1 INTRODUCTION

The star V647 Her is a bright component (V = 11\(^{{\text{m}}}_{.}\)2) in the astrometric binary system Gl 669 AB. Along with another star V639 Her (V = 12\(^{{\text{m}}}_{.}\)93), it forms a wide pair separated in projection by 16.8\('' \) [1, 2], and they both are studied as non-interacting single objects. These are flaring red dwarfs [3]; however, observations in different spectral ranges have revealed differences in manifestations of their activity [4], which are explained by their internal structure. Theoretical calculations [5] showed that stars with masses M < 0.35\({{M}_{ \odot }}\) are completely convective. According to the mass and effective temperature, V647 Her (M3.5), having a developed convective zone, still retains a radiative core, and V639 Her (M4.5) belongs to fully convective stars. The conditions for the development of activity in such stars are different, as well as mechanisms of its generation. This is confirmed by radio observations of both stars [4]. An important parameter that determines the topology of magnetic fields and the level of stellar activity is the rotation velocity of a star [6]. The rotation periods of many stars are determined from a series of spectral and photometric observations in the optical range [7, 8]. There are a small number of studies for both Gl 669AB stars, and the obtained results differ significantly [4]. The rapid rotation of the star V647 Her with a period of 0.95 days was reported in [9] based on the results of the analysis of data from the ASAS catalogue, but later a period of 20.14 days was adopted [10]. A similar value (19.81 days) was obtained from the SuperWASP photometric series [8]. In [11], when analyzing a sample of V-values from the SuperWASP catalog, a rotation period of 1.09 days was suspected. Photometric observations obtained with the 1.25-m telescope of the Crimean Astrophysical Observatory (CrAO) in 2019 showed the presence of rotational brightness modulation with a period of 20.69 days and a low probability of periodicity of 1.098 days [12]. In 2022, a new series of CCD observations was obtained at CrAO with the aim of determining the characteristics of the star’s brightness variability and studying their relation with activity processes.

This paper presents the results of an analysis of the brightness and color variations of the star V647 Her. It is shown that the observed rotational modulation with a period of 20.69 days is due to the presence of cool starspots. Using the 2019, 2022, and 2004 phase curves (SuperWASP catalogue), the distribution of starspots on the stellar surface at different epochs was examined, and their parameters were calculated within the framework of the zonal model.

2 PHOTOMETRIC OBSERVATIONS OF V647 HER AND COMPARISON STARS

Photometric observations of the star were carried out at the 1.25-m telescope AZT-11 of the Crimean Astrophysical Observatory using a CCD photometer equipped with the GE-2048 BI CCD camera. The specifications of the used СCD are as follows: (format 2k × 2k, pixel size 13.5 × 13.5 μm, field in the frame 9\(^{'}_{.}\)7 × 9\(^{'}_{.}\)7, image scale 0\(^{''}_{.}\)57/pixel with a 2 × 2 binning). Observations were carried out in the BV(RI)c bands in the Johnson–Cousins system.

Since July 5 to November 15, 2022 we obtained the photometric data for 48 observational nights. On each date, at least five records were made sequentially in each filter; the exposure time of one frame in the BV(RI)c filters was 60, 30, 10, and 5 s, respectively. In each filter, the resulting array of observations contains 609 frames; the journal of observations is presented in Table 1. In September and October, for the seven dates indicated in Table 2, observations were carried out in the monitoring mode lasting 1–3.5 hours. In this case, the filter was changed after recording one frame, and the exposure time in the corresponding filters remained the same.

Table 1.   Observations of V647 Her and comparison stars in 2022
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Table 2.   Brightness of the check star and V647 Her based on monitoring results in September and October 2022
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Image processing was performed using the MaximDL program; nearby stars TYC 2082-2143-1, (V = 11\(^{{\text{m}}}_{.}\)22) and TYC 2082-2142-1 (V = 11\(^{{\text{m}}}_{.}\)99) (SIMBAD database) were taken as comparison stars. Our estimates of brightness for V647 Her and the reference star TYC 2082-2142-1 were obtained in the instrumental system, and we also determined the differential values relative to the comparison star to rule out the influence of atmospheric extinction and erroneous measurements. Based on the results of monitoring the program and comparison stars, light curves were constructed according to which no regular variability during the night was revealed for both stars. The average star brightness values during the night were determined with an accuracy of 0\(^{{\text{m}}}_{.}\)006 (Table 2). Over the entire observation interval, the average brightness of the check star does not exceed 2σ; the average brightness level remains constant, equal to 0\(^{{\text{m}}}_{.}\)591 (±0.007). According to the light curves of the star V647 Her, its average brightness varies from night to night. Figure 1 shows the light curves for both stars based on observations in September–October; the \({{\langle {v}\rangle }_{{{\text{ch}}}}}\) values are shifted, ∆Vch = \({{\langle {v}\rangle }_{{{\text{ch}}}}}\) – 0\(^{{\text{m}}}_{.}\)31.

Fig. 1.
figure 1

Changes in the average brightness values of V647 Her in September–October 2022. The brightness values of the check star (triangles) are given for a zero-point, equal to –0.31; bars show standard deviation; dashed lines indicate monitoring dates.

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3 ANALYSIS OF BRIGHTNESS AND COLOR FOR V647 HER

The behavior of the brightness of V647 Her, according to the results of photometry in July–November 2022, is presented in instrumental values in Fig. 2a. The preliminary processing allowed us to exclude eight values related to the flare (JD 2459789) and random deviations from the data series (N = 609), and then the average values for the observation dates (N = 47) were determined. To compare with the 2019 results published in [12], we calculated the differential values relative to the brightness of the comparison star (Fig. 2b). The behavior of the star’s brightness variability in 2022 is the same as that in 2019; on both light curves the level of maximum brightness retains, but at some epochs the maximum and minimum values are not reached. In October–November, in the time span JD 2459854–2459899, the maximum brightness values were lower than the maximum level by ~7%, and the depth of minima became smaller by ~10–12%. The largest changes in brightness ∆V reached 0\(^{{\text{m}}}_{.}\)066, which is slightly different from these values in 2019, where ∆V = 0\(^{{\text{m}}}_{.}\)07. The average brightness level remains equal to 0\(^{{\text{m}}}_{.}\)17 (0.016).

Fig. 2.
figure 2

The behavior of the brightness of V647 Her according to observations in 2019 and 2022: (a) observation results for 2022; (b) series of ∆V-values after primary data processing for 2019 and 2022, ∆V are difference values relative to the comparison star TYC 2082-2143-1. The dotted line indicates the maximum level of brightness.

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An analysis of the light curve of the star by the Yurkevich, Scargle and Hartley methods in 2019 has shown that the ∆V-values vary with a period of 20.69 (0.07) days [12]. The same methods were used to analyze the light curve in 2022. The results of a search for periods in the range from 1 to 40 days confirmed the found value of the photometric period. Figure 3a shows the light curve in 2022 and the presence of periodic variability, represented by a sinusoid with a period of 20.69 days (Fig. 3b). The inset shows the Lomb–Scargle periodogram with a high peak at the frequency corresponding to this period. The lines indicate the FAP significance levels (0.3, 0.05, and 0.01) corresponding to 1σ, 2σ, and 3σ. A convolution of all data was performed with photometric elements HJD = 2453128.5102 + 20.69E, adopted in [12]. Taking into account that the amplitude of variability in October–November decreases, we constructed phase curves for this interval and for data obtained in July–September. The approximations of these curves by polynomials of the 4th and 5th degrees are presented in Fig. 3c. It can be seen that in October–November there were not only changes in the amplitude of variability but also in the shape of the phase curve, which shows another minimum to appear. Data for a series of residuals obtained after subtracting variability with a period of 20.69 days do not show significant changes exceeding the 2σ level (Fig. 3d). No further analysis was performed on a series of residuals.

Fig. 3.
figure 3

Changes in the brightness of V647 Her with a period of 20.69 days: (a) light curve based on observations in 2022 and errors in ∆V-values averaged on the observation date; (b) changes in the brightness of V647 Her with a period of 20.69 days, and the inset shows a period of 20.69 days according to the Lomb–Scargle analysis; (c) convolution of data on the intervals 05.07–28.09 (crosses) and 1.10–15.11 (filled circles), and lines show approximating polynomials; (d) a series of residuals after subtracting variability with P = 20.69 d and the standard deviation for the residuals. Dotted lines indicate ±2σ levels.

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The observed features of the brightness variability of V647 Her, such as small amplitude and a change in the shape of the curve, are typical for the red dwarfs with cool starspots on the surface. The presence of such starspots leads to a reddening of the star, which is clearly visible in its color indices in the red region of the spectrum. Figure 4a shows the brightness changes and V–I indices according to the V647 Her observations in 2022. The color indices vary in the range of 2.7–2.75, while at brightness minima the star becomes redder. A convolution of V–I values with a period of 20.69 days is shown in Fig. 4b. The amplitude of variability is ~0\(^{{\text{m}}}_{.}\)04, and the phase minimum is 0.70. After subtracting the contribution of the 20.69 d periodicity, a number of residuals did not show changes exceeding 2σ (Fig. 4c).

Fig. 4.
figure 4

Changes in the V–I color index with a period of 20.69 days: (a) changes in brightness and color index V–I and the corresponding rms; (b) convolution of V–I data with a period of 20.69 days and fitting of the phase curve by the 4th order polynomial (solid line); (c) a series of ∆(V–I) residuals after accounting for periodicity 20.69 d. Dashed lines mark σ-value and ±2σ levels.

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4 DISTRIBUTION OF STARSPOTS ON THE SURFACE OF THE STAR AND ESTIMATES OF THEIR PARAMETERS

The brightness and color of V647 Her, according to the Crimean observations in 2019 and 2022 and according to the 2004 data from the SuperWASP catalog, vary with a period of 20.69 days, which allows us to consider this value as a rotation period of the star. The phase curves plotted with this period represent the characteristics of rotational modulation produced due an inhomogeneous distribution of starspots on the surface of the star. We found that the shape of the phase curve, amplitude, and phase of the minimum vary, remaining stable for 40–100 days (Figs. 3c, 5). According to the phases of minimum, two types of phase curves can be distinguished: with one minimum, when rotational modulation is caused by the appearance of an area with a great starspot concentration on one of the hemispheres; and two minima, when such areas were observed on both hemispheres, as it was in October–November 2022. Table 3 shows data on the amplitudes and phases of minimum at the indicated intervals.

Fig. 5.
figure 5

Rotational modulation in brightness in 2019 and 2022. The phase curves (represented by polynomials) show changes in the amplitude and phase of minima in 2019 (thin line) and 2022 (thick line).

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Table 3.   Characteristics of rotational modulation in the brightness of V647 Her at different epochs (Prot = 20.69 days)
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The characteristics of rotational modulation change both on a short time scale and on a longer one, expressed in years. The maximum amplitude of rotation modulation increases by 30% in 2019 and 2022 as compared to 2004. Seasonal changes in the amplitude and phase of minima are caused by the evolution of starspots and their distribution on the surface. Changes on a longer scale indicate variations in the intensity of processes of starspot formation.

To estimate the parameters of starspots within the framework of the zonal model, the following photometric data are required: the value of the maximum brightness and its changes in the observation epoch and the values of the color indicators B–V, V–R, V–I [13]. Over a limited time interval, we can observe a certain maximum level of brightness corresponding to the minimum spottedness of the star at a given epoch, but the brightness in the absence of starspots (Vmax) is determined from long-term observations. For V647 Her, we constructed the combined light curve using the data from 1939 to 2018, and it shows that Vmax = 11\(^{{\text{m}}}_{.}\)1(±0.1) [14].

According to this value of maximum brightness and required input parameters, taking Teff = 3300 K [15] for the photosphere in the absence of starspots, we obtained the following estimates: the area occupied by starspots in 2004 is ~15% of the total surface area of the star, and in 2019 and 2022 it increases to 30%; the temperature of starspots is 2700–2800 K. According to the low-amplitude seasonal variations in brightness, the difference between the maximum and minimum values of the spotted area is 1–2%. The detailed calculations of the starspot parameters are being prepared for publication.

5 CONCLUSIONS

Photometric studies of the M dwarf V647 Her, carried out by us from the results of CCD observations in 2019 and 2022 at CrAO, have showed the presence of low-amplitude brightness variability with a period of 20.69 days. The phase of minimum and amplitude retain over 40–100 days. The V–I color indices change with the same period, and in the minimum of brightness, the star becomes redder. This type of variability indicates the presence of cool starspots on the surface of the star and their uneven distribution, leading to a modulation of brightness with the rotation period. We studied the rotational modulation in the light curve of the star for several years of observation and determined the maximum brightness level. The amplitude of rotational modulation does not exceed 0\(^{{\text{m}}}_{.}\)05. According to the phase curves, spottedness zones are usually found only on one of the hemispheres, at phases 0.6–0.7 at some epochs or at phases 0.1–0.2 at others. However, in October–November 2022, the concentration of starspots was observed in the indicated phases on both hemispheres. In 2004 (SuperWASP catalogue), one of the hemispheres remained more spotted, with starspot areas located at phases 0.43 and 0.17.

Based on the long-term data, including additions from publications and photometric catalogs, we estimated the maximum brightness of the star Vmax = 11\(^{{\text{m}}}_{.}\)1 and calculated the area and temperature of starspots within the framework of the zonal model. In 2004, starspots occupied 15% of the total surface area of the star, and in 2019 and 2022 the area increased up to 30%; the temperature of starspots was 2700–2800 K at a temperature of the quiet photosphere of 3300 K. The difference in the spottedness of the hemispheres of the star caused by an uneven seasonal distribution of starspots is 1–2%. Changes in the average annual brightness over a time span of several years indicate a change in the intensity of starspot formation processes, which is noticeable when comparing the starspot area in 2004 and at the present epoch.