Magnetic fields and cosmic rays in M 31

II. Strength and distribution of the magnetic field components^⋆

Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany

^⋆⋆ Corresponding author: rbeck@mpifr-bonn.mpg.de

Received: 4 April 2025
Accepted: 1 July 2025

Abstract

Context. Interstellar magnetic fields play an important role in the dynamics and evolution of galaxies. The nearby spiral galaxy M 31 is an ideal laboratory for extensive studies of magnetic fields.

Aims. We measure the strength and distribution separately for the various magnetic field components: total, ordered, regular, isotropic turbulent, and, for the first time, anisotropic turbulent.

Methods. Based on radio continuum observations of M 31 at 3.6 cm and 6.2 cm wavelengths with the Effelsberg 100–m telescope, plus combined observations with the VLA and Effelsberg telescopes at 20.5 cm, the intensities of total, linearly polarized, and unpolarized synchrotron emission are measures of the strengths of total, ordered, and isotropic turbulent fields in the sky plane. We used two assumptions about equipartition between the energy densities of total magnetic fields and total cosmic rays, i.e. local equipartition and overall equipartition on the scale of order 10 kpc and more. Faraday rotation measures (RMs) provided a model of the regular field. The quadratic difference between ordered and regular field strengths yields the strength of the anisotropic turbulent field.

Results. The average equipartition strengths of the magnetic field in the emission torus, between 8 kpc and 12 kpc radius in the galaxy plane, are (6.3 ± 0.2) μG for the total, (5.4 ± 0.2) μG for the isotropic turbulent, and (3.2 ± 0.3) μG for the ordered field in the sky plane. The total, isotropic turbulent, and ordered field strength decrease exponentially with radial scale lengths of ≃14–15 kpc. The average strength of the axisymmetric regular field, B_reg, derived from the RMs in the emission torus, is (2.0 ± 0.5) μG and remains almost constant between 7 kpc and 12 kpc radius. Quadratic subtraction of the component B_reg, ⊥ in the sky plane from the ordered field, B_ord, ⊥, yields the strength of the anisotropic turbulent field, B_an, ⊥, which is (2.7 ± 0.7) μG on average in the emission torus. Our test with an extreme non-equipartition case assuming constant CREs along the torus enhances the magnetic field fluctuations.

Conclusions. The average strength of the regular field between 7 kpc and 12 kpc radius is about 40% smaller than the equipartition strength of the ordered field (containing regular and anisotropic turbulent fields). As those two quantities were measured with independent methods, our results are consistent with the assumption of equipartition. Furthermore, our estimate of the diffusion length of cosmic-ray electrons (CREs) emitting at λ3.6 cm of ≲0.34 kpc in the sky plane sets the lower limit for the validity of the equipartition assumption. The average magnetic energy density in the emission torus is about five times larger than the thermal energy density of the diffuse warm ionized gas, while the magnetic energy density is similar to the kinetic energy density of turbulent motions of the neutral gas. Magnetic fields are a primary dynamical agent in the interstellar medium of M 31. The ratio between regular and isotropic turbulent fields is a measure of the relative efficiencies of the large-scale and the small-scale dynamos. The average value of ≃0.39, almost constant with azimuth in the emission torus as well with radius in the range 7–12 kpc, is consistent with present-day dynamo models. The ratio between anisotropic and isotropic turbulent fields is ≃0.57 on average and is almost constant with the azimuth in the emission torus as well as with the radius in the range 7–10 kpc. This indicates that anisotropic turbulent fields are generated by the shearing of isotropic turbulent fields.