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In the previous chapter, the Euler equation was minimized around a background state. In this chapter, this background state is further examined. In particular, we assume a relationship between pressure and mass density that is refered to as a polytrope of index unity. Then, a Helmholtz equation for the background density is derived and an explicit solution is given for the case of spherical symmetry.

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The Static Model

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  • 发表日期：

    2026年

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  • Tim-Jonas Peter

摘要

In the previous chapter, the Euler equation was minimized around a background state. In this chapter, this background state is further examined. In particular, we assume a relationship between pressure and mass density that is refered to as a polytrope of index unity. Then, a Helmholtz equation for the background density is derived and an explicit solution is given for the case of spherical symmetry.