再论中子星r模不稳定性的随机引力波背景
Stochastic Gravitational Wave Background from Neutron Star r-mode Instability Revisited
摘要：
我们重新审视的可能性和可探测性的随机引力波背景（SGWB）所产生的宇宙学人口的新生中子星（NS）与r-模不稳定性。我们发现，由此产生的SGWB是不敏感的CSFR模型的选择，但强烈依赖于CSFR在低红移的演变行为。我们的结果表明，无量纲能量密度$Ω_{\rm{GW}}$在频率范围$(200-1000)$ ~Hz内可能有一个峰值振幅$\simeq (1-3.5) \times10^{-8}$。然而，这样高的模式振幅是不现实的，因为已知最大值小得多并且至多为$10^{-2}$。$Ω_{\rm{GW}}$的实际估计值应至少低4个数量级（$\sim 10^{-12}$），这导致r模式背景检测的悲观前景。我们考虑不同的对地面干涉仪（IFO），并比较两种方法来结合多个IFO，以评估这GW背景的可探测性。与此机制相关的总发射GW能量的约束，以产生一个可检测的随机背景是$\sim 10^{-3} M_{\odot} c^2$的两个共同定位的先进LIGO探测器，和$2 \times 10^{-5} M_{\odot} c^2$的两个爱因斯坦望远镜。这些约束也可以适用于与NS中的振荡或不稳定性相关的替代GW发射机制，这取决于发射大多数GW的频带。
英文摘要：
We revisit the possibility and detectability of a stochastic gravitational wave background (SGWB) produced by a cosmological population of newborn neutron stars (NSs) with r-mode instabilities. We show that the resultant SGWB is insensitive to the choice of CSFR models, but depends strongly on the evolving behavior of CSFR at low redshifts. Our results show that the dimensionless energy density $Ω_{\rm{GW}}$ could have a peak amplitude of $\simeq (1-3.5) \times10^{-8}$ in the frequency range $(200-1000)$~Hz. However, such a high mode amplitude is unrealistic as it is known that the maximum value is much smaller and at most $10^{-2}$. A realistic estimate of $Ω_{\rm{GW}}$ should be at least 4 orders of magnitude lower ($\sim 10^{-12}$), which leads to a pessimistic outlook for the detection of r-mode background. We consider different pairs of terrestrial interferometers (IFOs) and compare two approaches to combine multiple IFOs in order to evaluate the detectability of this GW background. Constraints on the total emitted GW energy associated with this mechanism to produce a detectable stochastic background are $\sim 10^{-3} M_{\odot} c^2$ for two co-located advanced LIGO detectors, and $2 \times 10^{-5} M_{\odot} c^2$ for two Einstein Telescopes. These constraints may also be applicable to alternative GW emission mechanisms related to oscillations or instabilities in NSs depending on the frequency band where most GWs are emitted.
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