利用卡尔曼滤波器快速估计自旋漂移的二分量中子星模型参数
Rapid parameter estimation of a two-component neutron star model with spin wandering using a Kalman filter
摘要：
中子星的经典的、双组分的地壳超流体模型可以被公式化为噪声驱动的线性动力学系统，其中地壳和超流体的角速度使用应用于电磁脉冲定时数据和引力波数据的卡尔曼滤波器来跟踪。在这里，它显示了如何结合卡尔曼滤波器和嵌套采样的边缘似然估计六个模型参数的全后验分布，扩展以前的分析的基础上的最大似然方法。使用蒙特卡罗模拟在天体物理学上合理的参数域上测试该方法。它恢复注入的参数为$\lesssim 10$ %的时间序列包含$\sim 10^3$样本，典型的长期脉冲星定时运动。它在$\mathcal O(1)$ CPU-hr中高效运行，可处理上述大小的数据集。在目前的观测情况下，当电磁数据是唯一可用的，该方法准确地估计三个参数：弛豫时间，系综平均自旋下降的系统，和施加到地壳的随机扭矩的幅度。在未来的观测场景中，也可以获得引力波数据，该方法还可以估计地壳和超流体的惯性矩之间的比率，施加到超流体的随机扭矩的幅度，以及地壳-超流体滞后。这些经验结果与线性动力系统的形式可辨识性分析是一致的。
英文摘要：
The classic, two-component, crust-superfluid model of a neutron star can be formulated as a noise-driven, linear dynamical system, in which the angular velocities of the crust and superfluid are tracked using a Kalman filter applied to electromagnetic pulse timing data and gravitational wave data, when available. Here it is shown how to combine the marginal likelihood of the Kalman filter and nested sampling to estimate full posterior distributions of the six model parameters, extending previous analyses based on a maximum-likelihood approach. The method is tested across an astrophysically plausible parameter domain using Monte Carlo simulations. It recovers the injected parameters to $\lesssim 10$ per cent for time series containing $\sim 10^3$ samples, typical of long-term pulsar timing campaigns. It runs efficiently in $\mathcal O(1)$ CPU-hr for data sets of the above size. In a present-day observational scenario, when electromagnetic data are available only, the method accurately estimates three parameters: the relaxation time, the ensemble-averaged spin-down of the system, and the amplitude of the stochastic torques applied to the crust. In a future observational scenario, where gravitational wave data are also available, the method also estimates the ratio between the moments of inertia of the crust and the superfluid, the amplitude of the stochastic torque applied to the superfluid, and the crust-superfluid lag. These empirical results are consistent with a formal identifiability analysis of the linear dynamical system.
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