AI 中文总结
研究银河系致密双星在LISA毫赫兹频段形成的前景对SGWB推断的影响，通过构建目录残余频谱等方法，分析源功率集中等因素，得出其对\(\Omega_0\)不确定性的影响及相关数值结论。
AI 中文摘要
银河系致密双星预计会在激光干涉空间天线（LISA）的毫赫兹频段形成主要前景。未达采用的恢复标准的注入源的残余功率会使随机引力波背景（SGWB）推断产生偏差或增加其不确定性。我们利用LISA数据挑战2A桑格利亚注入和埃雷博尔比较表，构建了0.4至6.0毫赫兹之间的目录残余频谱，采用轨道平均长波长迈克尔逊\(X\)源功率。每个频率 bin 中的源功率集中决定了随机相位源总和的超额峰度；仪器噪声和基准SGWB功率在大多数 bin 中强烈降低了产生的超额峰度。残余频谱在平均 bin 功率中也与各向同性幂律SGWB重叠。我们使用通过对独立傅里叶模式功率方差求和得到的固定协方差。对于基准幅度\(\Omega_0 = 10^{-11}\)的频率无关SGWB，当残余功率在每个 bin 的傅里叶频率上均匀分布时，对无量纲残余功率因子\(\beta\)进行边缘化会使\(\Omega_0\)不确定性增加\(13.6\%\)。将这种增加限制在\(10\%\)的最大高斯先验标准差\(\beta\)为\(0.0073\)。傅里叶频率之间更集中的残余功率分布会减少这种增加，反映出未解决的频率结构。在协方差固定时省略基准残余会使最佳拟合\(\Omega_0\)偏移\(119.5\)倍于\(\beta\)固定时获得的不确定性。这种残余频谱到SGWB频谱上的投影不是后验检测显著性。数值取决于目录级标量功率模型、固定仪器噪声和独立模式功率协方差。
英文摘要
Galactic compact binaries are expected to form a dominant foreground in the millihertz band of the Laser Interferometer Space Antenna (LISA). Residual power from injected sources that do not meet the adopted recovery criteria can bias stochastic gravitational-wave background (SGWB) inference or increase its uncertainty. We use LISA Data Challenge 2A Sangria injections and the Erebor comparison table to construct a catalog residual spectrum between 0.4 and 6.0 mHz with orbit-averaged long-wavelength Michelson \(X\) source powers. The source power concentration in each frequency bin determines the excess kurtosis of a random-phase source sum; instrumental noise and fiducial SGWB power strongly reduce the resulting excess kurtosis in most bins. The residual spectrum also overlaps an isotropic power-law SGWB in the mean binned power. We use a fixed covariance obtained by summing independent Fourier-mode power variances. For a frequency-independent SGWB with fiducial amplitude \(Ω_0=10^{-11}\), marginalizing over the dimensionless residual-power factor \(β\) increases the \(Ω_0\) uncertainty by \(13.6\%\) when the residual power is distributed uniformly over the Fourier frequencies in each bin. The largest Gaussian prior standard deviation on \(β\) that limits this increase to \(10\%\) is \(0.0073\). More concentrated distributions of the residual power among Fourier frequencies reduce the increase, reflecting unresolved frequency structure. Omitting the fiducial residual with the covariance held fixed shifts the best-fitting \(Ω_0\) by \(119.5\) times the uncertainty obtained with \(β\) fixed. This projection of the residual spectrum onto the SGWB spectrum is not a posterior detection significance. The numerical values are conditional on the catalog-level scalar power model, fixed instrumental noise, and independent mode-power covariance.
Comments16 pages, 6 figures, and 2 tables
