arXiv subjects

Marijke Haverkorn

Publications and source records attributed to Marijke Haverkorn.

At least 19 recordsLinked to original sources

arXiv2026

Faraday depth similarities across scales with LoTSS & DRAGONS

Faraday rotation of diffuse Galactic synchrotron emission is a powerful tracer of the complex, magnetised interstellar medium (ISM), whose structures span a wide range of spatial scales, requiring both interferometric and single-antenna broadband radio polarisation observations for full characterisation. We compare Faraday rotation in the interferometric LOw-Frequency ARray Two-Metre Sky Survey (LoTSS; 120-168 MHz) and the single-antenna Dominion Radio Astrophysical Observatory Global Magneto-Ionic Medium Survey of the Northern Sky (DRAGONS; 350-1030 MHz), which are complementary in their sensitivity to spatial and Faraday-depth scales. We calculate first moments (M1) of polarised intensity versus Faraday depth, producing polarised-intensity-weighted mean Faraday depth maps of the regions common to both surveys. These maps show remarkable agreement between the surveys despite the lack of overlap in frequency or spatial-scale coverage. In the northern Galactic region, the M1 maps are morphologically similar with only small spatial shifts in the boundaries between positive and negative M1, and strong pixel-by-pixel correlation. In the southern Galactic region, both surveys trace the Faraday-depth gradient with Galactic longitude previously identified in LoTSS. Faraday depth spectra show consistent numbers and locations of peaks for more than half of the pixels. The strong structural similarity between the surveys, demonstrated by computing structure functions, suggests coupling across spatial scales in the magnetised ISM, enabling both interferometric and single-antenna observations to trace the same features. Instances of differences point to ISM configurations where observational effects such as depolarisation dominate or where this coupling breaks down due to local physical conditions.

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arXiv2026

3D Magnetic Field Vectors in Space: Bubbles, Clouds, and Filaments

Magnetic fields play important roles in the star-formation process across different spatial scales. The interplay between magnetic field strength (a key component of the interstellar medium's energy budget) and field orientation relative to density structures impacts how interstellar material evolves toward star formation. To understand galactic evolution toward stars, planets, and ultimately life, we need to map three-dimensional (3D) magnetic field vectors in 3D space. However, determining full vector information remains challenging due to projection effects and the complex relationship between observable tracers and field geometry. We outline the observational techniques that can be used to probe the 3D magnetic field structures of objects such as supernova remnants (SNR), superbubbles, HII regions, and HI filaments in the diffuse interstellar medium (ISM), and objects in the dense ISM such as molecular clouds, filaments, and cores. The main SKA-specific observational techniques include synchrotron emission and Faraday rotation of both compact sources and the diffuse emission. We discuss how SKA AA4 will allow implementation of the techniques we describe, leveraging the vastly improved sensitivity, resolution and uv-coverage compared to existing datasets. This will enhance our ability to reconstruct 3D magnetic field vectors, advancing our understanding of magnetic fields in Galactic evolution and star formation.

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arXiv2026

The magnetic field in the Milky Way Galaxy: from large to small scales

The Milky Way is the galaxy in which we can study its magnetic field to the finest details, providing an ideal laboratory to understand the fundamental questions: how magnetic field is generated and evolves, and how it influences other components in the Galaxy. An SKA-Mid polarization survey will produce an all-sky rotation measure (RM) grid with a density of about 100 per square degree, which is approximately two orders of magnitude larger than what is currently available, and produce total intensity, polarized intensity, and RM all-sky images of diffuse emission covering scales from about 10 arcseconds upward after combination with single-dish observations. The dense RM grid and images of diffuse emission will allow us to determine the most complete picture of the magnetic field in the southern Galactic hemisphere from large to small scales.

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arXiv2026

Small-scale Magnetic Fields in the Milky Way and Nearby Galaxies

Magnetic fields in galaxies span decades in physical scale, from the coherent magnetic fields on galactic scales (> kpc) to the random magnetic fields from 100 pc to the resistive scale of the galactic plasma (i.e. ~1e6 cm). While many radio studies to date have placed more emphasis on the large-scale galactic magnetic fields than the small-scale counterparts, the emerging SKA will greatly facilitate accurate, detailed studies of the small-scale (< 100 pc) galactic magnetic fields. In this Chapter, we highlight the importance of understanding the small-scale galactic magnetic fields in furthering our understanding of star formation, galaxy evolution, and the fundamental physics of magnetohydrodynamics. Furthermore, we discuss some open questions in the research field and outline several possible large observation programmes with the SKA Array Assembly 4 (AA4).

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arXiv2026

The magnetic field of the Milky Way: an observational perspective

Magnetic fields are an important and enigmatic component of the Milky Way's ecosystem. Mostly frozen into interstellar plasma, they play key roles in (turbulent) gas dynamics, star formation, energy household, evolution of interstellar objects, and cosmic-ray propagation. This paper reviews recent progress on measuring and characterizing these Galactic magnetic fields, limited to the larger-scale fields in mostly diffuse media, and to an observational perspective. On Galaxy-wide scales, the magnetic field roughly follows the spiral arms in the Galactic disk, and includes an additional component perpendicular to the disk away from the Galactic plane. The field configuration is different in the Galactic disk and the Galactic gaseous halo, qualitatively consistent with different dominating dynamo modes. Deviations from this idealized model are ubiquitously observed and include anomalously high Faraday rotation, variable magnetic field orientations and field reversals on kiloparsec scales. On smaller scales, the magnetic field is turbulent, anisotropic and intermittent. Much used descriptions of the turbulent magnetic field such as power laws and Gaussianity are being replaced by higher-order statistics that better capture the complexities of the field. Magnetic field orientations and possibly strength are correlated with both cold and warm components of the multi-phase interstellar gas, and with the interstellar dust distribution. The near future will bring a large increase in observational data in rotation measure grids, Faraday Tomography data and measurements of interstellar polarization of optical starlight, promising exciting developments in characterizing and understanding magnetic fields in the Milky Way in the next few years.

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arXiv2026

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

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.

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arXiv2026

A Robust Analysis of QU-fitting Behavior for 800-1088 MHz and 1296-1440 MHz

QU-fitting is a powerful tool for interpreting spectro-polarimetric radio continuum observations by linking them to physical models, enabling estimates of the magnetic fields in, for example, the Milky Way, galaxy clusters, and radio jets. We present a comprehensive investigation into the effectiveness and limitations of QU-fitting within the ASKAP POSSUM survey frequency ranges (800-1088 MHz and 1296-1440 MHz) with projections to other spectro-polarimetric radio observations. We simulate different physical polarization sources: Faraday simple, Burn slab, internal turbulence, external turbulence, and two-component models in the POSSUM frequencies, and assess their observational degeneracies and fit accuracies. Our results highlight the model-dependent nature of reliable fitting and identify specific regions of parameter space where model selection, and therefore characterization of the physical medium, becomes ambiguous. For QU-fitting we find the Bayes factor, computed using the marginal likelihood, outperforms more traditionally used goodness-of-fit metrics such as Bayesian Information Criterion (BIC), Akaike Information Criterion (AIC), and chi-squared for model selection. We provide empirical relationships to delineate the boundaries where model distinguishability is impossible. Finally, we evaluate how accurately QU-fitting recovers model parameters and their associated uncertainties, thereby assessing its ability to correctly characterize the Faraday-rotating medium in both point and extended sources in Faraday depth space.

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arXiv2026

GMIMS-DRAGONS: A Faraday Depth Survey of the Northern Sky Covering 350-1030 MHz

Polarized synchrotron emission at meter to centimeter wavelengths provides an effective tracer of the Galactic magnetic field. Calculating Faraday depth, the most useful parameter for mapping the line-of-sight magnetic field, requires observations covering wide frequency bands with many channels. As part of the Global Magneto-Ionic Medium Survey (GMIMS), we have observed polarized emission spanning 350-1030 MHz over the northern sky, in the declination range ${-20^{\circ}}\leqδ\leq{90^{\circ}}$. We used the 15 m telescope at the Dominion Radio Astrophysical Observatory (DRAO), equipped to receive orthogonal circular polarizations, with the Onsala Space Observatory band 1 feed developed for the SKA Project. Angular resolution varies across the band from $1.3^{\circ}$ to $3.6^{\circ}$. A digital spectrometer provided 42 kHz frequency resolution. Data were taken with the telescope moving rapidly in azimuth and are absolutely calibrated in intensity. Approximately 25% of the data were lost due to radio-frequency interference. The resolution in Faraday depth is $\sim6$ rad m$^{-2}$, and features as wide as $\sim38$ rad m$^{-2}$ are represented. The median sensitivity of the Faraday depth cube is 11 mK. Approximately 55% of sight-lines in this survey show Faraday complexity. This dataset, called ``DRAO GMIMS of the Northern Sky'' (DRAGONS), is the first to probe Faraday depth of the northern sky in its frequency range and will support many scientific investigations. The data will be used to calibrate surveys with higher angular resolution, particularly Galactic foreground maps from the Canadian Hydrogen Intensity Mapping Experiment, and to provide information on large structures for aperture-synthesis telescopes, particularly the DRAO Synthesis Telescope. The data are available through the Canadian Astronomy Data Centre.

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arXiv2025

Magnetic fields in planetary nebulae detected through non-thermal radio continuum emission

Context. Planetary nebulae are shells ejected by low- and intermediate-mass stars. The slow wind ejected by the asymptotic giant branch star is compressed by a fast stellar wind to produce an expanding gaseous shell surrounding a hot bubble. The shell is a source of thermal radio emission which shows a spectral index between -0.1 and 2. Only two planetary nebulae are known to show non-thermal radio emission indicating magnetic fields and non-thermal electrons. Aims. The aim of this paper is verification of presence of magnetic fields of planetary nebulae. Magnetic fields can have a significant influence on shaping planetary nebulae. Methods. We observed a sample of northern planetary nebulae in radio continuum at 144 MHz with the Low Frequency Array. We combined our observations with archival observations at higher frequencies. Results. The spectral indices in 30 planetary nebulae were below -0.1, indicating non-thermal radio emission. The majority of this sample consists of bipolar planetary nebulae, which are known to originate from binary central stars. Most of the nebulae have sizes larger than 20 arcsec. Magnetic fields and nonthermal emission may be common in smaller planetary nebulae, but can be suppressed by thermal emission. Our results suggest that different mechanisms can be responsible for the origin of magnetic fields and non-thermal emission in planetary nebulae.

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arXiv2025

A pioneering experiment combining single-antenna and aperture-synthesis data to measure Faraday rotation with GMIMS and the CGPS

Structures in the magnetoionic medium exist across a wide range of angular sizes owing to large-scale magnetic fields coherent over the Galactic spiral arms combined with small-scale fluctuations in the magnetic field and electron density resulting from energy injection processes such as supernovae. For the first time, we produce diffuse Galactic synchrotron emission Faraday rotation maps covering all spatial scales down to $3'$ resolution for magnetic field studies. These maps complement total and polarized intensity maps combining single-antenna and interferometric data that have been produced, such as the Canadian Galactic Plane Survey (CGPS). Combined maps have sensitivity to large scales from the single-antenna component and angular resolution from the interferometric component. We combine Global Magneto-Ionic Medium Survey High-Band North single-antenna and CGPS aperture-synthesis polarization data after spatial filtering, producing Stokes $Q$ and $U$ maps for the four CGPS frequency channels. We calculate rotation measures (RMs) for all pixels using a linear fit to polarization angle versus wavelength squared. Smooth polarized emission regions require the large-scale sensitivity of the single-antenna to illuminate the Faraday rotation, while aperture synthesis reveals small-scale RM variability. While these maps show magnetic field structures on the full range of spatial scales they probe, the RM values should be interpreted with caution, as the narrow $λ^2$ coverage limits sensitivity to Faraday complexity. Despite this limitation of the CGPS 35 MHz bandwidth, we demonstrate that useful Faraday rotation information can be obtained from the combined dataset, highlighting the important synergy between future broadband interferometric and single-antenna polarization surveys.

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arXiv2025

The Polarisation Sky Survey of the Universe's Magnetism (POSSUM): Science Goals and Survey Description

The Australian SKA Pathfinder (ASKAP) offers powerful new capabilities for studying the polarised and magnetised Universe at radio wavelengths. In this paper, we introduce the Polarisation Sky Survey of the Universe's Magnetism (POSSUM), a groundbreaking survey with three primary objectives: (1) to create a comprehensive Faraday rotation measure (RM) grid of up to one million compact extragalactic sources across the southern ~50 per cent of the sky (20,630 deg$^2$); (2) to map the intrinsic polarisation and RM properties of a wide range of discrete extragalactic and Galactic objects over the same area; and (3) to contribute interferometric data with excellent surface brightness sensitivity, which can be combined with single-dish data to study the diffuse Galactic interstellar medium. Observations for the full POSSUM survey commenced in May 2023 and are expected to conclude by mid-2028. POSSUM will achieve an RM grid density of around 30-50 RMs per square degree with a median measurement uncertainty of ~1 rad m$^{-2}$. The survey operates primarily over a frequency range of 800-1088 MHz, with an angular resolution of 20'' and a typical RMS sensitivity in Stokes $Q$ or $U$ of 18 $μ$Jy beam$^{-1}$. Additionally, the survey will be supplemented by similar observations covering 1296-1440 MHz over 38 per cent of the sky. POSSUM will enable the discovery and detailed investigation of magnetised phenomena in a wide range of cosmic environments, as well as the interplay between these components. This paper reviews the current science case developed by the POSSUM Collaboration and provides an overview of POSSUM's observations, data processing, outputs, and its complementarity with other radio and multi-wavelength surveys, including future work with the SKA. [Abstract abridged]

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arXiv2025

A magnetised Galactic halo from inner Galaxy outflows

Magnetic halos of galaxies are crucial for understanding galaxy evolution, galactic-scale outflows, and feedback from star formation activity. Identifying the magnetised halo of the Milky Way is challenging because of the potential contamination from foreground emission arising in local spiral arms. Additionally, it is unclear how our magnetic halo is influenced by recently revealed large-scale structures such as the X-ray emitting eROSITA Bubbles. Here we report the identification of several kpc-scale magnetised structures based on their polarized radio emission and their gamma-ray counterparts, which can be interpreted as the radiation of relativistic electrons in the Galactic magnetic halo. These non-thermal structures extend far above and below the Galactic plane and are spatially coincident with the thermal X-ray emission from the eROSITA Bubbles. The morphological consistency of these structures suggests a common origin, which can be sustained by Galactic outflows driven by active star-forming regions located in the Galactic Disc at 3-5 kpc from the Galactic Centre. These results reveal how X-ray-emitting and magnetised halos of spiral galaxies can be related to intense star formation activities and suggest that the X-shaped coherent magnetic structures observed in their halos can stem from galaxy outflows.

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arXiv2025

The Southern Twenty-centimetre All-sky Polarization Survey (STAPS): survey description and maps

We present data processing and verification of the Southern Twenty-centimetre All-sky Polarization Survey (STAPS) conducted with Murriyang, the Parkes 64-m telescope. The survey covers the sky area of -89<Dec<0 and the frequency range of 1.3-1.8 GHz split into 1-MHz channels. STAPS was observed commensally with the S-band Polarization All-Sky Survey (S-PASS). The survey is composed of long azimuth scans, which allows us to absolutely calibrate Stokes Q and U with the data processing procedure developed for S-PASS. We obtain I, Q, and U maps in both flux density scale (Jy/beam) and main beam brightness temperature scale (K), for the 301 frequency channels with sufficiently good data. The temperature scale is tied to the Global Magneto-ionic Medium Survey (GMIMS) high-band north sky survey conducted with the Dominion Radio Astrophysical Observatory 26-m telescope. All the STAPS maps are smoothed to a common resolution of 20 arcmin. The rms noise per channel ranges from about 16 mK to 8 mK for I, and from about 8 mK to 5 mK for Q and U at frequencies from 1.3 to 1.8 GHz. The rms noise in Q and U varies with declination and reaches minimum at declination of -89 degree. We also run rotation measure (RM) synthesis and RM clean to obtain peak polarized intensity and Faraday depth maps. The whole STAPS data processing is validated by comparing flux densities of compact sources, pixel flux density versus pixel flux density for Cen A, pixel temperature versus pixel temperature for the entire survey area, and RMs of extragalactic sources between STAPS and other measurements. The uncertainty of the flux density scale is less than 10%. STAPS delivers an L-band (20 cm) multi-frequency polarization view of the Galaxy, and will help advance our understanding of the Galactic magnetic field and magnetized interstellar medium.

astro-ph.GA↗

arXiv2024

Disentangling the Faraday rotation sky

Magnetic fields permeate the diffuse interstellar medium (ISM) of the Milky Way, and are essential to explain the dynamical evolution and current shape of the Galaxy. Magnetic fields reveal themselves via their influence on the surrounding matter, and as such are notoriously hard to measure independently of other tracers. In this work, we attempt to disentangle an all sky map of the line-of-sight parallel component of the Galactic magnetic field from the Faraday effect, utilizing several tracers of the Galactic thermal electron density. Additionally, we aim to produce a Galactic electron dispersion measure map and quantify several tracers of the structure of the ionized medium of the Milky Way. We rely on compiled catalogs of extragalactic Faraday rotation measures and Galactic pulsar dispersion measures, a well as data on bremsstrahlung and the hydrogen $α$ spectral line to trace the ionized medium of the Milky Way. We present the first full sky map of the line-of-sight averaged Galactic magnetic field. Within this map, we find LoS parallel and LoS-averaged magnetic field strengths of up to 4 $μ$G, with an all-sky root-mean-square of 1.1 $μ$G, which is consistent with previous local measurements and global magnetic field models. Additionally, we produce a detailed electron dispersion measure map, which agrees with already existing parametric models at high latitudes, but suffers from systematic effects in the disk. Further analysis of our results with regard to the 3D structure of $n_{th}$ reveals that it follows a Kolmogorov-type turbulence for most of the sky. From the reconstructed dispersion measure and emission measure maps we construct several tracers of variability of $n_{th}$ along the LoS.

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arXiv2024

Faraday tomography with CHIME: the `tadpole' feature G137+7

A direct consequence of Faraday rotation is that the polarized radio sky does not resemble the total intensity sky at long wavelengths. We analyze G137+7, which is undetectable in total intensity but appears as a depolarization feature. We use the first polarization maps from the Canadian Hydrogen Intensity Mapping Experiment. Our $400-729$ MHz bandwidth and angular resolution, $17'$ to $30'$, allow us to use Faraday synthesis to analyze the polarization structure. In polarized intensity and polarization angle maps, we find a "tail" extending $10^\circ$ from the "head" and designate the combined object the "tadpole". Similar polarization angles, distinct from the background, indicate that the head and tail are physically associated. The head appears as a depolarized ring in single channels, but wideband observations show that it is a Faraday rotation feature. Our investigations of H I and H$α$ find no connections to the tadpole. The tail suggests motion of either the gas or an ionizing star through the ISM; the B2(e) star HD 20336 is a candidate. While the head features a coherent, $\sim -8$ rad m$^2$ Faraday depth, Faraday synthesis also identifies multiple components in both the head and tail. We verify the locations of the components in the spectra using QU fitting. Our results show that $\sim$octave-bandwidth Faraday rotation observations at $\sim 600$ MHz are sensitive to low-density ionized or partially-ionized gas which is undetectable in other tracers.

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arXiv2024

Faraday tomography of LoTSS-DR2 data: III. Revealing the Local Bubble and the complex of local interstellar clouds in the high-latitude inner Galaxy

In this work, we present a new mosaic created with the second release of LOFAR Two-Metre Sky Survey data (LoTSS-DR2), which probes polarised synchrotron emission in the high-latitude inner Galaxy. Our objective is to characterise the observed emission through multi-tracer analysis to better understand the volume and the structures that may be observed with LOFAR. Furthermore, we exploit Faraday depth as a unique tool to probe the diffuse magnetised structure in the local ISM. We produced a mosaic Faraday cube of LoTSS-DR2 data by applying a rotation measure synthesis algorithm. From the cube, we constructed Faraday moment maps to characterise the nature of spectra. Additionally, we quantified the linear depolarisation canals using the Rolling Hough transform and used them to search for alignment with other data sets. Utilising LoTSS-DR2 observations alongside complementary data sets including Planck polarisation data, HI emission maps, and starlight polarisation measurements, we estimated the distance to the Faraday structures. The Faraday cube reveals an ordered structure across two-thirds of the observed area, whose orientation aligns well with that of both the HI filaments and the magnetic field. We estimate the minimum distance to the Faraday structures to be between 40 and 80 pc, which puts them in the vicinity of the Local Bubble wall. The emission is organised in a large gradient in Faraday depth whose origin we associate with the curved wall of the Local Bubble. Comparing our data with a model of the Local Bubble wall, we conclude that we might be probing a contribution of the medium inside the Local Bubble cavity as well, corresponding to the complex of local interstellar clouds. Moreover, we propose a toy model incorporating an ionised front of finite thickness into the Local Bubble wall, as a curved, cold neutral shell alone is insufficient to produce the observed gradient.

astro-ph.GA↗

arXiv2024

Faraday tomography of LoTSS-DR2 data: II. Multi-tracer analysis in the high-latitude outer Galaxy

We conducted a follow-up study on the analysis of the LOw Frequency ARray (LOFAR) Two-metre Sky Survey (LoTSS) mosaic in the high-latitude outer Galaxy presented in the first paper of this series. Here, we focus on the search for alignment between the magnetic field traced by dust, HI filaments, starlight optical linear polarisation, and linear depolarised structures (depolarisation canals) observed in low-frequency synchrotron polarisation. This alignment was previously found in several smaller fields observed with LOFAR, offering valuable insights into the nature of the interstellar medium and the 3D spatial distribution of the diffuse ionised medium. We aim to determine whether the alignment of the interstellar medium (ISM) phases observed through multiple tracers is a common occurrence or an exception. Additionally, in areas where depolarisation canals align with the magnetic field, we use starlight polarisation to constrain the distance to the structures associated with the observed canals. We employed the Rolling Hough Transform (RHT) and projected Rayleigh statistics (PRS) to identify and quantify the alignment between the different tracers. On the scale of the whole mosaic, we did not find any evidence of a universal alignment among the three tracers. However, in one particular area, the western region (Dec between $29^\circ$ and $70^\circ$ and RA between $\mathrm{7^h44^m}$ and $\mathrm{9^h20^m}$), we do find a significant alignment between the magnetic field, depolarisation canals, and HI filaments. Based on this alignment, we used the starlight polarisation of stars with known parallax distances to estimate that the minimum distance to the structures observed by LOFAR in this region lies within the range of 200 to 240 pc. We associate these structures with the edge of the Local Bubble.

astro-ph.GA↗

arXiv2023

Tomographic Imaging of the Sagittarius Spiral Arm's Magnetic Field Structure

The Galactic global magnetic field is thought to play a vital role in shaping Galactic structures such as spiral arms and giant molecular clouds. However, our knowledge of magnetic field structures in the Galactic plane at different distances is limited, as measurements used to map the magnetic field are the integrated effect along the line of sight. In this study, we present the first-ever tomographic imaging of magnetic field structures in a Galactic spiral arm. Using optical stellar polarimetry over a $17' \times 10'$ field of view, we probe the Sagittarius spiral arm. Combining these data with stellar distances from the $Gaia$ mission, we can isolate the contributions of five individual clouds along the line of sight by analyzing the polarimetry data as a function of distance. The observed clouds include a foreground cloud ($d < 200$ pc) and four clouds in the Sagittarius arm at 1.23 kpc, 1.47 kpc, 1.63 kpc, and 2.23 kpc. The column densities of these clouds range from 0.5 to $2.8 \times 10^{21}~\mathrm{cm}^{-2}$. The magnetic fields associated with each cloud show smooth spatial distributions within their observed regions on scales smaller than 10 pc and display distinct orientations. The position angles projected on the plane-of-sky, measured from the Galactic north to east, for the clouds in increasing order of distance are $135^\circ$, $46^\circ$, $58^\circ$, $150^\circ$, and $40^\circ$, with uncertainties of a few degrees. Notably, these position angles deviate significantly from the direction parallel to the Galactic plane.

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