) as squares for photographic observations and small filled circles for other observations, with vertical error bars of O-C residuals.

The O-C diagrams have the form of parabolas. Based on the times of maximum light from Table 4, we inferred the quadratic ephemerides listed in Table 5, which we use to draw the parabolas in the top panels of Figs. 2 and`3. The bottom panels of these figures show the residuals from these parabolas. We use the linear parts of these ephemerides to compute the O-C residuals in the fifth column of Table 4.

We use the data from Table 4 to compute the differences between the times of maximum light in the band (and also in photographic, pg, magnitudes whose photometric system is close to that of the band), and and bands relative to the band; the corresponding corrections are listed in Table 6. We used these corrections when drawing Figs. 2 and 3 and computing the ephemerides (Table 5), which therefore apply to the -band variations.

We use the method published by Lombard and Koen (1993) to confirm the reality of the changes in the pulsation period. To this end, we compute the differences of consecutive O-C residuals from Table 4, , and plot the dependences of on for both oscillations of V367 Sct (Figs. 4 and 5). The values, which have the meaning of average period in the epoch interval -, correspond to the behavior of the O-C residuals in Figs. 2 and 3, and hence the period increases found are real.

The quadratic terms (Table 5) allow us to compute the rates of evolutionary period increase for the fundamental tone and first overtone of V367 Sct, which are listed in the fifth column of Table 5. These period increase rates are consistent with theoretical computations for the third crossing of the instability strip (Turner et al., 2006; Fadeyev, 2014).

4. Conclusions

To study the period changes of the bimodal Cepheid V367 Sct, we acquired 379 CCD frames in filters with the 60-cm telescope of Caucasian Mountain Observatory and made 282 magnitude estimates on photographic plates of Sternberg Astronomical Institute (Moscow); in addition, we compiled 4329 published photometric observations. We used the Hertzsprung method to determine 203 times of maximum light for both oscillations, which allowed us to construct O-C diagrams spanning a 113-year time interval. The O-C diagrams have the form of parabolas, which allowed us, for the first time, to determine the quadratic ephemerides and to compute the rates of evolutionary period changes: s/year and s/yr for the fundamental tone and the first overtone of V367 Sct, respectively, which is consistent with the theoretical results for the third crossing of the instability strip. The pulsation stability test proposed by Lombard & Koen (1993) confirmed that the increase of periods was real.

Acknowledgments

This study was made using equipment acquired within the framework of the Development Program of M.V. Lomonosov Moscow State University.

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Table 1. Parameters of -, -, -, and -band light curves of both oscillations of V367 Sct

Table 2. Fourier coefficients (cosine expansion) of the -, -, -, and -band light curves of the fundamental mode ( ) and first overtone ( ) of V367 Sct.

Table 3. Observational data for V367 Sct.

Table 4. Times of maximum light for V367 Sct

Table 5. Quadratic ephemerides in the form for the fundamental mode and first overtone of V367 Sct and period change rates

Table 6. Differences between the times of maximum light in the - and -band filters relative to the -band filter for the fundamental mode and first overtone of V367 Sct

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