有限积分时间下的Transit光变曲线：Fisher信息分析
Transit Light Curves with Finite Integration Time: Fisher Information Analysis
摘要：
开普勒以其对15万多颗目标恒星前所未有的光度精度彻底改变了凌日行星的研究。开普勒探测到的大多数凌日行星候选者都被观测为长节奏目标，积分时间为30分钟，即将到来的凌日系外行星调查卫星（TESS）将以类似的积分时间记录全帧图像。30分钟的积分会影响凌日的形状，特别是对于小行星和低信噪比的情况。使用Fisher信息矩阵技术，我们推导出解析近似的方差和协方差的过境参数从拟合光变曲线测光收集有限的积分时间。我们发现，分箱的光变曲线可以显着增加的不确定性和协方差的推断参数时，比较方案与恒定的总信噪比（恒定的总积分时间，在没有读噪声）。与瞬时采样的光变曲线相比，在30分钟的积分时间内，地球大小的行星的过境进入/离开时间增加了34倍，而类太阳恒星周围的行星大小的行星增加了3.4倍。类似地，地球和小行星过境时间的不确定性增加了3.9和1.4倍。不受传播深度的影响很大程度上不受有限积分时间的影响。虽然通过深度、进入持续时间和通过持续时间之间的相关性都随着积分时间的增加而增加，但是中间通过时间与其他参数保持不相关。我们在www.its.caltech.edu/~eprice上提供了Python和Mathematica的代码，用于预测方差和协方差。
英文摘要：
Kepler has revolutionized the study of transiting planets with its unprecedented photometric precision on more than 150,000 target stars. Most of the transiting planet candidates detected by Kepler have been observed as long-cadence targets with 30 minute integration times, and the upcoming Transiting Exoplanet Survey Satellite (TESS) will record full frame images with a similar integration time. Integrations of 30 minutes affect the transit shape, particularly for small planets and in cases of low signal-to-noise. Using the Fisher information matrix technique, we derive analytic approximations for the variances and covariances on the transit parameters obtained from fitting light curve photometry collected with a finite integration time. We find that binning the light curve can significantly increase the uncertainties and covariances on the inferred parameters when comparing scenarios with constant total signal-to-noise (constant total integration time in the absence of read noise). Uncertainties on the transit ingress/egress time increase by a factor of 34 for Earth-size planets and 3.4 for Jupiter-size planets around Sun-like stars for integration times of 30 minutes compared to instantaneously-sampled light curves. Similarly, uncertainties on the mid-transit time for Earth and Jupiter-size planets increase by factors of 3.9 and 1.4. Uncertainties on the transit depth are largely unaffected by finite integration times. While correlations among the transit depth, ingress duration, and transit duration all increase in magnitude with longer integration times, the mid-transit time remains uncorrelated with the other parameters. We provide code in Python and Mathematica for predicting the variances and covariances at www.its.caltech.edu/~eprice.
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