The equipartition magnetic field formula in starburst galaxies: accounting for pionic secondaries and strong energy losses

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.

Equipartition and cosmic ray energy densities in central molecular zones of starbursts

“…This close correlation between the magnetic and radiation fields is critical for the far-infrared-radio relationship to hold and indicates that the magnetic field strength is tied directly to SFRs, e.g., as discussed in Lacki (2013). This trend is consistent with models where UB is set by turbulence in the ISM which in turn depends on the intensity of star formation and structure of the system (e.g., Balsara et al 2004; Thompson et al 2006;Lacki & Beck 2013). …”

“…Thus, the underlying assumptions of both methods imply that UB ∼ UCR and that leptonic (e ± ) cosmic rays ⋆ E-mail: yoasthull@wisc.edu (CRs) mainly lose energy via synchrotron radiation (e.g., Schober et al 2015). Recent revisions to the original formula take into account additional energy losses from inverse Compton cooling and bremsstrahlung and the production of secondary e ± CRs, both of which are significant in dense environments with intense radiation fields (e.g., Torres 2004;Beck & Krause 2005;de Cea del Pozo et al 2009;Lacki & Beck 2013;Persic & Rephaeli 2014). These additional losses, in combination with galactic winds, reduce the energy density in leptonic CRs such that an increase in UB is needed to produce sufficient synchrotron radiation.…”

Probing the magnetic field of the nearby galaxy pair Arp 269

“…bfeld uses following parameters: total pathlength through the source D, proton-to-electron energy density ratio K0, non-thermal spectral index α, and the mean synchrotron surface brightness of the chosen region. For K0 we used the typical value of 100, which is right even for the starburst galaxies (Lacki & Beck 2013). It should be noted here, that D is not very well known; this prevented us from creating a map of the magnetic field.…”

M 82 – A radio continuum and polarisation study

“…While this may be uncertain by an order of magnitude for the above-mentioned reasons, it is of the same order as the value derived by Klein et al (1988) (B eq ≈ 50 µG). Lacki & Beck (2013) suggested a revised equipartition formula for starburst galaxies, which includes pion decay processes and the generation of secondary electrons. They calculated a magnetic field strength of B eq = 250 µG, but this value was derived by using the integrated flux over the whole galaxy, not distinguishing between the core and halo emission, and using a constant scalelength of l = 500 pc.…”