An observational test for correlations between cosmic rays and magnetic fields

TL;DR

This study investigates the relationship between cosmic rays and magnetic fields in the Milky Way and M33, finding that cosmic ray distribution is nearly uniform at small scales and that energy equipartition may only hold at larger, kiloparsec scales.

Contribution

It provides observational and theoretical analysis showing cosmic rays are nearly uniform at small scales, challenging local energy equipartition assumptions and suggesting scale-dependent magnetic field estimates.

Findings

Cosmic ray fluctuations are small at scales >100 pc.

Magnetic field fluctuations are large at these scales.

Energy equipartition likely applies only at >1 kpc scales.

Abstract

We derive the magnitude of fluctuations in total synchrotron intensity in the Milky Way and M33, from both observations and theory under various assumption about the relation between cosmic rays and interstellar magnetic fields. Given the relative magnitude of the fluctuations in the Galactic magnetic field (the ratio of the rms fluctuations to the mean magnetic field strength) suggested by Faraday rotation and synchrotron polarization, the observations are inconsistent with local energy equipartition between cosmic rays and magnetic fields. Our analysis of relative synchrotron intensity fluctuations indicates that the distribution of cosmic rays is nearly uniform at the scales of the order of and exceeding $100\p$, in contrast to strong fluctuations in the interstellar magnetic field at those scales. A conservative upper limit on the ratio of the the fluctuation magnitude in the cosmic ray number density to its mean value is 0.2--0.4 at scales of order 100\,pc. Our results are consistent with a mild anticorrelation between cosmic-ray and magnetic energy densities at these scales, in both the Milky Way and M33. Energy equipartition between cosmic rays and magnetic fields may still hold, but at scales exceeding 1\,kpc. Therefore, we suggest that equipartition estimates be applied to the observed synchrotron intensity smoothed to a linear scale of kiloparsec order (in spiral galaxies) to obtain the cosmic ray distribution and a large-scale magnetic field. Then the resulting cosmic ray distribution can be used to derive the fluctuating magnetic field strength from the data at the original resolution. The resulting random magnetic field is likely to be significantly stronger than existing estimates.