AI 中文总结
研究由三分量非相对论矢量场引力玻色 - 爱因斯坦凝聚形成的普罗卡星内部自旋极化，通过模拟分解孔径平均自旋，发现凝聚产生的普罗卡星有可观但非最大极化，核心自旋受主导凝聚模式极化控制。
AI 中文摘要
我们研究了由三分量非相对论矢量场的引力玻色 - 爱因斯坦凝聚形成的普罗卡星的内部自旋极化。在理想化的周期盒模拟中，我们将孔径平均自旋分解为相干净分数、局部极化分数及其比率，从而区分真正的相干核心极化与孔径内方向抵消的局部自旋密度。对于独立矢量分量，凝聚产生的普罗卡星具有可观但非最大的极化。在独立分量模拟系综中，相干核心自旋分数的平均值为$\langle\chi_{\rm net}\rangle\simeq0.62$，实现到实现之间存在显著散射。我们将这种散射解释为主导分量空间模式的随机椭圆极化的结果，而不是普遍普罗卡星自旋分数的证据。这种解释得到了核心极化矩阵的支持：其主导特征向量提供了理想单模自旋分数的估计，而该估计与直接积分的相干自旋之间的差异跟踪核心与一阶分量空间状态的偏离。测量的主导特征向量自旋分数与各向同性随机复矢量参考大致兼容，与等幅随机相位参考不太兼容。相关和圆形初始数据将主导分量空间模式推向圆极化边界，给出独立→相关→圆形的顺序。这些结果表明，内部极化是引力凝聚的非相对论普罗卡星的真正矢量自由度，并且由此产生的核心自旋由主导凝聚模式的极化控制，而不是由固定的普遍值控制。
英文摘要
We study the internal spin polarization of Proca stars formed by gravitational Bose--Einstein condensation of a three-component nonrelativistic vector field. In idealized periodic-box simulations, we decompose the aperture-averaged spin into a coherent net fraction, a local polarization fraction, and their ratio, thereby distinguishing genuine coherent core polarization from local spin density whose direction cancels inside the aperture. For independent vector components, condensation produces Proca stars that are sizably but not maximally polarized. Across an independent-component simulation ensemble, the coherent core-spin fraction has mean $\langleχ_{\rm net}\rangle\simeq0.62$, with substantial realization-to-realization scatter. We interpret this scatter as the outcome of random elliptical polarization of the dominant component-space mode, rather than as evidence for a universal Proca-star spin fraction. This interpretation is supported by the core polarization matrix: its leading eigenvector provides an estimate of the ideal single-mode spin fraction, while the difference between this estimate and the directly integrated coherent spin tracks the departure of the core from a rank-one component-space state. The measured leading-eigenvector spin fractions are broadly compatible with an isotropic random-complex-vector model and less compatible with an equal-amplitude random-phase model. Correlated and circular initial data drive the dominant component-space mode toward the circular-polarization bound, giving the ordering independent $\rightarrow$ correlated $\rightarrow$ circular. These results show that internal polarization is a genuine vector degree of freedom of gravitationally condensed nonrelativistic Proca stars, and that the resulting core spin is controlled by the polarization of the dominant condensed mode rather than by a fixed universal value.
Comments15 pages, 4 figures
