本论文主要分为两部分:激变变星星族合成研究与相接双星的测光研究。激变变星是由一颗白矮星和一颗充满洛希瓣的次星组成的半相接密近双星系统，得益于奇特的观测特征与内部复杂的物理过程，它吸引着众多天文学家的关注。在本论文中，我们使用恒星演化程序MESA (Modules for Experiments in Stellar Astrophysics) 计算了吸积氦白矮星的演化，得到相应的稳定燃烧带，然后我们使用快速恒星演化程序BSE与MESA对激变变星进行了星族合成研究，主要研究成果如下:(1)我们构建了氦白矮星的吸积模型，并分析其在不同吸积率下的演化，得到了氦白矮星的稳定吸积带。(2)我们计算了激变变星中白矮星的质量变化，对激变变星进行了星族合成研究，发现部分白矮星可以在吸积中显著地增加质量。我们得到的激变变星中白矮星的平均质量为0.78 M⊙，与观测中白矮星的平均质量0.83 M⊙很接近。在我们模型的假设下白矮星质量小0.5 M⊙的激变变星样本仅占很小一部分，约为3.5%。(3)我们考虑了在观测选择效应下激变变星的周期分布。在假设激变变星的探测概率正比于物质转移率的情况下，星族合成结果虽然能呈现激变变星2-3小时左右的周期空隙，但整体上不能与观测很好的符合。上述选择效应可能不足以描述观测时的复杂性，需要考虑其它形式的选择效应。相接双星是两颗子星都充满洛希瓣的密近双星系统。由于两颗子星共享一个公共包层，两颗子星有相近的表面有效温度，所以相接双星具有EW型光变曲线。我们使用云南天文台的一米光学望远镜对两个相接双星样本进行了测光观测，然后使用W-D程序对样本进行了解轨分析，得到了相关物理参量，主要研究成果如下:(1)通过对AR Boo在BVR波段的光变曲线分析，我们发现AR Boo是一颗质量比 q=m2/m1=1.865的W次型相接双星，相接度为 f=12.7%。通过 O-C方法的周期分析，我们发现 AR Boo的轨道周期以2.04×10-7 days yr-1长期增加并伴随39.05年的周期性变化，我们分析了可能引起这种周期变化的两种机制(光时效应和磁活动调制)并给出了相关参数。(2)我们使用W-D程序对AV Pup的VRcIc波段的光变曲线进行了分析， 结果显示AV Pup 是一颗特殊的A次型相接双星系统：它具有较大的质量比 (q=m2/m1=0.896)和较低的相接度(f=10%)。O-C分析结果显示AV Pup的周期以 dP/dt=4.83×10-7 days yr-1的速率长期增加，这可能是从小质量子星向大质量子星的物质转移引起的。
其他摘要
This thesis consists of two parts: the population synthesis of cataclysmic variables (CVs) and the photometric study of contact binaries.CVs are close binaries consisting a white dwarf (WD) and a Roche lobe overflowing donor star. Owing to the peculiar observation characteristics and complex physical processes inside, CVs draw attention of many astronomers. In this thesis, we use the stellar evolution code MESA (Modules for Experiments in Stellar Astrophysics) calculate the evolution of accreting Helium WDs and get the steady burning region, then we use rapid stellar evolution code BSE and MESA to conduct the population synthesis for CVs, the main results are as follows:(1) We build the accreting models for Helium WDs and analysis the evolution for different accreting rates. By these procedures, we get the steady burning region for Helium WDs.(2) We consider the mass increase of WDs in CVs and perform population synthesis for CVs. The result shows that part of WDs can get a significant mass increase in the accreting process. The mean mass of WDs in our analysis is 0.78 M⊙, which is close to the value of observation 0.83 M⊙. According our assumption, only a small fraction (3.5%) of CVs have a WD mass less than 0.5 M⊙.(3) We calculate the period distribution of CVs in the influence of selection effects. We assume the detectability is proportional to the mass transfer rate. The results can reproduce the 2-3 h period gap, but the distribution are significantly different from the observation. It is suggested that the selection effect mentioned above can not describe the complexity of observation, we need to try some other formats of selection effect.Contact binaries are interacting binaries in which two components are overflowing their own Roche lobes. The two components of contact binary share a common envelope and have nearly identical effect temperatures, which make contact binaries show EW-type light curves. We carry out photometric observations for two contact binaries by using the 1 m telescope in Yunnan Observatories. We analyze the obtained light curves through Wilson-Devinney (W-D) code and get the physical parameters, and the main results are as follows:(1)We perform the photometric analysis for the contact binary AR Boo in BVR bandpasses. The solution shows that AR Boo is a W-subtype W UMa contact binary system with a mass ratio of q=m2/m1=1.865 and a fill-out factor of 12.7%. The O-C analysis shows that the orbital period of AR Boo has a continuous increase at a rate of 2.04×10-7 days yr-1, together with a cyclic variation with a period of 39.05 yr. The two mechanisms responsible for the period changes in the orbital period of AR Boo (light-travel-time effect and magnetic modulation) are discussed and the corresponding parameters are given.(2) We use W-D code to conduct the photometric analysis for AV Pup in VRcIc passbands. The solutions suggest that AV Pup is a peculiar A-subtype W UMa contact binary with a high mass ratio (q=m2/m1=0.896) and a low fill-out factor (f = 10%). The O-C analysis shows that the orbital period of AV Pup is increasing at a rate of 4.83×10-7 days yr-1, which can be explained by mass transfer from the less massive component to the more massive one.
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