微透镜光变曲线中扩展源效应的快速计算卷积方法
Fast Computational Convolution Methods For Extended Source Effects In Microlensing Lightcurves
摘要：
当源穿过临界线时，在引力透镜事件中可以看到扩展源效应。这些事件探测恒星强度分布，并可用于测量临边暗化系数，以检验恒星模型的预测。为了正确地减去行星瞬变事件中的恒星通量，需要一个精确测量的恒星轮廓数据库。在当前和未来的微透镜测量中，从空间和地面产生的数据量需要能够快速计算不同源透镜配置的光变曲线的算法。基于卷积方法，我们描述了一个通用的形式主义来计算这些曲线的单透镜。我们开发的椭圆积分，我们通过解决相关的一阶微分方程的积分近似。我们构造的临边暗化的解析解，第一次，为一个抛物线的配置文件是准确的$\sim 1-3\%$和$0.5\%$水平，分别。这些解决方案可以计算数量级快于其他集成例程。它们可以在处理大数据集的管道中实现，以实时提取恒星参数。
英文摘要：
Extended source effects can be seen in gravitational lensing events when sources cross critical lines. Those events probe the stellar intensity profile and could be used to measure limb darkening coefficients to test stellar model predictions. A data base of accurately measured stellar profiles will be needed to correctly subtract the stellar flux in planetary transient events. The amount of data that is being and will be produced in current and future microlensing surveys, from the space and the ground, requires algorithms that can quickly compute light curves for different source-lens configurations. Based on the convolution method we describe a general formalism to compute those curves for single lenses. We develop approximations in terms of quadratures of elliptic integrals that we integrate by solving the associated first order differential equations. We construct analytic solutions for a limb darkening and, for the first time, for a parabolic profile that are accurate at the $\sim 1-3\%$ and $0.5\%$ level, respectively. These solutions can be computed orders of magnitude faster than other integration routines. They can be implemented in pipelines processing large data sets to extract stellar parameters in real time.
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