The minimum jet power and equipartition

TL;DR

This paper develops a method to accurately estimate the minimum jet power and magnetic field strength in astrophysical jets by incorporating bulk motion and ion rest-mass energy, improving upon previous static-source models.

Contribution

It introduces a new approach for calculating minimum jet power based on observed synchrotron spectra, accounting for bulk motion and ion rest-mass energy, which yields more robust estimates.

Findings

Minimum jet power is independent of jet radius when ion rest-mass energy dominates.

The method allows determination of source size, power, and magnetic field from observed spectra.

Different equipartition parameters are derived when considering ion rest-mass energy versus energy content minimization.

Abstract

We derive the minimum power of jets and their magnetic field strength based on their observed non-thermal synchrotron emission. The correct form of this method takes into account both the internal energy in the jet and the ion rest-mass energy associated with the bulk motion. The latter was neglected in a number of papers, which instead adopted the well-known energy-content minimization method. That method was developed for static sources, for which there is no bulk-motion component of the energy. In the case of electron power-law spectra with index >2 in ion-electron jets, the rest-mass component dominates. The minimization method for the jet power taking it into account was considered in some other work, but only based on either an assumption of a constant total synchrotron flux or a fixed range of the Lorentz factors. Instead, we base our method on an observed optically-thin synchrotron spectrum. We find the minimum jet power is independent of its radius when the ion rest-mass power dominates, which becomes the case below certain critical radius. This allows for robust minimum power estimates. We also present results for the case with observed turnover frequency, at which the source becomes optically thick. This method allows a determination of the source size, in addition to the power and the magnetic field. We also point out that when the ion rest-mass power dominates, the estimates of the minimum power lead to very different equipartition parameters than those based on minimization of the energy content. The former and latter lead to approximate equipartition between the internal energy in magnetic field and in particles including and excluding, respectively, their rest mass energy.