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Larson-Penston Self-similar Gravitational Collapse.
Yan Guo1, Mahir Hadžić2, Juhi Jang3,4
1Division of Applied Mathematics, Brown University, Providence, RI 02912 USA.
Communications in Mathematical Physics
|November 1, 2021
Summary
Researchers rigorously proved the existence of the Larson-Penston solution, a self-similar model for collapsing self-gravitating fluids under Newtonian gravity with an isothermal equation of state.
Area of Science:
- Astrophysics
- Fluid dynamics
- Mathematical physics
Background:
- The Larson-Penston solution, discovered in 1969, describes the gravitational collapse of fluids.
- This solution is based on an isothermal equation of state and Newtonian gravity.
- Previous work relied on numerical integration to find this self-similar solution.
Purpose of the Study:
- To rigorously prove the existence of the Larson-Penston self-similar solution.
- To provide a formal mathematical foundation for the previously discovered collapse model.
Main Methods:
- The study employs rigorous mathematical analysis.
- Numerical integration methods were used in prior work, but this study focuses on analytical proof.
Main Results:
- The existence of the Larson-Penston solution is rigorously proven.
- This confirms the validity of the self-similar model for collapsing self-gravitating fluids.
Conclusions:
- The mathematical existence of the Larson-Penston solution is established.
- This rigorous proof supports further theoretical and observational studies of gravitational collapse.
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