锂元素丰度是恒星物理领域最重要的观测参数之一，它的演化过程指示了恒星内部的 物质传输、混合机制。标准恒星模型中只考虑对流作为物质混合机制一定程度上揭示了恒 星的内部结构，但是与之相悖的锂元素观测现象，比如疏散星团中锂元素丰度弥散、衰减 现象、锂间隙 (Li-Gap) 以及巨星中的富锂现象等，暗示了其他物质传输和混合机制, 例如 转动、磁场、重力波、扩散等可能的作用。近年来星震学测量的红巨星内部转动轮廓展示 出与模型预测的巨大差异这一结果表明我们大大低估了角动量传输的效率，也因而让我们 继续把目光聚焦于转动这一重要的物质传输机制。尽管对于锂元素丰度与转动的关系的研 究已持续多年，但受限于数据质量和数据数量，二者的关系仍不明确。但是一方面，多年 来的大望远镜观测和例如 LAMOST 这样的大型光谱巡天项目积累了大量锂元素丰度的观 测，另一方面，如 Kepler 卫星为我们提供了大量长时序高精度的光度观测数据，为研究恒 星转动提供了良好的样本，为我们带来了研究锂丰度和转动关系的良好契机。
首先， 我们研究了主序阶段疏散星团中的锂元素丰度与转动的关系， 此文通过从 Kepler 卫星观测的 K2 数据中提取出的转动周期数据，分别研究了三个中等年龄以下疏散 星团：昴星团、M35、毕星团锂间隙区域、锂丰度弥散区域的锂丰度与转动关系，利用光 度数据进一步确认了前人研究中从光谱数据中发现的二者的相关性。在前人研究的结果 外，我们利用自转周期确认了昴星团中型 F 型星锂间隙区域中二者的关系：转动快的星倾 向于消耗更多的锂元素。
其次，我们研究了场星中富锂巨星锂丰度与转动的关系，首次从自转周期数据确认了 锂元素丰度与转动存在的关系:(1) 在锂増丰程度较弱时，自转周期分布比较弥散，强锂増 丰的星倾向于快速转动;(2) 富锂巨星和极富锂巨星的转动速度随锂增丰强度或许存在两个 演化序列, 在极富锂巨星侧显示出更明显的随转动加快锂增丰越强的特点。由于样本量较 少的原因, 还需要更多的观测确认, 如果此现象确实存在, 或许暗示二者不同的形成机制。
与此同时，基于 Kepler 的优质数据也为大样本星震学研究的发展提供了契机。此文还 介绍了一种利用机器学习，卷积神经网络来进行亚巨星类太阳振动的模球谐度证认的的算 法。这种新的算法可以高效、快速、准确的进行振动模的球谐度证认，为更为细致的大样 本星震学的分析提供一种可行的算法支持。

The abundance of lithium is one of the most important observation parameters in the field of stellar physics, and its evolutionary process indicates the mechanism of transport and mixing within the star. The standard stellar model only considers convection as a mixing mechanism, which reveals the internal structure of the star to a certain extent, but the observations of lithium abundance, such as the dispersion of the lithium abundance, the depletion, and the lithium gap (Li-Gap) in the open star cluster. And the lithium-rich giants in the field, suggesting possible other material transport and mixing mechanisms, such as rotation, magnetic fields, gravity waves, diffusion and etc. In recent years, the internal rotation profile of red giant stars measured by asteroseismology has shown a huge difference from the model prediction. This result shows that we have greatly underestimated the efficiency of angular momentum transfer, and thus let us continue to focus on the important role of rotation. Although the research on the relationship between the abundance of lithium and rotation has continued for many years, the relationship between the two is still not clear due to the quality and quantity of data. But on the one hand, large ground-based telescope observations over the years and large-scale spectral survey projects such as LAMOST have accumulated a large amount of observations of lithium abundance. On the other hand, the Kepler satellite provides us with a large number of long-time and high-precision photometric data. The observation data provides a good sample for studying stellar rotation, and brings us a good opportunity to study the relationship between lithium abundance and rotation.
First, we studied the relationship between the lithium abundance and rotation of the main-sequence stars in the open cluster. In this paper, we study the rotation period extracted from the K2 data observed by Kepler satellite. The lithium abundance and rotation relations within lithium gap area and lithium dispersion area of open clusters under the middle age: the Pleiades, M35 and Hyades are re-examed. The use of photometric data to further confirm the previous research found from the spectral data. In addition to the results of previous studies, we used the rotation period to confirm the relationship between the two in the lithium gap region of the mid-F star: fast-rotating stars tend to deplete more lithium.
Secondly, we study the relationship between the lithium abundance and rotation of the lithiumrich giant stars in the field. For the first time, we confirmed the relationship between the abundance of lithium and rotation from the photometric data derived rotation period: (1) The less Li-enriched stars have a relatively dispersed rotation period and giants with high Li enrichment concentrated on the rapidly rotating area, which are consistent with earlier studies; (2) The rotation speed of the lithium-rich giant star and the super lithium-rich giant star may have two evolutionary sequences with the intensity of lithium enrichment, which is more obvious on the side of the extremely lithium-rich giant star. Due to the small sample size, more observations are needed to confirm. If this phenomenon does exist, it may imply a different formation mechanism between the li-rich giants and super li-rich giants.
At the same time, such high quality data observed by Kepler also provides an opportunity for the ensemble asteroseismology research. This article also introduces an algorithm that uses machine learning, convolutional neural networks, to identify the mode angular degrees of subgiants’ solar-like oscillation. This new algorithm can efficiently, quickly and accurately verify the mode angular degrees, and provides a feasible algorithm support for the analysis of ensemble asteroseismology.