Search for Evolutionary Period Changes in the Double-mode Cepheid V367 Sct Текст научной статьи по специальности «Физика»

Peremennye Zvezdy ( Variable ¡Stars) 44, No. 3, 2024 Received 28 April; accepted 24 May.

DOI: 10.24412/2221-0474-2024-44-28-41

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

L. N. Berdnikov1, A. A. Belinskii1, A. K. Dambis 1, E. N. Pastukhova2, M. A. Burlak1, N. P. Ikonnikova1, E. O. Mishin1, N. I. Shatskii1

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

For both periods of the bimodal Cepheid V367 Sct, O-C diagrams spanning a 113-year time interval are constructed. The O-C diagrams have the form of parabolas, allowing quadratic ephemerides and evolutionary period change rates to be determined for the first time, dPFu/dt = +0.233 (±0.020) s/yr and dPio/dt = +0.244 (±0.025) s/yr, for the fundamental tone and first overtone of V367 Sct, respectively, which are consistent with the results of theoretical computations for the third crossing of the instability strip. The test for stability of pulsations proposed by Lombard and Koen confirmed the reality of the evolutionary change of the periods.

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 5M©) 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 P = 4?946 and P = 4?685, 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 Pfu = 1?738 and P\O = 1"?270, 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 BVg'r'-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 (Ppu = 6d293) and the first overtone (P1O = 4d385) is described by Berdnikov et al. (2021).

Table 1 lists the BVg'r'-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 PFu fall within the domains of classical (DCEP) Cepheids and those for PO1, 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 E and the O-C residual, respectively; the sixth and seventh columns are the number of observations N 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 B band (and also in photographic, pg, magnitudes whose photometric system is close to that of the B band), and g' and r' bands relative to the V 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 V-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 A(O — C)j of consecutive O-C residuals from Table 4, A(O — C)j = (O — C)i+1 — (O — C)j, and plot the dependences of Pi = A(O — C)i/(Ei+1 — Ei) on Ej = (Ei + Ei+1)/2 for both oscillations of V367 Sct (Figs. 4 and 5). The Pj values, which have the meaning of average period in the epoch interval Ei - Ei+1, 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 BVg'r' 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: dP^/dt = +0.233 (±0.020) s/year and dP1O/dt = +0.244 (±0.025) 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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Figure 1: Phased B, V, g', and r' light curves for both oscillations of V367 Sct.

Figure 2: The O-C diagram for V367 Sct for linear (top panel) and quadratic (bottom panel) ephemeris of the fundamental tone (Table 5). The curve shows the parabola corresponding to the ephemeris (Table 5). Symbols are explained in the text.

Figure 3: The O-C diagram for V367 Sct for linear (top panel) and quadratic (bottom panel) ephemeris of the first overtone (Table 5). The curve shows the parabola corresponding to the ephemeris (Table 5). Symbols are explained in the text.

Figure 4: The dependence of P'(Fu) = ((O - C)m - (O - C)i)/(Em - E) on Ei = (E + Ei+1)/2 for the fundamental tone. The line corresponds to the behavior of O - C residuals in Fig. 2.

Figure 5: The dependence of P'(1O) = ((O - C)i+1 - (O - C)i)/(Ei+1 - E,) on E' = (E, + Ei+1)/2 for the first overtone. The line corresponds to the behavior of O-C residuals in Fig. 3.

Table 1. Parameters of B-, V-, g'-, and r'-band light curves of both oscillations of V367 Sct

Oscillation mode Filter Magnitude at Amplitude Intensity-mean

maximum light magnitude

Fundamental mode B 13.117 0.531 13.385

Fundamental mode V 11.433 0.379 11.618

Fundamental mode g' 12.292 0.438 12.505

Fundamental mode r' 10.551 0.303 10.704

First overtone B 13.225 0.352 13.385

First overtone V 11.486 0.244 11.618

First overtone g' 12.346 0.288 12.505

First overtone r' 10.607 0.201 10.704

Table 2. Fourier coefficients (cosine expansion) of the B-, V-, g'-, and r'-band light curves of the fundamental mode (PFu = 6?2866) and first overtone (PlO = 4?3863) of V367 Sct.

Oscillation Filter Ä21 R31 R41 021 031 041

mode Error Error Error Error Error Error

Fundamental mode B 0.11100 0.02040 0.01350 4.27050 2.29911 4.09857

±0.00081 ±0.00081 ±0.00031 ±0.00194 ±0.02297 ±0.05099

Fundamental mode g' 0.15596 0.03487 0.01320 4.48043 2.36722 6.24081

±0.00053 ±0.00053 ±0.00053 ±0.00356 ±0.01529 ±0.04022

Fundamental mode r' 0.16781 0.00839 0.02262 4.22781 1.72122 0.12706

±0.00002 ±0.00002 ±0.00002 ±0.00012 ±0.00232 ±0.00086

First overtone B 0.03281 0.00873 0.00002 5.40537 3.85542 2.34633

±0.00002 ±0.00002 ±0.00002 ±0.00056 ±0.00212 ±0.95915

First overtone V 0.12838 0.00423 0.00188 3.74491 1.48809 1.90353

±0.00060 ±0.00060 ±0.00060 ±0.00486 ±0.14274 ±0.32162

First overtone g' 0.08753 0.00652 0.00015 3.66465 3.60980 2.29634

±0.00002 ±0.00002 ±0.00002 ±0.00023 ±0.00308 ±0.13095

First overtone r' 0.03161 0.01210 0.02313 0.61989 2.03573 3.30126

±0.00003 ±0.00003 ±0.00003 ±0.00093 ±0.00243 ±0.00128

Table 3. Observational data for V367 Sct.

Data source Number of Type of JD interval

observations observations

Caucasian Mountain Observatory (this paper) 379 CCD, BVg'r' 2459403-2459438

Sternberg Astronomical Institute (this paper) 282 Photographic, pg 2432826-2448179

Published 314 Photographic, pg 2418529-2441926

Published 860 Photoelectric, BV 2437549-2453118

ASAS-3 223 CCD, V 2452135-2453228

ASAS-SN 2932 CCD, Vg' 2457061-2460044

Table 4. Times of maximum light for V367 Sct

Maximum, HJD Error, days Filter E O —C, days N Reference

V367 Sct-Fu

2424718.3580 0.0656 Pg -2794 0.1022 58 Efremov, KholoPov (1975)

2429752.9944 0.1084 Pg -1994 0.1966 35 Efremov, KholoPov (1975)

2433277.1252 0.0949 Pg -1434 0.1479 22 Sternberg Astronomical Institute

2433295.9548 0.1011 Pg -1431 0.0980 22 Efremov, KholoPov (1975)

2437707.3317 0.0315 V -730 -0.0578 25 Roslund, Pretorius (1962)

2437713.6682 0.0351 B -729 0.0007 24 Roslund, Pretorius (1962)

2438896.7396 0.0446 Pg -541 -0.0453 57 Efremov, KholoPov (1975)

2439035.2246 0.0469 Pg -519 -0.0101 78 Sternberg Astronomical Institute

2440344.1875 0.0396 Pg -311 -0.0282 75 Efremov, KholoPov (1975)

2440709.2236 0.0334 Pg -253 +0.0036 71 Sternberg Astronomical Institute

2441244.1650 0.0518 Pg -168 +0.0249 45 Efremov, KholoPov (1975)

2441665.7087 0.0586 Pg -101 -0.0743 35 Efremov, KholoPov (1975)

2441772.7581 0.0353 Pg -84 -0.0089 81 Sternberg Astronomical Institute

2442055.9425 0.0362 V -39 -0.0327 37 Madore, van den Bergh (1975)

2442062.1848 0.0447 B -38 -0.0684 36 Madore, van den Bergh (1975)

2442515.3697 0.0322 B 34 +0.0078 54 Madore et al. (1978)

2444346.7675 0.0243 B 325 +0.0908 124 Moffett, Barnes (1984)

2444365.6087 0.0118 V 328 +0.0373 44 Moffett, Barnes (1984)

2445699.7099 0.0165 V 540 -0.0151 50 Berdnikov (1986)

2446618.5607 0.0315 B 686 +0.0470 27 Berdnikov (1992a)

2446618.5714 0.0234 V 686 +0.0424 27 Berdnikov (1992a)

2447417.7103 0.0196 B 813 -0.0369 30 Berdnikov (1992b)

2447417.7136 0.0264 V 813 -0.0488 30 Berdnikov (1992b)

2447757.5945 0.0118 B 867 +0.0156 41 Berdnikov (1992c)

2447757.6289 0.0101 V 867 +0.0348 41 Berdnikov (1992c)

2447864.4644 0.0617 Pg 884 -0.0985 30 Sternberg Astronomical Institute

2448116.2532 0.0267 B 924 -0.0368 38 Berdnikov (1992d)

2448116.3004 0.0212 V 924 -0.0049 19 Berdnikov (1992d)

2448512.8153 0.0284 B 987 +0.0552 31 Berdnikov (1992e)

2448512.8284 0.0137 V 987 +0.0530 62 Berdnikov (1992e)

2448877.8204 0.0052 B 1045 +0.0559 824 Berdnikov, Ibragimov (1994a)

2448877.8671 0.0130 V 1045 +0.0875 83 Berdnikov, Ibragimov (1994a)

2449129.5138 0.0670 V 1085 +0.0070 45 Arellano Ferro et al. (1998)

2449223.9098 0.0123 V 1100 +0.0053 50 Berdnikov, Ibragimov (1994b)

2449223.9571 0.0108 B 1100 +0.0679 98 Berdnikov, Ibragimov (1994b)

2449538.5617 0.0663 V 1150 -0.0017 10 Berdnikov, Turner (1995a)

2449544.9139 0.0098 B 1151 +0.0726 164 Berdnikov et al. (1995)

2449551.2100 0.0122 V 1152 +0.0603 83 Berdnikov et al. (1995)

2449815.4734 0.0527 B 1194 +0.0255 15 Berdnikov, Turner (1995b)

2449815.5299 0.0644 V 1194 +0.0667 15 Berdnikov, Turner (1995b)

2449947.6206 0.0271 B 1215 +0.0160 56 Berdnikov et al. (1997)

2449960.2264 0.0525 V 1217 +0.0201 23 Berdnikov et al. (1997)

2450325.2512 0.0224 V 1275 +0.0407 33 Berdnikov et al. (1998)

2450325.2634 0.0136 B 1275 +0.0681 133 Berdnikov et al. (1998)

2450369.2132 0.0132 B 1282 -0.0343 28 Berdnikov, Turner (1998a)

2450369.2757 0.0162 V 1282 +0.0129 28 Berdnikov, Turner (1998a)

2450577.0441 0.0185 V 1315 +0.1064 35 Berdnikov, Turner (1998b)

2450809.9265 0.0225 V 1352 +0.1413 45 Ignatova, Vozyakova (2000)

2450816.1151 0.0302 B 1353 +0.0520 44 Ignatova, Vozyakova (2000)

2450904.1837 0.0210 B 1367 +0.0161 94 Berdnikov, Turner (2000)

2450904.2879 0.0271 V 1367 +0.1051 48 Berdnikov, Turner (2000)

2451269.2451 0.0352 B 1425 +0.0731 23 Berdnikov, Turner (2001)

2451653.1203 0.0108 V 1486 +0.0493 21 Berdnikov, Caldwell (2001)

2451653.1456 0.0256 B 1486 +0.0898 42 Berdnikov, Caldwell (2001)

2452074.7521 0.0155 V 1553 +0.0382 54 ASAS

2452414.5353 0.0282 V 1607 -0.0102 50 ASAS

Table 4. Continued

Maximum, HJD Error, days Filter E O-C, days N Reference

V367 Sct-Fu

2452704.0885 0.0190 V 1653 +0.0568 66 Berdnikov et al. (2019)

2452704.1182 0.0191 V 1653 +0.0865 48 ASAS

2453031.3463 0.0198 V 1705 +0.0694 59 ASAS

2457172.3183 0.0037 V 2363 +0.1306 110 ASAS-SN

2457543.6319 0.0035 V 2422 +0.1467 99 ASAS-SN

2457575.1390 0.0072 V 2427 +0.1880 60 ASAS-SN

2457795.3714 0.0083 V 2462 +0.1591 60 ASAS-SN

2457927.5295 0.0028 V 2483 +0.1604 154 ASAS-SN

2458009.3293 0.0083 V 2496 +0.1490 60 ASAS-SN

2458254.7019 0.0083 V 2535 +0.0876 62 ASAS-SN

2458311.4215 0.0035 V 2544 +0.1687 120 ASAS-SN

2458336.4655 0.0130 g' 2548 +0.1373 60 ASAS-SN

2458399.3794 0.0093 g' 2558 +0.1194 59 ASAS-SN

2458525.2606 0.0105 g' 2578 +0.1370 55 ASAS-SN

2458613.3781 0.0112 g' 2592 +0.1501 60 ASAS-SN

2458619.6996 0.0076 g' 2593 +0.1784 70 ASAS-SN

2458625.9558 0.0110 g' 2594 +0.1414 55 ASAS-SN

2458669.9773 0.0129 g' 2601 +0.1107 74 ASAS-SN

2458695.2601 0.0240 g' 2605 +0.2208 59 ASAS-SN

2458714.0785 0.0070 g' 2608 +0.1596 60 ASAS-SN

2458764.4038 0.0078 g' 2616 +0.1395 70 ASAS-SN

2458764.4232 0.0093 g' 2616 +0.1589 54 ASAS-SN

2458865.1417 0.0135 g' 2632 +0.1866 59 ASAS-SN

2459016.1705 0.0095 g' 2656 +0.1791 69 ASAS-SN

2459060.1976 0.0094 g' 2663 +0.1539 74 ASAS-SN

2459097.9658 0.0062 g' 2669 +0.1631 70 ASAS-SN

2459135.7134 0.0098 g' 2675 +0.1516 60 ASAS-SN

2459204.9781 0.0186 g' 2686 +0.1914 58 ASAS-SN

2459223.7966 0.0075 g' 2689 +0.1303 55 ASAS-SN

2459362.2602 0.0079 g' 2711 +0.1440 69 ASAS-SN

2459362.2899 0.0085 g' 2711 +0.1737 84 ASAS-SN

2459362.3011 0.0138 g' 2711 +0.1850 60 ASAS-SN

2459412.5887 0.0106 g' 2719 +0.1271 55 ASAS-SN

2459418.9106 0.0174 g' 2720 +0.1558 60 ASAS-SN

2459425.2103 0.0121 g' 2721 +0.1624 54 ASAS-SN

2459437.8389 0.0212 g' 2723 +0.2046 93 Sternberg Astronomical Institute

2459438.0193 0.0153 V 2723 +0.2877 95 Sternberg Astronomical Institute

2459444.2310 0.0096 B 2724 +0.2214 91 Sternberg Astronomical Institute

2459569.9590 0.0125 g' 2744 +0.1680 56 ASAS-SN

2459576.2545 0.0073 g' 2745 +0.1703 70 ASAS-SN

2459595.1616 0.0216 g' 2748 +0.1979 60 ASAS-SN

2459607.7585 0.0138 g' 2750 +0.2084 66 ASAS-SN

2459645.4690 0.0089 g' 2756 +0.1599 65 ASAS-SN

2459802.7950 0.0158 g' 2781 +0.1564 57 ASAS-SN

2459809.1282 0.0082 g' 2782 +0.1965 73 ASAS-SN

2459853.1872 0.0111 g' 2789 +0.2031 68 ASAS-SN

2459872.0948 0.0111 g' 2792 +0.2312 72 ASAS-SN

2459878.3109 0.0111 g' 2793 +0.1542 61 ASAS-SN

V367 Sct-1O

2424465.1663 0.0778 pg -4035 +0.1996 53 Efremov, Kholopov (1975)

2430077.6886 0.0999 pg -2755 +0.2456 29 Efremov, Kholopov (1975)

2433278.3314 0.0630 pg -2025 +0.0229 22 Sternberg Astronomical Institute

2433295.8936 0.0844 pg -2021 +0.0461 22 Efremov, Kholopov (1975)

2437702.5100 0.0354 V -1016 -0.0132 25 Roslund, Pretorius (1962)

2437742.2970 0.0297 B -1007 +0.3159 20 Roslund, Pretorius (1962)

2439031.1910 0.0379 pg -713 +0.0942 77 Sternberg Astronomical Institute

2439044.1764 0.0342 pg -710 -0.0747 70 Efremov, Kholopov (1975)

2440649.0281 0.0495 pg -344 -0.0404 71 Efremov, Kholopov (1975)

2440706.0701 0.0321 pg -331 -0.0001 71 Sternberg Astronomical Institute

2441477.8078 0.0418 pg -155 +0.0220 67 Efremov, Kholopov (1975)

2441771.5517 0.0328 pg -88 -0.0121 81 Sternberg Astronomical Institute

2442052.0901 0.0361 V -24 -0.1023 37 Madore, van den Bergh (1975)

2442056.4832 0.0456 B -23 -0.0892 36 Madore, van den Bergh (1975)

2442442.3659 0.0771 B 65 -0.0643 54 Madore, van den Bergh (1975)

2442468.6626 0.0373 V 71 -0.0807 31 Madore et al. (1978)

2442951.1169 0.0722 B 181 +0.0561 8 Dean (1977)

2442951.2034 0.0464 V 181 +0.1378 8 Dean (1977)

2444358.5741 0.0202 B 502 +0.0094 118 Moffett, Barnes (1984)

2444362.9616 0.0135 V 503 +0.0074 44 Moffett, Barnes (1984)

2445695.7986 0.0172 V 807 -0.1186 50 Berdnikov (1986)

2445695.9764 0.0574 B 807 +0.0639 23 Berdnikov (1986)

2446621.1122 0.0283 B 1018 +0.0180 27 Berdnikov (1992a)

2446621.1396 0.0260 V 1018 +0.0407 27 Berdnikov (1992a)

Table 4. Continued

Maximum, HJD Error, days Filter E O —C, days N Reference

V367 Sct-1O

2447419.1307 0.0294 У 1200 +0.0078 30 Berdnikov (1992b)

2447419.1368 0.0166 B 1200 +0.0186 30 Berdnikov (1992b)

2447756.7685 0.0109 B 1277 +0.0248 41 Berdnikov (1992c)

2447756.7889 0.0118 V 1277 +0.0404 41 Berdnikov (1992c)

2447861.9297 0.0377 PG 1301 -0.0480 30 Sternberg Astronomical Institute

2448111.9421 0.0270 B 1358 +0.0338 38 Berdnikov (1992d)

2448112.0003 0.0232 V 1358 +0.0873 19 Berdnikov (1992d)

2448510.8983 0.0309 V 1449 -0.0266 62 Berdnikov (1992e)

2448510.9268 0.0110 B 1449 +0.0066 31 Berdnikov (1992e)

2448879.2528 0.0154 V 1533 +0.0090 83 Berdnikov, Ibragimov (1994a)

2448879.2664 0.0044 B 1533 +0.0273 823 Berdnikov, Ibragimov (1994a)

2449133.4953 0.0611 V 1591 -0.0638 47 Arellano Ferro et al. (1998)

2449133.6899 0.0450 B 1591 +0.1356 59 Arellano Ferro et al. (1998)

2449221.3067 0.0283 V 1611 +0.0526 50 Berdnikov, Ibragimov (1994b)

2449221.3502 0.0078 B 1611 +0.1009 98 Berdnikov, Ibragimov (1994b)

2449545.7154 0.0098 B 1685 -0.0052 164 Berdnikov et al. (1995)

2449545.7869 0.0135 V 1685 +0.0616 83 Berdnikov et al. (1995)

2449817.4896 0.0214 B 1747 -0.0853 15 Berdnikov, Turner (1995b)

2449949.1196 0.0066 B 1777 +0.0023 56 Berdnikov et al. (1997)

2449962.2720 0.0384 V 1780 -0.0043 23 Berdnikov et al. (1997)

2450321.8331 0.0152 B 1862 +0.0123 133 Berdnikov et al. (1998)

2450321.8959 0.0296 V 1862 +0.0703 33 Berdnikov et al. (1998)

2450370.0671 0.0217 B 1873 +0.0140 28 Berdnikov, Turner (1998a)

2450370.1146 0.0216 V 1873 +0.0568 28 Berdnikov, Turner (1998a)

2450576.2106 0.0143 V 1920 +0.0697 35 Berdnikov, Turner (1998b)

2450812.9499 0.0347 B 1974 +0.0373 45 Ignatova, Vozyakova (2000)

2450813.0184 0.0300 V 1974 +0.1011 45 Ignatova, Vozyakova (2000)

2450905.0017 0.0156 B 1995 +0.0095 94 Berdnikov, Turner (2000)

2450905.2123 0.0108 V 1995 +0.2153 48 Berdnikov, Turner (2000)

2451273.2650 0.0364 B 2079 -0.0460 23 Berdnikov, Turner (2001)

2451655.0424 0.0299 V 2166 +0.2537 21 Berdnikov, Caldwell (2001)

2451655.0956 0.0200 B 2166 +0.3116 42 Berdnikov, Caldwell (2001)

2452128.4385 0.0219 V 2274 +0.0970 71 ASAS

2452374.1251 0.0498 B 2330 +0.2426 18 Berdnikov et al. (2019)

2452584.3868 0.0179 V 2378 +0.0317 83 ASAS

2452702.9445 0.0220 V 2405 +0.2012 66 Berdnikov et al. (2019)

2453027.2664 0.0272 V 2479 +0.0518 61 ASAS

2457175.3384 0.0032 V 3425 +0.1529 110 ASAS-SN

2457543.6916 0.0046 V 3509 +0.1873 99 ASAS-SN

2457578.8474 0.0096 V 3517 +0.2653 60 ASAS-SN

2457798.0453 0.0108 V 3567 +0.2257 60 ASAS-SN

2457929.5932 0.0028 V 3597 +0.2312 154 ASAS-SN

2458012.8846 0.0125 V 3616 +0.2124 60 ASAS-SN

2458253.9979 0.0137 V 3671 +0.1646 62 ASAS-SN

2458306.6982 0.0041 V 3683 +0.2480 120 ASAS-SN

2458398.7412 0.0078 g' 3704 +0.1678 59 ASAS-SN

2458438.2560 0.0122 g' 3713 +0.2200 100 ASAS-SN

2458547.9484 0.0091 g' 3738 +0.2936 80 ASAS-SN

2458622.4468 0.0046 g' 3755 +0.2513 70 ASAS-SN

2458675.0362 0.0125 g' 3767 +0.2237 69 ASAS-SN

2458692.5485 0.0108 g' 3771 +0.1971 60 ASAS-SN

2458710.1785 0.0148 g' 3775 +0.2881 79 ASAS-SN

2458727.6876 0.0108 g' 3779 +0.2582 100 ASAS-SN

2458767.1457 0.0044 g' 3788 +0.2535 70 ASAS-SN

2458859.1765 0.0114 g' 3809 +0.2047 58 ASAS-SN

2459017.0831 0.0064 g' 3845 +0.2604 70 ASAS-SN

2459060.9275 0.0125 g' 3855 +0.2573 71 ASAS-SN

2459205.5950 0.0121 g' 3888 +0.2282 58 ASAS-SN

2459227.5498 0.0039 g' 3893 +0.2592 137 ASAS-SN

2459240.7298 0.0105 g' 3896 +0.2850 79 ASAS-SN

2459328.3894 0.0152 g' 3916 +0.2496 100 ASAS-SN

2459359.1290 0.0127 g' 3923 +0.2960 73 ASAS-SN

2459433.5973 0.0109 g' 3940 +0.2236 57 ASAS-SN

2459442.4081 0.0157 g' 3942 +0.2649 93 Sternberg Astronomical Institute

2459442.4219 0.0060 B 3942 +0.3268 91 Sternberg Astronomical Institute

2459442.4360 0.0231 V 3942 +0.3363 95 Sternberg Astronomical Institute

2459464.3326 0.0138 g' 3947 +0.2657 100 ASAS-SN

2459530.1323 0.0088 g' 3962 +0.2942 80 ASAS-SN

2459573.9479 0.0065 g' 3972 +0.2623 70 ASAS-SN

2459587.0331 0.0118 g' 3975 +0.1932 54 ASAS-SN

2459731.8671 0.0116 g' 4008 +0.3306 143 ASAS-SN

2459810.6978 0.0183 g' 4026 +0.2358 52 ASAS-SN

2459810.7060 0.0074 g' 4026 +0.2441 71 ASAS-SN

2459823.9061 0.0124 g' 4029 +0.2899 88 ASAS-SN

2459845.8942 0.0164 g' 4034 +0.3543 78 ASAS-SN

Table 5. Quadratic ephemerides in the form MaxHJD = HJDo + P • E + q • E2 for the fundamental mode and first overtone of V367 Sct and period change rates dp/dt

Oscillation mode HJDo P, days q, days dp/dt, s/yr

Error Error Error Error

Fundamental tone 2442301.4091 6.293177564 0.23276399 • 10-°Y 0.2334

±0.0068 ±0.000004929 ±0.2039 • 10-°8 ±0.0205

First overtone 2442157.4263 4.384747197 0.16984058 • 10-°7 0.2445

±0.0116 ±0.000006137 ±0.1764 • 10~8 ±0.0254

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

Oscillation mode ATB, days Error ATg', days Error

Fundamental tone +0.0152 +0.0974

±0.0478 ±0.0478

First overtone +0.0047 -0.0434

±0.0943 ±0.0636