General relativistic study of astrophysical jets with internal shocks

Mukesh K. Vyas, Indranil Chattopadhyay

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16 Scopus citations


We explore the possibility of the formation of steady internal shocks in jets around black holes. We consider a fluid described by a relativistic equation of state, flowing about the axis of symmetry (θ = 0) in a Schwarzschild metric. We use two models for the jet geometry: (i) a conical geometry and (ii) a geometry with non-conical cross-section. A jet with conical geometry has a smooth flow, while the jet with non-conical cross-section undergoes multiple sonic points and even standing shock. The jet shock becomes stronger, as the shock location is situated farther from the central black hole. Jets with very high energy and very low energy do not harbour shocks, but jets with intermediate energies do harbour shocks. One advantage of these shocks, as opposed to shocks mediated by external medium, is that these shocks have no effect on the jet terminal speed, but may act as possible sites for particle acceleration. Typically, a jet with specific energy 1.8c2 will achieve a terminal speed of v∞ = 0.813c for jet with any geometry, where, c is the speed of light in vacuum. But for a jet of non-conical cross-section for which the length scale of the inner torus of the accretion disc is 40rg, then, in addition, a steady shock will form at rsh ~ 7.5rg and compression ratio of R ~ 2.7. Moreover, electron-proton jet seems to harbour the strongest shock. We will discuss possible consequences of such a scenario.

Original languageEnglish
Pages (from-to)3270-3285
Number of pages16
JournalMonthly Notices of the Royal Astronomical Society
Issue number3
StatePublished - 11 Aug 2017
Externally publishedYes

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© 2017 The Authors.


  • Black holes physics
  • Hydrodynamics
  • ISM: jets and outflows
  • Shock waves


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