| 摘要 | 𝛾 Dor 型脉动变星是上世纪九十年代发现的一类主序变星。观测研究发现该 类型脉动变星的脉动周期约为 0.3−3.3 天，光变振幅约为 0.01 星等，光谱范围为 A7−F5，质量范围为 1.5 M⊙-1.8 M⊙, 光度等级为 IV−V。𝛾 Dor 型脉动变星通常表现出由对流阻塞效应驱动的 g 模式脉动，可用于探测恒星的内部结构。这类变星在赫罗图上位于经典脉动不稳定带底部与主序带的交界处，且还与𝛿 Sct 型脉动变星的红边界存在重叠区域。观测发现一些位于该重叠区域内的变星，被称 为 𝛾 Dor 和 𝛿 Sct 混合型脉动变星，它们同时存在着 g 模式和 p 模式脉动。g 模式和 p 模式脉动可以分别反应恒星内核和恒星外包层的情况，故而这类恒星也 是星震学研究的重点对象。密近双星是求解恒星基本物理参量最准确和可靠的天体系统。当 𝛾 Dor型脉动变星处于密近双星系统中时，可准确地确定其物理参量，便于精确地确定其脉动模式，进一步分析恒星的内部结构和演化。也可以通过建立恒星模型来模拟密近双星中脉动子星的脉动模式，得出其基本物理参量， 再结合测光分析来反推密近双星系统的物理特征。此外，密近双星系统外可能存在的第三天体，对密近双星形成和演化的影响不可忽视。由于 𝛾 Dor 型脉动变星的脉动周期长，变幅小等原因，已知的含有 𝛾 Dor型脉动变星的密近双星样本数较少，具有详细分析研究的样本更少。随着 TESS 和 Kepler 等空间巡天望远镜 高精度连续测光数据的释放，将空间望远镜和地基望远镜的测光分光观测数据、 LAMOST光谱巡天数据以及欧洲 Gaia卫星的天体测量信息结合起来分析，将会增加含 𝛾 Dor 型脉动变星密近双星的样本数，提高求解含 𝛾 Dor型脉动变星的密近双星系统物理参数的可靠性。本文采用以上研究策略，对含有 𝛾 Dor 型脉动变星的密近双星系统 HZ Dra 和 RX Dra 进行了观测分析研究。获得的主要研究结果如下：1. 基于 TESS 空间巡天数据等，对密近双星系统 HZ Dra 的轨道周期变化进行分析，发现其 O-C 曲线呈现出长期变化叠加周期性变化的趋势。长期变化揭 示 HZ Dra 的轨道周期正以 2.45×10−8d/yr 的速率增加，导致轨道周期长期增加的原因可能是系统中两子星间的物质转移和由星风导致的物质损失。周期性变化成分揭示了该双星系统外可能存在近距离的第三天体，该第三天体在偏心轨道 上围绕与双星系统的公共质心运动（a3max=0.92 au, 𝑒3 = 0.28）。我们利用 W-D 等解轨程序拟合TESS光变曲线，发现第三天体对系统的光度贡献约为29%，这与理论计算值相符。与此同时，本文还发现主星上存在由于物质转移撞击而产生的热斑；在次星上存在由于磁活动造成的黑子。热斑和黑子的位置随时间演化并关于内拉格朗日点对称，这可用于解释系统中显著的 O ′ Connell 效应。基于 TESS 光变曲线进行的频率分析得出了 110 个频率成分，本文从其中 10 个独立频率中证认了 7 个非径向和1 个径向 p 模式脉动以及 1个非径向 g 模式脉动。我们还使用 MESA 程序对主星建立了恒星模型，得到的物理参数与通过 W-D双星模型求解的参数值相符。最终研究结果显示 HZ Dra 的主星是一颗处于零龄主序附近的𝛾 Dor 和 𝛿 Sct 混合型脉动变星。2. 基于 TESS 巡天测光数据，本文使用 W-D程序建立了 RX Dra 的分离双星模型，给出了该双星系统的质量比（0.90）、有效温度比（0.93）、光度比 （𝐿1 /Ltotal=71 %）和轨道倾角 (88∘ .73) 等参数。其次，基于 Gaia 卫星的大气参数， 本文使用 MESA 程序对 RX Dra 建立了恒星模型，由此证认了 20 个 g 模式脉动频率，其中有 16 个频率（F1-F7，F11-F20）被证认为偶极 g 模式，2 个频率（F21， F22）被证认为四极 g 模式，另外 2 个频率（F23，F24）被证认为六极 g 模式。结合双星模型的参数，本文首次给出该系统的物理参量：𝑀1 = 1.53 M⊙, 𝑀2 = 1.38 M⊙, 𝑇1 = 7240 K, 𝑇2 = 6747 K, 𝑅1 = 1.8288 R⊙, 𝑅2= 1.3075 R⊙, 𝐿1 = 8.2830 L⊙ 和 𝐿2= 3.4145 L⊙。最后，本文首次确认（1）该系统的主星是一颗处于主序演化阶段的 𝛾 Dor 型脉动变星，自转周期约为 5.7 天，长于轨道周期（3.78 天），其对流核半径估算为 0.14 R⊙；（2）次星处于赫罗图中的类太阳脉动变星区域，可能是一颗类太阳型脉动变星。 |
| 其他摘要 | 𝛾 Dor pulsating stars were found in the 1990s to be a class of main-sequence variable stars. Observational evidence suggests that this type of pulsating variable stars have a pulsating period of 0.3 to 3.3 days, a light variation amplitude of about 0.01 mag, a spectral range of A7 - F5, a mass range of 1.5 M⊙-1.8 M⊙, and a luminosity class of IV-V. Their gravity (g) modes driven by the convective blocking mechanism can be used to probe the interior of stars. On the Hertzsprung-Russel (H-R) diagram, 𝛾 Dor stars lie in the lower part of the classical instability strip, which partially overlaps the main-sequence strip and the cool edge of the 𝛿 Sct instabillity strip. Some variables have been found to lie in the overlapping area of 𝛾 Dor and 𝛿 Sct pulsating stars by observations, which are called hybrid pulsating stars. They pulsate in both p and g modes, where p modes can be used to probe the envelope of stars, while g modes can be used to probe the core of stars. So this makes them an important target for asteroseismological research. Close binary stars are the most accurate and reliable celestial systems for determinating the fundamental physical parameters of stars. If 𝛾 Dor pulsating stars are in close binary systems, their physical parameters can be determined accurately , facilitating the precise determination of their pulsation modes and further analysis of the stars’ internal structures and evolutions. It is also possible to calculate the pulsation modes of pulsating stars in close binaries by constructing stellar models to derive their funda mental physical parameters, which can then be combined with photometric analysis to infer the physical properties of close binary systems. In addition, the possible existence of a third body around the close binary stars has a non-negligible role on the formation and evolution of close binaries. Due to the long pulsation period and small pulsation amplitude of 𝛾 Dor pulsating stars, the sample of known close binaries containing 𝛾 Dor pulsators is relatively small, and there are fewer samples with detailed analysis. With the release of high-precision continuous photometric data from space survey telescopes such as TESS and Kepler, we can combine the photometric and spectroscopic data of space and ground-based telescopes, LAMOST spectral survey data, and the astrometric information of Gaia satellite for analysis. This will increase the sample numbers of 𝛾 Dor pulsating stars in close binaries, and improve the reliability of solving the physical parameters of close binary systems containing 𝛾 Dor pulsating stars. In this thesis pa per, we use the above research strategy to carry out an observation and analysis of the close binary systems HZ Dra and RX Dra containing 𝛾 Dor pulsating stars. The main results are as follows: 1. Based on TESS space survey data, etc, this paper carried out an analyses of orbital period changes for the close binary system HZ Dra. We found that the O-C curve shows a trend of long-term period variation superimposed on a cyclic variation. Long-term period variation indicates that the orbital period of HZ Dra is increasing at a rate of 2.45×10−8d/yr, which could be due to the transfer of mass between the two components and the stellar wind mass loss. The periodic variation reveals the possible existence of a close-in third body around the binary system, moving in an eccentric orbit around a common centre of mass with the binary (a3max = 0.92 au, 𝑒3 = 0.28). We fit the TESS light curve using the W-D program and find that the third light contribution to the system is about 29 %, which is in agreement with the theoretical calculation value. Meanwhile, we found a hot spot on the primary star due to mass transfer impacts; and a black spot on the secondary star due to magnetic activity. Their positions evolve with time and are symmetric about the inner Lagrangian point, which can be used to explain the significant ′ O Connell effect in the system. Frequency analyses based on the TESS light curve show 110 frequency components, of which 7 non-radial and 1 radial p-mode pulsations and 1 non-radial g-mode pulsation are identified from 10 independent frequencies. We also gave a stellar model for the primary using the MESA program, and the obtained physical parameters are consistent with the parameter values solved via the W-D binary model. The final results show that the primary star of HZ Dra is a hybrid of 𝛾 Dor and 𝛿 Sct pulsating star near the zero-age main sequence. 2. Based on photometric data from the TESS survey, we use the W-D program to construct a detached binary model for RX Dra. The mass ratio (0.90), the effective temperature ratio (0.93), the luminosity ratio (𝐿1 /Ltotal=71 %) and the orbital inclination (88∘ .73) of this binary system are derived. Combing on the atmospheric parameters of the Gaia satellite, we use the MESA program to build a stellar model of RX Dra. Twenty g-mode pulsation frequencies are identified, of which 16 frequencies (F1-F7, F11-F20) are identified as the dipole g mode, 2 frequencies (F21, F22) as the quadrupole g mode, and 2 frequencies (F23, F24) as the hexapole g mode. The physical parameters of the system are given for the first time in this paper：𝑀1 = 1.53 M⊙, 𝑀2 = 1.38 M⊙, 𝑇1 = 7240 K, 𝑇2 = 6747 K, 𝑅1 = 1.8288 R⊙, 𝑅2= 1.3075 R⊙, 𝐿1 = 8.2830 L⊙ and 𝐿2= 3.4145 L⊙. Finally, we confirms for the first time that (1) the primary star of the system is a 𝛾 Dor pulsating star in the main-sequence stage of evolution, with a rotation period of about 5.7 days, which is longer than the orbital period (3.78 days), and its convective core radius is estimated to be 0.14 R⊙; and (2) the secondary star is located in the region of solar-like pulsating star of the H-R diagram, and is likely to be a solar-like pulsating star. |
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