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arXiv 2305.09079astro-ph.HE
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脉冲星制动指数测量中的表观色散由计时噪声引起

Apparent dispersion in pulsar braking index measurements caused by timing noise

Andrés F. Vargas, Andrew Melatos

AI总结:

本文通过解析和蒙特卡洛模拟证明,计时噪声导致脉冲星制动指数测量出现表观色散,其方差与噪声幅度平方成正比,并给出异常区域的条件及对测量结果的影响。

摘要:

旋转供能脉冲星的自旋频率ν的随机时间游走(即与星际传播无关的计时噪声的无色分量)会影响对长期制动力矩测量的准确性。观测研究证实,具有异常制动指数|n|=|νddotν/dotν^2|≫1的脉冲星表现出更高水平的计时噪声,其中点号表示对时间的导数。本文通过解析计算和涉及合成数据及现代贝叶斯计时技术的蒙特卡洛模拟表明,测量到的n的方差⟨n^2⟩与计时噪声幅度σ_ddotν的平方成正比。异常区域⟨n^2⟩≫1对应于σ_ddotν^2≫10^{-60}(γ_ddotν/10^{-6} s^{-1})^2(dotν/10^{-14} Hz s^{-1})^4(ν/1 Hz)^{-2}(T_obs/10^8 s) Hz^2 s^{-5},其中γ_ddotν是恒星阻尼时间尺度,T_obs是总观测时间。当上述条件中的不等式反向时,n由长期制动力矩主导,如果长期制动力矩是电磁性的,计时测量返回n∼3。当驱动自旋涨落的随机过程不同于计时解中假设的红噪声模型(例如幂律谱密度)时,方差⟨n^2⟩更大。

英文摘要:

Stochastic temporal wandering of the spin frequency $ν$ of a rotation-powered pulsar (i.e.~the achromatic component of timing noise unrelated to interstellar propagation) affects the accuracy with which the secular braking torque can be measured. Observational studies confirm that pulsars with anomalous braking indices $\vert n \vert = \vert ν\ddotν / \dotν^2 \vert \gg 1$ exhibit elevated levels of timing noise, where an overdot symbolizes a derivative with respect to time. Here it is shown, through analytic calculations and Monte Carlo simulations involving synthetic data and modern Bayesian timing techniques, that the variance $\langle n^2 \rangle$ of the measured $n$ scales with the square of the timing noise amplitude $σ_{\ddotν}$. The anomalous regime $\langle n^2 \rangle \gg 1$ corresponds to $ σ_{\ddotν}^2 \gg 10^{-60} (γ_{\ddotν}/10^{-6} \, {\rm s^{-1}})^2 (\dotν / 10^{-14} \, {\rm Hz \, s^{-1}})^4 (ν/ 1 \, {\rm Hz})^{-2} (T_{\rm obs} / 10^8 \, {\rm s}) \, {\rm Hz}^2{\rm s}^{-5 }$, where $γ_{\ddotν}$ is a stellar damping time-scale, and $T_{\rm obs}$ is the total observing time. When the inequality in the above condition is reversed, $n$ is dominated by the secular braking torque, and timing measurements return $n\sim 3$, if the secular braking torque is electromagnetic. The variance $\langle n^2 \rangle$ is greater, when the stochastic process driving spin fluctuations differs from the red noise model (e.g. power-law spectral density) assumed in the timing solution.

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