Determination of an Instability Strip of Long Period Variables

自20世纪70年代末以来，对大麦哲伦星云中Mira变量的红外光度研究得到了广泛的开展。由于LMC中的恒星与我们的距离几乎相等，我们可以通过只处理相对光度来讨论这些恒星的一些特性，而不需要对绝对星等进行精确的热光度校正。通过这种方式，SAAO的天文学家在观测上获得了LMC中Mira变量的周期-光度关系。在本研究项目中，我们证明了Mira变量应该存在周期-质量-光度关系，而不是简单的周期-光度关系。最近观测得到的这些恒星的周期-光度关系应被认为是周期-质量-光度关系在（周期，光度）平面上的投影，周期-光度关系在观测拟合线周围的散射应部分解释为样本恒星的质量分布。更多地，我们可以推断出HR图中每颗恒星的质量和位置。观测得到的Mira变星的周期-光度关系表明这些恒星存在不稳定带。我们还提出了一种可能的解释，解释了天琴座RR变星的Blazhko效应，这一问题在很长一段时间内都没有得到解决。我们假设这些恒星有一个偶极磁场，这个磁场斜向恒星的旋转轴，并检查这个磁场对径向基本振荡模式的影响作为一个小的扰动。我们证明了观测到的布拉齐科效应可以通过考虑本征函数的扰动来很好地解释。我们估计解释布拉齐克效应所需的磁场强度。如果探测到这样的磁场，这个模型将是正确的。我们也将这个模型应用于快速振荡的Ap星。大多数Ap星被认为至少有一个四极磁场，外加一个主要的偶极成分。在本研究中，我们考虑一个一般的极向磁场，并研究它作为扰动对振荡的影响。将目前的结果与观测数据进行比较，为我们提供了这些恒星的星震学信息。最后，我们研究了类太阳恒星振荡的随机激发机制，得到了不同恒星振荡模式的激振频率范围。我们预计，这种半规则和/或不规则的光度变化可能是这种机制激发的振荡的一种表现。少

Infrared photometric investigation of Mira variables in the Large Magellanic Cloud has been extensively carried out since the late 1970s. Since stars in LMC are almost equally distant from us, we can discuss some properties of these stars by dealing with only relative luminosity without accurate knowledge of bolometric correction for absolute magnitudes. In this way, astronomers in SAAO obtained observationally a period-luminosity relation of Mira variables in LMC.In the present research project, we show that there should exist a period-mass-luminosity relation rather than a simple period-luminosity relation for Mira variables. A recent observationally obtained period-luminosity relation for these stars should be considered as a projection of the period-mass-luminosity relation on the (period, luminosity)-plane, and the scatter around an observationally fitted line of the period-luminosity relation should be interpreted partially as a mass distribution of the sample stars. We show that … More from this scatter we can deduce the mass and the position of each of the stars in the HR diagram. An observationally obtained period-luminosity relation of Mira variables implies the existence of an instability strip for these stars.We also propose a possible interpretation for the Blazhko effect in the RR Lyrae variables, which has remained to be solved for a very long time. We assume that these stars have a dipole magnetic field, which is oblique to the rotation axis of the star, and examine the effect of this field on the radial fundamental oscillation mode as a small perturbation. We demonstrate that the observed Blazhko effect is well interpreted by taking account of the perturbation to the eigenfunction. We estimate the magnetic field strength necessary to explain the Blazhko effect. This model will be justified if such magnetic fields will be detected. We also apply this model to the rapidly oscillating Ap stars. Most of Ap stars are believed to have, at least, a quadrupole magnetic field in addition to a main dipole component. In this research, we consider a general poloidal magnetic field and investigate its effect upon oscillations as a perturbation. Comparing the present results with the observational data provides us with asteroseimological information of these stars. We finally investigate the stochastic excitation mechanism of oscillations in the solar-like stars, and obtain the frequency range of the excited oscillation modes in a various stars. We expect that the semi-regular and/or irregular luminosity variation in late type stars may be a manifestation of the oscillations excited by this mechanism. Less