Oscillations of rapidly rotating stars

这个研究项目是为了了解快速旋转恒星的振荡。如果我们能够使用恒星振荡的观测数据来测试和发展我们对恒星结构和演化的理解，那么获得这种理解是至关重要的。恒星振荡的频率是由它们的内部结构和角速度决定的，所以通过测量这些频率，我们原则上可以绘制或限制它们的内部结构和旋转。这就是恒星地震学（或星震学）。恒星振荡的频率可以通过测量光输出或表面速度在很长一段时间内的微小变化来确定。对于一些恒星，这可以在地面上完成，但太空实验可以产生更高的精度和更长的不间断观测。为了使用这些数据，我们需要了解恒星的振荡特性。对于非旋转或缓慢旋转的恒星来说，这是相对直接的，每次振荡都由一个特定的表面几何因子（球谐）和适合恒星的波长数量来指定。这类恒星模型的频率很容易计算出来，而且已经开发出了利用这些数据绘制这类恒星内部地图的技术。但对于旋转的恒星，情况要复杂得多；振荡模态是由几个几何因子（表面谐波）组成的，这使得振荡频率的计算变得更加困难。进一步的旋转分裂振荡频率，产生更大的频率集。解决大旋转问题的唯一方法是制作旋转恒星的二维计算机模型，并对其振荡特性进行完整的二维计算。这就是拟议的研究方案的目标。由于Roxburgh建立快速旋转恒星的真实模型的技术的发展，这个计划现在是可能的，其中恒星内部的旋转不一定是恒定的，以及LIgnieres， Rieutord和Reese的技术的发展，以确定简单（多向）恒星模型的振荡，其中恒星内部的旋转是恒定的。在这两项进展的基础上，我们应该能够确定非均匀旋转的现实恒星模型的振荡特性。在研究了这些恒星模型的特性之后，我们将能够开发诊断技术，利用观测确定的频率来绘制或限制快速旋转恒星的内部结构和旋转，类似于那些非旋转恒星。Roxburgh在开发球型恒星诊断技术方面有相当丰富的经验。应该强调的是，快速旋转并不是那么快。在里斯对多向性模型的研究中，他发现，对于赤道自转速度大于50公里/秒的恒星，需要进行完整的二维研究。许多（实际上是大多数）中等质量和较大质量的恒星的速度都大于这个数值。提议是让里斯和罗克斯伯格一起去玛丽皇后学院进行这个研究项目。

This research programme is to understand the oscillations of rapidly rotating stars. Gaining this understanding is crucial if we are to be able to use observational data on stellar oscillations to test and develop our understanding of the structure and evolution of stars. The frequencies of oscillation of stars are determined by their internal structure and angular velocity, so by measuring these frequencies we can in principle map, or place constraints on, their internal structure and rotation. This is stellar seismology (or asteroseismology). The frequencies of oscillations of a star can be determined from measurements of the small variations in light output, or surface velocity, over a long interval of time. For some stars this can be done from the ground, but space experiments can yield much higher precision and much longer uninterupted observations. To use this data we need to understand the oscillation properties of stars. For non-rotating, or slowly rotating stars this is relatively straight forward, each oscillation is specified by a particular surface geometrical factor (a spherical harmonic) and the number of wavelengths that fit into the star. The frequencies of models of such stars are easily calculated, and techniques have been developed for using the data to map the interiors of such stars. But for stars that are rotating the situation is much more complex; an oscillation mode is made up of several geometrical factors (surface harmonics) which makes the calculation of the oscillation frequencies much more difficult. Further rotation splits the oscillation frequencies producing a much larger frequency set. The only way to address this problem for large rotation is to make 2-dimensional computer models of rotating stars and full 2-dimensional calculations of their oscillation properties. This is the objective of the proposed research programme. This programme is now possible due to the development of techniques by Roxburgh for building realistic models of rapidly rotating stars where the rotation is not necessarily constant inside the star, and the development of techniques by LIgnieres, Rieutord and Reese to determine the oscillation of simple (polytropic) stellar models where the rotation is constant inside the star. By building on these two developments we should be able to determine the oscillation properties of realistic stellar models in non-uniform rotation. Having investigated the properties of such stellar models we will then be in a position to develop diagnostic techniques for using observationally determined frequencies to map, or place constraints on, the internal structure and rotation of rapidly rotating stars, analagous to those for non-rotaing stars. Roxburgh has considerable experience in the development of diagnostic techniques for spherical stars. It should be emphasised that rapid rotation is not that rapid. In the work of Reese on polytropic models he found that full 2-dimensional studies were needed for stars with equatorial rotation speeds greater than 50 km/s. Many, indeed most, stars of moderate and large mass have speeds greater than this. The proposal is for Reese to join Roxburgh at Queen Mary to undertake this research programme.