孤立自洽恒星系统的反射对称性
Reflection symmetries of Isolated Self-consistent Stellar Systems
摘要：
孤立的，稳定状态的星系对应的Poisson-Vlasov系统的平衡解。我们表明：（i）所有的星系的分布函数只取决于能量必须是球对称的和（ii）所有的轴对称星系的分布函数取决于能量和角动量分量平行于对称轴也必须是反射对称的平面$z=0$。前一个结果是李希龙定理，这里推导的方法利用椭圆型偏微分方程的解的对称性，而后者的结果是新的。这些结果被归入对称性定理，该定理规定了如何在配置或速度空间的分布函数的对称性可以控制随后的恒星系统的反射对称的平面。
英文摘要：
Isolated, steady-state galaxies correspond to equilibrium solutions of the Poisson--Vlasov system. We show that (i) all galaxies with a distribution function depending on energy alone must be spherically symmetric and (ii) all axisymmetric galaxies with a distribution function depending on energy and the angular momentum component parallel to the symmetry axis must also be reflection-symmetric about the plane $z=0$. The former result is Lichtenstein's Theorem, derived here by a method exploiting symmetries of solutions of elliptic partial differential equations, while the latter result is new. These results are subsumed into the Symmetry Theorem, which specifies how the symmetries of the distribution function in configuration or velocity space can control the planes of reflection symmetries of the ensuing stellar system.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
