TianQin超大质量黑洞双星吸气参数估计精度的初步研究
Preliminary study on parameter estimation accuracy of supermassive black hole binary inspirals for TianQin
摘要：
利用Fisher信息矩阵方法计算了用于探测毫赫兹波段引力波的星载激光干涉探测器天琴对吸入型超大质量黑洞双星的参数估计精度。“限制”后牛顿波形，其中三阶后牛顿（3 PN）相位，包括自旋效应（自旋-轨道$β$和自旋-自旋$σ$）和一阶偏心率的贡献。用$10^3$双星对质量在$({10^5},{10^7}){M_ \odot }$和宇宙学红移$z=0.5$范围内的质量对进行蒙特卡罗模拟，结果表明啁啾质量$M_c$和对称质量比$η$的均方根误差分布的中位数分别在$\sim 0.02\% - 0.7\% $和$\sim 4\% - 8\% $范围内.光度距离$D_L$可确定为$\sim 1\% - 3\% $，源$ΔΩ$的角分辨率优于12度$^2$。对随信噪比降低而退化的$z=1.0$和$2.0$也给出了相应的结果。结果表明，自旋参数的加入降低了质量参数（${M_c}$，$η$）、合并时间和轨道相位（$t_c$，$ϕ_c$）的测量精度;与圆形情况相比，对相位的一阶偏心率修正降低了估计精度。通过比较二阶和三阶后牛顿相的结果，我们还展示了后牛顿阶对参数估计精度的影响。此外，我们还计算了天琴超大质量黑洞双星的视界距离。
英文摘要：
We use the Fisher information matrix method to calculate the parameter estimation accuracy of inspiraling supermassive black holes binaries for TianQin, a space-borne laser interferometric detector aimed at detecting gravitational waves in the millihertz frequency band. The `restricted' post-Newtonian waveform in which third order post-Newtonian (3PN) phase including spin effects (spin-orbit $β$ and spin-spin $σ$) and first-order eccentricity contribution is employed. Monte Carlo simulations using $10^3$ binaries for mass pairs with component masses in the range of $({10^5},{10^7}){M_ \odot }$ and cosmological redshift $z=0.5$ show that the medians of the root-mean-square error distributions for the chirp mass $M_c$ and symmetric mass ratio $η$ are in the range of $\sim 0.02\% - 0.7\% $ and $\sim 4\% - 8\% $, respectively. The luminosity distance $D_L$ can be determined to be $\sim 1\% - 3\% $, and the angular resolution of source $ΔΩ$ is better than 12 deg$^2$. The corresponding results for $z=1.0$ and $2.0$, which are deteriorated with the decreasing of the signal-to-noise ratio, have also been given. We show that adding spin parameters degrades measurement accuracy of the mass parameters (${M_c}$, $η$), and the time and the orbital phase of coalescence ($t_c$, $ϕ_c$); the inclusion of the first-order eccentricity correction to the phase worsens the estimation accuracy comparing with the circular cases. We also show the effects of post-Newtonian order on parameter estimation accuracy by comparing the results based on second order and third order post-Newtonian phases. Moreover, we calculate the horizon distance of supermassive black hole binaries for TianQin.
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