Probing the magneto-ionic medium of the Milky Way using pulsars

TL;DR

This study uses RM and DM measurements from a large sample of pulsars to map the Milky Way's magneto-ionic medium. It develops a joint analytic framework that decomposes both magnetic fields into large-scale and small-scale components and electron density into mean and fluctuating parts, introducing correlation lengths ${\ell_{b}}$ and ${\ell_{\delta n_e}}$ to quantify small-scale structure. The authors find a roughly constant large-scale magnetic field strength $|B| \approx 1.2~\mu$G and mean electron density $\langle n_e\rangle \approx 0.05\,\rm cm^{-3}$ within $\sim$20 kpc, while small-scale magnetic fluctuations occur on ${\ell_{b}} \approx 20$–$30$ pc and small-scale electron-density fluctuations on ${\ell_{\delta n_e}} \approx 250$–$300$ pc; RM shows $|RM| \propto DM$ and the inferred $\langle B_{\\parallel}\\rangle$ remains roughly distance-independent. The work demonstrates that magnetic and density fluctuations occupy distinct scales, providing a framework to interpret extragalactic RMs and offering constraints on the Galactic magnetic field and ISM turbulence. Overall, the results robustly constrain the small- and large-scale structure of the Milky Way's magneto-ionic medium and highlight the potential of pulsar RM/DM analyses for future surveys.

Abstract

Magnetic fields are fundamental to the dynamics of the interstellar medium (ISM) in spiral galaxies and are often separated into large-scale, regular ($\boldsymbol{B}$) and small-scale, random ($\boldsymbol{b}$) components. The thermal electron density, $n_{\rm e}$, can also be divided into large-scale, diffuse, $\langle n_{\rm e} \rangle$, and small-scale, clumpy, $δn_{\rm e}$, components. Estimating the properties of $b$ and $δn_{\rm e}$ from observations, even within the Milky Way, has long been challenging. This work addresses the challenge using pulsars, which probe the Milky Way's magneto-ionic medium. Using data of more than 1200 pulsars from the Australia Telescope National Facility pulsar catalogue, we combine dispersion (${\rm DM}$) and rotation (${\rm RM}$) measures with theoretical models to estimate both small- and large-scale properties of the Galactic magnetic field and thermal electron density. We find no significant correlation between the average parallel magnetic field strength, $\langle B_{\parallel} \rangle [μ{\rm G}] = 1.232\,{\rm RM}\,[{\rm rad\,m^{-2}}]/{\rm DM}\,[{\rm pc\,cm^{-3}}]$, and pulsar distance. For pulsars within $20\,{\rm kpc}$, we estimate $|B| \approx 1.2\,μ{\rm G}$ and $\langle n_{\rm e} \rangle \approx 0.05\,{\rm cm}^{-3}$. More importantly, we determine correlation lengths of small-scale components, $\ell_{b} \approx 20$ -- $30\,{\rm pc}$ and $\ell_{δn_{\rm e}} \approx 250$ -- $300\,{\rm pc}$. At smaller distances, $B$ remains roughly constant, while $\langle n_{\rm e} \rangle$ increases and both length scales decrease. These results refine our understanding of fundamental scales in the magneto-ionic medium, aiding the interpretation of extragalactic ${\rm RM}$s and providing insights into the role of magnetic fields in galaxies.

Figures (6)

• Figure 1: Comparison of three different correlation functions, ${\mathcal{C}_{1}}$, ${\mathcal{C}_{2}}$, and ${\mathcal{C}_{3}}$ (forms in the legend), as functions of the separation distance, $s$, in ${\mathrm{pc}}$ with a characteristic scale length, $\ell = 10\,{\mathrm{pc}}$ and the dimensionless constant, ${\mathcal{C}_{0}}=1$. All the correlation functions start from $1$ at $s=0$ and approach $0$ (dashed, black line) as $s \to \infty$. ${\mathcal{C}_{2}}$ goes to zero at a smaller separation than ${\mathcal{C}_{1}}$ and ${\mathcal{C}_{3}}$ allows the correlation to be negative before approaching zero. This illustrates the distinct behaviours of each correlation function at different separation distances, emphasising their functional forms, relative amplitudes, and decay rates (see Sec. \ref{['mainmethod3']} for further discussion on differences).
• Figure 2: Pulsar data, ${\mathrm{RM}}$ (a, c) and ${\mathrm{DM}}$ (b, d), for both data sets, $\mathrm{\mathrm{L}}_{{\mathrm{DM}}} \le 20\,{\mathrm{kpc}}$ (a, b) and $\mathrm{\mathrm{L}_{Ind}}$ (c, d) with spiral arm model used in the NE2001 thermal electron density model NE2001. As expected, most detected pulsars are concentrated around the Sun and thus the surrounding area is more sampled by the data. Our statistical analysis is, by extension, probing those regions more compared to the other parts of the Milky Way.
• Figure 3: Distribution of data for ${\mathrm{RM}}$, ${\mathrm{DM}}$, and $\mathrm{\mathrm{L}}_{{\mathrm{DM}}}$. Figures (a), (b) and (c) illustrate the histograms of ${\mathrm{RM}}$, ${\mathrm{DM}}$, and $\mathrm{\mathrm{L}}_{{\mathrm{DM}}}$, respectively. All distributions observe moderate skewness except (b), which is more symmetric. In all figures, we also observe a ${\mathcal{K}} > 0$, suggesting that the data exhibits features of a non-normal distribution.
• Figure 4: Same as Fig. \ref{['data distdm']} but for $\mathrm{\mathrm{L}_{Ind}}$. Here too, except ${\mathrm{RM}}$, both distributions show skewness ($\mathcal{S}$). Based on the computed kurtosis (${\mathcal{K}}$), all distributions show non-normal traits (note the negative ${\mathcal{K}}$ for $\mathrm{\mathrm{L}_{Ind}}$, which is probably due to a smaller number of samples in the histogram).
• Figure 5: (a): A log-log plot of $|{\mathrm{RM}}|$ versus ${\mathrm{DM}}$ for the $\mathrm{\mathrm{L}}_{{\mathrm{DM}}}$ dataset, with a linear fit in the log-log space shown as the red dashed line and the one-sigma deviations are shown as a pink band around it. The best-fit line is given by $|{{\mathrm{RM}}}| = (1.12 \pm 0.68)\,{\mathrm{DM}}^{(0.86 \pm 0.14)}$. (b) A plot of the absolute value of the average parallel magnetic field $|\langle B_{\parallel} \rangle|$ versus distance, calculated using equation \ref{['bp average']}. The best-fit line is shown as the red dashed line with one-sigma deviations as a pink band around it. The best-fit line is given by $|{\langle B_{\parallel} \rangle}|=(-0.02 \pm 0.01)\,\mathrm{\mathrm{L}}_{{\mathrm{DM}}} + (1.23 \pm 0.02)$. From these results, we conclude that $|{\mathrm{RM}}| \propto {\mathrm{DM}}$ and $|{\langle B_{\parallel} \rangle}| \propto \mathrm{\mathrm{L}}_{{\mathrm{DM}}}^0$. From (b), on an average, $|{\langle B_{\parallel} \rangle}|| \approx 1.2\,{\mu\mathrm{G}}$ (intercept of the fitted line).