| 摘要 | 星震学是目前为止为数不多能够直接探测恒星内部结构状态及其演化状态的研究方法和手段之一。它是通过机械波在恒星内部的传播情况来对恒星内部进行研究。这些波在恒星内部传播会引起整个恒星交替发生膨胀收缩运动，从而影响恒星表面光度以及视向速度。通过对光变或视向速度进行分析便可获得该恒星的震荡信息，如频率、振幅等，它们都是由恒星的内部结构状态所决定的。从震荡信息中提取的震荡参量可用来确定恒星的质量M、半径R、年龄τ、表面重力加速度g以及平均密度ρˉ等基本参量。 随着WIRE、MOST、CoRoT、Kepler等空间观测计划的进行，越来越多的类太阳震荡恒星已被观测到。这开启了一个新的研究领域――大样本星震学。所谓大样本星震学，就是根据的恒星某种性质将恒星进行归类并通过星震学方法进行研究。这使得星震学的研究从对单个恒星的研究走向对大样本的研究。 星团恒星常被看作同时形成于星际空间的一团气体尘埃，因此星团成员星之间拥有很多相似的性质，如相同的元素组成、相同的年龄以及距离等。这些相似性使得星团中的所有成员星或是星团内处于某个演化阶段的恒星的集群构成一个特殊的自然样本。这些恒星之间拥有场星所不具备的相似性，这些相似性将会对恒星模型或是计算提供更为严格的限制。同时，由于星团中成员星质量之间存在差异，不同质量的恒星演化状态不同，它们将处在不同的演化阶段，因此整个星团恒星构成一个完整的演化序列，这有利于我们结合恒星结构演化理论对星团恒星进行星震学分析。 在本论文中，我们结合星震学、恒星结构演化理论以及恒星的光度测光理论，运用大样本星震学的方法对Kepler视场中星团NGC6791和NGC6819中的红巨星分支恒星进行研究。在理论上获得一系列的新关系式，它们可以用来解释观测到的大频率间隔-最大功率谱频率以及视星等-大频率间隔等关系。另外，通过对星团恒星所特有的限制条件的运用，我们利用理论上所获得的新关系式确定了星团的金属丰度、距离以及星团红巨星分支恒星的质量。最后通过星震学方法估算星团恒星的星际消光。 基于恒星结构演化理论中的Hayashi线关系我们在红巨星分支恒星中获得一个关于恒星有效温度、质量、半径以及金属丰度类似于Hayashi线关系的关系。通过将该'HayaShi线关系’和类太阳震荡性质(大频率间隔关系、最大功率谱频率关系)相结合,我们推导出一系列关于恒星震荡大频率间隔和最大功率谱频率的新关系式。基于这些关系式的分析有如下结论： ·我们的研究方法提供直接的观测证据证实星团中红巨星分支恒星的质量在它们误差允许范围内是相等的。 ·红巨星的质量M、半径R和重力加速度g可以通过震荡参量——大频率间隔△v和最大功率谱频率Vmx——和非震荡参量——金属丰度Z确定。它们的误差主要来自震荡参量的测量误差,金属丰度的误差对计算结果影响非常小。 ·利用关于△v、vmax、M以及Z的新关系式,我们可对观测中获得的关系△v=αvβmax及其相应的参数α、β进行解释。参数α依赖于恒星的质量和金属丰度,即α(M,Z)。参数β几乎是一常数。 ·我们将星团中的恒星看作一个整体进行分析。基于这种新方法,我们以一种自洽的方式从大频率间隔△v和最大功率谱频率Vmax获得星团NGC6791和NGC6819的金属丰度和它们红巨星分支恒星的质量。 通过将'Hayashi线关系’、类太阳震荡性质以及恒星光度测光理论相结合,我们获得一个关于恒星的视星等V、热改正BC、大频率间隔△v、最大功率谱频率vmax、距离模数(m—M)0以及金属丰度Z的新关系式。通过分析,我们主要获得如下结论： ·通过该新关系式,我们可以解释观测中视星等-大频率间隔之间的变化关系,以及它们在不同波段之间的弥散差异。 ·通过将星团所有恒星看作一个整体进行分析,我们分别获得星团NGC6791和NGC6819的距离模数。 在新关系式中，金属丰度对距离模数的影响非常小。[Fe/H]中0.10dex的变化仅仅引起距离模数0.06星等的变化。 这种新方法可以用来作为星团成员星的识别的辅助判据。 基于前面获得的关于视星等、大频率间隔的关系式，我们运用星震学方法对星团NGC6791和NGC6819中恒星的星际消光影响进行计算。最后，通过高斯平滑插值方法处理后，我们获得一个随赤经赤纬变化的二维网格表。根据该网格表，我们可以通过插值获得该视场内任意赤经赤纬恒星的星际消光。 |
| 其他摘要 | Asteroseismology is a powerful tool and method to directly obtain different kinds of detailed information about the stellar internal structure and status and the evolutionary state of stars. It is through the propagation of mechanical waves in the stellar interior to detect and research the internal structure and status of stars. The propagation of waves in stellar internal will leads to stars alternately expansion and contraction and further to the change of stellar lightness and their radial velocities along with time. From the light curve or the radial velocity curve, the stellar oscillation information, which are dominated by the stellar internal structure and status, including oscillation frequencies and amplitudes, can be obtained. These oscillation information (oscillation parameters) can be used to determine the stellar fundamental parameters, such as stellar mass $M$, radius $R$, age $\tau$, surface gravity $g$, and mean density $\bar{\rho}$. Thanks to the space-based observations from instruments, such as \textit{WIRE}, \textit{MOST}, \textit{CoRoT}, and \textit{Kepler}, more and more stars with solar-like oscillations have been observed with an observational mode of high precision and uninterrupted photometric. This has opened a new research area in which it is possible to study large samples of stars which have same properties in certain aspect, i.e., so-called ensemble asteroseismology. Stars in a cluster are usually thought to be formed coevally from the same interstellar cloud of gas and dust. They are therefore expected to have many common properties which did not exist in ordinary field stars, such as the same chemical compositions, ages, distances. These common properties strengthen our ability to constrain the theoretical models and/or to determine the cluster fundamental parameters, such as cluster distance, age, and metallicity. In addition, the stars of different masses staying at different evolutionary phase, thus all of the stars in a cluster compose a completed evolutionary series. Cluster stars are therefore used to test the theory of stellar evolution. So, we can combine the theory of stellar structure and evolution with asteroseismology to study cluster stars. These mentioned properties in the above make cluster stars to be of a special natural sample. In the present thesis, combining the asteroseismology, the theory of stellar structure and evolution, and the theory of stellar photometric observations, we obtain a series of new relations. These new relation can be used to interpret the observational phenomenons which are the correlations between the large frequency separations and the frequency of maximum oscillation power and between apparent magnitudes and large frequency separations. At the same time, based on these new relations and combining the common properties of cluster, through analyzing the red giant stars of cluster NGC 6791 and NGC 6819, which are observed by \textit{Kepler}, with the method of ensemble asteroseismology, we determine the cluster fundamental parameters, including their metallicities, distance moduli, and RGB masses. In addition, we estimate the interstellar extinctions of the two clusters' stars with asteroseismology. \vskip 15pt Based on a relation for stars on the Hayashi track ($\sqrt{T_{\rm eff}}\sim g^pR^q$), we obtain a similar relation on the red giant branch respect to stellar effective temperature $T_{\rm eff}$, mass $M$, radius $R$, and metallicity $Z$ from the theory of stellar structure and evolution. Combining the new effective temperature relation with the solar-like oscillations, we derive a series of new relations respect on $\Delta\nu$, $\nu_{\rm max}$, $Z$, $M$, $R$, and $g$. Based on these new relations, we obtain the following conclusions: \begin{itemize} \item Our method provides direct observational evidence to confirm the theoretical argument that the masses of RGB stars in a cluster are the same within their uncertainty. \item Th |
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