Magnetic Activity and Period Variation Studies of the Short-period Eclipsing Binaries. II. V1101 Her, AD Phe, and NSV 455 (J011636.15–394955.7)

In this paper, we present new BVRI light curves of short-period contact eclipsing binaries V1101 Her and AD Phe from our observations carried out from 2014 to 2015 using the SARA KP and SARA CT telescopes. There is an eclipsing binary located at α(2000) = 01h16m36.ˢ15 and δ(2000) = −39°49′55.″7 in the field of view of AD Phe. We derived an updated ephemeris and found there a cyclic variation overlaying a continuous period increase (V1101 Her) and decrease (AD Phe). This kind of cyclic variation may be attributed to the light time effect via the presence of the third body or magnetic activity cycle. The orbital period increase suggests that V1101 Her is undergoing a mass-transfer from the primary to the secondary component (dM1/dt = 2.64(±0.11) × 10−6 M⊙ yr−1) with the third body (P3 = 13.9(±1.9) years), or 2.81(±0.07) × 10−6 M⊙ yr−1 for an increase andmagnetic cycle (12.4(±0.5) years). The long-term period decrease suggests that AD Phe is undergoing a mass-transfer from the secondary component to the primary component at a rate of −8.04(±0.09) × 10−8 M⊙ yr−1 for a period decrease and the third body (P3 = 56.2(±0.8) years), or −7.11(±0.04) × 10−8 M⊙ yr−1 for a decrease and magnetic cycle (50.3(±0.5) years). We determined their orbital and geometrical parameters. For AD Phe, we simultaneously analyzed our BVRI light curves and the spectroscopic observations obtained by Duerbeck & Rucinski. The spectral type of V1101 Her was classified as G0 ± 2V by LAMOST stellar spectra survey. The asymmetry of the R-band light curve of AD Phe obtained by McFarlane & Hilditch in 1987 is explained by a cool spot on the primary component.


Introduction
Short-period binaries play an important role in studying stellar physical parameters and evolution. These types of systems often have high levels of magnetic activity, manifested in the form of plages, flares, and starspots (Pribulla et al. 2003;Hall 2008;Pi et al. 2014). Short-period contact binaries are believed to have formed from initially short-period detached binaries via angular momentum loss caused by the magnetic braking (Guinan & Bradstreet 1988). However, in many of these kinds of stars, details of the magnetic activity phenomena are not well understood. Photometric and spectroscopic studies ofshort-period contact binaries are important methods for determining their physical properties. Therefore, studying these systems can help us understand the dynamical evolution of short-period binaries.
V1101 Her (GSC 03528-00044, ROTSE1 J180733.29 +465435.0) was discovered to be a variable star by the ROSAT-1 survey (Akerlof et al. 2000).  obtained the first CCD light curve in white light and concluded that it is an EW-type W UMa system. They also obtained a period of P=0.382659 days. Since then, times of minimum light for V1101 Her have been published by many investigators Hübscher et al. 2012;Nelson 2016;etc.). AD Phe (GSC 07534-00579, 2MASS J01163807-3942312) was discovered to be a variable star by Hoffmeister (1963) and Strohmeier & Bauernfeind (1969). They also determined their orbital period. Cerruti (1986) improved the ephemeris and obtained the rate of period decrease. McFarlane & Hilditch (1987) obtained the first multi-band light curves and obtained a preliminary photometric solution using two different photometric mass ratios q=0.5 and 1.0. Wolf et al. (2000) presented a period analysis of the W UMa-type eclipsing binary AD Phe and found no period variation. In 2007, Duerbeck & Rucinski (2007) carried out a medium precision radial velocity observation and obtained a spectroscopic mass ratio as q=0.37 (±0.01) for the system. Deb & Singh (2011) analyzed a V-band light curve observation obtained by the All Sky Automated Survey (ASAS). They obtained the physical parameters of AD Phe. Overall, the observational data for AD Phe are limited. NSV 455 was found to be an EW-type system and the light elements were given as T 0 =2454338 2900 and P (days)=0.320236 (Watson et al. 2007).
To better understand the magnetic activities and period variations of the eclipsing binaries, we need to monitor them by multi-color CCD photometry using 1m class optical telescopes. For this purpose, we present new BVRI CCD light curves for AD Phe, V1101 Her, and a star located at α=01: 16:36.15 and δ=−39:49:55.7 (J011636.15-394955.7), similar to our previous published paper on the magnetic activity and orbital period variation of the short-period eclipsing binary DV Psc ).

Observations and Data Reduction
We carried out new CCD photometric observations of two short-period eclipsing binaries from 2014 to 2015. We observed AD Phe using the SARA 60cm telescope at the Cerro Tololo Inter-American Observatory in Chile on 2014 October 07. We observed V1101 Her using the SARA 91.4cm telescope at the Kitt Peak National Observatory in USA on 2015 June 29 and 30, and October 10. The CCD cameras on both telescopes have a 2048×2048 pixel CCD with the Bessell BVRI filters. We used it in 2×2 binning mode, resulting in an effective resolution of 1024×1024 pixels. We have listed our observation details in Table 1. We reduced all our observed CCD images using the IRAF 4 package in the standard fashion (bias subtraction and flat-field correction). The magnitudes of three short-period eclipsing binaries, the comparison, and the check stars were determined using the Apphot sub-package in IRAF. In the process of analyzing AD Phe images, we found that the star located at α=01: 16:36.15 and δ=−39:49:55.7 in the field of AD Phe (see Figure 1) is an eclipsing binary (we label itNSV 455). From the 2MASS map, the NSV 455 is essentially a visual binary. We plotted the three sets of complete BVRI light curves (LCs) in Figure 2, with different symbols representing the corresponding dates. The differential magnitudes of the objects and their comparison stars versus HJD are listed in Table 2.
The Large Sky Area Multi-object Fiber Spectroscopic Telescope (LAMOST) provides many low-dispersion spectroscopic observations for a large number of eclipsing binary objects (Zhang et al. 2017a). We can use them to discuss stellar chromospheric activity (Zhang et al. 2017b). A spectrum of V1101 Her was obtained on 2014 April 20. We downloaded it from the LAMOST website (http://dr3.lamost.org) (Luo et al. 2012;Cui et al. 2012;Zhao et al. 2012). We found the spectral type of V1101 Her to be G0 ± 2V using comparisons of different spectra published by Pickles (1998). We plotted the comparison spectrum G0V and G2V data from Pickles (1998) in Figure 3. There are strong absorptions in the H α , H β , and H γ lines. Hence, there was no obvious chromospheric activity.

Orbital Period Study
From our photometric data, we determined several new lightof-minima times for V1101 Her, AD Phe, and NSV 455 using the method of Kwee & Van Woerden 1956 with the polynomial fitting and the interpolation method included in the program published by Nelson (2007). Table 3 tabulates these individual data and their errors. We also collected all published minimum times from the literature and the Eclipsing Binaries Minima Database (Paschke and Brát 2006) to calculate updated ephemerides and study period variations. We have listed those individual light-of-minima times and their uncertainties in Table 4. We have also listed the minima types (Pri: primary or Sec: secondary), the observational method (pg: photograph, pe: photometric or CCD: charge-coupled device), and epochs of these minima times in Table 4.

Period Analysis of V1101 Her
For V1101 Her, we collected a total of 27 CCD light-ofminima times, which are listed in Table 4 (7) of Table 4. We plotted (O-C) 1 versus epoch in Figure 4. The (O-C) 1 residuals show an upward parabolic variation with a possible oscillation, which indicates that there exists a cyclic variation overlaying a continuous period increase. The largescale variation of V1101 Her might be caused by the third body. We do not take this into consideration because of the lack of data and will analyze it in the future. There are two physical mechanisms for this cyclic variation. One mechanism is the quadratic ephemeris + the light time effect (LITE), which is caused by distance variations due to the third body. Fitting the (O-C) 1 values based on quadratic ephemeris+LITE (Pribulla & Rucinski 2006;Yang et al. 2007) gives In Equation (3), = A a i c sin 12 represents the semi-amplitude of the LITE, a 12 is the semimajor axis of the eclipsing-pair orbiting the common center of mass with the third body, and c is the speed of light. The other parameters of the third body are i, e, and ω, which represent the inclination, eccentricity, true anomaly, and longitude of the periastron, respectively. In order to obtain these related parameters of Equations (2) and (3) simultaneously, the Levenberg-Marquardt techniques were used (Press et al. 1992;Yang et al. 2011); the results are listed in Table 5. The calculated residuals (O-C) 2 values are listed in column (8) of Table 4 and plotted in Figure 4. The orbital period of the third body was obtained as P 3 =13.9(±1.9) years.
Another mechanism for this cyclic variation is the magnetic activity, and we assume this cycle is sinusoidal. The polynomial + sine function gives: The sinusoidal term of the above equation reveals a periodic oscillation with an amplitude of A=0.0020 (6) days. Using T=2π×P/ω, where P denotes the orbital period of V1101 Her in years and ω (rad −1 ) is the coefficient of E, the period of the oscillation T was calculated to be 12.4(±0.5) years. The calculated residuals (O-C) 2 values are listed in column (9) of Table 4 and are plotted in Figure 4.

Period Analysis of AD Phe
For AD Phe, we collected a total of 63 light-of-minima times, including 31 photographic (pg), 24 photoelectric (pe), and 8 CCD measurements, which are also listed in Table 4. Considering the various measurement accuracies, weights 5 and 10 are assigned to pg and pe/CCD data, respectively. Using a least-squares fitting method, we then improved the new ephemeris to be: The computed residuals of (O − C) 1 are listed in Table 4. Figure 4 shows its (O − C) 1 variation, whose shape may suggest a downward parabolic curve with a possible oscillation. The large-scale variation (parabolic curve) of V1101 Her might also be caused by the third body. Fitting the (O-C) 1 values based on quadratic ephemeris+LITE gives: The corresponding residuals of (O − C) 2 are also listed in Table 4. The obtained parameters for Equation (3) are listed in Table 5. The orbital period of the third body is P 3 =56.2(±0.8) years. We also used a polynomial + sinusoidal function for fitting (O-C) 1 , which led to the following equation: The corresponding residuals of (O-C) 2 are also listed in Table 4 and shown in Figure 4. The modulated period for this oscillation is T=50.3(±0.5) years. As a bonus when studying AD Phe, we found that the star NSV 455 in the field of view of AD Phe is also an eclipsing binary. The orbital period of NSV 455 is obtained by means of the phase dispersion minimization method of Stellingwerf (1978) as P=0.31616 (6) days. Our period is smaller than the result derived by Watson et al. (2007).

Photometric Analyses
As can be seen from Figure 2, the three sets of light curves have complete phase coverage and high time resolution. We analyzed their individual LCs with the updated version of the W-D program (Wilson & Devinney 1971;Wilson & Devinney 1979;Wilson 1990Wilson , 1994Wilson & Van Hamme 2004. The temperature of the primary component (T 1 ) was obtained using J and H magnitudes from the 2MASS All Sky Catalog (Skrutskie et al. 2006)using the relation derived by Collier Cameron et al. (2007): In this equation, we obtained J and H magnitudes values from the 2MASS All Sky Catalog (Skrutskie et al. 2006). For NSV 455, we see an optical companion located near the system in the 2MASS map. By assuming that the brighter companion is NSV 455, we determined the effective temperature of the primary component as T 1 =5183 K. In the RAVE 5th data release by Kunder et al. (2017) the temperature for AD Phe was given as T 1 =6155 K, which is obtained spectroscopically. For V1101 Her, the LAMOST survey derived the temperature of the primary component as T 1 =5920±167 K and the spectra type as G0±2V using automated methods and software based on the LAMOST stellar spectral template library (Wu et al. 2011). The temperature corresponds to about the G1V spectral type (Cox 2002). At these temperatures, the radiation is mainlyconvective. As a result, we set the fixed parameters in the W-D program as follows: the bolometric albedo A 1 =A 2 =0.5 (Rucinski 1969) and the gravity-darkening coefficients g 1 =g 2 =0.32 (Lucy 1967). The linear limbdarkening law was used to compute the limb-darkening coefficients for the B, V, R, and I bands (Van Hamme 1993), respectively. Based on the previous results of AD Phe and V1101 Her, and the LC shapes for NSV 455, we used Mode3 (overcontact mode) to analyze their LCs. For AD Phe, we simultaneously analyzed our BVRI light curves and the radial velocities published by Duerbeck & Rucinski (2007) to obtain the mass ratio and other orbital parameters. For V1101 Her and NSV 455, we conducted an extensive q-search to determine the best mass ratio q=M 2 /M 1 . We calculated a series of models with different mass ratios q from 0.2 to 4.6. We plotted the fitting residuals å-q) in Figure 6. The minimum residuals occur at the mass ratios q=0.8 and 2.0 for V1101 Her and NSV 455, respectively. The adjustable parameters are the orbital inclination (i), the secondary component's temperature (T 2 ), the surface potentials of both components (Ω 1 =Ω 2 ), and the different bandpass luminosities for the primary component Because NSV 455 has an optical companion and we know the JHK magnitudes of both objects, we estimate the light contribution at these filters as 30%.
Because the optical companion cannot be seen in our observations, the differential magnitudes of NSV 455 are contained by both objects. Because of the JHK magnitudes and colors of the optical companion, we expect the contribution of the third light to be smaller for BVRI filters. We used the light contribution as the third light in the LC analysis and reobtained the parameters. The light contribution of the optical companion is found to be 12.3%, 14.9%, 16.5% and 17.0% for the B, V, Rand I bands, respectively. The procedures for calculating the orbital and starspot parameters are similar to those in previous works on RT And (Zhang & Gu 2007) and DV Psc . Since it is difficult to obtain the starspot latitude by photometric observation, we assumed its latitude to be 90°. This means that we assumed the starspot is located on the equator of the component. We only adjusted the other three parameters: starspot longitude, temperature, and radius. We adjusted the spot parameters separately until the theoretical curves fit the observed ones well. For NSV 455, we explain our light curves with the contact model. For AD Phe, we simultaneously analyzed the BVRI light curves and the radial velocities published by Duerbeck & Rucinski (2007). We plot the observed radial velocity obtained by Duerbeck & Rucinski (2007) using one of the primary minima obtained near the dates (2451417.4681) and our theoretical fit using the WD Program in Figure 7. For AD Phe, the type of system is changed from W to A-type W Uma. At the primary minima the high-mass (high luminosity) companion is eclipsed by the low-mass companion. We can successfully model the observed LCs without a starspot since there is almost no asymmetry in our light curves.  mag and can be assumed to be the same for both light curves. But we see that for McFarlane & Hilditch's (1987) light curve the level of the secondary minima is nearly the same with the primary minima. Additionally, the secondary maxima are lower than the primary maxima. This shows us that around secondary minima and secondary maxima there must be extra light loss that can be modeled by a cool starspot or spots. These might also be caused by a cool spot on one of the components. The light curve variation might be caused by magnetic activity and mass-transfer from the primary to the secondary component, which is consistent with the period decrease. We fixed the orbital parameters and only adjusted the starspot parameters with a cool spot on the primary (Case1 in Table 6). For V1101 Her, we added a cool spot on the primary to explain the phenomenon that the Max.I at phase 0.25 is brighter than the Max.II at phase 0.75. However, we also add another starspot on the primary to explain the light curve distortion at phase around 0.25. Finally, we used two starspots model to explain our light curves of V1101 Her. We have listed the corresponding parameters of the three eclipsing binaries in Table 6 and the spot parameters in Table 7. We have plotted their theoretical and observed LCs in Figure 8. We have graphed the threedimensional models of Roche geometry at phases 0.25 and 0.75 in Figure 9.

Discussions and Conclusions
We have presented our new CCD B, V, R, and I LCs of three short-period eclipsing binaries (V1101 Her, AD Phe, and NSV 455). We have also observed the spectrum of V1101 Her and presented it in this text. Additional discussions are provided below.

Period Variations
To clarify the period change, we first considered the possibility of the period variation. For V1101 Her, the (O-C) diagram suggests a continuous increase to the orbital period with the cyclic oscillation: the period increase rates are dP/dt=7.58(±0.31)×10 −7 days yr −1 for the polynomial and LITE function (Equation (2)), and dP/dt=8.07(±0.19)× 10 −7 days yr −1 for the polynomial and sine function (Equation (4)). Since V1101 Her is a contact system, the mass-transfer from the primary component to the secondary component would be expected to be the cause of this period change. We can derive the mass-transfer rate (Ṁ 1 ) using the    following equation (Kwee 1958): The mass of the primary component is determined to be M 1 =1.05 M e , using the relationship between the mass and the spectral types (Cox 2002 1 for Equation (4). The first (O-C) analysis of AD Phe was carried out by Cerruti (1986) and found a period decrease at a rate of −1.23×10 −7 days yr −1 . Later, Wolf et al. (2000) analyzed the system again and decided the parabolic variation was a less probable event. We found that the period of AD Phe decreases at a rate of dP/dt=−1.52(±0.01)×10 −7 days yr −1 for Equation (6) and dP/dt=−1.34(±0.01)×10 −7 for Equation (7), which are close to the values of Cerruti (1986). On one hand, the period variation may be caused by masstransfer from the primary to the secondary component. In the case of mass-transfer, using the physical parameters listed in Table 5 Equation (9)  1 for Equation (7). On the other hand, the period decrease could be explained by magnetic braking (Applegate 1992;Lanza et al. 1998;Zhang et al. 2014).
The oscillating characteristics may be caused by the light time effect (LITE) due to the existence of the third body or the magnetic activity cycles of the system (sine). We shall consider LITE first. The semi-amplitude K RV of the changes in the systemic velocity accompanied by LITE is given by Mayer (1990)  where K RV is in kilometers per second, a 12 is in kilometers, and P 3 is in seconds. Using this equation and Equation (3), the mass function of the third component f(m) given in Table 5  We obtained the mass of the third body from the above equation, which also depends on the orbital inclination i′. We plotted the mass of the third body with respect to the orbital inclination in Figure 5. Using i′=90°we obtained the minimal mass of the third body M 3,min as 0.128 M e and 0.257 M e for V1101 Her and AD Phe, respectively. Using Allen's Astrophysical Quantities (Cox 2002) and assuming the third bodies are dwarf stars, the estimated spectral types are M6-M7 and M4-M5 for V1101 Her and AD Phe, respectively. For this case, it is difficult to find direct evidence of the third body by spectroscopic and photometric observation. If the additional tertiary component is true, V1101 Her and AD Phe both might be a third system. The second possibility for the cyclic oscillation in the O-C diagram is magnetic activity cycles. Using the relation  (1) and (2)). The dashed lines represent the quadratic fit, and the solid lines represent the quadratic fit superimposed on a cyclic variation (the third body or magnetic cycle).  (Cox 2002). Using the mean fractional radii given in Table 6  The values of the quadrupole moment for V1101 Her and AD Phe are smaller than the typical values (10 51 -10 52 g cm 2 ) for active binaries (Lanza and Rodonò 1999). Therefore, these cyclic variations could be attributed to LITE via a third body. However, we cannot rule out that these variations might be caused by the magnetic activity cycles.  Note.Parameters not adjusted in the solution are denoted by the symbol (a). The asterisk ( * ) indicates that we used AD Phe's orbital parameters to adjust the 1982 data. Case1 means a cool spot in the primary and Case2 means a hot spot in the secondary component.

Absolute, Geometrical, and Starspot Parameters
For V1101 Her, we were able to model the asymmetry in its LCs using a contact model with a cool spot on the primary and a hot spot on the secondary component separately. We obtained its geometrical parameters for the first time. The orbital inclination was obtained as 71°.1(±0.1). The temperature of the secondary component was obtained as T 2 =5690(±7) K. There is a temperature difference of about 230K between the primary and secondary components, and the difference might be become smaller as the mass-transfer continues. The mass ratio is about 0.80(±0.10), which is assumed by the region of the nearly same residuals obtained from the q-search method. As can be seen from Figure 6, the minimum region is very flat. Therefore, we need spectroscopic observations to confirm its mass ratio. The ratios of the luminosity of the primary component to its total value of the eclipsing binary are 0.6119 for the Bfilter, 0.5958 for V, 0.5872 for R, and 0.5806 for I. The dimensionless potentials are Ω 1 =Ω 2 =3.353(±0.003). We obtained a contact factor of f (%)=14.2(±0.6) using f=(Ω in -Ω)/(Ω in -Ω out ). We found the spectrum of V1101 Her to be G0V from LAMOST spectroscopic data. There is no evidence of emission at the H α , H β , and H γ lines, which indicate that V1101 Her does not have obvious chromospheric activity. The period increase and physical models of V1101 Her are similar to LY And (Lu et al. 2017), BB Peg (Kalomeni et al. 2007;Lu & Rucinski 1999), DD Indus (Samec et al. 2016), DD Com (Zhu et al. 2010), and V453 Mon (Köse et al. 2009).
By solving multi-band light and radial velocity curves simultaneously the WD program can calculate the absolute and geometrical parameters of the components at the same time (Wilson 1979). In analyzing the orbital physics for AD Phe, we included both our newly acquired BVRI light curves and the radial velocities published by McFarlane & Hilditch (1987). Comparing our new LCs and the first V-band LC obtained by McFarlane & Hilditch (1987), we see a long-term variation. There are magnitude differences for the primary and secondary minima, and for Max.I-Min.I. We also used cool spots on the component to explain the phenomenon. We successfully explained the asymmetry in its light curves. The spectroscopic mass ratio is q=0.378, which is similar to the results obtained by Duerbeck & Rucinski (2007) and Deb & Singh (2011). The  orbital inclination is 76°.05(±0.08), which is close to the results (72°.8∼75°.0) of McFarlane & Hilditch (1987) and 74°.0 by Deb & Singh (2011). The temperature of the secondary component is T 2 =5835(±6)K. The temperature difference is about 320 K between the two components, which is also similar to the results of 223K obtained by Deb & Singh (2011). The bandpass luminosities of the primary component to the total light are 0.7665 for B, 0.7517 for V, 0.7434 for R, and 0.7370 for I band. According to the radial velocity curve published by Duerbeck & Rucinski (2007), at the primary minima the lowmass companion is eclipsed. This requires that the low-mass companion have higher luminosity in the system. According to the light and radial velocity curve solution given in Table 7, we found that at the primary minima the more luminous and highmass component is eclipsed. With this information we can say that the system is essentially an A-type W UMa, which is different than the previous classification. The dimensionless potential is Ω 1 =Ω 2 =2.591(±0.003). The fillout parameter is found to be f (%)=15.4(±1.3). We obtained the absolute parameters (the semimajor axis a=2.456 R e ; the mass M 1 =1.004 M e , M 2 =0.378 M e ; the radius R 1 =1.17 R e , R 2 =0.76 R e ). These results are different from the results derived by Deb & Singh (2011) because the type of system is changed from W-to A-type W UMa. Similar rates of period decrease and contact degrees have been found in other binary   systems: BX Peg (Li et al. 2015), KQ Gem (Zhang 2010), RU UMi (Lee et al. 2008), and BL Leo (Yang et al. 2013). We discovered that the star (J011636.15-394955.7) is an eclipsing binary and presented its BVRI light curves. The coordinates of the star (J011636.15-394955.7) coincide with NSV 455 (an RR Lyrae type variable). It is possible that it was erroneously classified as an RR Lyr type variable (Gessner & Meinunger 1975;Demartino et al. 1996;Gavrilchenko et al. 2014). Watson et al. (2007) classified the system as an EW-type binary with a period (P(days)=0.350236). We determined its period as P=0.31616(6) days, and its (J-H) color indicates that this system is a late F-type W UMa. The photometric solution shows that NSV 455 is a contact binary (i=83°.068, q=2.00, f (%)=23.2(±2.5)). NSV 455 is essentially a visual/optical binary and this can be seen in 2MASS data. These three objects were overcontact binaries with low contact factors.
In summary, we have performed period analysis and photometric study of both V1101 Her and AD Phe. We have found that both the period and the light curves of AD Phe systems show intrinsic variations. The multiple changes in the period indicate that there may exist mass-transfer between the components, the third body, and/or the magnetic activity in both systems. The distortion in the light curves can be explained by spot activity.
Large numbers of photometric observations of the shortperiod eclipsing binaries are very important for studying orbital parameters and period variations. In the future, we will make simultaneous photometric and high-resolution spectroscopic observations to better understand the photospheric and chromospheric activities. We will also continue to study their physical mechanisms for orbital period variation.