论文标题
校准不确定性对重力波观测的影响
Calibration Uncertainty's Impact on Gravitational-Wave Observations
论文作者
论文摘要
我们校准电流尺度的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通过高斯过程很好地描述了。我利用此描述来分析校准不确定性的影响。鉴于观察到的数据和天体物理信号（天体物理校准）以及给定信号的数据（在校准不确定性上集成），我得出了校准误差的条件可能性的封闭形式表达式。我表明，校准不确定性总是会降低搜索灵敏度以及有关天体物理信号的可用信息。此外，校准不确定性从根本上限制了响应信号的限制的精度，这是考虑提议的第三代干涉仪的科学潜力时的关键因素。 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 $。在此信噪比下，与仅固定的高斯噪声相比，校准不确定性将$σ_ {\tildeλ} $增加$ 2 $。此外，1 \％校准不确定性将精度限制为始终为$σ_ {\tildeλ} \ gtrsim 0.5 $。我还展示了如何最好地选择应精确限制校准的频率，以最大程度地减少有关天体物理参数丢失的信息。在所有频率下，都不需要限制校准误差以对单个信号进行精确的天体物理推断。
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.
