多体耦合系统光变曲线的精确计算及Rossiter-McLaughlin效应
Accurate Computation of Light Curves and the Rossiter-McLaughlin Effect in Multi-Body Eclipsing Systems
摘要：
我们在这里提出了一个有效的方法来计算每个机构在一个多体食事件的所有常用的临边昏暗的法律可见光通量。我们的方法遵循了Wu（2012）提出的思想，将格林定理应用于临边暗化积分，从而将可见圆盘上的二维通量积分转换为可见边界上的一维积分。我们实现这一想法，通过一个迭代过程相结合的快速方法来描述每个机构的可见边界的快速数值积分计划计算的积分。对于两体情况，我们的方法在速度上与Mandel & Agol（2002）和Gimenez（2006 a）的方法都比较好。该方法的优点在于，它适用于任何数量的球体，其计算精度可以通过使用公差参数进行调整。最重要的是，该方法提供了两个主要的优势，以前使用的技术：（i）它可以采用大量的肢体黑暗的法律，包括所有常用的;（ii）它可以计算Rossiter-McLaughlin效应的刚体旋转与任意方向的旋转轴，使用任何这些肢体黑暗的法律。此外，我们可以计算Rossiter-McLaughlin效应的恒星表现出差异的旋转，使用二次临边昏暗的法律。我们提供的方法的数学背景，并详细解释如何实现该技术的帮助下，我们提供的几个例子和代码。
英文摘要：
We present here an efficient method for computing the visible flux for each body during a multi-body eclipsing event for all commonly used limb darkening laws. Our approach follows the idea put forth by Pal (2012) to apply Green's Theorem on the limb darkening integral, thus transforming the two-dimensional flux integral over the visible disk into a one-dimensional integral over the visible boundary. We implement this idea through an iterative process which combines a fast method for describing the visible boundary of each body with a fast numerical integration scheme to compute the integrals. For the two-body case, our method compares well in speed with both that of Mandel & Agol (2002) and that of Gimenez (2006a). The strength of the method is that it works for any number of spherical bodies, with a computational accuracy that is adjustable through the use of a tolerance parameter. Most significantly, the method offers two main advantages over previously used techniques: (i) it can employ a multitude of limb darkening laws, including all of the commonly used ones; (ii) it can compute the Rossiter-McLaughlin effect for rigid body rotation with an arbitrary orientation of the rotation axis, using any of these limb darkening laws. In addition, we can compute the Rossiter-McLaughlin effect for stars exhibiting differential rotation, using the quadratic limb darkening law. We provide the mathematical background for the method and explain in detail how to implement the technique with the help of several examples and codes which we make available.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
