Magnetic Activity and Orbital Period Study for the Short-period RS CVn–type Eclipsing Binary DV Psc

Using 27 sets of new multiband photometry light curves acquired from our long-term photometric campaign carried out in the last 5 yr and high-resolution spectroscopic data from seven nights, we analyzed the physical mechanisms of period variation, starspot cycle, optical flares, and chromospheric activities of the eclipsing binary DV Psc. Our updated O − C diagram covering a period of approximately 20 yr shows an oscillation in its orbital period. This variations might be caused by a third body with an orbital period of 14.58 ± 0.28 yr. There are two active regions of starspots at longitude belts of about 90° and 270°. We obtained its starspot cycles with periods of 3.60 ± 0.03 yr and 3.42 ± 0.02 yr at about 90° and 270°, respectively. Moreover, the magnitude difference of Max. I–Max. II shows cyclic oscillation of 5.15 ± 0.01 yr. During our decade long photometric campaign, we observed DV Psc a total of 326.4 hr, detected 18 outbursts (12 of them have never been reported) with flare energies in the range of (6.62–1106.85) × 1024 J. The slope of the relationship between the phase of the max flare and spots is 0.842 ± 0.083, implying a correlation between spots and flares. We discovered evidence for a correlation between the rotation period and the activity cycle for the short-period eclipsing binaries. Our high-resolution spectroscopic observations of DV Psc show obvious emissions above continuum in the Hα line and small self-reversal emissions of the Ca ii IRT lines.


Introduction
For short-period RS CVn eclipsing binaries (EBs), it is useful to study the light curve (LC) variations caused by starspots using BVRI multiband photometry and spectra properties using high-resolution spectroscopic observations (e.g., Berdyugina 2005;Strassmeier 2005;Hall 2008;Butler et al. 2015). We can obtain simultaneous orbital solutions (stellar masses, temperatures, radii of two components, and orbital inclination) of both components using the radial velocity and LCs (Irwin et al. 2009;Kim et al. 2014;Wilson et al. 2017). Long-term photometric observations are very useful for studying starspot parameters (the spot longitude, temperature, area, and latitude), starspot evolution, starspot statistic properties, and the flare rate and their phase distributions (e.g., Qian et al. 2014a;Wang et al. 2015). We usually used the chromospheric activity indicators of Ca II H&K, H α , and Ca II IRT lines in the optical wavelengths (Montes et al. 2000;Frasca et al. 2010) to discuss their chromospheric activities. There are variabilities in the equivalent widths (EWs) of the H α emissions for some EBs (Özeren et al. 2001;Kjurkchieva et al. 2004 etc.), which show clear rotational modulation (e.g., Flores et al. 2015). There are spatial correlations between chromospheric activity regions and photospheric spots (Şenavci et al. 2018). High-resolution spectroscopic observations are used to study activity behavior of chromospheric activity indicators and their properties. These phenomenon are also important for studying magnetic activity and their properties by putting constraints on current theoretical solar and stellar theoretical models.
Optical photometric and spectroscopic monitoring are important tools for studying magnetic activity cycles (Berdyugina 2005;Lanza 2010). Baliunas et al. (1995) detected that many stars show stellar activity cycles from the Mount Wilson observatory H&K project. Oláh et al. (2016) found some stars showing multiple and changing cycles. Some of the methods for obtaining magnetic cycles include using the brightness of stars, starspot parameters, active longitudes, and the light minima of EBs ). There is a positive correlation between the rotation and cycle (Oláh et al. 2009). There are also a positive correlation between chromospheric activity cycle and brightness variability (Lockwood et al. 2007). Therefore, it is important to determine the magnetic cycles of EBs. Flares are the violent and sudden events that release magnetic energy, which are detected by long-term photometric and spectroscopic monitoring (Davenport et al. 2012). The flare events have also been detected in many EBs (e.g., Nelson & Caton 2007;Dimitrov & Kjurkchieva 2010;Qian et al. 2012b). These researchers determined flare properties, such as flare amplitudes, flare duration (the flare rise time, decay time, and total duration), orbital phases of the flare events, and flare rates (e.g., Qian et al. 2012bQian et al. , 2015Parimucha et al. 2016b;Kunt & Dal 2017;Šmelcer et al. 2017). There is a possible correlation between the flare amplitude and its duration (e.g., Qian et al. 2014a). They determined the phase distribution of individual flares of GJ 3236 (Šmelcer et al. 2017) and CSTAR 038663 .
There is a position correlation between the stellar spots and flares (Dimitrov & Kjurkchieva 2010). Quasi-periodic pulsations were also found in some EBs to release energy (Qian et al. 2012b;Kunt & Dal 2017). The variability of RS CVn binary DV Psc has been known since late 20th century. Robb et al. (1999) observed the first LCs of DV Psc with at least one spot on one of the components. DV Psc was first classified as a K4-5 star by Stephenson (1986). Later, additional properties for DV Psc were discovered, such as LC asymmetries (Robb et al. 1999;Vaňko et al. 2007;Parimucha et al. 2010), chromospherical activities as indicated by Ca II H and K emissions (Beers et al. 1994;Pi et al. 2014), and strong X-ray emissions (Bade et al. 1998). The asymmetric LCs were explained with a starspot by  Salchi & Edalati (2003). Lu et al. (2001) obtained the mass ratio of 0.702±0.014 by the radial-velocity curve of DV Psc. Later,  revised the orbital parameters of DV Psc using BVR charge-coupled device (CCD) photometric observations together with previously published radial velocity. Moreover, Parimucha et al. (2010) obtained considerable spot variations. Pi et al. (2014) obtained a magnetic cycle with a period of about 4.88±0.32 yr by examining the values of phase 0.25 (Max. I)-phase 0.75 (Max. II) and determined the probability of a flare to be about 0.082 flares per hour.  found a weak downward parabola in the O−C diagram of orbital period. However, Pi et al. (2014) found an upward parabola. They interpreted them by mass transfer or magnetic braking. Pribulla et al. (2012) also hoped to detect extra-solar planets in the DV Psc system using timing of the minima. DV Psc is an interesting target, which deserves long-term monitoring for studying stellar magnetic activity and period variation.
In this paper, we will present 27 new LCs from our photometric campaign for DV Psc from 2013 November-2018 January, high-resolution spectroscopic observations from seven nights, and our analyses starspot activities (evolution), flare events, chromospheric emissions, and evolutionary stages.

CCD Photometry
We carried out our new multicolor CCD photometric campaign of DV Psc using a multitude of telescopes from Asia, North and South America, and Europe: the 85 cm (see Zhou et al. 2009) and 60 cm (Zhang 2018)       November 20 to 2018 January 28 using the standard BVRI filters; the exposure times are 15-45 s, 5-30 s, 3-10 s, and 1-7 s in BVRI filters, respectively. We listed the photometry observation log in Table 1, which includes the observational date, the corresponding Heliocentric Julian Date (HJD), orbital phases, passband, and telescopes. We reduced all of these CCD images by the IRAF 5 package in the standard manner. We selected GSC0008-743 and GSC0008-949 as the comparison and check stars, respectively. The resulting LCs in BVRI passbands are shown in Figure 1 from 2008 November 21 to 2018 January 28, which includes the previously published data from Pi et al. (2014).
The HJD and the difference magnitudes of DV Psc are listed in Table 2.

Spectroscopy
We obtained high-resolution spectra (HRS) for DV Psc during seven nights (2017 January 3, 4, 11, 12, 13, 14, and 17) using the echelle spectrograph on the 2.16 m telescope (Fan et al. 2016) of  Note. We set the mean error for the minima, where error not given is marked by "a." References.
(1) * Paschke (0,home), (2) Robb et al. (1999), (3)   NAOC. A 4096×4096 pixel CCD with a pixel size of 12 μm is used, and the spectrograph has a resolution of R=49, 800 with a slit width of 0.19 mm (corresponding to 1 8). We also reduced the spectra using the IRAF package. We observed some inactive stars (HR 617 (K2 III), HR 222 (K2.5 V), HR 248 (M0 III), HR 1614 (K3 V), HR 3304 (K5 III) and HR 753 (K3 V)) whose spectral types and luminosity classes are similar to those for DV Psc. We used them to build the synthesized spectra as the photospheric line of DV Psc. We normalized each spectrum to its continuum using a polynomial function, which are plotted in Figure 2 (the first and third panels). We listed the HRS observation log of DV Psc in Table 3, which includes observational date, HJD, exposure times, and the signal-to-noise ratios (S/Ns).

Period Study
We obtained 65 new CCD light minimum times from our photometric observations for DV Psc from 2013 November 20 to 2018 January 28 with 1 m class telescopes. From these LCs, we extracted light minimum times by the method of polynomial fitting (Kwee & van Woerden 1956;Nelson 2007). We listed them in Table 4. To update ephemerides and period variations, we also collected the minimum times from the Minima Database (Paschke & Brat 2006) and other literature. We listed all of them in Table 5. Base on the 271 CCD minimum times, we obtained an updated liner ephemeris for DV Psc as follows: where the values in parentheses are the uncertainties in the last digits of the preceding quantities, and E is the epoch number.
We calculated their fitting residual (O−C) 1 values and listed them in the fifth column of Table 5. We used the error-weight method to fit them. If no errors were available for some data, we use the mean errors from all data points with errors. We plotted these (O−C) 1 values in Figure 3, where primary and secondary minima times are marked by different symbols. The (O−C) 1 residuals of DV Psc shows an oscillatory trend, which indicates that a cyclic oscillation exists for the system's period variation.
For the cyclic oscillation of period variation, we used two possible physical mechanisms to interpret our result. One is the light-travel time effect (LITE) caused by a hypothetical third body. Because of the asymmetric LC of the secondary component, we assigned weight factors 5 and 10 for the secondary and primary minima, respectively, in our fitting.
In the above equation, A=a i c sin 12 represents the semiamplitude, c is the light speed, and a 12 is the semimajor axis. The parameters of the third body are e, i, and ω, which are the eccentricity, inclination, true anomaly, and longitude of the periastron, respectively. We used the Levenberg-Marquart technique (Press et al. 1992;Yang et al. 2011) to fit our (O−C) 1 data and listed the resulting parameters in Table 6. The residual (O−C) 2(3rd body) values are also listed in the sixth column of Table 5 and plotted in Figure 3 (left panel). The period cycle of the third body is P 3rd =14.58±0.28 yr.
Another mechanism for the period oscillation is magnetic activity. We used a sine function to fit our (O−C) 1 values and obtained 0.0006±0.0001 Note. Parameters not adjusted in the solution are denoted by "a." P-Primary, S-Secondary.

Analysis
In this section, we will analyze DV Pscs photospheric starspot activities, energies of flares, and chromospheric activities.

Starspot Activities
We analyzed our LCs utilizing the W-D code (Wilson & Devinney 1971;Wilson 1990Wilson , 1994Wilson & Van Hamme 2014). We simultaneously fitted our photometric data from BVRI bands (excluding the flares). Because the radial-velocity resolution of  was computed based on the (B, V, and R) LCs, Max. II is darker than Max. I, which may affect the W-D program accuracy. To obtain our orbital solution, we used our B, V, R, and I LCs with best symmetry from 2011 November 12 and 13 ) and the published radial velocity by Lu et al. (2001), and we revised the orbital parameters (such as a mass ratio of 0.668 ± 0.003). We fixed the temperature of the primary component at 4450 K, which was published by previous authors Parimucha et al. 2010). The temperature of the secondary component at 3692 K, the orbital inclination at 74 . 2  , and the dimensionless potentials of both components were taken from previous work (Zhang et al. 2010b). Consequently, we obtained the system velocity as 27.47±0.34 km s −1 . We plotted the radial-velocity curves and their fits in Figure 4 and listed the revised absolute parameters in Table 7. Our results are similar to those obtained by . Because there is an orbital period cycle, we have tried to look for the third body luminosity contribution to all 27 sets of LCs. The resulting third body luminosity is very small (l l 0.107% ). Hence, the contribution of the third body to the overall luminosity cannot be confirmed.
We used two spots on the primary component to explain our LCs. We only adjusted the starspot parameters and fixed the orbital parameters. The same method was used to study starspots of other eclipsing binaries (Pribulla et al. 2000(Pribulla et al. , 2001Zhang & Gu 2007), where one can find a detailed description of this method. In our analyses, we first tried to use two cool spots to explain the asymmetric LCs of DV Psc. After numerous attempts, we were unable to fit our observed LCs to the theoretical model. Then, we used a hot and a cool spot to fit our observed LCs to the theoretical model and succeeded. Hot spots have also been believed to be associated with the magnetic activities of stars (Kouzuma 2019). Solar faculae are often observed on areas that surround cool spots. We listed the resulting starspot parameters of DV Psc in Table 8. In Table 8, for the data set from 2006 September 27,  also used a hot spot with a temperature of about 6898 K on the secondary to explain the observed LCs. Here, we also used a hot spot to explain our new LCs. Since the spot temperature is highly correlated with its radius and the latitude, the spot temperature obtained this way usually contains large uncertainty. The most reliable parameters of a spot are the spot longitude for studying the evolution of spot and stellar activity cycles (Eker 1999;Berdyugina 2005). We plotted the theoretical curves (solid lines) and observed LCs (open circles) in Figure 5.

Optical Eruptions
Stellar flares are strong and sudden events in stellar atmospheres, which eject hot materials into space and release accumulated magnetic energy. The released bolometric energy in the flare events ranges from 10 to 10 24 27 J (Pettersen 1989). During our new observations, we detected 15 new flares. We employed the same flare detection criterion as previous researchers (Qian et al. 2012b;Pi et al. 2014;Parimucha et al. 2016a;Šmelcer et al. 2017). We plotted a typical DV Psc flare event in Figure 6, and we plotted the phase distribution of all flare events obtained from 2008 to 2018 in Figure 7.
To estimate the energy released during these outbursts, the Planck law of the energy distribution of flare emission was used. The temperature and luminosity of both components are

F F
where L 1 2 + ( ) F is the total luminosity of DV Psc Δm(t) is the time magnitude evolution of the flare, and we integrated from the beginning, t B , to the end of the flares, t E . We calculated the total flare energies and listed them in Table 9. The flare energies that we detected range from (6.62-1106.85)×10 24 J, where some of them are larger than that of the solar flare energy (Benz 2017).

The Chromospheric Activity Analysis
All of the 27 observed spectra (see Figure 2) exhibit clear deep absorptions with small core emissions in the Ca II IRT lines and strong emission features above the continuum in both components of DV Psc in the H α lines. We calculated the EWs of the H α line and the corresponding orbital phases using our updated ephemeris. We listed the results in Table 10. Because we could not distinguish the source of emission from the primary or secondary components for most of spectra, we have to attribute the results as the total intensity from both components. The same methods for calculating the EWs are used in the previous papers (Gu et al. 2002;Pi et al. 2016;Zhang et al. 2016 etc.).We plotted the observed EWs of DV Psc versus the phase or HJD in Figure 8   We analyzed the spectra of DV Psc with a synthetical spectral subtraction technique (Barden 1985;Montes et al. 1995Montes et al. , 1997Montes et al. , 2000Montes et al. , 2004. The synthesized spectra were built from radial-velocity shifted and rotationally broadened spectra of two inactive stars, HR 753 (K3 V) and HR 248 (K5 III), which are the best template stars for the primary and the secondary of DV Psc, respectively. We obtained the initial intensity weights (0.883/0.117) from our photometric modeling. We obtain its rotational velocity (v sin i) using many metallic spectra lines in the range of 6401-6513 Å (Zhang & Gu 2008). The (v sin i) values for the primary component is 114.35 and 85.95 km s −1 for the secondary. All of the observed, synthesized, and subtracted spectra of DV Psc are also plotted in Figure 2. The subtracted spectra all show excess emissions. We listed the parameters of these excess emissions in Table 11, which include HJD, the phase, EWs of H α , Ca II IRT lines, and the ratio of Ca II EW 8542 to EW 8498 . We plotted them in Figure 8

Discussions and Conclusions
We reported and analyzed new long-term multicolor photometric observations and HRS of DV Psc. In this section, based on our new results, we will discuss the period variation mechanism, starspot evolution, flare properties, and any relationship between the magnetic cycle and orbital period of EBs. We will end by discussing the chromospheric properties and evolutionary status of DV Psc.

The Period Variation Mechanisms
As discussed in Section 3, the (O−C) diagram suggests a cyclic oscillation (Figure 3). The oscillating characteristic may be caused by magnetic activity cycles or the LITE due to a possible third body. Let us consider the LITE first. Mayer (1990) The mass of the third body depends on the orbital inclination, i′, and the minimal value, M 3,min , of the DV Psc system is 0.107 M e when i′=90°. The corresponding spectral type was about a M6-M7 dwarf, not an extraplanet (Cox 2002). The second possible mechanism is the magnetic activity cycle. Applegate (1992)  -)gcm 2 for active stars (Lanza & Rodonò 1999). Hence, these cyclic variations are most probably caused by the LITE via a third body.

Starspot Evolution
Two activity longitude belts around the quadrature longitude (90°and 270°) were found by the long-term photometric monitoring on RS CVn binaries (e.g., Zeilik et al. 1988Zeilik et al. , 1989Zeilik et al. , 1994Oláh et al. 1989;Henry et al. 1995;Lanza et al. 2002 etc.). Berdyugina & Tuominen (1998) found that the active longitudes show a periodic change from one active longitude to the other (a flip-flop cycle). To explain this phenomenon, Moss (2004) proposed a mechanism of an oscillating quadrupole mode. For the spot parameters of DV Psc from 2008 to 2018, we found that the spots are around the longitudes 90°and 270°(the third and eighth columns in     Table 8), forming two active longitude belts, which means there are possible cycle of the spots oscillating around quadrature positions. The longitude of the spots can be used to search for a possible magnetic cycle (Pribulla et al. 2000;Rodonò et al. 2000;e.g.,). For DV Psc, the positions of the spots within the two "belts" seem to be periodic. We used the quadratic trend combined with a sine wave to fit them. We obtain a period of 3.60±0.03 yr and 3.42±0.02 yr for the   "belts" around 90°and 270°, respectively. The optimal fits are shown in Figure 9. The starspot-preferred longitudes might be explained by tidal effects of the dynamics for magnetic flux tubes (Holzwarth & Schüssler 2002). The cycles found from sine waves fitted to active longitude belts have 3.42-3.60 yr of periods. The magnetic activity cycles found from the (O − C) analyses is 13.26 yr. The magnetic cycles from active longitudes are smaller than that from the (O − C) analyses. Therefore the periods found from the active longitudes belts support the hypothesis that the sinusoidal variation seen in the O − C residuals are caused by a third body. Therefore, we prefer the explanation that the cyclic variations of (O − C) values are caused by the LITE via a third body.
To investigate the variations in the out-of-the-eclipse part of the LCs of DV Psc, we calculated the values of Max. I-Max. II from the previous observations Parimucha et al. 2010;Pi et al. 2014), as well as the 27 new sets of LCs, and listed them and their errors of B, V, R, and I bands, respectively, in Table 12. We used these results to search for the magnetic cycle. We used the sinusoidal function   Figure 11. Distribution as a function of spectral types for eclipsing binaries with period and magnetic cycles likely caused by stellar activity.
to fit Max. I-Max. II values. This technique was also used by other researchers (Pribulla et al. , 2011Yang et al. 2012;Pi et al. 2014). Most of the Max. I-Max. II data were acquired from observations after 2017. Because of the uneven distribution of data points, we added a weighting factor based on the number of data points in each year and listed them in Table 12. The resulting magnetic cycle periods are 5.24±0.01 yr in the B band, 5.13±0.01 yr in the V band, 4.91±0.01 yr in the R band, and 5.31±0.02 yr in the I band. Their average value is 5.15±0.01 yr. We plotted the Max. I-Max. II magnetic cycle in Figure 10. The adjusted residual square is 0.65, which is smaller than 1. The fit is not good after 2007. This implies that there might be multiple and/or changing cycles in its activities. Multiple and changing cycles were also found in other late-type stars (Hathaway 2015;Oláh et al. 2016). Future observations are needed to confirm the multiple cycles of DV Psc activities. To check the periodicity of the values of Max. I-Max. II., we also performed a Fourier analysis using the software package period04 (Lenz & Breger 2005). The values of cycles are consistent with our result from a sine fitting.
The rotational period and cyclic length are two important properties of active stars. The existence of a relationship between the rotational period and cyclic length had been studied for a long time. Baliunas et al. (1996) suggested using P P cyc rot to discuss their relationship. Recently, there is evidence to suggest a correlation between the rotational period and cyclic length Suárez et al. 2016). We collected all of the known short-period EBs with possible magnetic cycles in Table 13, which includes spectral types of EBs, their types (Algol, W Uma, RS CVn binary, cataclysmic variables (Ca V), and low-mass eclipsing binaries (L EB)), the orbital period, and the obtained method of magnetic cycles, such as orbital period variations (Pv), spot-phase migration variations (Spmv), and brightness variations (Bv). One hundred sixty-six EBs have at least one cycle, and 42 EBs show more than one cycle; all of them have spectral types from B to M type except 16 cataclysmic variable stars. We plotted the EB distribution as a function of the spectral type in Figure 11. Here, we made an implicit assumption that these cyclic variations are attributed to magnetic activities. In a direct References.
(1) Robb et al. (1999), (2)   comparison of the rotational period versus the cyclic period, the top panel of Figure 12 shows the number distribution of cycle lengths versus orbital periods. The cyclic length ranges from approximately 1 to 180 yr of those short-period EBs with rotational periods from 0.1 to 8 days. At first glance, one may conclude that there is no apparent correlation between these two quantities. The bottom panel of Figure 12 shows the relationship between the log-log scale of P P cyc orb versus P 1 orb . Now, we see clear linear correlation between these two quantities. The slope for our results is 0.711±0.047, which confirms that there is indeed a weak correlation between these two quantities. This maybe imply a common dynamo for these short-period EBs. Although the Sun is a single star, the magnetic activity detected on these stars is solved by considering the Standard Solar Dynamo Model. Therefore, we also collected solar activity cycles of 11 and 3.65 yr from Oláh et al. (2016) and 44 and 88 yr from Messina & Guinan (2002). We also plotted the Sun cycle in Figure 12. As can be seen from Figure 12, the Sun support the distribution seen in the current figure. This relationship should put a constraint on theoretical solar and stellar models in the future.

Flare Activity
By the end of 2018 January, we have photometrically monitored DV Psc for about 326.4 hr and detected a total of 21 flares (see Table 9), which revealed the flare frequency of 0.064 flares per hour. The flare rate is slightly smaller than the previous result of about 0.082 flares per hour  and the flare rate of 0.10 of GJ 3236 (Parimucha et al. 2016a). This flare rate is similar to 0.057 flares per hour for CM Dra (Nelson & Caton 2007) and 0.05 flares per hour for CU Cnc (Qian et al. 2012b). The flare durations are 3.9-22.3 minutes, 4.5-17.3 minutes, 4.6-15.6 minutes, 1.8-8.1 minutes, and 8.9-10.8 minutes in BVRr′I bands, respectively. The corresponding amplitudes are 0.042-0.734 mag, 0.021-0.273 mag, 0.014-0.197 mag, 0.023-0.116 mag, and 0.048-0.108 mag in the BVRr′I bands. We plotted the distribution of energies of individual flares with the duration time in Figure 13, where the horizontal axis is the reciprocal of the duration time (ν=1/ (duration time)). The fact that we observe flares in B, V, R, r′, I filters suggests their high-energy nature (see Figure 14). The total energy of the flares detected ranged from 6.62×10 24 to 1106.85×10 24 J. The slope of the linear fit for the energies is −1.529±0.190. There are no broken power laws, as seen in GJ 3236 (Šmelcer et al. 2017). More flare events are needed to make a definite conclusion. We also listed the phases of the max flare and spot of the system in columns 3 and 4 of Table 9 and updated the relationship between the phases of the flare and spot positions. We fitted the phases of flares and spots to a straight line using the least-squares method and plotted the result in Figure 14. The slope of the relation is 0.842±0.083, which is close to 1. This indicates that the phase of flares were close to the position of spots for DV Psc. This confirmed a correlation of spots and flares.      Baraffe et al. (2015). Solid circle represents the primary component, and empty circle represents the secondary component of DV Psc.

Chromospheric Activity
From the first high-resolution spectroscopic observations of DV Psc, we see strong emissions above continuum in the H α lines and minor self-reversal emissions in the Ca II IRT lines. The subtracted spectra exhibit clear emissions in the H α line and Ca II IRT lines. The largest emission in H α lines with an EW of 2.584±0.015 Å (see Table 10) and 3.539±0.052 Å for the excess emission (see Table 11) of the system occurred on 2017 January 4. The varying and strong chromospheric excess emissions in these chromospheric lines proved its high level of chromospheric activities. The values of the ratio (EW EW 8542 8498 ) was useful for distinguishing the source of this activity from a plage or prominence. In Table 11, these ratios are in the range of 0.965 ∼ 2.704, which indicates that the emissions arose from plages. These were also found in other stars (e.g., Arévalo & Lázaro 1999;Montes et al. 2001;Gálvez et al. 2007;Pi et al. 2016).

Evolutionary Stage
Combining photometric and spectroscopic solutions, we obtained absolute parameters of DV Psc and listed them in Table 7. In Figure 15, we plotted radius versus mass and L L log  ( ) versus T eff diagrams for several theoretical isochrones taken from Baraffe et al. (2015) and indicated the positions of both primary and second components. We found that the parameters of the primary component are in good agreement with the 0.050 Gyr tracks of the theoretical model. The secondary component is located just slightly under the 0.050 Gyr tracks, which might be a discrepancy of the radii of low-mass stars between the observation and theoretical models (López-Morales & Ribas 2005).