The fine structure of the mean magnetic field in M31

TL;DR

This work advances the understanding of M31's large-scale magnetic field by performing a Bayesian Fourier-mode analysis of multi-wavelength polarization data across four rings in the disk. The axisymmetric component ($m=0$) dominates and exhibits a near-constant trailing spiral with a pitch of about $p_0 oughly -15^ ext{o}$ to $-16^ ext{o}$, while higher-order modes ($m=1$–$3$, and $4$ in the outermost ring) contribute subtler, irregular variations consistent with local perturbations rather than global dynamo action. The analysis introduces depolarization parameters $oldsymbol{\xi_{11}}$ and $oldsymbol{\xi_{20}}$ to isolate the magnetic-field signal from Faraday effects, and validates the method with simulations, demonstrating reliable mode-counting via Bayesian complexity. The results align with mean-field dynamo predictions while highlighting the role of local structures (e.g., spiral arms, a hole near M32) in shaping non-axisymmetric components, and they provide a practical framework for analyzing depolarization-affected polarized emission in other galaxies. Overall, the paper strengthens the link between observed regular-field structure and dynamo theory in spiral galaxies and offers a robust methodological path for future magneto-ionic analyses.

Abstract

To explore the spatial variations of the regular (mean) magnetic field of the Andromeda galaxy (M31), we use Fourier analysis in azimuthal angle along four rings in the galaxy's plane. The Fourier coefficients give a quantitative measure of strength of the modes, enabling us to compare expectations from mean-field dynamo models of spiral galaxies. Earlier analyses indicated that the axisymmetric magnetic field (azimuthal Fourier mode $m=0$) is sufficient to fit the observed polarization angles in a wide range of galactocentric distances ($r$). We apply a Bayesian inference approach to new, more sensitive radio continuum data at $λ\lambda3.59$, $6.18$, and $11.33$ cm and the earlier data at $λ20.46$ cm to reveal sub-dominant contributions from the modes $m=1$, 2, and 3 along with a dominant axisymmetric mode. Magnetic lines of the axisymmetric mode are close to trailing logarithmic spirals which are significantly more open than the spiral arms detectable in the interstellar dust and neutral hydrogen. The form of the $m=0$ mode is consistent with galactic dynamo theory. Both the amplitudes and the pitch angles of the higher azimuthal modes ($m>1$) vary irregularly with $r$ reflecting local variations in the magnetic field structure. The maximum strength of the mean magnetic field of $1.8-2.7 μ$G (for the axisymmetric part of the field) occurs at $10-14$ kpc but we find that its strength varies strongly along the azimuth; this variation gives rise to the $m=1$ mode. We suggest a procedure of Bayesian inference which is independent of the specific nature of the depolarization and applies when the magneto-ionic layer observable in polarized emission is not symmetric along the line of sight because emission from its far side is completely depolarized.

Figures (17)

• Figure 1: Polarized intensity maps at various wavelengths in the sky plane. An overlay of azimuthal sectors of 20∘$^\circ$ width, as used in this paper, in the galactic plane is shown. The ellipses are the projections of circles in the galaxy plane, with radii of 6, 8, 10, 12, and 14 kpc. Polarized background sources have been subtracted. Straight line segments for the polarization orientation, with the length proportional to the degree of polarization, are shown only where total intensity is greater than three times the rms noise ($I \geq 3 \sigma_{I}$). They are shown in red where the polarized intensity is greater than three times the rms noise in the Stokes parameters $Q$ and $U$ ($\text{PI} \geq 3 \sigma_{Q,U}$) and in black if the polarized intensity is greater than ten times rms noise in the Stokes parameters $Q$ and $U$. A segment of the length corresponding to 20 per cent polarization and the beam corresponding to the resolution used in this paper are shown at the bottom left, while the linear scale is at the bottom right.
• Figure 2: The simulated polarization angles for Case II of \ref{['sec:sim']} (circles with error bars for the $1\sigma$ uncertainty) as a function of the azimuthal angle $\theta$ at four wavelengths, $\lambda \lambda 3.59$, $6.18$, $11.33$, and $20.46\,\text{cm}$ from top to bottom. The black solid line represents the best-fitting model derived using the Bayesian inference.
• Figure 3: The variation of the maximum likelihood $\mathcal{L}_\text{G}$ (left-hand axis, continuous lines; higher likelihood corresponds to a larger value of the quantity shown) and the complexity parameter $\mathcal{C}$ (right-hand axis, open symbols) with the number of magnetic modes $n_m$ in the validation procedure of \ref{['sec:sim']}: Case I (red curve and circles) and Case II (blue curve and squares). The dashed grey line corresponds to $\mathcal{C} =3n_m+2$, the number of the model parameters.
• Figure 4: The variation of depolarization as a function of the azimuthal angle: $\text{DP}_{20/3}$ at 3 HPBW (top panel), $\text{DP}_{20/6}$ at 3 HPBW (middle panel), and $\text{DP}_{11/6}$ at 5 HPBW (bottom panel). The median depolarization across the azimuthal angles per radial range is shown with the grey dashed line. Left to right: the radial ranges 6--8, 8--10, 10--12 and 12--14 kpc.
• Figure 5: The model likelihood (curves with symbols) and complexity parameter (symbols) as functions of the number of Fourier modes for $r=$6--8 kpc (red circles), 8--10 kpc (blue squares), 10--12 kpc (orange diamonds) and 12--$14\,\text{kpc}$ (black hexagons). The complexity parameter increases almost linearly, as $\mathcal{C}=3n_m+2$ up to $n_m=5$. Together with the variation of the likelihood, this suggests $n_m=3$ for $r=6\text{--}12\,\text{kpc}$ and $n_m=4$ for $r=12\text{--}14\,\text{kpc}$.