论文标题
关于天体物理系统的对数正常通量分布的测定
On the determination of log-normal flux distributions for astrophysical systems
论文作者
论文摘要
确定天体物理源的通量分布是高斯还是对数正态，可以对其可变性的性质进行关键见解。对于中等长度（$ <10^3 $）的灯光曲线，一个有用的首先分析是通过估计偏度并应用Anderson-Darling（AD）方法来测试通量的通量和对数的高斯性。我们对具有不同长度，可变性，高斯测量误差和功率谱指数$β$（即$ p（f）\ propto f^{ - β} $）的光曲面进行广泛的模拟，以提供可靠使用这两种测试的处方和指南。我们提供了经验拟合，用于偏度的预期标准偏差和列表的AD测试临界值$β= 0.5 $和$ 1.0 $，这与文献中给出的白噪声（$β= 0 $）的值不同。此外，我们表明，对于白噪声，对于大多数实际情况，这些测试是毫无意义的，因为binning在时间上改变了通量分布。对于$β\ gtrsim 1.5 $，偏度方差不会随长度而减小，因此测试不可靠。因此，此类测试只能应用于$β\ gtrsim 0.5 $和$β\ Lessim 1.0 $的系统。作为这项工作中给出的处方的一个示例，我们重新确认了Blazar的Fermi数据，3FGL \，J0730.2-1141，表明其$γ$ ray的通量与log-Normal分布一致，并且与高斯人不一致。
Determining whether the flux distribution of an Astrophysical source is a Gaussian or a log-normal, provides key insight into the nature of its variability. For lightcurves of moderate length ($< 10^3$), a useful first analysis is to test the Gaussianity of the flux and logarithm of the flux, by estimating the skewness and applying the Anderson-Darling (AD) method. We perform extensive simulations of lightcurves with different lengths, variability, Gaussian measurement errors and power spectrum index $β$ (i.e. $P(f) \propto f^{-β}$), to provide a prescriptionand guidelines for reliable use of these two tests. We present empirical fits for the expected standard deviation of skewness and tabulated AD test critical values for $β= 0.5$ and $1.0$, which differ from the values given in the literature which are for white noise ($β= 0$). Moreover, we show that for white noise, for most practical situations, these tests are meaningless, since binning in time alters the flux distribution. For $β\gtrsim 1.5$, the skewness variance does not decrease with length and hence the tests are not reliable. Thus, such tests can be applied only to systems with $β\gtrsim 0.5$ and $β\lesssim 1.0$. As an example of the prescription given in this work, we reconfirm that the Fermi data of the blazar, 3FGL\,J0730.2-1141, shows that its $γ$ ray flux is consistent with a log-normal distribution and not with a Gaussian one.
