在大量的通常由内部的辐射区和对流包层构成的晚型恒星上，黑子活动是普遍存在的现象。受到恒星自转调制的黑子活动不仅会带来光变，同时也会影响光谱观测。对于晚型分离食双星而言，人们不仅可以通过测光和光谱数据确定其绝对物理参数，如质量和半径，而且可以通过分析由黑子活动带来的光变去探究黑子的属性（如黑子的大小，寿命），以黑子为代表的恒星活动周以及恒星表面的较差自转。同时，对于不同光谱型的分离食双星的研究，有助于了解不同物理属性下的黑子活动。特别是对于小质量的分离食双星而言，其黑子活动比较显著，会影响视向速度的测量，进而影响恒星物理属性的测定。研究小质量的分离食双星，有助于理解小质量恒星中的半径膨胀效应这一难题，即与标准的恒星演化模型相比，小质量恒星的半径比模型预测值高出约10%。
本论文基于Kepler/TESS 的测光和LAMOST 光谱数据，开展了晚型分离食双星的黑子活动研究。研究对象为Kepler 天区的两颗光谱型为F 型的分离食双星KIC 8301013 和KIC 6525196，以及TESS 天区的一颗光谱型为K 型的分离食双星TIC 157376469。本论文取得的主要成果如下：

（1）对F 型分离食双星KIC 8301013，解轨得到了该双星的物理参数，首次得到了该双星系统的黑子活动强度和衰减时标。
基于Kepler 为期4 年光变曲线和LAMOST-Kepler 项目的中低分辨率光谱数据，利用Wilson–Devinney（WD）程序，我们对轨道周期约为4.4 天的F 型的分离食双星KIC8301013 构建了一个双星模型，首次得到了该双星系统的基本参数以及食外残差的光变曲线。主星和次星的质量和半径分别为M1 = 1.29 ± 0.02M⊙, R1 = 1.45 ± 0.01R⊙,M2 =1.11 ± 0.05M⊙, R2 = 1.20 ± 0.01R⊙。利用ACF 和Lomb-Scargle periodogram，对食外残差进行了周期分析、时频分析以及黑子演化分析，首次发现该双星系统在大多数时间里有两个主要的经度相差约为180 度的黑子活动区，活动区的衰减时标的量级约为几十天，用食外残差光变的均方差表示的活动区的平均大小为0.002 mag，活动区的转动周期与双星的轨道周期接近。这两个活动区转动的周期的差异和变化与较差自转和活动区的迁移有关。与太阳黑子相比，该F 型主序双星的黑子的活动性明显较强。与F 型单星相比，其活动水平没有显著的差异。

（2）对F 型分离食双星KIC 6525196，通过解轨得到了双星的物理参数，首次获得了该双星系统的黑子活动周期。
利用与分析KIC 8301013 相同的方法，对F 型分离食双星KIC 6525196 进行了双星模型以及食外残差分析得出，主星和次星的质量和半径分别为M1 = 1.02 ± 0.01M⊙,R1 = 1.13 ± 0.01R⊙,M2 = 0.95 ± 0.01M⊙, R2 = 1.07 ± 0.01R⊙。首次在KIC 6525196 上发现了两个经度相差约为180 度的黑子活动区，并得到了该活动区的衰减时标（量级在几十天）和活动区的平均大小（0.002 mag）。F 型主序食双星KIC 6525196 的黑子活动水平与KIC 8301013 的黑子活动水平相当，强于太阳黑子，与F 型单星并无显著差异。通过KIC 6525196 的食外残差的光变振幅的周期分析，首次发现该双星系统的黑子活动存在一个约244 天的周期。

（3）对K 型分离食双星TIC 157376469，通过解轨得到了双星的物理参数，首次发现了该双星系统的主星的半径膨胀。
基于TESS 的时长约27 天的测光数据和LAMOST 的中低分辨率光谱数据，我们对一个短周期（1.3 天）的分离食双星TIC 157376469 进行了测光和光谱分析，得出了一个新的线性历元。利用WD 程序，对光变曲线和视向速度曲线进行同时拟合，结果表明TIC157376469 由两个光谱型为K 型的小质量主序星构成，并且主星是一个具有黑子活动的恒星。主星和次星的质量和半径分别为：M1 = 0.704 ± 0.028M⊙,R1 = 0.754 ± 0.010R⊙,M2 = 0.539 ± 0.021M⊙, R2 = 0.543 ± 0.007R⊙。与PARSEC v1.2 等年龄线相比，首次发现主星的半径膨胀了约～ 16%，大于通常的小于10% 的半径膨胀。而次星的半径则与模型的预言基本一致。

Starspot activity is usually common on late-type stars with inner radiative region and outer convective envelope. Starspot activity modulated by stellar rotation not only bring light variation, but also have a effect on spectroscopic measurement. For late-type detached eclipsing binary, the absolute properties of the binary (such as masses and radii) can be determined by using photometric and spectroscopic data. The light curves with starspot modulation can be used to study the properties of the starspots (e.g. spotsize and lifetime), starspot activity cycle and difference rotation.Furthermore, the study of detached eclipsing binaries with different spectral types is helpful in understanding the starspot activity with different physical properties. Especially for low-mass detached eclipsing binaries, the statspot activity is significant, which will affect the measurement of radial velocities, and thus affect the determination of the physical properties of the binaries. The study of low-mass detached eclipsing binaries helps to understand radius expansion effects in low-mass eclipsing binaries, namely, the radii of low-mass stars obtained from photometric and spectroscopic observations is about 10% higher than those predicted by stellar models.

Based on Kepler/TESS photometric and LAMOST spectral data, this paper studies starspot activity in late-type detached eclipsing binary. The study objects of this paper are two F-type detached eclipsing binary, KIC 8301013 and KIC 6525196, and a K-type detached eclipsing binary TIC 157376469, respectively. The main achievements of this paper are as follows.

(1)For KIC 8301013, we obtain the physical properties of the binary system, the intensity and decay timescale of starspot activity on the binary for the first time. Based on Kepler four-year light curves and spectroscopic data from LAMOST-Kepler project and using the Wilson-Devinney (WD) code and, we construct a binary model for KIC 8301013 with orbital period of P ≈ 4.4 days to determine absolute properties of the binary and the out-of-eclipse flux residuals. The masses and radii for the primary and secondary are, respectively, M1 = 1.29 ± 0.02M⊙, R1 = 1.45 ± 0.01R⊙, M2 = 1.11 ± 0.05M⊙, R2 = 1.20 ± 0.01R⊙. Using autocorrelation function (ACF) and Lomb-Scargle periodograms, we carry out period analysis, time-frequency analysis, starspot evolution analysis for the out-of-eclipse residuals. The results shows that there are two active region with longitudes separated by 180? in most of time for the first time. The decay time-scale of active region and their mean size are determined to be tens of days and 0.002 mag, respectively. The rotation period of the active regions are close to the orbital period of the binary. The rotation period difference between the two active regions and the variation of the two periods are related to difference rotation and the latitude migration of active regions. Comparisons with the sunspot, the starspot activity level on F-type the binary is significantly stronger. There no big difference of starspot activity level between the F-type binary and the F-type individual star.

(2)For KIC 6525196, we obtain the physical properties of the binary system. The starspot activity cycle on the binary system is obtained for the first time. Using the same method as the analysis of KIC 8301013, a binary model for F-type eclipsing binary KIC 6525196 is constructed and the out-of-eclipse residuals are analysed. The masses and radii of two components are, respectively, M1 = 1.02 ± 0.01M⊙, R1 = 1.13 ± 0.01R⊙,M2 = 0.95 ± 0.01M⊙, R2 = 1.07 ± 0.01R⊙. Two active region with longitudes separated by 180 is also found on KIC 6525196. The decay timescale of active region are determined to be tens of days. The mean size of the active region is 0.002 mag. Similar to the activity level of KIC 8301013, the activity level of KIC 6525196 is stronger than that of sunspots, and isn't significantly different from that of the F-type single stars. The periodic analysis of the light variation of out-of-eclipse residuals of KIC6525196 shows that the starspot activity of the binary has an activity cycle of about 244 days for the first time.

(3)For TIC 157376469, we obtain the physical properties of the binary system. The radius inflation of the primary is found for the first time. Using the TES S light curves (27 days long) and LAMOST data, we perform a photometric and spectroscopic analysis for the short-period (～ 1.3 days) eclipsing binary TIC 157376469. A new linear ephemeris is obtained. Using the WD code to fit the light curves and radial velocity curves, the results show that TIC 157376469 is composed of two K-type low-mass main-sequence stars. The masses and radii of the primary and secondary are, respectively, determined to be M1 = 0.704 ± 0.028M⊙, R1 = 0.754 ± 0.010R⊙, M2 = 0.539 ± 0.021M⊙, R2 = 0.543 ± 0.007R⊙. The primary is a star with starspot activity. Compared with the PARSEC v1.2 isochrones, we found for the first time that the radius of the primary is oversized of ～ 16%, which is larger than the usual sub-10% radius inflation. While, the radius of the secondary is almost consistent with the models.