[Paper Review] Statistical Analysis of Extra-galactic Rotation Measures

M. Johnston‐Hollitt, Christopher Hollitt+1 more|arXiv (Cornell University)|Oct 27, 2004

Historical Geography and Cartography1 references3 citations

TL;DR

This study presents a statistical analysis of 800 reliable extra-galactic rotation measures (RMs) to map the large-scale Galactic magnetic field. Using interpolated all-sky RM mapping and Fourier analysis, it finds that the Milky Way's magnetic influence extends up to ±30° from the Galactic plane, with excess power at spatial scales of 30°, 46°, and 50°, and rejects strong support for a bisymmetric spiral magnetic field. The high-latitude RM distribution follows an exponential, not Gaussian, distribution, indicating underestimated intrinsic RM populations.

ABSTRACT

We have performed a statistical analysis of a sample of 1100 extra-galactic rotation measures (RMs) obtained from the literature. Using a subsample of approximately 800 reliable RMs we compute a rotation measure sky and determine reliable large scale features for the line of sight Galactic magnetic field. We find that the influence of the Milky Way can be seen up to roughly 30 degrees on either side of the Galactic plane. Furthermore we observe an excess of RM on spatial scales between 30 degrees and 50 degrees in the region of the Galactic Plane. Additionally, the support for a bisymmetric spiral Galactic magnetic field is significantly reduced in our analysis.

Motivation & Objective

• To map the large-scale structure of the Galactic magnetic field using extra-galactic rotation measures (RMs) as tracers of line-of-sight magnetic fields.
• To determine the spatial extent of the Milky Way's magnetic field influence on extragalactic RM measurements.
• To test the hypothesis of a bisymmetric spiral magnetic field in the Milky Way using statistical analysis of RM data.
• To characterize the intrinsic distribution of RMs beyond the Galactic plane, particularly assessing whether it follows a Gaussian or exponential form.
• To improve the reliability of RM sky maps by applying a culling algorithm based on median modulus and three-sigma deviation to remove outliers.

Proposed method

• Compiled a sample of 1100 extra-galactic RMs from multiple literature catalogues, selecting only those with reliable fits over at least three wavelengths.
• Removed RMs associated with lines of sight through galaxy clusters to avoid contamination from cluster magnetic fields.
• Applied a culling algorithm that removed sources with a three-sigma deviation from the local median modulus RM, using the median rather than mean to estimate sigma.
• Generated an all-sky interpolated RM map by solving the 2D Poisson’s equation with a resolution of one pixel per square degree due to low source density (~0.013 sources/deg²).
• Conducted Fourier analysis on RM maps across different Galactic latitude strips to detect excess power at specific spatial scales.
• Performed chi-squared testing on the RM distribution at high Galactic latitudes (|b| ≥ 30°) to assess goodness-of-fit to exponential and Gaussian models.

Experimental results

Research questions

• RQ1 To what extent does the Milky Way’s magnetic field influence extra-galactic rotation measures, and how far does this influence extend in Galactic latitude?
• RQ2 Are there statistically significant large-scale spatial structures in the RM sky, particularly at scales of 30°–50°, that reflect the underlying Galactic magnetic field structure?
• RQ3 Does the observed RM distribution at high Galactic latitudes (|b| ≥ 30°) follow a Gaussian or exponential distribution, and what does this imply about the intrinsic RM population?
• RQ4 Is there statistical support for a bisymmetric spiral magnetic field configuration in the Milky Way based on current RM data?
• RQ5 How do the results compare with previous studies, particularly those using less selective data or different analysis techniques?

Key findings

• The influence of the Milky Way’s magnetic field on extra-galactic RMs is statistically significant up to approximately ±30° from the Galactic plane.
• Excess power in the RM sky is detected at spatial scales of 30°, 46°, and 50°, particularly within ±30° of the Galactic plane, indicating large-scale magnetic field structures.
• The data show only marginal evidence for a bisymmetric spiral magnetic field, significantly reducing support for this model compared to earlier studies.
• At high Galactic latitudes (|b| ≥ 30°), the RM distribution follows an exponential form with a fit of Number of occurrences = 289 × exp(–0.037 × RM), confirmed at >99.9% confidence level.
• The standard deviation of RMs at |b| ≥ 30° is 10 rad m⁻², consistent with local measurements and indicating minimal Galactic contribution at these latitudes.
• The exponential distribution of high-latitude RMs suggests that intrinsically high RMs are more common than previously assumed, challenging the prior expectation of a Gaussian distribution.