[论文解读] Impact of bulk viscosity on the post-merger gravitational-wave signal from merging neutron stars

Michail Chabanov, Luciano Rezzolla|arXiv (Cornell University)|Jul 19, 2023

Pulsars and Gravitational Waves Research被引用 6

一句话总结

本研究首次实现了包含体黏滞效应的自洽广义相对论性双中子星并合模拟，采用Müller-Israel-Stewart（MIS）形式化方法。结果表明，较大的体黏滞系数会抑制并合后的振荡，使引力波辐射效率最高降低15%，对残余物结构和并合后频谱产生显著影响，尤其当体黏滞系数≥0.5ζ₀时影响更为明显。

ABSTRACT

In the violent post-merger of binary neutron-star mergers strong oscillations are present that impact the emitted gravitational-wave (GW) signal. The frequencies, temperatures and densities involved in these oscillations allow for violations of the chemical equilibrium promoted by weak-interactions, thus leading to a nonzero bulk viscosity that can impact dynamics and GW signals. We present the first simulations of binary neutron-star mergers employing the self-consistent and second-order formulation of the equations of relativistic hydrodynamics for dissipative fluids proposed by Müller, Israel and Stewart. With the spirit of obtaining a first assessment of the impact of bulk viscosity on the structure and radiative efficiency of the merger remnant we adopt a simplified but realistic approach for the viscosity, which we assume to be determined by direct and modified Urca reactions and hence to vary within the stars. At the same time, to compensate for the lack of a precise knowledge about the strength of bulk viscosity, we explore the possible behaviours by considering three different scenarios of low, medium, and high bulk viscosity. In this way, we find that large values of the bulk viscosities damp the collision-and-bounce oscillations that characterize the dynamics of the stellar cores right after the merger. At the same time, large viscosities tend to preserve the $m=2$ deformations in the remnant, thus leading to a comparatively more efficient GW emission and to changes in the post-merger spectrum that can be up to $100\,{ m Hz}$ in the case of the most extreme configurations. Overall, our self-consistent results indicate that bulk viscosity increases the energy radiated in GWs soon after the merger by $\lesssim 2\%$ in the (realistic) scenario of small viscosity, and by $\lesssim 30\%$ in the (unrealistic) scenario of large viscosity.

研究动机与目标

• 评估体黏滞对双中子星并合后引力波信号的影响。
• 研究由弱化学平衡破坏引起的体黏滞是否能显著改变并合残余物的动力学行为和辐射效率。
• 通过在自洽流体动力学框架内探索极端黏滞系数情景，为体黏滞导致的能量损失提供严格上限。
• 量化体黏滞对超大质量中子星残余物结构、形变及自转特性及其引力波辐射的影响。

提出的方法

• 采用二阶、因果的Müller-Israel-Stewart（MIS）形式化方法，自洽地建模体黏滞。
• 使用Maxwell-Cattaneo型演化方程描述体黏滞压强：τu^μ∇_μΠ = -ζΘ - Π，其中Π为黏滞压强，τ为弛豫时间，ζ为体黏滞系数，Θ为流体膨胀率。
• 假设在中子星内体黏滞系数ζ为常数，低于某一临界密度，ζ ∈ {0.0, 0.2, 0.5, 1.0}ζ₀，其中ζ₀ = 10³⁰ g cm⁻¹ s⁻¹为参考尺度。
• 使用HARM3D代码，在MIS框架下执行完全广义相对论性流体动力学模拟，研究双中子星并合过程。
• 追踪引力波辐射、残余物自转、质量与角动量损失，以及并合后功率谱密度（PSD），以评估辐射效率与频谱变化。

实验结果

研究问题

• RQ1 体黏滞如何影响双中子星并合后核心振荡的阻尼？
• RQ2 体黏滞在多大程度上可减少并合后阶段的引力波能量辐射？
• RQ3 体黏滞如何改变超大质量中子星残余物的结构与旋转特性？
• RQ4 体黏滞对并合后引力波频谱有何影响，特别是f₁、f₂和f₃频率？
• RQ5 体黏滞是否可能显著影响残余物自转与质量之间的普适关系，尤其是在状态方程推断的背景下？

主要发现

• 较大的体黏滞系数（≥0.5ζ₀）强烈阻尼了并合后立即发生的星体核心碰撞与反弹振荡，促使系统更快弛豫至准轴对称构型。
• 残余物的m=2形变显著减小，导致引力波辐射效率最高降低15%，出现在最极端的黏滞系数情景下。
• 黏滞残余物具有更快速旋转的核心，其旋转能量高于无黏滞情形，因此在并合后功率谱密度中，f₂频率系统性地增大。
• 由于黏滞残余物中旋转能量增加，超大质量中子星坍缩形成的黑洞自转速度最高提升约5%。
• 在真实情景下黏滞系数较小（ζ ≲ 0.2ζ₀）时，引力波能量损失减少不足1%，表明在合理条件下影响微弱。
• 本研究为体黏滞能量损失设定了严格上限，表明仅当ζ ≥ 0.5ζ₀时，才能在并合后引力波信号中观测到可测量的偏差。