AI 中文总结
本研究通过统一数值比较四种理论描述，确定了轴子星结构在不同耦合强度下适用的理论框架，为选择牛顿、相对论修正或广义相对论描述提供了系统基准。
AI 中文摘要
轴子星的质-半径关系通常使用不同阶的相对论近似来计算，因此确定这些描述在何处仍然可靠变得非常重要。我们对实标量场的牛顿薛定谔-泊松描述、一阶和二阶相对论有效场论以及完整的爱因斯坦-克莱因-戈登系统中的轴子星基态构型进行了统一的数值比较。在所有四种描述中使用相同的吸引四次自相互作用，我们扫描$|\widetilde{\lambda}|=(M_{\rm Pl}/f_a)^2$并确定最大质量及相应的包围质量半径。所有描述都恢复了常见的大$|\widetilde{\lambda}|$稀薄星标度，而在弱耦合和中等耦合下出现了显著差异。相对论有效场论系统地插值于牛顿结果和完整广义相对论结果之间。对于最大质量序列中$\max|\phi|/f_a=O(1)$的部分，我们在完整广义相对论中明确测试了时间谐波和势截断。高次谐波展开显示出快速收敛，而恢复完整的单余弦势仅将最大质量改变约百分之几，$R_{95}$改变约几个百分点。连同相对论有效场论描述向完整广义相对论的系统收敛，这些结果表明，与薛定谔-泊松预测的大弱耦合偏差反映了非相对论结构描述的失效。我们的结果为确定何时需要牛顿、相对论修正或完全广义相对论描述轴子星结构提供了系统基准。本工作中使用的数值实现可在Axion Star Solvers仓库中获取，网址为https://this https URL。
英文摘要
Axion-star mass-radius relations are commonly computed using different orders of relativistic approximation, making it important to determine where these descriptions remain reliable. We perform a unified numerical comparison of axion-star ground-state configurations in the Newtonian Schrödinger-Poisson description, first- and second-order relativistic effective field theories, and the full Einstein-Klein-Gordon system for a real scalar field. Using the same attractive quartic self-interaction in all four descriptions, we scan $|\widetildeλ|=(M_{\rm Pl}/f_a)^2$ and determine the maximum masses and corresponding enclosed-mass radii. All descriptions recover the common large-$|\widetildeλ|$ dilute-star scaling, while substantial differences appear at weak and moderate coupling. The relativistic EFTs interpolate systematically between the Newtonian and full-GR results. For part of the maximum-mass sequence where $\max|ϕ|/f_a=O(1)$, we test the temporal-harmonic and potential truncations explicitly in full GR. The higher-harmonic expansion shows rapid convergence, while restoring the complete single-cosine potential changes the maximum mass only at the percent level and $R_{95}$ at the several-percent level. Together with the systematic convergence of the relativistic EFT descriptions toward full GR, these results show that the large weak-coupling departure from the Schrödinger-Poisson prediction reflects the breakdown of the nonrelativistic structural description. Our results provide a systematic benchmark for determining when Newtonian, relativistically corrected, or fully general-relativistic descriptions are required for axion-star structure. The numerical implementation used in this work is available in the Axion Star Solvers repository at https://github.com/Parisa-Arabameri/AxionStar.
Comments22 pages, 10 figures, 1 table
