刻度不确定度对引力波观测的影响
Calibration Uncertainty's Impact on Gravitational-Wave Observations
摘要：
我们校准当前千分之一级干涉仪的能力可能会混淆天体物理信号的推断。当前的校准不确定性很好地描述了高斯过程。我利用这个描述来分析检验校准不确定性的影响。我推导出封闭形式的表达式的校准误差给定的观测数据和天体物理信号（天体物理校准）的条件可能性，以及给定的信号（集成的校准不确定性）的数据的边际可能性。我表明，校准的不确定性总是降低搜索灵敏度和有关天体物理信号的信息量。此外，校准不确定性将从根本上限制强信号的精度，这是考虑拟议的第三代干涉仪的科学潜力时的一个关键因素。例如，我估计，在探测器响应的幅度和相位中具有$1\%$不确定性的情况下，对于信噪比为$\gtrsim 10^4$的信号，人们只能测量1.4+1.4 $\,M_\odot$系统的领先阶潮汐参数（$\tildeΛ$），以优于$\pm 1$（$\sim 0.2\%$相对不确定性）。在该信噪比下，与单独的平稳高斯噪声相比，校准不确定性使$σ_{\tildeΛ}$增加$2$的因子。此外，1\%的校准不确定度限制了精度始终为$σ_{\tildeΛ} \gtrsim 0.5$。我还展示了如何最好地选择校准的频率应精确地限制，以尽量减少有关天体物理参数的信息丢失。为了对单个信号进行精确的天体物理推断，没有必要在所有频率下都将校准误差限制为很小。
英文摘要：
Our ability to calibrate current kilometer-scale interferometers can potentially confound the inference of astrophysical signals. Current calibration uncertainties are well described by a Gaussian process. I exploit this description to analytically examine the impact of calibration uncertainty. I derive closed-form expressions for the conditioned likelihood of the calibration error given the observed data and an astrophysical signal (astrophysical calibration) as well as for the marginal likelihood for the data given a signal (integrated over the calibration uncertainty). I show that calibration uncertainty always reduces search sensitivity and the amount of information available about astrophysical signals. Additionally, calibration uncertainty will fundamentally limit the precision to which loud signals can be constrained, a crucial factor when considering the scientific potential of proposed third-generation interferometers. For example, I estimate that with $1\%$ uncertainty in the detector response's amplitude and phase, one will only be able to measure the leading-order tidal parameter ($\tildeΛ$) for a 1.4+1.4$\,M_\odot$ system to better than $\pm 1$ ($\sim 0.2\%$ relative uncertainty) for signals with signal-to-noise ratios $\gtrsim 10^4$. At this signal-to-noise ratio, calibration uncertainty increases $σ_{\tildeΛ}$ by a factor of $2$ compared to stationary Gaussian noise alone. Furthermore, 1\% calibration uncertainty limits the precision to always be $σ_{\tildeΛ} \gtrsim 0.5$. I also show how to best select the frequencies at which calibration should be precisely constrained in order to minimize the information lost about astrophysical parameters. It is not necessary to constrain the calibration errors to be small at all frequencies to perform precise astrophysical inference for individual signals.
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