发表机构
Max Planck Institute for Gravitational Physics (Albert Einstein Institute); Weizmann Institute of Science（马克斯·普朗克引力物理研究所（爱因斯坦研究所）; 魏茨曼科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究推导了冷却相对论流的新自相似解，明确其与Blandford-McKee解的因果边界，证明该解在激波附近的自洽性。
AI 中文摘要
Blandford-McKee（BM）解描述了强球形爆震波后方的极端相对论性自相似流，该爆震波传播至外部密度剖面∝r⁻ᵏ（其中k<4，r为距中心的距离）的介质中，但该解仅适用于紧邻激波的热壳；在激波后方足够深处，流体将脱离BM regime。由于相似剖面仅由激波条件决定，未对内部端点施加任何条件，因此该解在激波附近的有效性取决于BM regime之外的流能否在该热壳上留下印记。对于浅密度剖面（k<k_g≃2.062），BM解的特征结构已阻止非BM内部的前行声信号在极端相对论阶段到达激波；对于更陡的剖面（k_g<k<4），热状态方程在流仍处于相对论性且与激波相连时失效。在此，我们推导了冷却相对论流的新自相似解，该解具有自身的相似尺度、方程和特征结构，它在靠近激波处与热BM解重叠，并在该重叠区域之外达到声速点。这个临界点将与激波相连的BM加冷却复合流与更深处的下游区域分隔开，因此在临界点之外产生的声信号无法向激波传播。该机制在k=7/2时是明确的，此时可解析得到冷却解。因此，这种因果结构使得BM解得以成立，即使它未全局描述整个下游流，仍能在激波附近保持自洽性。
英文摘要
The Blandford--McKee (BM) solution describes the ultra-relativistic self-similar flow behind a strong spherical blast wave propagating into an external density profile $\propto r^{-k}$, where $k<4$ and $r$ is the distance from the center, but it applies only to the hot shell adjacent to the shock, sufficiently deep behind it, the fluid leaves the BM regime. Since the similarity profiles are determined solely by the shock conditions, with no conditions imposed at the inner end, the validity of the solution near the shock depends on whether the flow beyond the BM regime can imprint on this hot shell. For shallow density profiles, $k<k_g\simeq 2.062$, the characteristic structure of the BM solution already prevents forward-going acoustic information from the non-BM interior from reaching the shock during the ultra-relativistic stage. For steeper profiles, $k_g<k<4$, the hot equation of state fails while the flow is still relativistic and shock-connected. There, we derive a new self-similar solution for the cooling relativistic flow, which has its own similarity scale, equations, and characteristic structure. It overlaps with the hot BM solution toward the shock, and reaches a sonic point beyond this overlap. This critical point separates the shock-connected BM-plus-cooling composite from the deeper downstream region, so acoustic signals generated beyond it cannot propagate toward the shock. The mechanism is explicit at $k=7/2$, for which the cooling solution is obtained analytically. This causal structure is therefore what enables the BM solution, which remains self-consistent near the shock even though it does not globally describe the full downstream flow.
Comments14 pages, 6 figures, submitted to Physics of Fluids
