The radial component of the local Galactic magnetic field in 3D

Abstract

We present a distance-resolved reconstruction of the local line-of-sight Galactic magnetic field, $B_{||}$, by combining a 3D electron density ($n_{e}$) map derived from dust map-informed simulations and a full-sky map of Faraday rotation measure (RM). The forward model evaluates RM on the same 3D grid as the $n_{e}$ map and compares to the Galactic Faraday rotation sky. We infer $B_{||}$ with a Gaussian-process prior whose power spectrum is inferred from the data using geometric variational inference. The result is a local (within 1.25 kpc where $|b|>5^{\circ}$) map of $B_{||}$ with uncertainties. The reconstructed RM sky reproduces prominent features of Faraday rotation sky, with a root mean square average strength of $B_{||}$ of $1.63\pm 0.16$ $μ$G. In face-on views, the magnetic field exhibits coherent patches with alternating sign and hints of kpc-scale modulations, but with significant structure seen on scales of order 100 pc. The $B_{||}$ field is seen to exhibit a 3D power spectrum with an average slope of $-2.73 \pm 0.19$. We validate our $B_{||}$ reconstruction with Galactic pulsars. Predicted RMs (computed by integrating $n_{e}B_{||}$ to each pulsar's distance) correlates with observed RMs, and predicted dispersion measures (DMs) from the $n_{e}$ map also correlate with measured DMs, albeit with significant scatter.

Figures (14)

• Figure 1: Selected slices through our reconstructed fields. These slices are one grid cell thick (approximately 10 pc). The left column shows the inferred structure of $B_{||}$, the second column shows slices of the relative standard deviation of $B_{||}$ as determined from our 120 samples, third column shows the electron density structure used for our reconstruction, and the rightmost column shows the 3D structure of RM contributions. All slices are in the $x-y$ plane, at Z-heights of $500$ pc, $250$ pc, $-250$ pc and $-500$ pc. Note that the $B_{||}$ field is only showing the strength of $B_{||}$ relative to the position of the sun, and that large values of $B_{||}$ at high altitude have a significant component point in the $z$-axis as well as in the $x-y$ plane.
• Figure 2: Maps derived from our reconstructed magnetic field structure in Galactic coordinates centred at $(l,b) = (0^{\circ},0^{\circ})$. Panel (a): the data-constrained extragalactic RM sky from hutschenreuter22. Panel (b): our reconstruction of the RM sky from our inferred 3D structure of $B_{||}$ and underlying 3D map of $n_{e}$. This map is derived from the mean $B_{||}$ field from the posterior samples. Panel (c): the total uncertainty in the recovered map of RM, defined as the pixel-by-pixel standard deviation from each of the posterior samples of our reconstruction. This takes into account the underlying uncertainties in the hutschenreuter22 map, uncertainties in the form of samples from the edenhofer23 dust map, and sample variance originating from the differing draws from the posterior. Panel (d): the normalized residual sky as a difference in RM in our posterior mean sky map and the sky of hutschenreuter22, normalized to the uncertainty in the reconstructed sky.
• Figure 3: The mean reconstructed 3D field of $n_{e} B_{||}$ integrated along the full $z$-axis of the reconstructed volume (excluding the $|b|<5^{\circ}$ masked mid-plane). This corresponds to a z-integrated contribution to the RM sky, shown in a face-on (top-down) view of the local volume. The Sun is at the centre of this image, and the Galactic centre is defined as being to the right. Positive $B_{||}$ is defined as pointing towards the Sun. Any voxels of the 3D grid which are behind our $|b| < 5^{\circ}$ midplane mask are not included in this integration. This can be considered a top down view of the Sun-centred hutschenreuter22 RM map, minus the midplane behind the $5^{\circ}$ mask. Some individual objects are labelled as in mccallum25, with the size and location of the Per-Tau shell from bialy21. Note that this is not equivalent to the RM which would be observed through the Galactic disc from above, as the direction of the parallel component of the B-field is here still defined using a heliocentric observer. An animated version of this figure is available online as supplementary material, showing the posterior mean from each electron density sample.
• Figure 4: The mean power spectrum of $B_{||}$ from our posterior samples, with the filled region representing $1\sigma$. The mean average slope of the power spectrum is $-2.73 \pm 0.19$. Also shown in black dashed lines are 10 samples from our prior.
• Figure 5: Validation results using local pulsars from the ATNF Pulsar Catalogue manchester05. Left panel shows the observed RM of each pulsar versus the RM predicted from the 3D GMF $B_{||}$ reconstruction. The right panel shows the observed DM (scales only with $n_{e}$) with the prediction from the underlying electron density map used as a fixed prior in our reconstruction. 1:1 match lines are shown on each panel. Observational uncertainties in RM and DM are negligible on the scales of these plots, so these error bars are not included.