Dynamical Properties of Internal Shocks Revisited

Asaf Pe'Er, Killian Long, Piergiorgio Casella

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

Internal shocks between propagating plasma shells, originally ejected at different times with different velocities, are believed to play a major role in dissipating the kinetic energy, thereby explaining the observed light curves and spectra in a large range of transient objects. Even if initially the colliding plasmas are cold, following the first collision, the plasma shells are substantially heated, implying that in a scenario of multiple collisions, most collisions take place between plasmas of non-zero temperatures. Here, we calculate the dynamical properties of plasmas resulting from a collision between arbitrarily hot plasma shells, moving at arbitrary speeds. We provide simple analytical expressions valid for both ultrarelativistic and Newtonian velocities for both hot and cold plasmas. We derive the minimum criteria required for the formation of the two-shock wave system, and show that in the relativistic limit, the minimum Lorentz factor is proportional to the square root of the ratio of the initial plasmas enthalpies. We provide basic scaling laws of synchrotron emission from both the forward and reverse-shock waves, and show how these can be used to deduce the properties of the colliding shells. Finally, we discuss the implications of these results in the study of several astronomical transients, such as X-ray binaries, radio-loud quasars, and gamma-ray bursts.

Original languageEnglish
Article number54
JournalAstrophysical Journal
Volume846
Issue number1
DOIs
StatePublished - 1 Sep 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017. The American Astronomical Society. All rights reserved.

Funding

We furthermore provided analytical expressions for the energy density and for the energy per particle in the shocked region. We found that for nonrelativistic collision, one needs to discriminate between three scenarios: “hot” plasma, for which A.P. wishes to thank Damien Bégué Felix Ryde, Ralph Wijers, and Bing Zhang for useful comments. This research was partially supported by the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreements n 618499 (AP) and n 322259 (PC).

FundersFunder number
Seventh Framework Programme618499, 322259
Seventh Framework Programme

    Keywords

    • X-rays: binaries
    • gamma-ray burst: general
    • hydrodynamics
    • plasmas
    • shock waves
    • stars: jets

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