Long-Term Cyclic Variability of YZ CMi in the Context of Solar and Stellar Physics

TL;DR

This study analyzes long-term photometric data of YZ CMi, revealing cyclic brightness variations, uneven spot distribution, and active longitude shifts, providing insights into stellar activity compared to the Sun.

Contribution

It presents a detailed long-term analysis of YZ CMi's activity cycles, spot distribution, and active longitude behavior, highlighting differences from solar activity.

Findings

27.5-year brightness cycle with 0.2-0.3 magnitude amplitude

Uneven spot distribution with higher concentration at specific longitudes

Active longitude shifts occurring approximately every 6 years

Abstract

Manifestations of activity on the YZ CMi (M4.5Ve) flare star which has a rotation period of 2.77 days and belongs to a group of activity-saturated stars, are considered from long-term photometric data together with photographic measurements from 1926 to 2009. Long-term changes in yearly mean brightness of the star are found on a time scale of 27.5 years with an amplitude of $0.2 - 0.3^m$ that indicate variations in development of surface inhomogeneities and a large degree of surface spottedness in the maximum activity. Spots are distributed unevenly over the surface, their concentration is higher at certain longitudes spaced by intervals equal to 0.6 phases of the rotation period. The recovery of active longitude (a possible "flip-flop" effect) occurs over a period of about 6 years. We note differences in activity of this star from typical for the Sun and solar-like stars, which are associated with its dynamic characteristics $P_{cyc}$ and $P_{rot}$ and its inner structure.

Figures

b presents the periodogram obtained by the Yurkevich method, which shows a significant peak corresponding to a period of 27.5 years. Figure 2 shows the data convolution for this period. The large scatter of values in the maximum and minimum leaves uncertainty in estimation of the cycle amplitude. According to our data in the maximum of the light curve, i.e. without spots, $B=12.71^{\textrm{m}}$, the same maximum level was noted by Alekseev (2001). The amplitude of cyclic variability is $0.2-0.3^{\textrm{m}}$, and the maximum of activity (the smallest brightness of the star) lasts for 4–5 years

Full text

1. 1 INTRODUCTION
2. 2 FLARE ACTIVITY
3. 3 DETECTION OF SURFACE INHOMOGENEITIES
4. 4 LONG-TERM VARIATIONS IN BRIGHTNESS OF YZ CMi; A SEARCH FOR THE CYCLE
5. 5 ROTATIONAL MODULATION IN BRIGHTNESS AND ACTIVE LONGITUDES
6. 6 CONCLUSIONS

1 INTRODUCTION

One of the key goals of solar and stellar physics is a study of physical processes on the surface of low-mass active stars within time scales comparable to their lifetimes. The analysis of observations in different spectral ranges can be used to test and develop the stellar dynamo theory. Thus, the study of X-ray fluxes from the coronae of active late-type stars on the main sequence as a function of the stellar rotation (Wright et al., 2011; Reiners et al., 2014) revealed two features in their behavior: fast-rotating stars having a very high level of coronal activity that practically is not changed when the speed of axial rotation decreases (stars with saturated activity) and stars with the solar-type activity that decreases when their rotation is decelerated (stars with entire complex of the solar-type activity, including a regular cycle). More refined analysis (Nizamov et al., 2017) has clearly shown that the transition from the saturated regime, which is typical for young stars, to the solar-type activity occurs in G, K, and M stars at different periods of the axial rotation. The saturated activity regime is replaced by the solar-type activity when the rotation periods are 1.1, 3.3, and 7.2 days for stars of G2, K4, and M3 spectral classes, respectively. A detailed examination of G–M dwarfs reveals a phenomenological similarity of their activity and differences due to physical parameters, interior structure, magnetic field intensity, and age.

On the whole, the level of stellar activity is characterized by such parameters as the flare energy, starspot area, and variations in radiation intensity in the optical and X-ray ranges. Baliunas et al. (1996) showed a relation between the observed parameters – the rotation period of a star ($P_{\textrm{rot}}$) and duration of its cycle ($P_{\textrm{cyc}}$) – and theoretical dynamo number $D$ expressed as $P_{\textrm{cyc}}/P_{\textrm{rot}}\sim D^{\,l}$. For F–G–K stars from the HK project with periods over 5 days and cycles no longer than 20 yr, $l=0.74$. This ratio allows us to choose a group of stars for which the number of revolutions necessary for development of a cycle is determined according to one law (with the same $l$).

For stars with long cycles, $l=0.84$ (Katsova et al., 2015); for M-dwarfs, $l=0.89$ (Suárez Mascareño, 2016). However, cycles of the considered M-dwarfs were found from the short time series; only some of them have several decades of available data.

In this context, observations of the long-term variability of the V833 Tau K-dwarf with saturated activity (Bondar, 2015; 2017) are of interest. This star is characterized by a very powerful corona: the coronal activity index $\log L_{\textrm{X}}/L_{\textrm{bol}}$ reaches –3.04. Alongside the precisely determined rotational modulation with a period of 1.79 days, long-term variations of optical radiation are revealed on a time scale of about 19 years. This indicates that in the saturated activity mode magnetic fields of different scales coexist and the process of cycle formation starts rather early when this regime has not yet been replaced by the solar-type activity.

There is another star with saturated activity, for which long-term data series are available; this makes it possible to draw conclusions about the character of surface activity associated with starspot distribution. This star is a rapidly rotating red dwarf YZ CMi ($V=11.05$, M4.5 Ve, $P_{\textrm{rot}}=2.77$ days) in the solar vicinity ($d=5.8$ pc). The star is young and is undergoing the stage of arriving of a red dwarf on the main sequence (Eggen, 1968). Its ratio of X-ray luminosity to bolometric luminosity is evaluated as $\log L_{\textrm{X}}/L_{\textrm{bol}}=-2.73$. Its mass and radius parameters, $M/M_{\odot}=0.31$, $R/R_{\odot}=0.29$, indicate that it belongs to fully convective stars. The ratio $M/M_{\odot}=0.35$ (Chabrier and Baraffe, 1997) determines the boundary between two groups of stars – those with radiative cores and those with fully convective cores. Other physical properties of YZ CMi are given by Gershberg et al. (1999) and Bychkov et al. (2017). Recently, the studies of red dwarf activity have paid great attention to the late M-stars and brown dwarfs. However, detailed studies of different ranges of the electromagnetic spectrum cover small time intervals, that are insufficient for the solution of fundamental problems related to the cyclic magnetic activity of low-mass stars.

YZ CMi belongs to a small group of M-dwarfs with long-term data series that allow us to make conclusions about their activity associated with the starspot distribution. This paper presents data on the frequency and energy of flares, surface spot area indicating a high star activity. The goal of this paper is to determine whether a process of starspot formation on this star is cyclic, to compare parameters of the cycle and the level of stellar activity with the activity of the Sun and solar-type stars. The research sets the following tasks: to analyze the long-term photometric data covering a time interval of more than 80 years, from 1926 to 2009; to search for the cycle and determine its parameters; to study the rotational modulation in brightness and distribution of spots at different epochs; to compare the level of magnetic activity of the star and solar-like stars by their dynamic characteristics $P_{\textrm{cyc}}$ and $P_{\textrm{rot}}$ associated with the dynamo number.

2 FLARE ACTIVITY

Development of flare activity in the YZ CMi star is detected at all wavelengths – from the X-ray to radio ranges. In the optical range, brightness variations can reach $1^{\textrm{m}}-3^{\textrm{m}}$ with a flare duration of tens of minutes; less bright flares ($<0.6^{\textrm{m}}$) are observed during several minutes and even fractions of a minute; series of flares with different amplitudes and durations are often detected also. The flare amplitude increases towards short wavelengths. The level of flare activity of YZ CMi is comparable to UV Cet, a star with powerful flares that lent its name to the entire class of red dwarfs with flaring activity. No time dependence was revealed in the activity of YZ CMi. The flare frequency is two to three events per 10 h, but sometimes the interval between flares is 20 min and periods of quiet brightness continue for several days or even tens of days. YZ CMi is one of the three stars closest to the Sun, the energy of powerful flares on which by several orders of magnitude exceeds the energy of the strongest solar flares ($E=10^{32}$ erg). These events can happen several times a year (Osten et al., 2016).

In 2008, the flare with a maximum duration of 1 hour and brightness variation up to 5.68${}^{\textrm{m}}$ was registered on the star (Zhilyaev et al., 2011), and in 2009 the brightness increased by almost 6${}^{\textrm{m}}$ during a flare that lasted for 7 h (Kowalski et al., 2010). The total energy of these flares was $\sim 10^{34}-10^{35}$ erg, and changes observed in the optical spectrum were accompanied by amplification of the emission in lines and in radiation in the continuum. This suggests that there are different mechanisms of heating, the effect of which varied within different phases of flares (Kowalski et al., 2010).

3 DETECTION OF SURFACE INHOMOGENEITIES

The kind of brightness variability of YZ CMi is typical for BY Dra-type stars. Active flare manifestations make it difficult to study the surface inhomogeneities, thereby systematic observations are required for the detection and examination of spots. Low-amplitude variations of YZ CMi luminosity with 2.77-day periods were discovered by Chugainov (1974) and confirmed by Pettersen et al. (1983). The phase light curves showed that the modulation of amplitude in 1972–1973 was 0.12–0.15${}^{\textrm{m}}$, while in 1979–1980 it was 0.18${}^{\textrm{m}}$. The brightness modulation with a rotation period is associated with the asymmetric starspot distribution.

A convincing evidence for the presence of starspots was obtained by observations in the IR range at a wavelength of $12\;\mu$m (Katsova and Tsikoudi, 1993) with the use of IRAS data. The IR excesses (differences between the flux $\lambda=12\;\mu$m calculated according to the surface temperature and the observed value) were compared with the X-ray radiation $\log(L_{\textrm{X}}/L_{\textrm{bol}})$ for 17 flare dM-stars and 14 G–K dwarfs. In the diagram $(m_{\textrm{obs}}-m_{\textrm{cal}})\lambda-\log(L_{\textrm{X}}/L_{\textrm{bol}})$, YZ CMi and other dM-stars are located in the saturation region, where $\log(L_{\textrm{X}}/L_{\textrm{bol}})=-3$, and they practically do not vary when the color excess increases. Among the studied stars, YZ CMi shows the greatest color excess. This feature indicates the presence of cool spots covering a considerable fraction of its surface (filling factor is close to 1). In models using observations from 1996–1997 (Zboril, 2003), cool spots with $T\sim 2800$ K cover 10–25% (for angles of inclination $i=60^{\circ}$ and $i=75^{\circ}$). The temperature of spots is 3000–3100 K based on the results of broad-band photometry (Alekseev and Bondar, 1998; Alekseev, 2001; Alekseev and Kozhevnikova, 2017); at certain epochs, the spots cover up to 38% of the star surface, concentrating near the latitudes of $10^{\circ}-15^{\circ}$.

One of the features of color characteristic of the star is that it becomes bluer at the epoch of higher activity. Observations by Amado et al. (2001) in 1996–1997 showed that color indicators $(U-B)$ and $(B-V)$ are changed in anti-correlation with $V$-values and color indicators in the red range. The star became bluer in the short wave range, when its color increased in the red part of the spectrum. This means that the active regions on the star surface include not only cool dark spots but facula regions also. Drawing an analogy with the known 11-year solar cycle, we can expect that the epochs of occurrence of large active regions on the surface of the star are changed by epochs of less spottedness. According to observations in 1926–1943 from the Harvard photographic collection Phillips and Hartmann (1978) suspected the cyclicity in spot development and estimated a cycle length of about 30 years. Data on measurements from the Sonneberg Observatory collection (Bondar, 1995; 1996), as well as photometric observations performed in 1994–1997 (Alekseev and Bondar, 1998), which supplement the photographic data, confirmed the variability in yearly mean brightness of the star over the indicated time span. However, due to the lack of observations during some years and the insufficient length of data series, these conclusions need further confirmation.

4 LONG-TERM VARIATIONS IN BRIGHTNESS OF YZ CMi; A SEARCH FOR THE CYCLE

Estimations of the YZ CMi brightness obtained from archives of the Harvard Observatory and the Sonneberg Observatory correspond to the photometric $B$-values. In order to study the behavior of brightness of the YZ CMi luminosity over a long interval, we supplemented these data by the results obtained at the Crimean Astrophysical Observatory in 1994–1997 with the 1.25-m telescope (Alekseev and Bondar, 1998), and taken from the published photometric data (Andrews, 1968; Amado, 2001) and the ASAS photometric catalog (Pojmanski, 1997). Based on all these data, the yearly mean $B$-values were calculated. The reduction of $V$-magnitudes from the ASAS catalog was performed with the value of $B-V=1.606$; the correction of $B$-values from Phillips and Hartmann (1978) was $-0.2^{\textrm{m}}$. The compiled light curve presents long-term variations from 1926 to 2009 (Fig. 1a).

The AVE software package [http://www.gea.cesca.es] was used to determine the periodicity based on a generated data series containing 65 points by the Yurkevich and Hartley methods for periods $<50$ years. Figure 1b presents the periodogram obtained by the Yurkevich method, which shows a significant peak corresponding to a period of 27.5 years. Figure 2 shows the data convolution for this period. The large scatter of values in the maximum and minimum leaves uncertainty in estimation of the cycle amplitude. According to our data in the maximum of the light curve, i.e. without spots, $B=12.71^{\textrm{m}}$, the same maximum level was noted by Alekseev (2001). The amplitude of cyclic variability is $0.2-0.3^{\textrm{m}}$, and the maximum of activity (the smallest brightness of the star) lasts for 4–5 years. The obtained result, $P_{\textrm{cyc}}=27.5(2)$ years, agrees with the 30-year cycle supposed earlier by Phillips and Hartmann (1978) and differs from the 10.6-year cycle by Suárez Mascareño et al. (2016). They found this value from the analysis of shorter row of data covering $\sim 9$ years.

5 ROTATIONAL MODULATION IN BRIGHTNESS AND ACTIVE LONGITUDES

According to Chugainov (1974) and Pettersen et al. (1983) the stellar brightness varies within $0.12-0.15^{\textrm{m}}$ with a period of 2.77 days, which is equal to the period of rotation. This type of variability is produced by the uneven spot distribution over the surface. The amplitude of modulation usually does not exceed 0.1${}^{\textrm{m}}$ (Alekseev, 2001), but it can increase up to 50% during some epochs. We studied the rotational modulation of brightness using the photometric data from the ASAS-catalog for 2001–2009. Upon processing, excluding measurements with a large error and flares, 533 $V$-values were included in the data series. Cyclic changes with a period of 27.5 years were subtracted from the initial series as the second-degree polynomial, and the obtained residuals of $\Delta V$ values are used to construct phase curves (Fig. 3) with the indicated rotation period and an arbitrarily chosen initial epoch $T_{0}=2452894.9005$.

We considered phase curves for the seasons of 2003–2009 with the densest data. The result presented in Fig. 4 shows the presence of rotational modulation with an amplitude $<0.1^{\textrm{m}}$. Spots cover both hemispheres and concentrate at active longitudes separated by $216^{\circ}$. The active region producing the highest amplitude of modulation was observed in 2003, 2006, and 2009 at phase $\varphi=0.25$; in 2008, the active region was amplified at phase $\varphi=0.85$, while it was weakly noticeable in 2004. In 2007, a concentration of spots with a phase of 0.5 was observed. The change of active longitude within about 3 years was registered by the observations during the 1993–1999 seasons (Alekseev, 2001). However, a cycle of change of the dominating longitude is not obvious, and we can only suppose that it is recovered within 3–6 years.

These results and the results published earlier have shown that the amplitude of rotational modulation of YZ CMi varies within the limits of 0.03-0.11${}^{\textrm{m}}$, increasing close to the maximum of activity and decreasing at the epoch of decreasing activity (Fig. 5). The data considered here do not cover all phases of the activity cycle, but they allow us to suggest that $A_{\textrm{mod}}$ changes cyclic as the amplitude of the cycle. This means that the unevenness of spot distribution increases upon cycle development, i.e. with an increasing of the total spottedness area; wherein one of the surfaces is more occupied by spots than the other one, while at minimum of activity spottedness of both hemispheres is almost equal and the rotational modulation is minimal. Calculations of starspot areas (Alekseev, 2001) show that at the maximum activity the area of starspots in one hemisphere is four times larger than in the other, and when the activity falls, the ratio of areas is $S_{\textrm{max}}/S_{\textrm{min}}\sim 1.5$.

6 CONCLUSIONS

YZ CMi is one of the few almost fully convective stars with a very strong magnetic field, about 4 kG (Reiners and Basri, 2007; Bychkov et al., 2017). The magnetic activity on YZ CMi is characterized as flares typical for the UV Cet-type stars and surface spots inherent to BY Dra-type stars. A length of the discovered activity cycle of the star associated with starspot formation is 27.5 years. In order to maintain this cycle, the star performs tens of times more turnovers than the Sun or other slowly rotating G–M dwarfs with cyclic activity. The considerable amplitude of the cycle (more than 0.2${}^{\textrm{m}}$) indicates an increasing of the star spottedness, up to 38%  of its total area in the maximum of the activity (Alekseev and Kozhevnikova, 2017). The large area and high flare energy are features of difference in the activity of this star from those typical for the Sun and other low-mass stars. Ratio $P_{\textrm{cyc}}/P_{\textrm{rot}}$ is about $3.6\times 10^{3}$, and the star does not belong to the G–K ensemble or early M-dwarfs, which have the similar relationship between $P_{\textrm{cyc}}/P_{\textrm{rot}}$ and $1/P_{\textrm{rot}}$. The existence of active longitudes, and probably their cyclic change within the range of $\sim 6$ years (manifestation of the “flip-flop” effect), is observed in the spot distribution over the stellar surface. This indicates the considerable role of the large-scale magnetic field in development of activity.

Thus, there are known two stars, V833 Tau and YZ CMi, K and M dwarfs, with activity saturation for which there is a long-term monitoring of optical variability. Being young fast-rotating objects, they possess very powerful coronae (the density at the corona base is tenfold higher than the solar value (Katsova et al., 1987), the ratio of X-ray to the bolometric luminosity $L_{\textrm{X}}/L_{\textrm{bol}}$ exceeds $10^{-3}$). These stars demonstrate a complex of non-stationary and quasi-stationary phenomena indicative of the presence of both large-scale and local magnetic fields. Their rate of axial rotation has not yet been decelerated to a level that would change their activity regime from the saturated to the solar type. However, both stars demonstrate signs of an incipient tendency towards more systematic and regular activity. These features of their activity set new tasks for observations and enhancement of theories of magnetic field generation in red dwarfs.

ACKNOWLEDGMENTS

The authors are grateful to M.A. Livshits and A.A. Shlyapnikov for discussions. The study was partially supported by the Russian Foundation for Basic Research, project no. 16-02-00689.