Batchelor, Saffman, and Kazantsev spectra in galactic small-scale dynamos

TL;DR

This paper investigates the presence and characteristics of Batchelor, Saffman, and Kazantsev spectra in small-scale galactic dynamos, revealing their coexistence during different dynamo stages and implications for magnetic field structures and polarization signals.

Contribution

It demonstrates that all three spectra are present in the small-scale dynamo and details their scale-dependent occurrence during the kinematic and saturated stages, including polarization properties.

Findings

All three spectra are observed during the dynamo process.

The saturated state shows a Saffman spectrum on large scales.

Polarization maps reveal non-Gaussian features and scale-dependent polarization excess.

Abstract

The magnetic fields in galaxy clusters and probably also in the interstellar medium are believed to be generated by a small-scale dynamo. Theoretically, during its kinematic stage, it is characterized by a Kazantsev spectrum, which peaks at the resistive scale. It is only slightly shallower than the Saffman spectrum that is expected for random and causally connected magnetic fields. Causally disconnected fields have the even steeper Batchelor spectrum. Here we show that all three spectra are present in the small-scale dynamo. During the kinematic stage, the Batchelor spectrum occurs on scales larger than the energy-carrying scale of the turbulence, and the Kazantsev spectrum on smaller scales within the inertial range of the turbulence -- even for a magnetic Prandtl number of unity. In the saturated state, the dynamo develops a Saffman spectrum on large scales, suggestive of the build-up of long-range correlations. At large magnetic Prandtl numbers, elongated structures are seen in synthetic synchrotron emission maps showing the parity-even E polarization. We also observe a significant excess in the E polarization over the parity-odd B polarization at subresistive scales, and a deficiency at larger scales. This finding is at odds with the observed excess in the Galactic microwave foreground emission, which is believed to be associated with larger scales. The E and B polarizations may be highly non-Gaussian and skewed in the kinematic regime of the dynamo. For dust emission, however, the polarized emission is always nearly Gaussian, and the excess in the E polarization is much weaker.