# The jet-disk symbiosis without maximal jets: 1-D hydrodynamical jets revisited

## TL;DR

This paper revisits the jet-disk symbiosis model, correcting previous algebraic mistakes and relaxing the maximal jet assumption, demonstrating that the core conclusions remain valid under more general conditions.

## Contribution

It corrects algebraic errors in the 1-D hydrodynamical jet model and shows the jet-disk symbiosis applies broadly without the maximal jet assumption.

## Key findings

- Corrections cause minor differences for small opening angles and Lorentz factors.
- Jet-disk symbiosis remains valid without the maximal jet assumption.
- Isothermal jets are necessary to reproduce flat radio spectra.

## Abstract

In this work we discuss the recent criticism by Zdziarski of the maximal jet model derived in Falcke & Biermann (1995). We agree with Zdziarski that in general a jet's internal energy is not bounded by its rest-mass energy density. We describe the effects of the mistake on conclusions that have been made using the maximal jet model and show when a maximal jet is an appropriate assumption. The maximal jet model was used to derive a 1-D hydrodynamical model of jets in agnjet, a model that does multiwavelength fitting of quiescent/hard state X-ray binaries and low-luminosity active galactic nuclei. We correct algebraic mistakes made in the derivation of the 1-D Euler equation and relax the maximal jet assumption. We show that the corrections cause minor differences as long as the jet has a small opening angle and a small terminal Lorentz factor. We find that the major conclusion from the maximal jet model, the jet-disk symbiosis, can be generally applied to astrophysical jets. We also show that isothermal jets are required to match the flat radio spectra seen in low-luminosity X-ray binaries and active galactic nuclei, in agreement with other works.