AI 中文总结
该研究构建了一种混合核心含暗物质的解析双不可压缩流体恒星模型，确定了其可允许参数空间与临界致密性，为暗物质混合中子星模型提供了有用基准。
AI 中文摘要
我们构建了一种解析相对论性双流体恒星，其特征为混合核心，其中普通物质与暗物质作为两种各自守恒的不可压缩理想流体共存，包层仅由普通物质构成。两种流体既不交换物质也不交换能量，仅通过共同的时空几何发生相互作用；普通组分延伸至核心-包层界面，而暗组分则被限制在核心内。尽管存在混合核心-单流体包层结构及内部界面，该系统仍保持解析可处理性，使我们能获得压强与度规函数的显式表达式，并直接探究暗物质占比与核心相对大小的影响。我们确定了物理上可允许的参数空间，并推导了与中心压强发散相关的类布赫达尔临界致密性，其值取决于暗物质相对密度与混合核心的大小。在对应的单流体极限下，可恢复史瓦西常密度恒星及其标准临界值2M/R=8/9。质量-半径分析进一步表明，具有相同整体致密性的构型可对应不同的内部物质分布。除了提供对核心受限第二组分的解析可控描述外，该构建还为识别后续可在更现实的暗物质混合中子星模型中研究的定性趋势提供了有用基准，而详细处理此类模型超出了本工作的范围。
英文摘要
We construct an analytical relativistic two fluid star characterized by a mixed core, where ordinary matter and dark matter coexist as two independently conserved incompressible perfect fluids, and an envelope composed exclusively of ordinary matter. The fluids exchange neither matter nor energy and interact only through the common spacetime geometry, with the ordinary component extending across the core envelope interface while the dark component is confined to the core. Despite the mixed core--single-fluid envelope structure and the internal interface, the system remains analytically tractable, allowing us to obtain explicit expressions for the pressures and metric functions and to follow directly the effects of the dark-matter fraction and relative core size. We determine the physically admissible parameter space and derive a Buchdahl like critical compactness associated with the divergence of the central pressure, whose value depends on the relative dark matter density and the size of the mixed core. The Schwarzschild constant density star and its standard critical value, $2M/R=8/9$, are recovered in the corresponding one fluid limit. The mass--radius analysis further shows that configurations with the same global compactness can correspond to distinct internal matter distributions. Beyond providing an analytically controlled description of a core-confined second component, the construction offers a useful benchmark for identifying qualitative trends that may subsequently be examined in more realistic dark matter admixed neutron star models, whose detailed treatment lies beyond the scope of the present work.
