论文标题
超偏见爆炸的非相对论内部：扩展到布兰福德·麦基解决方案
The Non Relativistic Interiors of Ultra-Relativistic Explosions: Extension to the Blandford McKee Solutions
论文作者
论文摘要
众所周知的Blandford-McKee溶液在球形几何形状中描述了超强大的冲击波的超层流流动的流体动力学。但是，这些解决方案在冲击波后面的距离$ \ sim r/2 $的距离上变得不准确，随着流量接近牛顿速度，$ r $是冲击半径。在这项工作中，我们找到了一种新的自相似溶液，该解决方案是Blandford-Mckee解决方案的扩展，并描述了爆炸波的内部部分，在该部分中，该流量与牛顿速度有些相对论。我们发现，流的内部部分的速度曲线不取决于冲击洛伦兹因子的值，$γ$，并且从$ r = 0 $降到$ r/γ^2 $的距离落后于冲击。尽管冲击波与其背后的整个流动的因果接触，但方程中出现了一个单数点。然而，解决方案并不需要通过单个点：对于较慢的较慢降低的环境密度，$ρ\ propto r^{ - k} $带有$ k <\ frac {1} {2} {2}（5- \ sqrt {10}}}} {10}）\ cong0.92 \ cong0.92 $，与二级冲击波浪形成了与interow the Ornon the Ornont the Ornon的二级冲击波。
The hydrodynamics of an ultrarelativistic flow, enclosed by a strong shock wave, are described by the well known Blandford-McKee solutions in spherical geometry. These solutions, however, become inaccurate at a distance $\sim R/2$ behind the shock wave, where $R$ is the shock radius, as the flow approaches Newtonian velocities. In this work we find a new self-similar solution which is an extension to the Blandford-McKee solutions, and which describes the interior part of the blast wave, where the flow reaches mildly relativistic to Newtonian velocities. We find that the velocity profile of the internal part of the flow does not depend on the value of the shock Lorentz factor, $Γ$, and is accurate from $r=0$ down to a distance of $R/Γ^2$ behind the shock. Despite the fact that the shock wave is in causal contact with the entire flow behind it, a singular point appears in the equations. Nevertheless, the solution is not required to pass through the singular point: for ambient density that decreases slowly enough, $ρ\propto r^{-k}$ with $k<\frac{1}{2}(5-\sqrt{10})\cong0.92$, a secondary shock wave forms with an inflow towards the origin.
