The First Photometric Investigation and Spectroscopic Analysis of Two Contact Binaries: ASAS J124343+1531.7 and LINEAR 2323566

W UMa type stars are close binary systems usually consisting of two late-type stars. The two stars fill or over-fill their Roche lobes, and there exists a common convective envelope(CCE) (Lucy 1968a, 1968b) around two components. Due to the existence of a CCE, there may be mass transfer and energy exchange between two components (e.g., Li et al. 2015; Liao et al. 2017; Lee & Park 2018; Li 2018). The mass and angular momentum may also be lost from the binary system (e.g., Vanǹt Veer 1979; Rahunen 1981; van Hamme 1982; Qian 2001a, 2001b, 2003). Thus a series of physical processes will occur, such as the O'Connell effect (O'Connell 1951), thermal relaxation oscillation (TRO) (e.g., Flannery 1976; Lucy 1976; Robertson & Eggleton 1977), orbital period change, short period cut-off etc. (e.g., Ruciński 1992, 2007; Stepień 2006; Jiang et al. 2012; Li et al. 2019). In addition, there also exists the Applegate mechanism (Applegate 1992) and light-time effect (LTTE) (e.g., Irwin 1959; Mayer 1990; Wolf et al. 1999), which can be used to explain the periodic changes of the orbital period of W UMa type stars. These physical characteristics make the contact binaries have a more complex evolutionary process. Accordingly, contact binaries are also of great significance for studying the formation and evolution of eclipsing binaries (e.g., Qian et al. 2017, 2018).

ASAS J124343+1531.7 (2MASS J12434277+1531375, PY Com) was classified as an EW type binary star by Gettel et al. (2006) using the ROTSE-I telescope. Its period was reported as 0.266155 days, and the maximum and minimum V magnitude are 13.18 mag and 13.63 mag respectively. Later, Hoffman et al. (2009) defined ASAS J124343+1531.7 as a W UMa type star with a period of 0.30718 days. Drake et al. (2014) obtained the period for 0.26616 days and the amplitude of variation for 0.4 mag. Minimal timings of ASAS J124343+1531.7 were obtained by Diethelm (2009, 2010, 2011, 2012). Nevertheless, the study of photometric solutions and the period variations have not been published yet. This paper presents the complete BVR_c light curves first obtained in 2018, 2019 and 2020. Thereafter, the O − C analyses of orbital period and photometric solutions were put forward.

LINEAR 2323566 (2MASS J11514615+4750292) was first observed by the asteroid survey LINEAR (Palaversa et al. 2013), it was identified as an eclipsing binary with a period of 0.232872 days. The median LINEAR magnitude and amplitude variation were determined as 15.24 mag and 0.8 mag respectively. Later, Drake et al. (2014) identified LINEAR 2323566 as an EW type binary star and determined a period of 0.23287 days by the Catalina Surveys Data Release-1 (CSDR1). It has no photometric analyses or period investigations. During our observations, two complete BR_c light curves were obtained in 2016 and 2020 to do the photometric solution. Due to the lack of minima from other literatures, we only analyzed the orbital period using our observation data.

2.1. Photometric Observations

We observed ASAS J124343+1531.7 and LINEAR 2323566 using the 0.84 m f/15 Ritchey–Chrétien telescope at Observatorio Astronómico Nacional, Sierra San Pedro Mártir (OAN-SPM), Baja California, México, coupled with the Mexman filter-wheel and the Marconi3 CCD detector, equipped with Standard Johnson–Cousin–Bessel UBVR_c I_c filters, in 2016 Febuary, 2018 April and 2019 January. As well as the WIYN 0.90 m f/7.5 Cassegrain telescope at Kitt Peak National Observatory (KPNO), Arizona, USA, coupled with the Harris UBVR_c I_c filter-wheel and the S2KB CCD detector followed up the observations in 2020 February. The log of observations is shown in Table 1. All these CCD images were reduced using the IRAF ⁴ package and has been corrected by bias and flat. In order to identify good comparison stars, and to determine the relative magnitudes of the variables, the field stars were calibrated during very photometric nights in which Landolt standard fields were also observed. Tables 2 and 3 list the HJD and the magnitudes of ASAS J124343+1531.7 and LINEAR 2323566. Figure 1 shows the light curves of the two objects in phase. The ephemeris used to convert time into phase is shown below,

where the is the primary minimum of light curve of each year. It can be seen from the light curves that both of them are W UMa type stars and show the O'Connell effect.

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Table 1. Information of Observation for ASAS J124343+1531.7 and LINEAR 2323566

Objects	R.A. Decl.	Date	Filter(Exposure Time (s))	Filter(Number of data points)
ASAS J124343+1531.7	12 43 42.77+15 31 37.46	2018 Apr 22	B(50), V(25), Rc (15)	B(63), V(63), Rc (63)
		2019 Jan 24,		B(86), V(87), Rc (87)
		2020 Feb 15		B(42), V(42), Rc (42)
LINEAR 2323566	11 51 46.16+47 50 29.45	2016 Mar 20	B(50&100), Rc (30)	B(263), Rc (131)
		2020 Feb 16		B(78), Rc (39)

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Table 2. Photometric Data of ASAS J124343+1531.7

B			V			R
HJD	M(mag)		HJD	M(mag)		HJD	M(mag)
2018 Apr 22
2458230.69130	14.287		2458230.69072	13.417		2458230.69031	12.976
2458230.69337	14.316		2458230.69279	13.438		2458230.69238	13.004
2458230.69544	14.372		2458230.69486	13.469		2458230.69445	13.026
2458230.69751	14.403		2458230.69693	13.510		2458230.69652	13.058
2458230.69958	14.449		2458230.69900	13.561		2458230.69859	13.087
⋯	⋯		⋯	⋯		⋯	⋯
2458895.02813	14.260		2458895.02665	13.372		2458895.02518	12.934
2458895.03320	14.363		2458895.03136	13.433		2458895.02982	12.985
2458895.03834	14.462		2458895.03626	13.527		2458895.03471	13.070
2458895.04435	14.585		2458895.04208	13.621		2458895.04039	13.162
2458895.05094	14.583		2458895.04856	13.674		2458895.04703	13.232

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Table 3. Photometric Data of LINEAR 2323566

B			R
HJD	M(mag)		HJD	M(mag)
2016 Mar 20
2457467.65545	16.732		2457467.65651	15.021
2457467.65731	16.710		2457467.65943	15.020
2457467.65835	16.706		2457467.66236	14.992
2457467.66023	16.730		2457467.66528	14.979
2457467.66127	16.683		2457467.66820	14.951
⋯	⋯		⋯	⋯
2458896.03358	17.004		⋯	⋯
2458896.03710	17.104		⋯	⋯
2458896.03902	17.128		⋯	⋯
2458896.04271	17.221		⋯	⋯
2458896.04459	17.307		⋯	⋯

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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We also tried to find other sky survey data for these two targets, for example, All Sky Automated Survey (ASAS) (Paczynski et al. 2006), All-Sky Automated Survey for Supernovae (ASAS-SN) (Shappee et al. 2014), Catalina Sky Surveys (CSS) (Drake et al. 2014), Transiting Exoplanet Survey Satellite (TESS) (Ricker et al. 2015), Northern Sky Variability Survey (NSVS) (Woźniak et al. 2004), etc. Although these two targets were both observed, the quality of survey data except TESS is not good enough to support subsequent analysis work. Finally, we adopted only the TESS data for ASAS J124343+1531.7. The TESS data processed by lightkurve package (Lightkurve Collaboration et al. 2018) were downloaded from the Mikulski Archive for Space Telescopes (MAST). ⁵ The time span is about 25 days from 2020 March 21 to 2020 April 15. In order to better show the overall light curve, we used Equation (1) to convert the BJD of TESS data into phase and obtained the complete light curves in one period plotted in Figure 2. Later, we also used this data for orbit period and photometric analysis.

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2.2. Spectroscopic Observations of LAMOST

Guoshoujing Telescope (the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST)) is a 4 m reflecting Schmidt telescope equipped with 4000 fibers with a 5° field of view (Cui et al. 2012; Zhao et al. 2012). The wavelength coverage ranges from 3700 Å to 9000 Å (Du et al. 2016), and the overall spectral resolution of LAMOST is approximately 1800. The data were reduced with LAMOST pipelines (Luo et al. 2012). And the LAMOST spectral analysis pipeline (also called 1D pipeline, LASP) is used to classify and measure the spectra (Luo & Zhao 2001; Luo et al. 2004, 2008, 2012; Wang et al. 2010). Through LASP, the observed stellar spectra are classified into different subclasses by matching with template spectra (Wei et al. 2014). The spectra and parameters of ASAS J124343+1531.7 and LINEAR 2323566 were obtained from Data Release 7 ⁶ (Luo et al. 2015). Table 4 lists the spectral information of these two targets, including the observational data, Heliocentric Julian date, phase, spectral type, effective temperature (T_eff), log(g), radial velocity (RV) and signal to noise ratio of r filter (S/N-r). We downloaded these spectra and plotted them in Figure 3.

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Table 4. The Spectral Information of ASAS J124343+1531.7 and LINEAR 2323566 Released by LAMOST

Targets	Obsdate	HJD(d)	Phase	Subclass	Teff(K)	log(g)	RV (km s−1)	S/N-r	EWs: Hα (Å)
ASAS J124343+1531.7	2014 Mar 9	2456726.12748	0.11390	G9	5221.76 ± 50.97	4.342	−24.29	93.2	3.019 ± 0.018
	2017 Dec 18	2458106.42784	0.05481	G9	5083.87 ± 27.15	4.230	−9.46	119.8	3.361 ± 0.033
LINEAR 2323566	2014 Jan 21	2456679.31742	0.39520	K5	4464.32 ± 88.88	4.428	27.85	48.2	4.663 ± 0.083

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The 2015 version of the Wilson–Devinney (W-D) (Wilson & Devinney 1971; Wilson 1979, 1990; van Hamme & Wilson 2007; Wilson et al. 2010; Wilson & van Hamme 2014) program was used to analyze the new multi-passband CCD photometry and obtained the model parameters. The effective temperatures used in the W-D program are from LAMOST listed in Table 4. Since ASAS J124343+1531.7 has two spectra, we assigned an average temperature of 5153 ± 153 K as the final effective temperature of the primary star. The effective temperature of the primary star used in calculation was 4464 ± 89 K for LINEAR 2323566. According to Lucy (1967) and Ruciński (1969), the gravity-darkening coefficients and bolometric albedo coefficients were set as g_1,2 = 0.32 and A_1,2 = 0.5, respectively. Bolometric limb-darkening and bandpass limb-darkening coefficients were obtained from van Hamme (1993). The TESS band is added to the limb-darkening table by Professor Van Hamme (2021, private communication with Dr. Wang, Z. H.). During our modeling, Mode 3 was chosen for the two binary systems. Other parameters include the orbital inclination i, the effective surface temperature of the secondary star T₂, the dimensionless potentials of two components Ω₁ = Ω₂ and the monochromatic luminosity of the primary star L₁ were set as adjustable parameters.

First, we used all the observed data from OAN-SPM, KPNO, and TESS for ASAS J124343+1531.7 and LINEAR 2323566 to do the q-search process respectively, to determine their mass ratios. Then, we obtained solutions with mass ratios ranging from 0.1 to 10 with an interval of 0.1. The relationship between their mass ratios and residuals is shown in Figure 4. The mass ratios corresponding to their minimum residuals are 3.6 and 1.4, respectively. Consequently, we set them as the initial values of q and adjustable, and thereafter, the convergent solutions for mass ratios 3.758 and 1.438 were obtained. The photometric solutions corresponding to these mass ratios are considered to be the final solution of these two objects, and are applied to determine the physical parameters and discuss the evolutionary status. All the parameters and errors of photometric solutions are listed in Table 5.

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Table 5. Physical Parameters of ASAS J124343+1531.7 and LINEAR 2323566

Star	ASAS J124343+1531.7	LINEAR 2323566
T1(K)	5153	4467
q(M2/M1)	3.758 ± 0.028	1.438 ± 0.040
T2	4833 ± 5	4382 ± 10
i(deg)	77.4 ± 0.2	87.4 ± 0.6
Ω1 = Ω2	7.404 ± 0.037	4.348 ± 0.063
L1B /LB	0.335 ± 0.003	0.465 ± 0.003
L1V /LV	0.314 ± 0.003	⋯
	0.299 ± 0.003	0.449 ± 0.003
L1TESS/LTESS	0.290 ± 0.001	⋯
r1	0.287 ± 0.001	0.358 ± 0.003
r2	0.515 ± 0.004	0.423 ± 0.013
f	31.8 ± 5.8 %	14.9 ± 10.9 %

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Since the two maxima of the light curves are not equal for these two objects, this indicates that they both exist O'Connell effect, which is generally caused by the existence of spots (e.g., V789 Her and V1007 Cas, Li et al. 2018). Therefore, we added spot parameters when using W-D program and fitted them according to observations at different times to study the changes of spots. We divide the data of ASAS J124343+1531.7 into three parts, 2018 and 2019, 2020 February for our observations and 2020 March and April for TESS, while the data of LINEAR 2323566 into two parts, 2016 and 2020 for our observations. Their mass ratios are respectively set to 3.758 and 1.438, then the spot parameters are adjusted to obtain the best fitting solution. We have tried adding cool spot or hot spot on the primary or secondary stars, and finally we obtained the best results when we used a single cool spot on the hotter star. The theoretical light curves of different times are plotted in Figure 5, it can be seen that the two maxima of light curves fit well, the residuals between observed data and theoretical light curves are almost flat. The spot parameters at different times are listed in Table 6.

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The geometric structure under different spot parameters at phase 0.25 and 0.75 are displayed in Figure 6, where the model of the binary systems and the location of the cool spot are displayed more intuitive. The dimension parameters of the corresponding geometric structure are also listed in Table 6. The errors obtained by the W-D method are mathematical fitting and have no physical meaning.

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In order to analyze the orbital period changes of ASAS J124343+1531.7 and LINEAR 2323566, we used the K-W method (Kwee & van Woerden 1956) to calculate the eclipsing times. However, the time resolution of TESS data for ASAS J124343+1531.7 is low, on account of the 30 minute observation cadence. Therefore, we used the phase shift method to apply higher density light curves. First, we divided TESS light curves into four parts, the BJD time span of these four parts are 2458929.51622 to 2458935.24541, 2458936.26624 to 2458940.82870, 2458946.74526 to 2458951.32849 and 2458951.34932 to 2458954.80755, and the number of points in each part is 234, 215, 165 and 166, respectively. Second, using the equation BJD = BJD₀ + P × E, where BJD is the observing time, BJD₀ is the reference time for each part, which are 2458932.120404, 2458938.245397, 2458948.620222 and 2458952.620118, and P is the orbital period of ASAS J124343+1531.7. Ultimately, we moved the long time-span data into one period and determined the four panels of Figure 7. Then, we obtained 8 eclipsing times from these four sets of light curves.

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Combining other literatures, public data and our own observations, we collected 16 and 4 minima for ASAS J124343+1531.7 and LINEAR 2323566 respectively shown in Table 7. The ephemerides used to calculate O − C (observation-calculation) values are:

Since the minimum moments of TESS data for ASAS J124343+1531.7 are given in BJD, we converted other observed minima from HJD to BJD. The calculated epoch and O − C values were also listed in Table 7, and the corresponding data points were plotted in Figure 8.

The trend of ASAS J124343+1531.7 shows slightly nonlinear variations. Therefore we fitted the O − C values with an upward parabola, where the revised ephemeris is as follows,

From Equation (3), the coefficients of second-order term are positive, indicating that the period of ASAS J124343+1531.7 is secular increase and the rate is calculated as dp/dt = 1.239 × 10⁻⁷ d · yr⁻¹. After removing the parabolic term from O − C trend, the residuals are plotted in the lower panel. The residuals are almost flat, which indicates the O − C values were fitted well. While LINEAR 2323566 has very few data points, and the distribution of data points shows no nonlinear change, as shown on Figure 8. Therefore, we only performed simple linear fitting on LINEAR 2323566, and obtained the new ephemeris as follows,

The residuals of the fitting are also displayed in the bottom panel of Figure 8, and the corresponding data are listed in Table 7.

Due to the 2015 version of the W-D program can also analyze the times of minima, then we included the minima data of these two objects during the W-D process to solve the epoch, period and orbital period variation. Then, we transformed the results into the form of Equations (3) and (4) as shown below,

Equation (5) is for ASAS J124343+1531.7, which exists a long-term increase in the orbital period, and the rate is calculated as dp/dt = 1.241×10⁻⁷ d · yr⁻¹. Equation (6) is for LINEAR 2323566, which obtained a new linear ephemeris. By comparison, it can be seen that the results of the two methods are almost the same.

Since both ASAS J124343+1531.7 and LINEAR 2323566 exhibit the O'Connell effect, we used a spot generally caused by magnetic activity to explain this phenomenon. In order to further confirm whether in these two objects exist magnetic activity, we analyzed the spectral lines below. The observed spectra not only shows chromospheric activity, but also mix in some spectral lines of photosphere. In order to use the intensity of H_α line to analyze their magnetic activity, we adopted a spectral subtraction technique conducted by Barden (1985). Some other objects also used this method, for example, ASAS J082243+1927.0 (Kandulapati et al. 2015), EPIC 202073314 (Sriram et al. 2018), V582 Lyr (Cheng et al. 2019); V384 Ser, AQ Psc, V480 Gem and 2MASS J07095549+3643564 (Zhang et al. 2020).

First, we selected some targets with a temperature difference of 100 K above or below our objects from a catalog of radial velocity standard stars (Huang et al. 2018). Then we used these targets to search in LAMOST Data Release 7. Finally, we obtained 7 and 8 template spectra for ASAS J124343+1531.7 and LINEAR 2323566, respectively, and used these inactive spectra to construct the synthesized spectra. Combining the object and template spectra, a total of 18 spectra were normalized by IRAF package Continuum. We obtained their residuals by subtracting the comprehensive spectra from the object spectra, and all the spectra exclude the region of H_α . Then the best template spectra were determined as 2MASS J19141861+4238492 and KIC 7446560 for the two objects respectively. The spectral type and temperature were determined as K1 and 5028K for 2MASS J19141861+4238492, K5 and 4377 K for KIC 7446560. We subtracted their best template spectra from the observed spectra to obtain the subtracted spectra, which is the chromospheric construction. All of the observed, synthesized and subtracted spectra are displayed in Figure 9. From the intensity of emission line H_α , LINEAR 2323566 has stronger chromospheric activity than ASAS J124343+1531.7. The equivalent widths (EWs) were calculated using IRAF package Splot, which are listed in Table 4.

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Using the light curve analysis, we determined the physical parameters of ASAS J124343+1531.7 and LINEAR 2323566, which are shown in Table 5. The mass ratio and fill-out factor are 3.758 ± 0.028 and 31.8% ± 5.8% for ASAS J124343+1531.7, 1.438 ± 0.040 and 14.9% ± 10.9% for LINEAR 2323566. Therefore, ASAS J124343+1531.7 is a W-subtype median contact binary, while LINEAR 2323566 is a W-subtype shallow contact binary. The O'Connell effect of these two systems prove that it may exist magnetic activity. Spectral analysis obtained the EWs of the emission line H_α , which confirmed the possibility of magnetic activity of these two objects.

According to Yakut & Eggleton (2005), the statistics show that the more massive stars of W-type and A-type low-temperature contact binaries (LTCBs) usually locate in the main sequence. Consequently, assuming the more massive star is a main sequence star and referring to Cox (2000), the spectral type of the more massive star is classified by the effective temperature as K3 and K5, then the mass was determined by the spectral type as M₂ = 0.75M_⊙, 0.68M_⊙. Subsequently the mass of less massive star is also calculated according to the mass ratio and the mass of more massive star, M₁ = 0.20M_⊙, 0.47M_⊙. Combining the mass and period, the orbital semimajor axis was determined using the third law of Kepler, M₁ + M₂ = 0.0134 × a³/P², a = 1.71R_⊙, 1.67R_⊙. Simultaneously, the radius and luminosity of the two components were computed by using the photometric solutions and Stefan-Boltzman law, R₁ = 0.49R_⊙, 0.60R_⊙, R₂ = 0.88R_⊙, 0.71R_⊙, L₁ = 0.15L_⊙, 0.13L_⊙, L₂ = 0.38L_⊙, 0.17L_⊙. The error bars are obtained by error transmission. All the absolute parameters of ASAS J124343+1531.7 and LINEAR 2323566 are listed in Table 8.

Both of the two targets have been observed by Gaia (Gaia Collaboration et al. 2016, 2018), we obtained the Gaia distances, 361.8 pc for ASAS J124343+1531.7 and 678.7 pc for LINEAR 2323566. Considering the interstellar extinction, we calculated their apparent magnitudes using luminosity from WD solution and Gaia distance, and obtained 13.536 mag for ASAS J124343+1531.7 and 15.838 mag for LINEAR 2323566. Our apparent magnitude of photometric values is about 13.20 mag for ASAS J124343+1531.7, while apparent magnitude from Drake et al. (2014) is 15.38 mag for LINEAR 2323566. The apparent magnitudes derived by the two methods are somewhat different, this may be caused by that there are some differences between the estimated absolute parameters and the real ones.

6.1. Mass Transfer Between two Components

According to the analysis of the orbital period, the overall trend of O − C shows an upward parabolic composition with a rate of dp/dt = 1.239×10⁻⁷ dyr⁻¹ for ASAS J124343+1531.7. The long-term increase can probably be explained by the mass transfer from the less massive to the more massive star. Then we used the following equation to calculate the rate of mass transfer,

dM₁/dt = −4.22 × 10⁻⁸ M_⊙ yr⁻¹ was determined. The negative sign indicates that the less massive star M₁ is losing mass, while the more massive star M₂ is receiving mass. Then we discuss the possible subsequent evolution of ASAS J124343+1531.7. As the mass transfer, mass ratio will increase and the distance between the two components will increase. Therefore, the degree of contact will gradually become smaller, ASAS J124343+1531.7 will evolve from the current contact binary to a semi-contact binary or detached binary. Consequently, ASAS J124343+1531.7 is a good target for studying the TRO model (Flannery 1976; Lucy 1976; Robertson & Eggleton 1977), follow-up observations are also needed to confirm this result.

6.2. Evolutionary Status

In order to study the evolutionary status of these two objects, the diagram of mass–luminosity and mass–radius were plotted in Figure 10. The solid and dotted lines show the zero age main sequence (ZAMS) and the terminal age main sequence (TAMS) constructed by the BSE Code (Hurley et al. 2002). Circles and rhombuses respectively represent 30 A-subtype and 42 W-subtype binary derived from Yakut & Eggleton (2005). Red stars and blue stars respectively represent the two components of ASAS J124343+1531.7 and LINEAR 2323566. All solid symbols represent the more massive components, whereas the open symbols denote the less massive ones. The positions of the two objects in the diagram are consistent with the trend of the other binaries. The more massive stars of ASAS J124343+1531.7 and LINEAR 2323566 locate above the ZAMS line and below the TAMS line. The less massive star of ASAS J124343+1531.7 locates above the TAMS line, while LINEAR 323566 locates above the ZAMS line and below the TAMS line. This manifests that the two components of LINEAR 2323566 are both slightly evolved stars. And for ASAS J124343+1531.7, the more massive star is a main sequence star, the less massive star has evolved out of the main sequence and is over-luminous and over-sized.

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In summary, the photometric solutions and period variation of ASAS J124343+1531.7 and LINEAR 2323566 were obtained first. Through light curve analysis, it is found that ASAS J124343+1531.7 is a W-subtype median contact binary, while LINEAR 2323566 is a W-subtype shallow contact binary. They both present the O'Connell effect, which can be explained by a cool spot on the primary star. The existence of the cool spot may be caused by magnetic activity, and at the same time, the weak H_α emission lines on the spectra also indicate that the two objects possess magnetic activity. Through the analysis of the orbital period, we obtained ASAS J124343+1531.7 exists a secular period increase, which is likely caused by the mass transfer from the less massive star to the more massive star. We obtained a new ephemeris for LINEAR 2323566. The two components of ASAS J124343+1531.7 are both main sequence stars. While for LINEAR 2323566, the more massive star is a main sequence star, the less massive star has evolved out of main sequence and is over-luminous and over-sized. In the future, more observations combining photometry and spectra are needed to verify the variations of orbital period and the evolution of ASAS J124343+1531.7 and LINEAR 2323566.

We are very grateful for the very helpful comments and suggestions of the referee. This work is supported by the Joint Research Fund in Astronomy (No. U1931103) under cooperative agreement between National Natural Science Foundation of China (NSFC) and Chinese Academy of Sciences (CAS), and by NSFC (No. 11703016), and by Young Scholars Program of Shandong University, Weihai (Nos. 20820171006), and by the Open Research Program of Key Laboratory for the Structure and Evolution of Celestial Objects (No. OP201704). RM acknowledges the financial support from the Universidad Nacional Autónoma de México (UNAM) and DGAPA under grant PAPIIT IN 100918.

We acknowledge the support of the staff of OAN-SPM. Based in part on observations at Kitt Peak National Observatory, NSF's NOIRLab, managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. The authors are honored to be permitted to conduct astronomical research on Iolkam Du'ag (Kitt Peak), a mountain with particular significance to the Tohono O'odham. The 0.9m telescope is operated by WIYN Inc. on behalf of a Consortium of partner Universities and Organizations (see www.noao.edu/0.9m for a list of the current partners). The WIYN Observatory is a joint facility of the University of Wisconsin–Madison, Indiana University, NSF's NOIRLab, the Pennsylvania State University, Purdue University, University of California, Irvine, and the University of Missouri. Guoshoujing Telescope (the Large Sky Area Multi-Object Fiber Spectroscopic Telescope LAMOST) is a National Major Scientific Project built by the Chinese Academy of Sciences. Funding for the project has been provided by the National Development and Reform Commission. LAMOST is operated and managed by the National Astronomical Observatories, Chinese Academy of Sciences. This paper includes data collected by the TESS mission, which are publicly available from the Mikulski Archive for Space Telescope (MAST). Funding for the TESS mission is provided by NASA's Science Mission directorate. We acknowledge the TESS team for its support of this paper. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC; https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.

The calculations in this work were carried out at Supercomputing Center of Shandong University, Weihai.