Self-similarity of the third type in ultra relativistic blastwaves
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913233390010368 |
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| author | Faran, Tamar Gruzinov, Andrei Sari, Re'em |
| author_facet | Faran, Tamar Gruzinov, Andrei Sari, Re'em |
| contents | A new type of self-similarity is found in the problem of a plane-parallel, ultra-relativistic blast wave, propagating in a powerlaw density profile of the form $ρ\propto z^{-k}$. Self-similar solutions of the first kind can be found for $k<7/4$ using dimensional considerations. For steeper density gradients with $k>2$, second type solutions are obtained by eliminating a singularity from the equations. However, for intermediate powerlaw indices $7/4<k<2$ the flow does not obey any of the known types of self-similarity. Instead, the solutions belong to a new class in which the self-similar dynamics are dictated by the non self-similar part of the flow. We obtain an exact solution to the ultra-relativistic fluid equations and find that the non self-similar flow is described by relativistic expansion into vacuum, composed of (1) an accelerating piston that contains most of the energy and (2) a leading edge of fast material that coincides with the interiors of the blastwave and terminates at the shock. The dynamics of the piston itself are self-similar and universal, and do not depend on the external medium. The exact solution of the non self-similar flow is used to solve for the shock in the new class of solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07978 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Self-similarity of the third type in ultra relativistic blastwaves Faran, Tamar Gruzinov, Andrei Sari, Re'em High Energy Astrophysical Phenomena A new type of self-similarity is found in the problem of a plane-parallel, ultra-relativistic blast wave, propagating in a powerlaw density profile of the form $ρ\propto z^{-k}$. Self-similar solutions of the first kind can be found for $k<7/4$ using dimensional considerations. For steeper density gradients with $k>2$, second type solutions are obtained by eliminating a singularity from the equations. However, for intermediate powerlaw indices $7/4<k<2$ the flow does not obey any of the known types of self-similarity. Instead, the solutions belong to a new class in which the self-similar dynamics are dictated by the non self-similar part of the flow. We obtain an exact solution to the ultra-relativistic fluid equations and find that the non self-similar flow is described by relativistic expansion into vacuum, composed of (1) an accelerating piston that contains most of the energy and (2) a leading edge of fast material that coincides with the interiors of the blastwave and terminates at the shock. The dynamics of the piston itself are self-similar and universal, and do not depend on the external medium. The exact solution of the non self-similar flow is used to solve for the shock in the new class of solutions. |
| title | Self-similarity of the third type in ultra relativistic blastwaves |
| topic | High Energy Astrophysical Phenomena |
| url | https://arxiv.org/abs/2402.07978 |