EDP Sciences logo
Subscriber Authentication Point
Search
Menu
Home All issues Volume 657 (January 2022) A&A, 657 (2022) A43 Full HTML
Free Access
Issue
A&A
Volume 657, January 2022
Article Number A43
Number of page(s) 14
Section Interstellar and circumstellar matter
DOI https://doi.org/10.1051/0004-6361/202140486
Published online 04 January 2022

© ESO 2022

1 Introduction

The Faraday effect describes the rotation of the polarization position angle propagating through magnetized plasma and provides information on the line-of-sight (LOS) component of magnetic fields weighted by the thermal electron density. These quantities are key puzzle pieces for the characterization and modeling of the structure of the Milky Way’s magnetic field and of many extra-Galactic astrophysical objects, such as galaxies (Beck 2015) and galaxy clusters (Durrer & Neronov 2013). A better understanding of these structures is not only an interesting topic on its own merit, but it may also provide a pathway to understanding the origin of the magnetic field in the Universe as a whole (Subramanian 2016). Thus, a primary objective of research on cosmic magnetism has been the investigation of the polarimetric properties of peculiar extra-Galactic objects in the hope of obtaining insights into their morphology and formation history.

Over the years, this pursuit has led to a dense coverage of Faraday rotation data across the whole sky, which have been cataloged in exhaustive compilations (Oppermann et al. 2012; Van Eck et al., in prep.). The characteristics of this data not only depend on the properties of the objects in question but on the integral of all environments through which the light has passed upon arriving at the telescope. This leads to a potential intertwining of information on completely different astrophysical environments, such as the intergalactic and interstellar media. In particular, the plasma of our Galaxy is responsible for a significant amount of Faraday rotation; we refer to Cooper & Price (1962) or Gardner & Davies (1966) for early detections of the Galactic Faraday rotation contribution and Haverkorn (2015) and Beck (2015) for reviews.

In order to disentangle the contributions to Faraday rotation from multiple sources, reconstruction procedures have been developed. Specifically in the case of the Galactic Faraday rotation sky, a useful measure for discerning Galactic and extra-Galactic components is the similarity of RM values of nearby sources on the sky. We expect that large angular correlations in Faraday data most likely result from local effects, implying that data resulting from extra-Galactic processes should be mostly uncorrelated on angular scales of arc-minutes or larger (Akahori & Ryu 2010). Exceptions to this might be caused by neighboring parts of the cosmic large-scale structure or large-scale magnetic fields in the intergalacticmedium in proximity to the Milky Way Xu et al. (2006). Past all-sky methods to reconstruct the Galactic Faraday sky were developed, for instance, by Frick et al. (2001), Johnston-Hollitt et al. (2004), Dineen & Coles (2005), Xu et al. (2006), Short et al. (2007), Pshirkov et al. (2011), Oppermann et al. (2012), Xu & Han (2014).

In this paper, we are continuing the work of Oppermann et al. (2012, 2015) and Hutschenreuter & Enßlin (2020). In the latter reference (henceforth HE20) the authors introduce two inference models. The simpler one is a generalization of the model used by Oppermann et al. (2012), while the more complicated one additionally restricts the amplitude of the Faraday sky with data on the emission measure (EM) of thermal electrons, as obtained from the Planck satellite (Planck Collaboration X 2016). These works use Bayesian inference schemes, which utilize the whole-sky correlation structure of the Galactic part of the Faraday rotation sky in order to (a) perform the aforementioned component separation and (b) to interpolate between data points on the sky. As the precise form of the correlation structure (which is necessary for the interpolation) is unknown, it is also inferred jointly with the sky map.

The aim of this paper is to provide the community with the most recent version of the Galactic Faraday sky with a minimal set of physical assumptions in unprecedented resolution and to draw attention to previously under-constrained sky regions, such as the Magellanic Clouds or peculiar substructures of the Galactic disc. The more complicated inferences using the algorithms developed in HE20 have also been repeated. However, discussing these results, particularly in light of the many options that exist for the inclusion of new data sets and modeling assumptions, exceeds the scope of this paper, which is to provide a methodologically clean update on the Faraday rotation sky with a specific focus on high resolution, specific Galactic structures, and statistical properties of the Faraday rotation sky. Thus, we perform the same analysis as in HE20, but are restricting ourselves to the model which uses Faraday data only. An accompanying publication is in preparation (Hutschenreuter & Ensslin, in prep.), which focuses on the aforementioned more complicated models and focuses on the analysis of the component maps. This present publication should therefore be regarded as the primary reference for the updated Faraday rotation sky, whereas the other aims to provide a physical interpretation of the component maps, which depends more on assumptions. The resulting posterior mean and uncertainty maps for the Faraday rotation sky are available for download either as full-sky maps1 or via a cutout server2.

We structure the paper as following: Sect. 2 summarizes the relevant physics and the modeling. Section 3 describes the data used in this work. Section 4 discusses the results and Sect. 5 gives a conclusive summary.

2 Modeling the Faraday rotation sky

2.1 Physics

To provide context for modeling the Faraday sky, we start with a short summary on important physical concepts and general data aquisition methods for Faraday data.

First, the differential angle of rotation, , by which the polarization plane of linearly polarized light is rotated between emission and detection can be described via between emission and detection can be described via: (1)

where λ is the observational wavelength, ψ0 is the intrinsic polarization angle, ψλ the angle observed at wavelength λ, and RM is the rotation measure (Burn 1966). Determining RMs has traditionally been done by observing ψλ at different wavelengths, and then determining the slope of in the λ2 space. In the ideal case of a thin non-emitting plasma screen being the only source for the rotation effect, the RM at redshift zero is equal to the Faraday depth: (2)

where nth is the thermal electron density and B∥ is the component of the magnetic field parallel to the LOS. The physical constants e, me, and c describe the elementary charge, the electron mass and the speed of light, respectively. We conform with the general sign convention that RM and ϕ are positive for Bparallel pointing toward the observer. Unfortunately, the relation RM = ϕ is generally not correct, for example, in the case of multiple components along the LOS. Measurements of ϕ are therefore often obtained via more elaborate reconstruction techniques, such as RM synthesis (Brentjens & de Bruyn 2005; Bell & Enßlin 2012). In this work, we use specific data for ϕ that were determined either with a simple slope fit in λ2 space or via RM synthesis. The sampling in λ2 space is often sparse, and this sparsity is generally understood to produce artificial features in the Faraday spectrum (Farnsworth et al. 2011). The likelihood of these being mistaken as true ϕ-values can be minimized through a careful analysis, but cannot completely be eradicated; hence, this aspect has to be considered when using the data.

In this work, we are interested in the Galactic component of the Faraday rotation sky ϕgal. Due to the additivity of ϕ, one can write the equation connecting the data dϕ with ϕgal as (3)

where the is a projection operator connecting the sky with data space and the (Gaussian) noise term nϕ contains the known observational error. The non-Galactic component ϕetc contains, for example, extra-Galactic, ionospheric contributions or unresolvable small-scale structures. Furthermore, it is absorbed together with the observational noise into an adapted noise term, , whose covariance needs to be estimated. It should be emphasized at this point that for the lack of accurate radial information connected to the RM data, our decision criterion on the discrimination between Galactic and extra-Galactic relies solely on angular correlations. This implies that relatively close-by extra-Galactic objects such as the Magellanic clouds can end up on the Galactic map, while unresolvable small scale Galactic structures might be erased by the noise estimation. A more accurate separation most likely would rely on a detailed three-dimensional (3D) modeling of the interstellar medium (ISM) and the inclusion of distance information, which by far exceeds the scope of this work. The noise estimation is done using the same noise estimation technique as first described by Oppermann et al. (2012), namely, by modeling the adapted noise standard deviations via (4)

where ηϕ is a parameter to be inferred via an inverse gamma model, (5)

as detailed by Oppermann et al. (2012) and HE20. The hyper-parameters, αϕ and βϕ, steer the ability of the noise estimation to increase the noise and, hence, down-weighted data points with large ϕetc in the likelihood. This is equivalent to setting a prior for our expectation that data excess should be explained by the sky map or an increase of the noise. In Oppermann et al. (2012) as well as in HE20, αϕ was set to a single number for the whole sky (1 and 2.5, respectively). As discussed in HE20, we need to adapt the hyper-parameters for the noise estimation when increasing the resolution to make up for the increase in degrees of freedom, that is, to allow for the representation of previously unresolvable small-scale structures. With the increase of the resolution to about 1.3 ×10−2deg2 or 46.8 arcmin2 in this work, we found that setting the parameter to a restrictive value leads to over-fitting in high latitude regions (i.e.,data points clearly dominated by the extra-Galactic component appearing as point sources in the sky map), while a looser choice makes it hard to represent the small scale-structure in the Galactic disc. This indicates that we have reached a resolution where a noise model with a universally chosen, αϕ, is not able to accurately represent the non-homogeneous statistics of the Faraday sky anymore. Hence, we decided to use a position-dependent noise estimation, which gets more restrictive in regions where we expect small-scale structures to be mostly Galactic, forinstance, towards the Galactic disc or the Magellanic clouds. We chose to use the logarithmic DM map of Yao et al. (2017) as a proxy for this prior, as it provides a natural scaling with Galactic latitude and includes at least some important structures such as the Magellanic clouds. This template is then rescaled such that it reaches 1 towards the poles (hence, complying with the global value for αϕ, chosen in Oppermann et al. 2012), but it reaches up to 3.5 towards the disc, implying a very restrictive prior for ηϕ in these regions. In accordance with the previous studies, βϕ is then set such that the prior mode of ηϕ is 1 for all data points.

This noise estimation procedure also takes care of uncorrelated systematic errors, as, for example, the nπ-ambiguity, demonstrated in HE20 for the data points identified by Ma et al. (2019). A potentially correlated systematic effect may come from the limited range in Faraday depth that most Faraday rotation surveys probe. Sources with a Faraday depth that are out of range are either ignored or misrepresented in the data sets, depending on the technique used to analyze the polarimetric data. Such effects are hard to model and cannot generally be remedied by the noise estimation. Hence, we do not correct for such systematics.

2.2 Nomenclature

Before proceeding with the modeling discussion, we would like to comment on the terminology used in this paper and its predecessor HE20. There, the authors use the term “Faraday data” for the data and refer to ϕ as the Faraday depth. Accordingly, the reconstructed sky is referred to as the “Galactic Faraday depth sky”. This reflects the common Bayesian ontology that clearly separates data and signal and relies on the assumption that the data are a noisy measurement of ϕ defined in Eq. (2). This nomenclature is independent of the way the data were obtained or the physical geometry of the LOS observed. The term “RM” is omitted by HE20 and implicitly reserved for the subset of the data that were obtained using slope fitting techniques. This unfortunately does not completely match the general way these terms are used in the astrophysical literature, where sometimes the naming convention is moreso determined by the LOS structure. The label “Faraday depth” for Eq. (2) is sometimes reserved for cases where rotation and emission are mixed and it is necessary to deal with complex Faraday spectra (e.g., see Van Eck 2018), while “RM” is often used in situations that can be explained with a single non-emitting Faraday screen (e.g., see Mao et al. 2010). This terminology is hard to maintain in our work as we are mixing these data sets and we are agnostic to the geometry along the LOS; but on the other hand the term “Faraday depth sky” as it is used in HE20 might give a false impression of what is actually inferred. Thus, we decided to again label Eq. (2) as “Faraday depth”, however, we refer to the reconstructed sky simply as the “Faraday rotation sky”.

2.3 Sky model

The sky model for ϕgal was mo by HE20. Here, we give a very short alternative motivation, which provides connection points for additional data sets (e.g., on theGalactic dispersion measure (DM)). An illustrative picture arises if we assume no correlation between nth and B∥, which is reasonable for the warm ionized medium of the Galaxy (Passot & Vázquez-Semadeni 2003; Harvey-Smith et al. 2011; Wu et al. 2015), Eq. (2) for the Galactic component can be expressed as: (6)

(Draine 2010), where DM = ∫LOSdl nth and is the LOS-parallel component of the magnetic field vector averaged along the LOS. This equation is used to motivate the simplest model for the Faraday sky, (7)

implemented for the first time in HE20. Here, ρ and χ are Gaussian fields on the sky with unknown correlation structure that needs to be determined. The log-normal field eρ is supposed to take over the role of the DM, while the sign field χ models the magnetic field average. As already noted by HE20, we cannot break the degeneracy between eρ and χ in this model and relate the component fields to the respective physical quantities without further information or assumptions. This approach is the basis of a separate work (Hutschenreuter & Ensslin, in prep.). We note that the assumption of no correlation between nth and B∥ is by no means necessary to motivate the model above, since a separation of the Faraday sky into an amplitude and a sign field is, of course, always possible, but is only used to give an illustrative image.

The inference of the correlation functions has been updated in accordance with recent developments in numerical information field theory; for more details, we refer to Arras et al. (2020). The new model is equally flexible in representing different power spectra, but has the advantage of more intuitive and better decoupled hyper-parameters. This inference was implemented in the newest version (v.7) of the NIFTy package (The NIFTy5 team, in prep.). Nifty is based on information field theory (IFT) and provides the user with a library of Bayesian signal inference techniques, mostly aimed at the evaluation of noisy and very high-dimensional problems. Specifically, it makes use of the MGVI algorithm (Knollmüller & Enßlin 2019) to approximate posterior distributions via variational inference. In addition, it contains a toolkit to implement complicated likelihoods and signal models. For a generic reference and introduction to IFT, we refer to Enßlin (2019).

3 Data

We used a newly compiled master catalog of published Faraday data from extra-Galactic sources such as AGNs3 that is to be published by Van Eck et al. (in prep.)4. This catalogwas assembled independently of the Oppermann et al. (2012) catalog, but contains most of the same sources along with many others published since then. A list of the individual catalogs included can be found online with the master catalog.

This new master catalog is not yet complete, with papers being prioritized for inclusion based on combination of catalog size, recency, andease of data access (i.e., Vizier or machine readable tables were preferred to LATEX or PDF tables, which, in turn, were preferred to images of tables). The version of the catalog used here includes data points from 38 papers, which encompasses nearly all of the catalogs published in the past 30 yr that contain more than 30 data points. Some papers with fewer data points were also included. Sources reported with multiple data points (from RM synthesis or QU-fitting) had all components included as separate entries in the catalog. This results in a catalog of 50 207 data points, which is a significant expansion on the 41 330 used by Hutschenreuter & Enßlin (2020); Oppermann et al. (2012). In accordance with Stil et al. (2011), the error bars of Taylor et al. (2009) were multiplied by 1.22.

Additionally, we were provided with yet unpublished catalogs, mostly including data compiled in 2020 by the LOFAR Two-metre Sky Survey (LoTSS) (O’Sullivan et al., in prep.; 2461 data points), by the Canadian Galactic Plane Survey (CGPS) (Van Eck et al. 2021; 2493 data points) and a small data set provided by Johnston-Hollit et al. (in prep.) (68 data points) which was already present in the Oppermann catalog. These data sets will become part of the catalog once published. We have decided in favor of including this data, as we would like our results to represent the most up-to-date state of the Galactic Faraday sky as of the end of the year 2020.

In summary, we therefore have 55190 data points from 41 surveys available. This number excludes 39 pulsars that were removed from the catalog, as they generally do not probe the full Galactic LOS (Sobey et al. 2019). We did not attempt to identify duplicate sources in the catalog: if a source appears in multiple catalogs, all measurements were kept. While multiple measurements of the same source provide valuable additional information, the noise estimation technique of Oppermann et al. (2012) is, strictly speaking, not optimal in these cases, since these sources probe the same part of the IGM and the assumption of independence for the error estimates, which includes the extra-Galactic signal, does not hold anymore. The severity of this issue depends on the number of duplicates, which is hard to determine without extensive source matching. We can, however, give an estimate on this number by counting the number of data points located in a sky pixel containing more than one data point. This results in a fraction of ≈ 0.6% of the data set being identified as potential duplicates at a resolution of about 0.1°. Only a small fraction of those may turn out to be actual duplicates; on the other hand, nearby sources might be correlated by the IGM on such scales even if they are not duplicates, as demonstrated by Akahori & Ryu (2010). We hence assume the number of data points with extra-Galactic correlations to be on the order of 1% and therefore deem the approximation of uncorrelated noise acceptable. In future studies of the Faraday sky, this might have to be revised. We assumed an a-priori noise level of 50% of |dϕ| for the 72 sources without or with zero-valued error bars, which were then subject to the same noise estimation procedure as all other data points. This is a rather cautious choice, but we deem the potential downsides of systematic effects introduced by “overconfident” data to be more significant than those of a potentially ignored data point as a result of overly large error bars. In any case, this choice is automatically corrected to some degree by the noise estimation. A projection of all data points, their error bars, and the source density on the sky is shown in Fig. 1.

4 Results and discussion

In the following, we present the results of the inference using the model introduced in Sect. 2 and the data presented inSect. 3.

4.1 The sky

We show the resulting Faraday rotation sky and uncertainties in Figs. 2 and 3 with different saturation scales to highlight the sky morphology at different latitude scales. For comparison, the previous result of HE20 is shown in Fig. 4a and a difference map between this figure and Fig. 2a is shown in Fig. 4b. On large scales, the results are in good agreement with each other, while on smaller scales many more structures are discernible in the new reconstruction. At higher latitudes, the largest deviations are discernible in the Southern sky, namely, the region south of − 40° in celestial declination, which was severely underconstrained in previous inferences but has since mostly been filled by Faraday data from Schnitzeler et al. (2019), although the region still has not reached a number density comparable to the Northern Hemisphere. Moreover, Fig. 4b demonstrates considerable differences in the Galactic disc, in part, in the morphology but also in amplitude. This can be well observed in Fig. 3a, which reveals a pronounced disc with absolute values often exceeding 1500 rad m−2. The maximum is close to 3000 rad m−2, which stands in strong contrast to the previous inference results of HE20, where a maximum magnitude was found to be slightly above 1000 rad m−2. The disc is further investigated in Sect. 4.2.1.

We further show the component fields eρ and χ in Fig. 5. Both show strong similarity to the analog component fields found in HE20. If we assume that our model in Eq. (7) is correct and that both maps are a proxy for the physical components of the Faraday sky, then, at least in terms of morphology, Fig. 5a should trace the Galactic DM map, while Fig. 5b should trace the LOS-averaged magnetic field strength. We give some evidence for this claim in Sect. 4.2.2 and Sect. 4.3.3, while a more detailed investigation is to be presented by Hutschenreuter & Ensslin (in prep.). The χ map shows some evidence for point-like structures with opposite sign to their diffuse surroundings, which, at high latitudes, we cannot exclude to be remaining extra-Galactic residuals. This indicates that our noise estimation routine was only partially successful, and that some precautions have to be taken if the maps are used as foreground reduction template.

4.2 Substructures

4.2.1 Inner disc

The inner Galactic disc is highlighted in more detail in Fig. 6. Here, we demonstrate the strong variability of the disc by plotting a fine slice along Galactic longitude together with data points falling in the same region. The plot also contains some color coded latitude information, in order to demonstrate that within the disc the same variability is observed when moving along latitudes, including frequent sign flips. The plot contains the approximate directions of the Galactic spiral arm tangents. We note two strong excesses in amplitude of the Faraday sky, one towards the Galactic center and another one towards the tangent point of the Sagittarius arm at around l ≈ 48° reaching almost 3000 rad m−2. The latter excess has been first reported by Shanahan et al. (2019), with the highest observed data point above 4000 rad m−2. Other arm locations also seem to be correlated with stronger values in ϕ, albeit in a much less clear way. The Sagittarius region has also been discussed extensively by Reissl et al. (2020), who investigate rotation measures as spiral tracers using simulations. In their work, the authors confirm the shape of the Sagittarius excess and attribute itssharp morphology to the geometry of the spiral arm relative to the observer. They furthermore predict somewhat more extended but nonetheless relatively strong Faraday rotation features for the other arms and an overall increase in Faraday depth towards the Galactic center and we note that these features are not visible in the results of Oppermann et al. (2012) or Hutschenreuter & Enßlin (2020). In this work, we do find stronger disc amplitudes of the Faraday sky, but cannot confirm the above mentioned overall morphology, as our results are dominated by much smaller structures. Assuming the consistency of our inference and that the simulations of Reissl et al. (2020) produce a correct representation of the Milky Way, the observations can only be explained by systematic effects in the data. For one, the longitude region with latitudes still has under-dense data coverage, as can be seen in Figs. 1c and 7. This might imply that several strong excess regions have not been noted yet as they have simply not been probed. Furthermore, as already noted by Reissl et al. (2020) for the Taylor et al. (2009) data set and previously discussed in Sect. 2.1, many Faraday rotation data sets have range limitations in dϕ and, hence, these might misrepresent regions with exceedingly large Faraday rotation. Modeling such systematics on the inference side, for example,as an extension of Eq. (7), have not been attempted and potentially would require strong prior assumptionson the disc, which would be opposed to our general approach of using generic sky models in order to maintain a high level of flexibility. Hence, it cannot be excluded that systematic effects are still present in the data, especially within the disc, and future Faraday rotation surveys are likely necessary to arrive at a complete picture.

thumbnail Fig. 1

Sky projections of the data set used in this work, the associated observational errors and the source density. Panel a shows the Faraday data, panel b the observed error bars. Data points falling into the same pixel have been averaged. These plot has been made with a four-times decreased resolution (corresponding to an pixel area of 0.21 deg2 or 7.56 × 102 arcmin2) compared to that of the inference in order to enable better visualization. Panel c shows the source density of the data set used in this work. The pixels in this map have an area of about 3.36 deg2 or 1.2 × 104 arcmin2, again for visualization purposes. These, and all subsequent maps, are presented in Galactic coordinates centered at .

4.2.2 Magellanic clouds

To investigate the correspondence of the Faraday sky with other tracers, we single out the Magellanic clouds as the specific objects of study given their relatively well-defined overall morphology and small-scale structure. The clouds are shown in Fig. 9 as excerpts of the Faraday rotation sky, the amplitude field, eρ, H α data (Finkbeiner 2003; Gaustad et al. 2001), and the EM sky as obtained by Planck (Planck Collaboration X 2016), where the latter is related to the thermal electron density as in analogy to the DM defined in Sect. 2.3. A comparison between Figs. 9b and 9d reveals that the amplitude field indeed seems to trace the morphology of dense Galactic structures also on intermediate scales, as both clouds are not only present in Fig. 9b, but also are weighted correctly. The excerpt on the Faraday sky has been offset by 20 rad m2, in order to highlight the structures of the clouds. A significant small scale correspondence of the Faraday rotation excerpt and the Hα is visible, which seems to indicate that even the very small-scale structures are not residuals of extra-Galactic contamination, but resemble existing structures. Furthermore, the region between the clouds seems to indicate a coherent region of Faraday rotation between the Magellanic clouds. This is, again, consistent with an additional coherent magnetic field structure between the clouds, as first reported by Mao et al. (2008), see also Kaczmarek et al. (2017).

thumbnail Fig. 2

Inference results for the posterior mean (panel a) and uncertainties (panel b) of the Galactic Faraday rotation sky using the updated data catalog. The color scale is saturated at ± 250 rad m−2 for the mean and at 80 rad m−2 for the uncertainties to highlight mid latitude features.
thumbnail Fig. 3

Inference results for the posterior mean (panel a) and uncertainties (panel b) of the Galactic Faraday rotation sky using the updated data catalog. The sky maps are the same as in Fig. 2, but the color scale is saturated at ± 1500 rad m−2 in the mean and 300 rad m−2 in the uncertainty to highlight the disk features of the Galactic Faraday rotation sky.
thumbnail Fig. 4

Comparison to previous results. Panel a shows the mean of the Galactic Faraday rotation sky as inferred by HE20, using the same saturation scale as in Fig. 2a. Panel b shows the difference between Figs. 2a and 4a.
thumbnail Fig. 5

Posterior means of the components defined in Eq. (7). Panel a shows the amplitude field eρ and panel b shows the sign field χ.
thumbnail Fig. 6

Slice in longitude (l ∈ (270°, 90°)) through the inner part of the Galactic disc from the Galactic Faraday rotation sky. The colored strips indicate equal latitude strips of the inferred Faraday sky within b ∈ (−1°, 1°). The plot also contains the data points falling in the same region indicated by grey crosses. Data points with ϕ > 3000 rad m−2 are indicated with black triangles at the upper end of the plot. The approximate locations of several spiral arm tangents (Hou et al. 2009; Vallée 2017) are indicated as grey lines, specifically these are the Local (Loc), Sagittarius (Sgr), Scrutum (Sct), and Norma (Nor) arms. We note that these positions are inferred from different tracers such as HII regions and hence do not necessarily coincide exactly with the tangent points traced by a potential excess in Faraday rotation. The region towards l ≈ 45° is also partly shown in Shanahan et al. (2019), where the strong excess in Faraday rotation in direction to the tangent of the Sagittarius arm was first noted.
thumbnail Fig. 7

Histogram of absolute values of the Galactic latitude positions of all data points used in this work.
thumbnail Fig. 8

Template for the noise estimation parameter, αϕ. The noise model is introduced in Eq. (5), the template is based on the Galactic electron model derived by Yao et al. (2017).

4.3 Statistical properties

4.3.1 Power spectra

The inference method employed in this work has seen a significant upgrade in correlation structure modeling. The resulting power spectrum is compared to previous results by plotting the power spectra in Fig. 10. The plot also contains the corresponding statistical uncertainties of our results. The plot shows a significant offset of the new spectrum towards small scales compared to its predecessors. In order to illustrate the result, Fig. 10 also contains a parametric maximum a posteriori fit to the new spectrum using the analytic formula (8)

which results in s = −2.4, ℓ0 = 34 and A =1.1 × 1014. While a similar power law slope of ≈ −2.17 was found by Oppermann et al. (2012), the power spectra on small scales were at least somewhat suppressed in HE20. This is consistent with the new small-scale structures visible in Fig. 2a as compared to Fig. 4a.

thumbnail Fig. 9

Magellanic Clouds in our results and as seen with different observables, respectively: panels a and b show the Faraday rotation (with a 20 rad m−2 offset) and the underlying amplitude field as inferred in this work. Panels c and d show the clouds in H α emission (Finkbeiner 2003; Gaustad et al. 2001), and in emission measure (EM), as obtained by the Planck satellite (Planck Collaboration X 2016), respectively. Panel c indicates the locations of the clouds.

4.3.2 Latitude correlations

An important consistency test for the convergence of our inference and a successful separation of the Galactic component of the Faraday sky is to check if there are any latitude correlations remaining in the residuals . Since a datapoint can either be fitted by adjusting the sky or by increasing the noise estimate, it is best to compare the noise-weighted residual, , as a dimensionless tracer of such correlations. The noise, , in this case is the standard deviation as defined in Eq. (4). This is investigated in Fig. 11, which shows a two-dimensional histogram between the logarithmic noise-weighted residuals and the absolute value of the Galactic latitude. For latitudes exceeding 3°, no notable correlation with latitude is discernible. This is not true for the scatter of the residual, which is strong in the disc and smaller at higher latitudes. Such an increase is, however, easily explained when viewing the distribution of data points along Galactic latitude as depicted in the histogram Fig. 7. Another peculiar feature of Fig. 11 is the relatively sharp decrease of the count density for log residuals of 0. This is an imprint of the distribution of our uncertainties in our Faraday data catalog, which sees a relatively hard cut towards large error bars.

4.3.3 Amplitude correlations

The inferences conducted in HE20 and (Hutschenreuter & Ensslin, in prep.) make use of the EM sky as a proxy for the amplitude of the Faraday sky. In order to test the extent to which this assumption is viable, we investigate the correlation between the amplitude field (shown in Fig. 5a) and both the DM sky and the square root of the EM sky, Fig. 12. The square root is motivated by the quadratic dependence of the EM on the thermal electron density, in contrast to the linear dependence of DM and RM. The latter was inferred from cosmic microwave data by the Planck survey (Planck Collaboration X 2016), while the former is calculated from a parametric model of the Galactic thermal electron density (Yao et al. 2017) based on pulsar DM data. Although the EM map of Planck is much more detailed and the DM map relies on very little data and strong modeling assumptions, we note much clearer correlations of the amplitude field with the DM map than with the map, aligning with both the model and the physical discussion presented in Sect. 2.3. This is confirmed by Spearman-rank cross-correlation coefficients of 0.88 for the log DM map and 0.72 for the log square root EM map. In the case of the DM map some of the missing correlation to the amplitude map can be explained by the fact that the Yao et al. (2017) electron model lacks small-scale structure as it relies on sparse data. The differences to the square root EM map, which itself contains a lot of small scale structure, are best explained by the missing volume filling factor that needs to be considered in order to equate the EM and DM skies. Gaensler et al. (2008) show that this factor is variable over the sky and ranges between 0.04 in the mid-plane to about 0.3 at larger distances from the Galactic disc. As demonstrated by HE20, the EM sky is nonetheless a valuable source of information on the Galactic electron density profile. It is however necessary to model these systematic volume effects by introducing additional degrees of freedom, as implemented phenomenologically by HE20. An improved version of this model that takes the above discussion into account will be given by Hutschenreuter & Ensslin (in prep.).

thumbnail Fig. 10

Power spectrum for the Faraday rotation sky derived in this work, compared with results from HE20 and Oppermann et al. (2012). Red dashed line indicates a parametric fit to the results of this work using Eq. (8). The uncertainties of the spectrum derived in this work are indicated by light-blue lines, which are only slightly offset from the dark-blue lines showing the mean.
thumbnail Fig. 11

2D histogram of logarithmic noise weighted residuals and absolute Galactic latitude.

5 Summary and conclusion

In this work, we reconstruct the Galactic Faraday rotation sky using a newly available Faraday rotation data set, comprising the catalog compiled by Van Eck et al. (in prep.) and including additional catalogs provided by O’Sullivan et al. (in prep.); Van Eck et al. (2021); Johnston-Hollit et al. (in prep.). This work is an update to the reconstructions by Oppermann et al. (2012) and HE20. In addition to the new data set, we made technical advancements by employing a new correlation structure model originally developed by Arras et al. (2020) and providing our results with an increased angular resolution. We found significant updates with regard to earlier results, such as an enhanced Galactic disc with Faraday rotation amplitudes near 3000 rad m−2 and drastically improved small-scale structures in the sky map. Apart from a morphological examination of the full sky and certain excerpts such as the Galactic disc and the Magellanic clouds, we further examined the statistical properties of our results by investigating the power spectrum of the resulting map and cross-correlations of the map and itscomponents with other ISM tracers. We found an additional motivation to the attempt initiated by HE20 to introduce additional tracers for more holistic Galactic sky inferences. Our results can be used as a foreground-reduction template for extra-Galactic Faraday data, however, we should note that some extra-Galactic residuals might still be present in the posterior mean maps. An ideal foreground-reduction pipeline should hence mirror the analysis of Oppermann et al. (2015), that is, by performing a joint analysis of the extra-Galactic, systematic and Galactic components to the variance. If such a procedure is deemed too expensive to implement, at least some smoothing should be applied to the maps, to lessen the effect of potential extra-Galactic residuals, especially athigher latitudes. Our analysis has furthermore demonstrated that future Faraday rotation sky inferences might strongly benefit from future surveys that remedy certain shortcomings of the existing data sets such as

  • the paucity of data with regard to parts of the Galactic disk, as well as the regions above and below the disk and the southern celestial sky (although the situation there has improved considerably in recent years, mainly due to the results of Schnitzeler et al. (2019).

  • the systematic biases introduced by several surveys due to their limited Faraday depth range, which might mean that several strong Faraday rotating regions have remained undetected.

These issues indicate a strong potential for the upcoming polarimetric surveys of ASKAP, MeerKAT, LOFAR, MWA, VLASS, and SKA to improve our knowledge of the Galactic Faraday rotation sky, as they will provide a vast catalog of new Faraday data (Heald et al. 2020). This information will then serve a pivotal role in constraining the Galactic magnetic field as well as providing an important input for upcoming reconstructions of the magnetized interstellar medium.

thumbnail Fig. 12

Histogram of sky pixels illustrating the correlation between the log amplitude field, ρ, and the logarithmic DM (panel a) and the logarithmic square root EM (panel b) skies, respectively. The former is calculated from a Galactic thermal electron model (Yao et al. 2017), while the latter is inferred by the Planck survey from extinction-free microwave data (Planck Collaboration X 2016).

Acknowledgment

The results in this publication have been derived using the NIFTy package (https://gitlab.mpcdf.mpg.de/ift/NIFTy, The NIFTy5 team, in prep.). Some of the images were produced using the CMasher library (https://github.com/1313e/CMasher, van der Velden 2020). We would like to thank Jennifer West and the CIRADA team providing the cutout server. S.H. would like to thank Philipp Frank, Philipp Arras, Martin Reinecke, Jakob Knollmüller, Reimar Leike, and the rest of the IFT team for valuable discussions and their continuous work on the NIFTy package. The noise estimation template in Fig. 8 was produced using the pygedm package (https://pypi.org/project/pygedm/, Yao et al. 2017). We thank Rainer Beck for his careful reading and valuable comments as the Max Planck Institute for Radio Astronomy (MPIfR) internal referee. S.H. and M.H. acknowledge funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 772663). The Australia Telescope is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO. J.M.S. acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), 2019-04848. J.B. acknowledges the support of the Natural Sciences and Engineering Research Council of Canada and the National Research Council of Canada. Basic research in radio astronomy at the US Naval Research Laboratory is supported by 6.1 Base funding. C.J.R. acknowledges financial support from the ERC Starting Grant “DRANOEL”, number 714245. C.L.H.H. acknowledges the support of the NAOJ Fellowship and JSPS KAKENHI grants 18K13586 and 20K14527. The Paul G. Allen Family Foundation, the US Naval Observatory and the US National Science Foundation grants AST-0321309, AST-0540690 and AST-0838268 have contributed to the ATA project. This paper has made use of the S-PASS/ATCA RM catalog Schnitzeler et al. (2019). The Dunlap Institute is funded through an endowment established by the David Dunlap family and the University of Toronto. C.V.E. and B.M.G. acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC) through grant RGPIN-2015-05948, of the Canada Research Chairs program, and of the Canada Foundation for Innovation 2017 Innovation Fund through Project 35999. LOFAR (van Haarlem et al. 2013) is the Low Frequency Array designed and constructed by ASTRON. It has observing, data processing, and data storage facilities in several countries, which are owned by various parties (each with their own funding sources), and which are collectively operated by the ILT foundation under a joint scientific policy. The ILT resources have benefited from the following recent major funding sources: CNRS-INSU, Observatoire de Paris and Université d’Orléans, France; BMBF, MIWF-NRW, MPG, Germany; Science Foundation Ireland (SFI), Department of Business, Enterprise and Innovation (DBEI), Ireland; NWO, The Netherlands; The Science and Technology Facilities Council, UK; Ministry of Science and Higher Education, Poland; The Istituto Nazionale di Astrofisica (INAF), Italy. This research made use of the Dutch national e-infrastructure with support of the SURF Cooperative (e-infra 180169) and the LOFAR e-infra group. The Jülich LOFAR Long Term Archive and the German LOFAR network are both coordinated and operated by the Jülich Supercomputing Centre (JSC), and computing resources on the supercomputer JUWELS at JSC were provided by the Gauss Centre for Supercomputing e.V. (grant CHTB00) through the John von Neumann Institute for Computing (NIC). This research made use of the University of Hertfordshire high-performance computing facility and the LOFAR-UK computing facility located at the University of Hertfordshire and supported by STFC [ST/P000096/1], and of the Italian LOFAR IT computing infrastructure supported and operated by INAF, and by the Physics Department of Turin university (under an agreement with Consorzio Interuniversitario per la Fisica Spaziale) at the C3S Supercomputing Centre, Italy.

References

  1. Akahori, T., & Ryu, D. 2010, ApJ, 723, 476 [NASA ADS] [CrossRef] [Google Scholar]
  2. Anderson, C. S., Gaensler, B. M., Feain, I. J., & Franzen, T. M. O. 2015, ApJ, 815, 49 [Google Scholar]
  3. Arras, P., Frank, P., Haim, P., et al. 2020, ArXiv e-prints [arXiv:2002.05218] [Google Scholar]
  4. Battye, R. A., Browne, I. W. A., Peel, M. W., Jackson, N. J., & Dickinson, C. 2011, MNRAS, 413, 132 [NASA ADS] [CrossRef] [Google Scholar]
  5. Beck, R. 2015, A&ARv, 24, 4 [Google Scholar]
  6. Bell, M. R., & Enßlin, T. A. 2012, A&A, 540, A80 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  7. Betti, S. K., Hill, A. S., Mao, S. A., et al. 2019, ApJ, 871, 215 [NASA ADS] [CrossRef] [Google Scholar]
  8. Brentjens, M. A., & de Bruyn A. G. 2005, A&A, 441, 1217 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  9. Broten, N. W., MacLeod, J. M., & Vallee, J. P. 1988, Ap&SS, 141, 303 [CrossRef] [Google Scholar]
  10. Brown, J. C., Taylor, A. R., & Jackel, B. J. 2003, ApJS, 145, 213 [NASA ADS] [CrossRef] [Google Scholar]
  11. Brown, J. C., Haverkorn, M., Gaensler, B. M., et al. 2007, ApJ, 663, 258 [NASA ADS] [CrossRef] [Google Scholar]
  12. Burn, B. J. 1966, MNRAS, 133, 67 [Google Scholar]
  13. Clarke, T. E., Kronberg, P. P., & Böhringer, H. 2001, ApJ, 547, L111 [NASA ADS] [CrossRef] [Google Scholar]
  14. Clegg, A. W., Cordes, J. M., Simonetti, J. M., & Kulkarni, S. R. 1992, ApJ, 386, 143 [CrossRef] [Google Scholar]
  15. Cooper, B. F. C., & Price, R. M. 1962, Nature, 195, 1084 [NASA ADS] [CrossRef] [Google Scholar]
  16. Costa, A. H., & Spangler, S. R. 2018, ApJ, 865, 65 [NASA ADS] [CrossRef] [Google Scholar]
  17. Costa, A. H., Spangler, S. R., Sink, J. R., Brown, S., & Mao, S. A. 2016, ApJ, 821, 92 [NASA ADS] [CrossRef] [Google Scholar]
  18. Dineen, P., & Coles, P. 2005, MNRAS, 362, 403 [NASA ADS] [CrossRef] [Google Scholar]
  19. Draine, B. T. 2010, Physics of the Interstellar and Intergalactic Medium, Princeton Series in Astrophysics (Princeton, NJ: Princeton University Press) [CrossRef] [Google Scholar]
  20. Durrer, R., & Neronov, A. 2013, A&ARv, 21, 62 [NASA ADS] [CrossRef] [Google Scholar]
  21. Enßlin, T. A. 2019, Annal. Phys., 531, 1800127 [CrossRef] [Google Scholar]
  22. Farnsworth, D., Rudnick, L., & Brown, S. 2011, AJ, 141, 191 [NASA ADS] [CrossRef] [Google Scholar]
  23. Feain, I. J., Ekers, R. D., Murphy, T., et al. 2009, ApJ, 707, 114 [Google Scholar]
  24. Finkbeiner, D. P. 2003, ApJS, 146, 407 [Google Scholar]
  25. Frick, P., Stepanov, R., Shukurov, A., & Sokoloff, D. 2001, MNRAS, 325, 649 [NASA ADS] [CrossRef] [Google Scholar]
  26. Gaensler, B. M., Dickey, J. M., McClure-Griffiths, N. M., et al. 2001, ApJ, 549, 959 [Google Scholar]
  27. Gaensler, B. M., Madsen, G. J., Chatterjee, S., & Mao, S. A. 2008, PASA, 25, 184 [NASA ADS] [CrossRef] [Google Scholar]
  28. Gardner, F. F., & Davies, R. D. 1966, Aust. J. Phys., 19, 129 [NASA ADS] [Google Scholar]
  29. Gaustad, J. E., McCullough, P. R., Rosing, W., & Van Buren D. 2001, PASP, 113, 1326 [NASA ADS] [CrossRef] [Google Scholar]
  30. Harvey-Smith, L., Madsen, G. J., & Gaensler, B. M. 2011, ApJ, 736, 83 [CrossRef] [Google Scholar]
  31. Haverkorn, M. 2015, IAU Symp., 407, 483 [NASA ADS] [Google Scholar]
  32. Heald, G., Braun, R., & Edmonds, R. 2009, A&A, 503, 409 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  33. Heald, G., Mao, S., Vacca, V., et al. 2020, Galaxies, 8, 53 [Google Scholar]
  34. Hou, L. G., Han, J. L., & Shi, W. B. 2009, A&A, 499, 473 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  35. Hutschenreuter, S., & Enßlin, T. A. 2020, A&A, 633, A150 [EDP Sciences] [Google Scholar]
  36. Johnston-Hollitt, M., Hollitt, C. P., & Ekers, R. D. 2004, in The Magnetized Interstellar Medium, eds. B. Uyaniker, W. Reich, & R. Wielebinski, 13 [Google Scholar]
  37. Kaczmarek, J. F., Purcell, C. R., Gaensler, B. M., McClure-Griffiths, N. M., & Stevens, J. 2017, MNRAS, 467, 1776 [NASA ADS] [Google Scholar]
  38. Kim, K. S., Lilly, S. J., Miniati, F., et al. 2016, ApJ, 829, 133 [NASA ADS] [CrossRef] [Google Scholar]
  39. Klein, U., Mack, K. H., Gregorini, L., & Vigotti, M. 2003, A&A, 406, 579 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  40. Knollmüller, J., & Enßlin, T. A. 2019, ArXiv e-prints [arXiv:1901.11033] [Google Scholar]
  41. Law, C. J., Gaensler, B. M., Bower, G. C., et al. 2011, ApJ, 728, 57 [NASA ADS] [CrossRef] [Google Scholar]
  42. Ma, Y. K., Mao, S. A., Stil, J., et al. 2019, MNRAS, 487, 3432 [CrossRef] [Google Scholar]
  43. Ma, Y. K., Mao, S. A., Ordog, A., & Brown, J. C. 2020, MNRAS, 497, 3097 [NASA ADS] [CrossRef] [Google Scholar]
  44. Mao, S. A., Gaensler, B. M., Stanimirović, S., et al. 2008, ApJ, 688, 1029 [NASA ADS] [CrossRef] [Google Scholar]
  45. Mao, S. A., Gaensler, B. M., Haverkorn, M., et al. 2010, ApJ, 714, 1170 [NASA ADS] [CrossRef] [Google Scholar]
  46. Mao, S. A., McClure-Griffiths, N. M., Gaensler, B. M., et al. 2012a, ApJ, 755, 21 [NASA ADS] [CrossRef] [Google Scholar]
  47. Mao, S. A., McClure-Griffiths, N. M., Gaensler, B. M., et al. 2012b, ApJ, 759, 25 [NASA ADS] [CrossRef] [Google Scholar]
  48. Minter, A. H., & Spangler, S. R. 1996, ApJ, 458, 194 [NASA ADS] [CrossRef] [Google Scholar]
  49. Oppermann, N., Junklewitz, H., Robbers, G., et al. 2012, A&A, 542, A93 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  50. Oppermann, N., Junklewitz, H., Greiner, M., et al. 2015, A&A, 575, A118 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  51. Oren, A. L., & Wolfe, A. M. 1995, ApJ, 445, 624 [NASA ADS] [CrossRef] [Google Scholar]
  52. O’Sullivan, S. P., Purcell, C. R., Anderson, C. S., et al. 2017, MNRAS, 469, 4034 [CrossRef] [Google Scholar]
  53. Passot, T., & Vázquez-Semadeni, E. 2003, A&A, 398, 845 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  54. Planck Collaboration X. 2016, A&A, 594, A10 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  55. Pshirkov, M. S., Tinyakov, P. G., Kronberg, P. P., & Newton-McGee, K. J. 2011, ApJ, 738, 192 [Google Scholar]
  56. Reissl, S., Stil, J. M., Chen, E., et al. 2020, A&A, 642, A201 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  57. Riseley, C. J., Lenc, E., Van Eck, C. L., et al. 2018, PASA, 35, 43 [Google Scholar]
  58. Riseley, C. J., Galvin, T. J., Sobey, C., et al. 2020, PASA, 37, e029 [Google Scholar]
  59. Rossetti, A., Dallacasa, D., Fanti, C., Fanti, R., & Mack, K. H. 2008, A&A, 487, 865 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  60. Roy, S., Rao, A. P., & Subrahmanyan, R. 2005, MNRAS, 360, 1305 [NASA ADS] [CrossRef] [Google Scholar]
  61. Schnitzeler, D. H. F. M., Carretti, E., Wieringa, M. H., et al. 2019, MNRAS, 485, 1293 [NASA ADS] [CrossRef] [Google Scholar]
  62. Shanahan, R., Lemmer, S. J., Stil, J. M., et al. 2019, ApJ, 887, L7 [NASA ADS] [CrossRef] [Google Scholar]
  63. Short, M. B., Higdon, D. M., & Kronberg, Philipp, P. 2007, Bayesian Anal., 2, 665 [NASA ADS] [Google Scholar]
  64. Simard-Normandin, M., Kronberg, P. P., & Button, S. 1981, ApJS, 45, 97 [NASA ADS] [CrossRef] [Google Scholar]
  65. Sobey, C., Bilous, A. V., Grießmeier, J. M., et al. 2019, MNRAS, 484, 3646 [Google Scholar]
  66. Stil, J. M., Taylor, A. R., & Sunstrum, C. 2011, ApJ, 726, 4 [NASA ADS] [CrossRef] [Google Scholar]
  67. Subramanian, K. 2016, Rep. Prog. Phys., 79, 076901 [NASA ADS] [CrossRef] [Google Scholar]
  68. Tabara, H., & Inoue, M. 1980, A&AS, 39, 379 [Google Scholar]
  69. Taylor, A. R., Stil, J. M., & Sunstrum, C. 2009, ApJ, 702, 1230 [Google Scholar]
  70. Vallée, J. P. 2017, Astron. Rev., 13, 113 [Google Scholar]
  71. van der Velden, E. 2020, J. Open Source Softw., 5, 2004 [Google Scholar]
  72. Van Eck C. 2018, Galaxies, 6, 112 [NASA ADS] [CrossRef] [Google Scholar]
  73. Van Eck, C. L., Brown, J. C., Stil, J. M., et al. 2011, ApJ, 728, 97 [Google Scholar]
  74. Van Eck, C. L., Haverkorn, M., Alves, M. I. R., et al. 2018, A&A, 613, A58 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  75. Van Eck, C. L., Brown, J. C., Ordog, A., et al. 2021, ApJS, 253, 48 [NASA ADS] [CrossRef] [Google Scholar]
  76. van Haarlem, M. P., Wise, M. W., Gunst, A. W., et al. 2013, A&A, 556, A2 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  77. Vernstrom, T., Gaensler, B. M., Vacca, V., et al. 2018, MNRAS, 475, 1736 [NASA ADS] [CrossRef] [Google Scholar]
  78. Wrobel, J. M. 1993, AJ, 106, 444 [NASA ADS] [CrossRef] [Google Scholar]
  79. Wu, Q., Kim, J., & Ryu, D. 2015, New Astron., 34, 21 [NASA ADS] [CrossRef] [Google Scholar]
  80. Xu, J., & Han, J.-L. 2014, Res. Astron. Astrophys., 14, 942 [Google Scholar]
  81. Xu, Y., Kronberg, P. P., Habib, S., & Dufton, Q. W. 2006, ApJ, 637, 19 [NASA ADS] [CrossRef] [Google Scholar]
  82. Yao, J. M., Manchester, R. N., & Wang, N. 2017, ApJ, 835, 29 [NASA ADS] [CrossRef] [Google Scholar]
4

This master catalog can be found online at https://github.com/Cameron-Van-Eck/RMTable; we used used version 0.1.8 of the catalog in this paper.

All Figures

thumbnail Fig. 1

Sky projections of the data set used in this work, the associated observational errors and the source density. Panel a shows the Faraday data, panel b the observed error bars. Data points falling into the same pixel have been averaged. These plot has been made with a four-times decreased resolution (corresponding to an pixel area of 0.21 deg2 or 7.56 × 102 arcmin2) compared to that of the inference in order to enable better visualization. Panel c shows the source density of the data set used in this work. The pixels in this map have an area of about 3.36 deg2 or 1.2 × 104 arcmin2, again for visualization purposes. These, and all subsequent maps, are presented in Galactic coordinates centered at .
In the text
thumbnail Fig. 2

Inference results for the posterior mean (panel a) and uncertainties (panel b) of the Galactic Faraday rotation sky using the updated data catalog. The color scale is saturated at ± 250 rad m−2 for the mean and at 80 rad m−2 for the uncertainties to highlight mid latitude features.
In the text
thumbnail Fig. 3

Inference results for the posterior mean (panel a) and uncertainties (panel b) of the Galactic Faraday rotation sky using the updated data catalog. The sky maps are the same as in Fig. 2, but the color scale is saturated at ± 1500 rad m−2 in the mean and 300 rad m−2 in the uncertainty to highlight the disk features of the Galactic Faraday rotation sky.
In the text
thumbnail Fig. 4

Comparison to previous results. Panel a shows the mean of the Galactic Faraday rotation sky as inferred by HE20, using the same saturation scale as in Fig. 2a. Panel b shows the difference between Figs. 2a and 4a.
In the text
thumbnail Fig. 5

Posterior means of the components defined in Eq. (7). Panel a shows the amplitude field eρ and panel b shows the sign field χ.
In the text
thumbnail Fig. 6

Slice in longitude (l ∈ (270°, 90°)) through the inner part of the Galactic disc from the Galactic Faraday rotation sky. The colored strips indicate equal latitude strips of the inferred Faraday sky within b ∈ (−1°, 1°). The plot also contains the data points falling in the same region indicated by grey crosses. Data points with ϕ > 3000 rad m−2 are indicated with black triangles at the upper end of the plot. The approximate locations of several spiral arm tangents (Hou et al. 2009; Vallée 2017) are indicated as grey lines, specifically these are the Local (Loc), Sagittarius (Sgr), Scrutum (Sct), and Norma (Nor) arms. We note that these positions are inferred from different tracers such as HII regions and hence do not necessarily coincide exactly with the tangent points traced by a potential excess in Faraday rotation. The region towards l ≈ 45° is also partly shown in Shanahan et al. (2019), where the strong excess in Faraday rotation in direction to the tangent of the Sagittarius arm was first noted.
In the text
thumbnail Fig. 7

Histogram of absolute values of the Galactic latitude positions of all data points used in this work.
In the text
thumbnail Fig. 8

Template for the noise estimation parameter, αϕ. The noise model is introduced in Eq. (5), the template is based on the Galactic electron model derived by Yao et al. (2017).
In the text
thumbnail Fig. 9

Magellanic Clouds in our results and as seen with different observables, respectively: panels a and b show the Faraday rotation (with a 20 rad m−2 offset) and the underlying amplitude field as inferred in this work. Panels c and d show the clouds in H α emission (Finkbeiner 2003; Gaustad et al. 2001), and in emission measure (EM), as obtained by the Planck satellite (Planck Collaboration X 2016), respectively. Panel c indicates the locations of the clouds.
In the text
thumbnail Fig. 10

Power spectrum for the Faraday rotation sky derived in this work, compared with results from HE20 and Oppermann et al. (2012). Red dashed line indicates a parametric fit to the results of this work using Eq. (8). The uncertainties of the spectrum derived in this work are indicated by light-blue lines, which are only slightly offset from the dark-blue lines showing the mean.
In the text
thumbnail Fig. 11

2D histogram of logarithmic noise weighted residuals and absolute Galactic latitude.
In the text
thumbnail Fig. 12

Histogram of sky pixels illustrating the correlation between the log amplitude field, ρ, and the logarithmic DM (panel a) and the logarithmic square root EM (panel b) skies, respectively. The former is calculated from a Galactic thermal electron model (Yao et al. 2017), while the latter is inferred by the Planck survey from extinction-free microwave data (Planck Collaboration X 2016).
In the text

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.