2020/12/31 by M. E. de la Cruz-Hernandez, Manuel E de la Cruz-Hernández, S. Mendoza
Physics and Astronomy · #Adiabatic process #Astrophysics and Cosmic Phenomena #Classical mechanics #Discontinuity (linguistics) #Gamma-ray bursts and supernovae #Geometry #Lorentz transformation #Mathematical analysis #Mechanics #Physics #Planar #Polytropic process #Pulsars and Gravitational Waves Research #Quantum mechanics #Shock (circulatory) #Shock wave #Surface (topology) #astro-ph.HE
paper · pdf · doi:10.1093/mnras/stab2158
10 pages. Accepted for publication in Monthly Notices of the Royal Astronomical Society (MNRAS)
arxiv created 2021/07/23 · openalex publication_date 2021/07/28 · arxiv updated 2021/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
ABSTRACT We show that the 1D planar ultrarelativistic shock tube problem with an ultrarelativistic polytropic equation of state can be solved analytically for the case of a working surface, i.e. for the case when an initial discontinuity on the hydrodynamical quantities of the problem form two shock waves separating from a contact discontinuity. The procedure is based on the extensive use of the Taub jump conditions for relativistic shock waves, the Taub adiabatic, and performing Lorentz transformations to present the solution in a system of reference adequate for an external observer at rest. The solutions are found using a set of very useful theorems related to the Lorentz factors when transforming between systems of reference. The energy dissipated inside the working surface is relevant for studies of light curves observed in relativistic astrophysical jets and so, we provide a full analytical solution for this phenomenon assuming an ultrarelativistic periodic velocity injected at the base of the jet.