iShocks: X-ray binary jets with an internal shocks model

In the following paper we present an internal shocks model, iShocks, for simulating a variety of relativistic jet scenarios; these scenarios can range from a single ejection event to an almost continuous jet, and are highly user configurable. Although the primary focus in the following paper is black hole X-ray binary jets, the model is scale and source independent and could be used for supermassive black holes in active galactic nuclei or other flows such as jets from neutron stars. Discrete packets of plasma (or `shells) are used to simulate the jet volume. A two-shell collision gives rise to an internal shock, which acts as an electron re-energization mechanism. Using a pseudo-random distribution of the shell properties, the results show how for the first time it is possible to reproduce a flat/inverted spectrum (associated with compact radio jets) in a conical jet whilst taking the adiabatic energy losses into account. Previous models have shown that electron re-acceleration is essential in order to obtain a flat spectrum from an adiabatic conical jet: multiple internal shocks prove to be efficient in providing this re-energization. We also show how the high frequency turnover/break in the spectrum is correlated with the jet power, $ u_b propto L_{textrm W}^{sim 0.6}$, and the flat-spectrum synchrotron flux is correlated with the total jet power, $F_{ u}propto L_{textrm W}^{sim 1.4}$. Both the correlations are in agreement with previous analytical predictions.