AN EFFICIENT METHOD FOR MODELING HIGH-MAGNIFICATION PLANETARY MICROLENSING EVENTS
AN EFFICIENT METHOD FOR MODELING HIGH-MAGNIFICATION PLANETARY MICROLENSING EVENTS
复制标题
高倍率行星微透镜事件建模的有效方法
DOI：
10.1088/0004-637x/716/2/1408
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
D. Bennett
中科院分区：
文献类型：
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作者：
D. Bennett
我提出了一个以前未发表的方法计算和建模多个透镜微透镜事件，是基于图像为中心的射线拍摄方法的班尼特和Rhie。它已被用来模拟各种各样的二元和三元透镜系统，但它的目的是有效地模拟高放大率的行星微透镜事件，因为这些高放大率的事件，到目前为止，最具挑战性的事件建模。它被设计为足够有效地处理复杂的微透镜事件，其中包括两个以上的透镜质量和透镜轨道运动。该方法使用极坐标积分网格，其在径向方向上的网格间距小于在角方向上的网格间距，并且其采用专门设计用于处理边缘变暗源的积分方案。我目前的测试表明，这些功能实现二阶精度的光变曲线的一些高放大率的行星事件。与在两个方向上具有相同网格间距（对于固定数量的网格点）的一阶积分方案相比，它们将计算精度提高了100倍以上。该方法还包括基于大都会算法的χ2最小化方法，其允许跳跃函数以允许快速收敛到χ2最小值的方式变化。最后，我介绍了一个全局参数空间搜索策略，允许光变曲线模型的参数空间的盲搜索，而不需要在一个大的网格的固定参数的χ2最小化。相反，参数空间是在初始条件的网格上探索的，用于使用完整的参数空间的一组χ2最小化。虽然这种方法可能比在一个大的参数网格上找到χ2最小值的方法要快一些，但我认为这种方法的主要优势在于具有多个行星信号的事件，必须探索更高维的参数空间才能找到正确的光变曲线模型。
I present a previously unpublished method for calculating and modeling multiple lens microlensing events that is based on the image centered ray-shooting approach of Bennett & Rhie. It has been used to model a wide variety of binary and triple lens systems, but it is designed to efficiently model high-magnification planetary microlensing events, because these high-magnification events are, by far, the most challenging events to model. It is designed to be efficient enough to handle complicated microlensing events, which include more than two lens masses and lens orbital motion. This method uses a polar coordinate integration grid with a smaller grid spacing in the radial direction than in the angular direction, and it employs an integration scheme specifically designed to handle limb-darkened sources. I present tests that show that these features achieve second-order accuracy for the light curves of a number of high-magnification planetary events. They improve the precision of the calculations by a factor of >100 compared to first-order integration schemes with the same grid spacing in both directions (for a fixed number of grid points). This method also includes a χ2 minimization method, based on the Metropolis algorithm, that allows the jump function to vary in a way that allows quick convergence to χ2 minima. Finally, I introduce a global parameter space search strategy that allows a blind search of parameter space for light curve models without requiring χ2 minimization over a large grid of fixed parameters. Instead, the parameter space is explored on a grid of initial conditions for a set of χ2 minimizations using the full parameter space. While this method may be somewhat faster than methods that find the χ2 minima over a large grid of parameters, I argue that the main strength of this method is for events with the signals of multiple planets, where a much higher dimensional parameter space must be explored to find the correct light curve model.