On the dynamic efficiency of internal shocks in magnetized relativistic outflows

TL;DR

This paper investigates how internal shocks in magnetized relativistic outflows convert kinetic energy into thermal and magnetic energy, revealing that moderate magnetization enhances efficiency and is largely independent of flow Lorentz factors.

Contribution

It provides a quantitative analysis of the dynamic efficiency of internal shocks in magnetized relativistic flows, highlighting the impact of magnetization and flow velocity on energy conversion.

Findings

Moderately magnetized shocks can achieve up to 40% efficiency.

Efficiency is largely independent of the slower shell's Lorentz factor.

Results are consistent across different plasma equations of state.

Abstract

We study the dynamic efficiency of conversion of kinetic-to-thermal/magnetic energy of internal shocks in relativistic magnetized outflows. We model internal shocks as being caused by collisions of shells of plasma with the same energy flux and a non-zero relative velocity. The contact surface, where the interaction between the shells takes place, can break up either into two oppositely moving shocks (in the frame where the contact surface is at rest), or into a reverse shock and a forward rarefaction. We find that for moderately magnetized shocks (magnetization $\sigma\simeq 0.1$), the dynamic efficiency in a single two-shell interaction can be as large as 40%. Thus, the dynamic efficiency of moderately magnetized shocks is larger than in the corresponding unmagnetized two-shell interaction. If the slower shell propagates with a sufficiently large velocity, the efficiency is only weakly dependent on its Lorentz factor. Consequently, the dynamic efficiency of shell interactions in the magnetized flow of blazars and gamma-ray bursts is effectively the same. These results are quantitatively rather independent on the equation of state of the plasma. The radiative efficiency of the process is expected to be a fraction $f_r<1$ of the estimated dynamic one, the exact value of $f_r$ depending on the particularities of the emission processes which radiate away the thermal or magnetic energy of the shocked states.