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arXiv 2302.06602astro-ph.GAphysics.plasm-ph
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盘星系中旋涡不稳定性的饱和

Saturation of spiral instabilities in disk galaxies

Chris Hamilton

AI总结:

本研究针对盘星系旋涡不稳定性的饱和机制问题,提出恒星在共转共振附近的非线性俘获是关键机制,解析推导了饱和条件与最大振幅公式,与N-体模拟吻合,解释了不同振幅旋涡的成因。

摘要:

旋涡密度波可作为底层恒星分布函数的线性不稳定性在星系盘中产生。这类不稳定性的振幅会以某一固定增长率$β$呈指数增长,随后发生非线性饱和。然而,饱和背后的机制以及由此产生的饱和旋涡振幅,此前受到的关注较少。本文提出,一种重要的饱和机制是恒星在旋涡共转共振附近的非线性俘获。在该机制下,我们通过解析证明,当共振俘获轨道的平动频率达到$ω_\text{lib} \text{~几} \times m^{1/2} β$时,$m$臂旋涡不稳定性将发生饱和。对于具有平坦旋转曲线的星系,这意味着最大相对旋涡面密度$|δΣ/Σ_0| \text{~几} \times (β/Ω_\text{p})^2 \tan α$,其中$Ω_\text{p}$为旋涡图案速度,$α$为其旋臂角。该结果与近期的$N$-体模拟结果合理吻合,表明由内部产生的不稳定性驱动的旋涡相对振幅最多为百分之几十;而像M51和NGC 1300这类更高振幅的旋涡,很可能是由极强的棒旋结构和/或潮汐扰动导致的。

英文摘要:

Spiral density waves can arise in galactic disks as linear instabilities of the underlying stellar distribution function. Such an instability grows exponentially in amplitude at some fixed growth rate $β$ before saturating nonlinearly. However, the mechanisms behind saturation, and the resulting saturated spiral amplitude, have received little attention. Here we argue that one important saturation mechanism is the nonlinear trapping of stars near the spiral's corotation resonance. Under this mechanism, we show analytically that an $m$-armed spiral instability will saturate when the libration frequency of resonantly trapped orbits reaches $ω_\mathrm{lib} \sim \mathrm{a\,\, few}\times m^{1/2} β$. For a galaxy with a flat rotation curve this implies a maximum relative spiral surface density $\vert δΣ/Σ_0\vert \sim \mathrm{a\,\,few} \times (β/Ω_\mathrm{p})^2 \cot α$, where $Ω_\mathrm{p}$ is the spiral pattern speed and $α$ is its pitch angle. This result is in reasonable agreement with recent $N$-body simulations, and suggests that spirals driven by internally-generated instabilities reach relative amplitudes of at most a few tens of percent; higher amplitude spirals, like in M51 and NGC 1300, are likely caused by very strong bars and/or tidal perturbations.

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