[论文解读] Spinning down newborn neutron stars: nonlinear development of the r-mode instability

R. Bondarescu, Saul A. Teukolsky+1 more|arXiv (Cornell University)|Sep 19, 2008

Pulsars and Gravitational Waves Research被引用 29

一句话总结

本文通过三模耦合（r-模与两个近共振惯性模）建模新生中子星中r-模不稳定的非线性饱和，表明自转减慢演化对粘性力和冷却机制高度敏感。研究发现，r-模的引力波辐射可能在新生后数年至数十年内被先进LIGO探测到，具体取决于内部耗散特性，非线性动力学导致复杂的热振荡，并且自转减慢 timescale 受超子超流性和边界层粘性的影响而变化。

ABSTRACT

We model the nonlinear saturation of the r-mode instability via three-mode couplings and the effects of the instability on the spin evolution of young neutron stars. We include one mode triplet consisting of the r-mode and two near resonant inertial modes that couple to it. We find that the spectrum of evolutions is more diverse than previously thought. The evolution of the star is dynamic and initially dominated by fast neutrino cooling. Nonlinear effects become important when the r-mode amplitude grows above its first parametric instability threshold. The balance between neutrino cooling and viscous heating plays an important role in the evolution. Depending on the initial r-mode amplitude, and on the strength of the viscosity and of the cooling this balance can occur at different temperatures. If thermal equilibrium occurs on the r-mode stability curve, where gravitational driving equals viscous damping, the evolution may be adequately described by a one-mode model. Otherwise, nonlinear effects are important and lead to various more complicated scenarios. Once thermal balance occurs, the star spins-down oscillating between thermal equilibrium states until the instability is no longer active. For lower viscosity we observe runaway behavior in which the r-mode amplitude passes several parametric instability thresholds. In this case more modes need to be included to model the evolution accurately. In the most optimistic case, we find that gravitational radiation from the r-mode instability in a very young, fast spinning neutron star within about 1 Mpc of Earth may be detectable by advanced LIGO for years, and perhaps decades, after formation. Details regarding the amplitude and duration of the emission depend on the internal dissipation of the modes of the star, which would be probed by such detections.

研究动机与目标

• 超越单模近似，研究新生中子星中r-模不稳定的非线性饱和。
• 确定粘性（超子体积粘性和边界层粘性）和冷却（直接URCA过程、中微子冷却）如何影响自转减慢演化与引力波辐射。
• 评估先进LIGO对距离约1 Mpc以内的年轻、高速自转中子星的r-模引力波探测能力。
• 探讨热平衡与参数不稳定阈值在塑造恒星自转与温度演化中的作用。

提出的方法

• 通过三模耦合建模r-模不稳定的非线性演化，包括r-模与两个近共振惯性模。
• 采用双相粘性模型：高温时（T ~ 10^9–10^10 K）为超子体积粘性，低温时（~3×10^8 K）为边界层粘性。
• 从高温（T ~ 10^10 K）且高速自转（接近开普勒频率）的中子星出发，模拟自转减慢演化。
• 通过引力波驱动、粘性加热与中微子冷却之间的能量平衡，确定热平衡状态。
• 利用引力波与粘性耗散率的解析近似，推导自转减慢timescale的标度律。
• 采用准稳态近似建模模态振幅演化，尤其在非线性效应占主导时。

实验结果

研究问题

• RQ1 与单模模型相比，引入三模耦合如何改变新生中子星的自转减慢演化？
• RQ2 在r-模稳定性曲线上，何种条件会导致热平衡？非线性效应在何时主导演化？
• RQ3 超子超流转变温度与边界层粘性变化如何影响r-模驱动引力波辐射的持续时间与振幅？
• RQ4 在何种条件下，r-模引力波辐射可在中子星形成后数年至数十年内被先进LIGO探测到？
• RQ5 与粘性强度和初始条件相关的自转减慢timescale由何种标度律支配？

主要发现

• r-模不稳定性可导致引力波辐射在新生后长达数十年内被先进LIGO探测到，具体取决于内部耗散特性。
• 当r-模振幅超过首个参数不稳定阈值时，非线性效应变得显著，导致超越单模模型的复杂动力学。
• 在r-模稳定性曲线上达到热平衡时，自转减慢行为呈现振荡特征，振幅逐渐减小，直至恒星稳定于该曲线。
• 在低粘性条件下，当r-模振幅多次通过参数不稳定阈值时，会出现发散行为，需引入更多模态才能实现准确建模。
• 当边界层粘性占主导时，最终自转频率几乎与超子体积粘性强度无关，自转减慢timescale满足 t_spin-down ∝ A_hb^(-1)。
• 在最乐观的情形下，距离约1 Mpc以内的年轻、高速自转中子星的引力波辐射可能在数年至数十年内被探测到，探测性取决于内部耗散特性。