标题： 发射线流量测量及其比值的概率分布函数 显示英文标题

标题： The probability distribution functions of emission line flux measurements and their ratios

摘要： 在天体物理学中，许多物理参数是通过两个观测量的比值来推导的。 如果测量的相对不确定度足够小，可以使用简化假设进行解析传播，但对于较大的正态分布不确定度，比值的概率分布会变得偏斜，其众数会偏离高斯不确定度传播所预期的值。 此外，比值A/B的最可能值不等于B/A的最可能值的倒数。 当分母的不确定度大于分子的不确定度时，这种效应最为明显。 我们展示了这一效应在对斯隆数字巡天的12,126个光谱分析中出现。 [O III]在4959和5007 ${\AA}$ 处的固有比值通常表示为较强线与较弱线的比值。 因此，分母的不确定度更大，导致非高斯概率分布。 通过考虑这一效应，我们得出了对固有5007/4959比值的改进估计。 我们得到一个值为3.012 $\pm$ 0.008，这比理论值2.98略高，并且在统计上显著。 我们进一步研究了在低信噪比下从发射线测得的流量存在强烈向上的偏差这一建议。 我们在SDSS的线流量测量中未能检测到这种效应，并且无法重现Rola和Pelat首次描述的这种偏差的结果。 我们认为这种效应的大小可能在很大程度上取决于所使用的特定拟合算法。 显示英文摘要

摘要： Many physical parameters in astrophysics are derived using the ratios of two observed quantities. If the relative uncertainties on measurements are small enough, uncertainties can be propagated analytically using simplifying assumptions, but for large normally distributed uncertainties, the probability distribution of the ratio become skewed, with a modal value offset from that expected in Gaussian uncertainty propagation. Furthermore, the most likely value of a ratio A/B is not equal to the reciprocal of the most likely value of B/A. The effect is most pronounced when the uncertainty on the denominator is larger than that on the numerator. We show that this effect is seen in an analysis of 12,126 spectra from the Sloan Digital Sky Survey. The intrinsically fixed ratio of the [O III] lines at 4959 and 5007 ${\AA}$ is conventionally expressed as the ratio of the stronger line to the weaker line. Thus, the uncertainty on the denominator is larger, and non-Gaussian probability distributions result. By taking this effect into account, we derive an improved estimate of the intrinsic 5007/4959 ratio. We obtain a value of 3.012 $\pm$ 0.008, which is slightly but statistically significantly higher than the theoretical value of 2.98. We further investigate the suggestion that fluxes measured from emission lines at low signal to noise are strongly biased upwards. We were unable to detect this effect in the SDSS line flux measurements, and we could not reproduce the results of Rola and Pelat who first described this bias. We suggest that the magnitude of this effect may depend strongly on the specific fitting algorithm used.