The Equipartition Magnetic Field Formula in Starburst Galaxies: Accounting for Pionic Secondaries and Strong Energy Losses

TL;DR

This paper derives a new equipartition formula for starburst galaxies accounting for pionic secondaries and energy losses, revealing similar magnetic field estimates to classical methods despite different assumptions.

Contribution

It introduces an equipartition expression tailored for hadronic environments like starbursts, considering secondary production and energy losses.

Findings

Derived a new equipartition formula for starbursts.

Found that magnetic field estimates are similar to classical results.

Explained the proton/electron ratio of ~100 in GHz-emitting electrons.

Abstract

Equipartition arguments provide an easy way to find a characteristic scale for the magnetic field from radio emission, by assuming the energy densities in cosmic rays and magnetic fields are the same. Yet most of the cosmic ray content in star-forming galaxies is in protons, which are invisible in radio emission. Therefore, the argument needs assumptions about the proton spectrum, typically that of a constant proton/electron ratio. In some environments, particularly starburst galaxies, the reasoning behind these assumptions does not necessarily hold: secondary pionic positrons and electrons may be responsible for most of the radio emission, and strong energy losses can alter the proton/electron ratio. We derive an equipartition expression that should work in a hadronic loss-dominated environment like starburst galaxies. Surprisingly, despite the radically different assumptions from the classical equipartition formula, numerically the results for starburst magnetic fields are similar. We explain this fortuitous coincidence using the energetics of secondary production and energy loss times. We show that these processes cause the proton/electron ratio to be ~100 for GHz-emitting electrons in starbursts.