Revised equipartition and minimum energy formula for magnetic field strength estimates from radio synchrotron observations

Abstract

Abstract. The commonly used classical equipartition or minimum-energy estimate of total magnetic fields strengths from radio synchrotron intensities is of limited practical use because it is based on the hardly known ratio K of the total energies of cosmic ray protons and electrons and also has inherent problems. We present a revised formula, using the number density ratio K for which we give estimates. For particle acceleration in strong shocks K is about 40 and increases with decreasing shock strength. Our revised estimate for the field strength gives larger values than the classical estimate for flat radio spectra with spectral indices of about 0.5-0.6, but smaller values for steep spectra and total fields stronger than about 10 µG. In very young supernova remnants, for example, the classical estimate may be too large by up to 10×. On the other hand, if energy losses of cosmic ray electrons are important, K increases with particle energy and the equipartition field may be underestimated significantly. Our revised larger equipartition estimates in galaxy clusters and radio lobes are consistent with independent estimates from Faraday rotation measures, while estimates from the ratio between radio synchrotron and X-ray inverse Compton intensities generally give much weaker fields. This may be explained e.g. by a concentration of the field in filaments. Our revised field strengths may also lead to major revisions of electron lifetimes in jets and radio lobes estimated from the synchrotron break frequency in the radio spectrum.

Detection of non-thermal emission from the massive protostellar jet HH80-81 at low radio frequencies using GMRT

“…In the above equation, the frequencies, νo, ν1 and ν2 are expressed in GHz. For estimation of the magnetic field, we assume K ∼ 40 for Fermi accelerated electrons typical of astrophysical environments (Beck & Krause 2005), η ∼ 0.5 to account for clumpiness within the condensations that is evident from the detailed structure of HH80 and HH81 objects (Heathcote, Reipurth & Raga 1998), and φ ∼ 34 • (Masqué et al 2012). We consider the GMRT flux densities at frequency of νo = 0.610 GHz (2016) while the cutoff frequencies are taken as ν1 = 0.01 GHz and ν2 = 100 GHz.…”

“…(1) would be revised from 2/7 to 1/(3 + α) (Beck & Krause 2005). Writing the energy of electron in terms of its Lorentz factor and considering γmin ∼ 100, the change in the magnetic field estimate is within 10%.…”

JVLA S- and X-band polarimetry of the merging cluster Abell 2256

“…We calculated the magnetic field strengths of the radio relic in Abell 2256 using the revised equipartition formula from Beck & Krause (2005). The total equipartition magnetic field strengths Bt is given by…”

“…where e is the elementary charge, me is the electron mass, c is the speed of light, γ is the spectral index of the electron energy spectrum which relates to the synchrotron spectral index α = −(γ − 1)/2, and i is the inclination of the magnetic fields with respect to the sky plane (Beck & Krause 2005).…”

Anisotropy of the extragalactic radio background from dark matter annihilation

“…In some models, cluster shocks are even capable of providing enough energy to explain the entirety of the ARCADE-2 signal through the reacceleration of thermal electrons. Additionally, cluster shocks provide the larger magnetic fields necessary in order to efficiently convert electron energy into synchrotron radiation [57][58][59]. However, these models depend sensitively on the properties of cluster shocks in both major and minor mergers.…”