Relativistic spherical shocks in expanding media

Taya Govreen-Segal*, Noam Youngerman, Ishika Palit, Ehud Nakar, Amir Levinson, Omer Bromberg*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate the propagation of spherically symmetric shocks in relativistic homologously expanding media with density distributions following a power-law profile in their Lorentz factor. That is,, where is the medium proper density, is its Lorentz factor, α > 0 is constant, and t, r are the time and radius from the centre. We find that the shocks behaviour can be characterized by their proper velocity,, where is the shock Lorentz factor as measured in the immediate upstream frame and is the corresponding three velocity. While generally, we do not expect the shock evolution to be self-similar, for every α > 0 we find a critical value for which a self-similar solution with constant U′ exists. We then use numerical simulations to investigate the behaviour of general shocks. We find that shocks with have a monotonously growing U′, while those with have a decreasing U′ and will eventually die out. Finally, we present an analytic approximation, based on our numerical results, for the evolution of general shocks in the regime where U′ is ultrarelativistic.

Original languageEnglish
Pages (from-to)313-318
Number of pages6
JournalMonthly Notices of the Royal Astronomical Society
Volume528
Issue number1
DOIs
StatePublished - 1 Feb 2024

Funding

FundersFunder number
Buchman Foundation1657/18 & 2067/22
JetNS
NSF-BSF2020747
Simons Foundation00001470
European Research Council818899
United States-Israel Binational Science Foundation2018312
Israel Science Foundation1995/21

    Keywords

    • (stars:) gamma-ray burst: general
    • hydrodynamics
    • methods: analytical
    • methods: numerical
    • shock waves
    • stars: jets

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