大${\rm Pm}$小尺度运动学发电机在中子星前身星中的应用
Large ${\rm Pm}$ small-scale kinematic dynamo in protoneutron stars
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中文总结 AI 辅助
本研究通过模拟和理论模型，探讨了中子星前身星中湍流对流发电机如何产生磁星强磁场，发现增长率随Pm和Ra增加，并预测在大Pm极限下增长率约1 ms⁻¹。
中文摘要 AI 辅助
磁星是年轻、孤立的脉冲星，拥有异常强的磁场，其表面偶极场强度约为$10^{15}$ G。产生如此强磁场的一个合理情景是在中子星前身星阶段，由湍流对流发电机进行指数放大。然而，对流的预期持续时间很短（约$10$ s），这对发电机增长率施加了严格限制。我们使用弹性近似进行了82次三维对流发电机模拟的广泛集合，并研究了运动学阶段以量化发电机增长率$\gamma$。我们发现$\gamma$随磁普朗特数${\rm Pm}$和瑞利数${\rm Ra}$的增加而增加，最不稳定模式变得高度非轴对称和多极。我们进一步观察到，随着磁雷诺数${\rm Rm}$的增加，从大尺度发电机逐渐过渡到小尺度发电机，导致磁场主要集中在小尺度上。当外部磁边界条件变化时，这一趋势保持不变。由于解析越来越小的尺度在数值上变得不切实际，我们采用理论上的小尺度Kazantsev发电机模型来探索中子星前身星特征的大${\rm Pm}$区域。该模型定性地捕捉了模拟中观察到的增长率行为，并且外推到大的${\rm Pm}$极限时，表明在中子星前身星中$\gamma$仅弱依赖于电阻率。在与中子星前身星相关的条件下，该模型预测磁能增长率约为$\sim 1$ ms$^{-1}$。
英文摘要
Magnetars are young, isolated neutron stars that possess an exceptionally strong magnetic field, with surface dipolar strengths on the order of $10^{15}$ G. One of the plausible scenarios for generating such a strong field is an exponential amplification by a turbulent convective dynamo during the protoneutron star phase. However, the short expected duration of the convection ($\sim 10$ s) imposes a stringent constraint on the dynamo growth rate. We perform an extensive set of 82 three-dimensional convective dynamo simulations in the anelastic approximation and investigate the kinematic phase to quantify the dynamo growth rate $γ$. We find that $γ$ increases with both the magnetic Prandtl number ${\rm Pm}$ and the Rayleigh number ${\rm Ra}$, with the most unstable mode becoming highly non-axisymmetric and multipolar. We further observe a gradual transition from large-scale to small-scale dynamo as the magnetic Reynolds number ${\rm Rm}$ increases, resulting in a magnetic field that is predominantly concentrated at small scales. The trend remains unchanged when the outer magnetic boundary condition is varied. Since resolving the increasingly small scales becomes numerically impractical, we employ the theoretical small-scale Kazantsev dynamo model to explore the large ${\rm Pm}$ regime characteristic of protoneutron stars. The model qualitatively captures the growth rate behaviour observed in simulations and, upon extrapolation to the large ${\rm Pm}$ limit, indicates that $γ$ is only weakly dependent on the resistivity in a PNS. Under conditions relevant to the PNS, this model predicts a magnetic energy growth rate of the order of $\sim 1$ ms$^{-1}$.
发表机构
- Indian Institute of Technology Kharagpur（印度理工学院哈格普尔分校）
- Indian Institute of Technology Madras（印度理工学院马德拉斯分校）
- Université Paris Cité, Université Paris-Saclay, CEA, CNRS, AIM（巴黎西岱大学、巴黎萨克雷大学、法国原子能和替代能源委员会、法国国家科学研究中心、天体物理学信息与方法研究所）
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