#### Abstract

First CCD photometry for the contact binary MT Cas is performed in 2013 in December. The spectral type of F8V is determined from the low-precision spectrum observed on 2018 Oct 22. With Wilson-Devinney code, the photometric solutions are deduced from light curves (LCs) and AAVSO’s and ASAS-SN’s data, respectively. The results imply that MT Cas is a W-type weak-contact binary with a mass ratio of and a fill-out factor of , respectively. The asymmetric LCs in 2013 are modeled by a dark spot on the more massive component. By analyzing the curve, it is discovered that the orbital period may be undergoing a secular increase at a rate of , which may result from mass transfer from the less massive component to the more massive one. With mass transferring, MT Cas may evolve into a broken-contact configuration as predicted by TRO theory.

#### 1. Introduction

W Ursae Majoris binary contains two components, which are embedded in a common envelope [1, 2]. Models for contact binary have been recently constructed by several investigators (e.g., see [3–5]). However, their evolutionary status still remains unclear because the spectra cannot be analyzed for abundances due to the extreme broadening and blending of spectral lines. Therefore, it is crucially important to observe contact binaries, which may provide some special phenomena and processes, such as magnetic activity [6], third body [7], angular momentum evolution [3], flare [8], and stellar coalescence [9]. It is helpful for us to understand their formation, structure, and evolution of contact binaries.

MT Cas (=SV SON 4671) was found by Götz & Wenzel [10] as a W UMa-type eclipsing binary. Its visual magnitude is mag, and the depths of both eclipses are mag and mag, respectively [11]. Hoffmann [12] photoelectrically observed this binary. Unfortunately, the light curves did not cover the complete period. Pribulla et al. [13] derived a linear ephemeris with a period of days, which was updated to be days [14]. Except for some photometric data performed by several amateur observers of AAVSO (https://www.aavso.org/data-download) and ASAS-SN database [15] (https://asas-sn.osu.edu/database/light_curves/335960), no additional observations for this binary have been presented up to now.

In this paper, the neglected binary MT Cas was studied photometrically and spectroscopically in Section 2. The orbital period variation is analyzed in Section 3, and three sets of light curves (i.e., LCs in 2013, AAVSO’s LC, and ASAS-SN LC) are modeled in Section 4. In Section 5, we estimated the absolute parameters and discuss mass transfer between two components and its evolutionary status.

#### 2. New Observations

##### 2.1. Photometry

CCD photometry for MT Cas was first carried out at six nights of 2013, with the 85-cm telescope [16] at the Xinglong station (XLs) of National Astronomical Observatories of China (NAOC). The standard Johnson-Cousins systems were mounted onto this telescope. During the observation, files are used in order to provide the enough high time resolution. The image reductions are done by using the Image Reduction (IMRED) and Aperture Photometry (APPHOT) packages in the Image Reduction and Analysis Facility (IRAF) in a standard mode. Differential magnitudes were then determined by aperture photometry.

In the observing process, we chose TYC 3657-1637-1 ( and ) and TYC 3657-1245-1 ( and ) as the comparison and check stars, respectively. Typical exposure times are adopted to be in band and in band, respectively. In total, we obtained 383 and 373 images in and bands. The standard uncertainties are mag in band and mag in band. All individual observations (i.e., and ) are listed in Table 1. The differential magnitudes* versus* orbital phases are displayed in Figure 1, where phases are computed by a period of (Kreiner et al. 2004). The LCs in 2013 imply that MT Cas is an UMa-type eclipsing binary, whose amplitudes of variable light are mag and mag in and bands, respectively. There exists an unequal height between both maxima, i.e., O’Connell effect [17, 18]. Max.II at phase is brighter than Max.I at phase up to mag and mag in and bands, respectively. This kind of stellar activity occurs on other W UMa-type binaries, such as VW Cep [19], DV CVn [20], V532 Mon [21], and BB Peg (Kalomeni et al. 2007), and DZ Psc [22].

##### 2.2. Low-Precision Spectrum

The low-precision spectrum for MT Cas was obtained by using the* Yunnan Faint Object Spectrograph and Camera* (YFOSC), which is attached to the 2.4-m telescope at Lijiang station (LJs) of Yunnan Astronomical Observatory of China (YNAO) at UT 15:50:13 of 2018 October 22. During the observing process, we chose a 140-mm-length slit and a* Grism*-3 with a wavelength range from to [23]. The exposure time is 10 minutes. The phase of 0.98 almost corresponds to the observed middle time HJD 245414.1634. Reduction of the spectra was performed by using IRAF packages, including bias subtraction, flat-fielding, and cosmic-ray removal. Finally, the one-dimensional spectrum was extracted. With the* winmk* software (http://www.appstate.edu/~grayro/MK/winmk.htm), we obtained a normalized spectrum, which is displayed in Figure 2. By comparing the spectra of standard stars [24], the spectral type is determined to be F8V for the primary (i.e., more massive component) of this binary because the secondary is eclipsed by the primary around phase 0.0 for the W-type contact binary (see Section 4).

#### 3. Eclipse Times and Period Analysis

From our new observations and AAVSO’s data, several times of primary and secondary minima are generally determined by using the method of Kwee & van Woerden [25]. From ASAS-SN database, we downloaded 134 data types in* V* band for this binary. With the Period04 package [26], we obtained the power spectrum, which is shown in Figure 3. The searched frequency is , corresponding to 0.156937 days (i.e., half of an orbital period). The derived epoch HJD 2457010.9922 (i.e., the secondary eclipse time) a bit differs from the given rough epoch HJD 2457011.76746 from the ASAS-SN database. The individual single-color minimum timings with their errors are listed in Table 2.

In order to construct the curve (i.e., observed values minus calculated ones), we collected all available light minimum times. From the gateway (http://var2.astro.cz/ocgate) and TIDAK [14] (http://www.as.up.krakow.pl/minicalc/CASMT.HTM), we accumulated 10 “pg” (i.e., photographic), 21 “pe” (i.e., photoelectric), and 34 CCD measurements. Table 3 lists all those eclipsing times, whose errors are not given for 10 pg, 4 pe, and 1 CCD from literature. The standard derivations for all pe and CCD data are averaged to be 0.00137 days. For light minimum times without errors, we adopted the errors of 0.0137 for 10 pg data and 0.0014 days for 4 pe and 2 CCD ones. Therefore, the used weights depend on their errors while fitting the curve.

By using the linear ephemeris [14],we compute the initial residuals, , which are listed in Table 3 and shown in Figure 4(a). From this figure, there exists a long gap between HJD 2430024.400 [10] and HJD 2451550.2943 [27], except for three data types [12]. However, the general trend of may be evidently described by an upward parabolic curve. A linear least-squares fitting method with weights leads to the following ephemeris:After being removed by Eq. (2), we obtained the final residuals of , which are listed in Table 3 and shown in Figure 4(b). If we neglected low-precision photographic data, we could find no regularity, such as sinusoidal variation, only from pe and CCD data, which can be directly seen from the right part of Figure 4(b) except for a bit scatter.

#### 4. Modeling Light Curves

From the AAVSO and ASAS-SN databases, two additional* V*-band LCs for MT Cas are available and are displayed in Figure 5. Therefore three sets LCs are applied to derive the photometric elements with the updated Wilson-Devinney binary star modeling program [28, 29] (W-D program can be accessed from the site of ftp://ftp.astro.ufl.edu/pub/wilson/lcdc2015.). Kurucz’s [30] stellar atmosphere model was applied. Based on the spectral type of F8V with a subtype error, we adopted a mean effective temperature for the more massive component (i.e., the primary) to be (the subscripts “p” and “s” refer to the primary component and the secondary one, respectively). We fixed the gravity-darkening coefficients of [31] and bolometric albedo coefficients of [32], which are appropriate for stars with convective envelopes. The logarithmic limb-darkening coefficients are interpolate from van Hamme’s [33] tables. Other adjustable parameters are , , , , and .

**(a)**

**(b)**

Due to lack of radial velocity curves, the “q-search” process is carried out by obtaining a series of tried solutions from light curves. Modeling calculations start to mode 2 (i.e., detached configuration) and always converge to mode 3 (i.e., contact one). For several fixed inclinations from to with a step of , we first performed a series of solutions. Five computed curves for are shown in Figure 6(a), in which a minimum squared residual, , occurs around and . As a free parameter for the orbital inclination, we obtained the relations of and (the fill-out factor for contact binary is defined by , in which and are inner and outer critical potentials, respectively), which are displayed in Figure 6(b). The mass-ratio of with a minimum value of indicates that MT Cas is a W-type contact binary (i.e., the less massive component eclipsed by the more massive component at the primary minima; see [34]). After is considered to be a free parameter, we deduced the photometric solution, which is listed in Table 4. The calculated light curves as dotted lines are shown in Figure 1. Because LCs in 2013 cause unequal heights between both light maxima up to Max.I-Max.II mag, a dark spot is added in modeling the asymmetric LCs. Assuming a cool spot on the equator of the more massive component (i.e., colatitude, ), we obtained the final photometric elements, which are given in Table 4, including other three parameters of spot (i.e., longitude , angular radius , and temperature factor ). The mass ratio and fill-out factor for MT Cas are and , respectively. The corresponding theoretical light curves as solid lines are plotted in Figure 1. The O’Connell effect for this binary can be attributed the activity of stellar spot. Its area is up to of the area of the more massive component. Therefore, the spotted solution is accepted to be the final solution due to its small value of . Additionally, we analyzed AAVSO’s and ASAS’ LCs, respectively. The derived photometric solutions are given in Table 4. The mass ratio and fill-out factor almost agree with the previous result from our light curves. The calculated LCs are plotted as continuous lines in Figure 6. Their mass-ratios approximate to the result of the photometric solution with a cool spot.

**(a)**

**(b)**

#### 5. Results and Discussions

Up to now no spectroscopic elements have been published, and the absolute parameters of this binary cannot be directly determined. Assuming the spectral type of F8V with a subtype uncertainty, the mass of the primary was roughly estimated to be [35]. Using the mass ratio and orbital period, the separation between components and the mass of the secondary are estimated to be and , respectively. Other absolute parameters for MT Cas are as follows: , , , and .

The mass-luminosity diagram is displayed in Figure 7, in which the zero-age main sequence (ZAMS) and the terminal-age main sequence (TAMS) are constructed by the binary-star evolution code [36]. The W-type low-temperature contact binaries (LTCBs; see [3]) are plotted as black open and filled circles. From this figure, the primary component of MT Cas is close to the TAMS line, implying that it is a normal main-sequence star. Meanwhile, the secondary component lies above the TAMS line, indicating that it may be a small helium star in an advanced evolutionary stage [4].

From Eq. (2), the orbital period of MT Cas may be undergoing a secular increase at a rate of . This case occurs in other weak-contact binaries, which are listed in Table 5. Therefore, the period increase rate for MT Cas may be a small value for this kind of binaries. The long-term period increases can be generally interpreted by mass transfer from the less massive component to the more massive one. Under conserved mass transfer assumption, the mass transfer rate can be computed by the following formula [37]:Inserting the values of , , , and into Eq. (3), the mass transfer rate is estimated to be . With the period increasing, the separation between two components will increase. Meanwhile, mass transfer from the secondary one to the primary one also causes the mass ratio to decrease. This may result in the inner and outer Roche lobes shrinking, which will cause the fill-out factor to decrease. Finally, the weak-contact configuration may be broken. Therefore, MT Cas may evolve into a broken-contact configuration, as predicted by TRO theory [3, 38–40]. In the future, it necessitates to obtain high-precision photometry and spectroscopy to identify the orbital period variations and to determine its absolute parameters.

#### Data Availability

The data used to support the findings of this study are included within the article.

#### Conflicts of Interest

The authors declare that they have no conflicts of interest.

#### Acknowledgments

This research is partly supported by the National Natural Science Foundation of China (grants Nos. 11873003 & 11473009), Natural Science Research Project of the Educational Department of Anhui Province (grant No. KJ2017A850), and the Outstanding Young Talents Program (grant No. gxyq2018161) of the Educational Department of Anhui Province. New observations of MT Cas were obtained by using the 60/85-cm telescopes at the Xinglong Station of NAOC and 2.4-m telescope at the Lijiang Station of YNAO.

#### Supplementary Materials

Table 1: CCD photometric observations in* V* and* R*_{c} bands.* (Supplementary Materials)*