Magnetic ﬁelds and UHECR propagation

. I review the main observational tools used to detect and measure magnetic ﬁelds in the interstellar medium of our Galaxy (considering both the Galactic disk and the Galactic halo), in the interstellar medium of external galaxies, and in the extragalactic medium. In each case, I present a summary of the most important results obtained with the di ﬀ erent tools, trying to lay the emphasis on the magnetic ﬁeld properties that are relevant to the propagation of ultra-high–energy cosmic rays (UHECRs)


Introduction
The existence of interstellar magnetic fields was first predicted as a means to confine and accelerate Galactic cosmic rays. Back in 1937, Hannes Alfvén 1 correctly pointed out that the confinement of cosmic rays in our Galaxy implied "the existence of a magnetic field in interstellar space". Twelve years later, Enrico Fermi [1] went one step further and argued that "cosmic rays are originated and accelerated primarily in the interstellar space of the Galaxy by collisions against moving magnetic fields." He also added, with surprising accuracy for the time, that "the magnetic field in the dilute matter is of the order of magnitude of 5 × 10 −6 gauss, while its intensity is probably greater in the heavier clouds." Thus, it appears that the history of interstellar magnetic fields is intimately linked to the history of cosmic rays.
Since cosmic rays are electrically charged particles, their trajectories are deflected by the interstellar magnetic field. This deflection is measured by the Larmor radius, where E is the energy of the particle, q its electric charge, B the magnetic field strength, and α the particle pitch angle (angle between the particle velocity and the magnetic field). For a 1 GeV (10 9 eV) cosmic ray, r g (0.2 AU) B 1 μG which is considerably smaller than both the dominant scale of the interstellar magnetic field, L B , and the scale height of the Galactic disk, H G . As a result, the cosmic ray has a mostly helical motion along magnetic field lines, with negligible drift, though with possible diffusion due to smallscale magnetic fields and collisions.
In contrast, for a 1 EeV (10 18 eV) cosmic ray, which is roughly comparable to both L B and H G . As a result, the motion of the cosmic ray is moderately deflected by the interstellar magnetic field, such that its trajectory is neither straight nor helical. Throughout this paper, the magnetic field vector is denoted by B, its component in the plane of the sky (PoS) by B ⊥ , and its component along the line of sight (LoS) by B . Furthermore, Galactic longitude and latitude are denoted by l and b, respectively.
In Sect. 2, I review the main observational methods employed to detect and measure interstellar magnetic fields in our own Galaxy, and I summarize what each of these methods has taught us about their typical strength, their direction/orientation, their spatial distribution, and their overall topology. In brief, the linear polarization of starlight and of dust thermal emission yields the orientation of B ⊥ in the general, dusty interstellar medium (ISM) (Sect. 2.1). Synchrotron emission, in combination with data or assumptions on the relativistic-electron density, is a tracer of B ⊥ in the general, cosmic-ray filled ISM (Sect. 2.2). Faraday rotation measures, in conjunction with the observed or modeled distribution of thermal electrons, lead to B in ionized regions (Sect. 2.3). Exploiting the Faraday rotation of the Galactic diffuse synchrotron emission makes it possible to perform Faraday tomography (Sect. 2.4). Zeeman splitting [e.g., 2] and the Goldreich-Kylafis effect [3,4] also offer important diagnostic tools of interstellar magnetic fields, but since they are not directly relevant to cosmic-ray propagation, I do not discuss them in this paper.
In Sect. 3, I present the main observational results obtained for interstellar magnetic fields in external galaxies (Sect. 3.1) and for extragalactic magnetic fields (Sect. 3.2).

Dust polarization
Interstellar dust grains generally have irregular, elongated shapes, which, in a directional stellar radiation field, cause them to feel radiative torques. These torques have two important effects [see, e.g., [5][6][7]. First, they spin up the grains to suprathermal rotation about their short axes. Second, they gradually bring the grain spin axes into alignment with the local interstellar magnetic field. As a result, dust grains tend to line up with their long axes perpendicular to the local magnetic field.
The magnetically aligned dust grains collectively act as a polarizing filter for starlight. Since they preferentially scatter and absorb the starlight component that is polarized parallel to their long axes (as seen in the PoS), the starlight that passes through is linearly polarized parallel to B ⊥ . In consequence, the measured polarization orientation of starlight directly gives the orientation of B ⊥ .
In addition to polarizing starlight, the magnetically aligned dust grains also emit infrared/submm thermal radiation in a dichroic manner. Since the emissivity is strongest for the radiation component that is polarized parallel to the grains' long axes (as seen in the PoS) [8], dust thermal emission is linearly polarized perpendicular to B ⊥ . Thus, the measured polarization orientation of dust thermal emission, rotated by 90 • , corresponds to the orientation of B ⊥ .
If B varies along the LoS and/or across the observed sky area, polarization data, from either starlight or dust thermal emission, smoothed in the PoS, provide the orientation of the PoS component of the ordered magnetic field, B ord . For future reference, we note that the ordered magnetic field, B ord , discussed in Sects. 2.1 and 2.2, differs from the regular magnetic field, B reg , discussed in Sect. 2.3, in the sense that B ord has a given orientation, but not necessarily a given direction, whereas B reg has both a given orientation and a given direction 2 .
Polarization data not only give the orientation of B ⊥ , but they also make it possible to estimate, under certain conditions, the inclination of B to the PoS [see, e.g., 9, and references therein]. This is because the polarization fraction, i.e., the ratio of polarized intensity to total intensity, varies as cos 2 γ B , where γ B is the inclination angle of B to the PoS. In particular, the signal has maximum polarization when B lies in the PoS (γ B = 0), while the signal is completely unpolarized when B lies along the LoS 2 The total magnetic field, B, is composed of a regular field, B reg , and a fluctuating field, B fluc : B = B reg + B fluc . The fluctuating field, in turn, has an isotropic component, B fluc,iso , and an anisotropic (or directional) component, B fluc,dir : B fluc = B fluc,iso + B fluc,dir . The ordered field, B ord , is composed of the regular field and the anisotropic fluctuating field: B ord = B reg + B fluc,dir . Thus, the total magnetic field can also be regarded as the superposition of the ordered field and the isotropic fluctuating field: The difficulty here is that the polarization fraction depends not only on γ B , but also on the optical properties of dust grains and on their alignment efficiency, and it is generally not straightforward to isolate the contribution from γ B .
Starlight polarimetry of a large number of stars within a few kpc of the Sun shows that B ord in the nearby Galactic disk is horizontal, i.e., parallel to the Galactic plane, and nearly azimuthal [10]. In the Galactic vicinity of the Sun, B ord is found to be oriented along the axis (l, b) (83 • , 0 • ) 3 [11]. The horizontal orientation of B ord in the nearby Galactic disk appears clearly in the all-sky map of starlight polarization from the compilation by [12] (see Figure 1). It also emerges from this map that B does not remain horizontal at high Galactic latitudes. Most strikingly, B ⊥ appears to follow approximately the shape of the North Polar Spur (NPS), which extends from the Galactic plane at l ≈ +20 • nearly all the way up to the north Galactic pole. More detailed polarization maps of the north and south Galactic polar regions reveal a significant asymmetry between both hemispheres, probably due to the Local Bubble and other local features [13]. Starlight polarization measurements, combined with stellar distances (e.g., from Gaia), open the way to probe the orientation of B ⊥ in 3D. The optical polarization survey PASIPHAE is expected to soon offer a large enough data set to perform such a tomographic analysis in a meaningful way [14].
Polarization measurements of the dust thermal emission provide a more complete and more detailed view of the orientation of B ⊥ across the sky, though without any information on its LoS variations. The all-sky 353 GHz polarization map obtained with the Planck satellite [15] (see Figure 2) is generally consistent with the starlight polarization map displayed in Figure 1. In the Galactic disk, B ord is again found to be horizontal, and this appears to 3 Faraday rotation studies, which give the sign of B , indicate that B ord actually points toward (l, b) (83 remain true out to large distances from the Sun. At high Galactic latitudes, the distorsion of B ⊥ toward the NPS is similar to that observed in the optical.

Synchrotron emission
Synchrotron emission is produced by relativistic electrons gyrating about magnetic field lines. The synchrotron emissivity at frequency ν due to a power-law energy spectrum of relativistic electrons, f (E) = K e E −γ , is given by where fc(γ) is a known function of γ and B ⊥ is the strength of B ⊥ [16]. The synchrotron total intensity is obtained by integrating the synchrotron emissivity along the LoS: Low-frequency radio maps of the Galactic synchrotron emission can be used to model the spatial distribution of the interstellar magnetic field, from the large Galactic scales down to the smallest scales resolved by radio telescopes. This modeling requires knowing the relativisticelectron spectrum, which can be derived either from cosmic-ray propagation models or from gamma-ray observations. Alternatively, one sometimes resorts to the double assumption that (1) relativistic electrons represent a fixed fraction of the cosmic-ray population and (2) cosmic rays and magnetic fields are in (energy or pressure) equipartition. While the second assumption can find some rough justification at large scales, 4 there is no guarantee that it holds at small scales. Nevertheless, direct measurements of the interstellar magnetic field [18] and of the Galactic cosmic-ray ion and electron spectra [19] by the Voyager spacecraft indicate that, in the very local ISM, magnetic fields and cosmic rays are indeed close to (pressure) equipartition, with a total magnetic field strength B ≈ 5 μG. 4 The argument usually put forward to justify the equipartition assumption is that energy equipartition corresponds almost exactly to the condition that the total (cosmic-ray + magnetic) energy is minimum [17].
An important property of synchrotron emission is that it is linearly polarized perpendicular to B ⊥ , so that information can also be gained on the orientation of B ⊥ . If the observing frequency happens to be low enough to be affected by Faraday rotation (see Sect. 2.3), the received polarized signal must somehow be "de-rotated" in order to retrieve the true orientation of B ⊥ . In addition, if B has a fluctuating component, the contributions from isotropic magnetic fluctuations to the polarized intensity cancel out, leaving only the contribution from the ordered magnetic field, B ord = B reg + B fluc,dir (see footnote 2). Thus, while the synchrotron total intensity yields the strength of the total magnetic field, the synchrotron polarized intensity yields the strength and the orientation of the ordered magnetic field (both in the PoS). In the Galactic vicinity of the Sun, the ratio of ordered to total magnetic field strength turns out to be B ord B ≈ 0.6 [20]. Together with B ≈ 5 μG, this ratio implies B ord ≈ 3 μG.
The reference all-sky map of the Galactic synchrotron emission remains the all-sky 408 MHz radio continuum emission map of [21] (displayed in Figure 3). Based on this map, [22] constructed an axisymmetric model of the spatial distribution of the Galactic synchrotron emissivity. When combined with the equipartition assumption, this model implies that the total magnetic field strength has a radial scale length 12 kpc and a vertical scale height 4.5 kpc near the horizontal position of the Sun [23]. Synchrotron emission at 408 MHz suffers strong depolarization by differential Faraday rotation along the LoS. As a result, the polarized intensity of the 408 MHz emission is very weak and only representative of the nearby ISM. To detect synchrotron emission in polarization from deeper in the Galaxy, one must turn to higher frequencies. Figure 4 shows an all-sky map of the polarized intensity measured by WMAP at 23 GHz -a frequency little affected by Faraday rotation. The two features that clearly stand out are the strongly polarized NPS in the middle and Fan region on the left. The orientation of B ⊥ inferred from synchrotron polarization is in broad agreement with the orientation inferred from dust polarization (see Figures

Faraday rotation
In ionized regions of the ISM, the interstellar magnetic field can be probed with Faraday rotation measures of Galactic pulsars and extragalactic sources of linearly polarized radio waves [24].
Faraday rotation of a linearly polarized radio wave occurs when the wave propagates through a magneto-ionized medium. This rotation results from the interaction of the wave with the thermal electrons, which systematically gyrate in a right-handed sense about magnetic field lines. The angle by which the orientation of polarization rotates is given by where λ is the observing wavelength and is the so-called rotation measure, with C a numerical constant, n e the thermal-electron density, B the LoS component of the magnetic field, and L the path length from the source to the observer. In practice, the rotation measure of a given radio source can be determined by measuring the polarization orientation of the incoming radiation at at least two different wavelengths. Rotation measures have now been obtained for about 1 200 Galactic pulsars and 45 000 extragalactic radio point sources. The big advantage of Galactic pulsars is that one can measure, in addition to their rotation measures, their dispersion measures, and their distances, L (with some uncertainty). The ratio of RM to DM directly yields the n e -weighted average value of B between the considered pulsar and the observer. By combining the average values of B toward pulsars with their measured distances, one can in principle map out the large-scale 3D distribution of B . The big advantage of extragalactic radio point sources is that they are much more numerous than pulsars, such that they give access to finer details in the magnetic field distribution. The fact that they lie beyond the Galaxy is both an asset and a drawback, in the sense that their rotation measures also probe the outskirts of the Galaxy, beyond the pulsar region, but they are contaminated by contributions from the host galaxy and from the intervening intergalactic medium. Another limitation is that extragalactic sources have no dispersion measures, so their rotation measures must be complemented with a model for the spatial distribution of thermal electrons. Rotation-measure studies have provided invaluable information on the strength, direction, and spatial configuration of the interstellar magnetic field in ionized regions. Low-latitude radio sources (both Galactic pulsars and extragalactic point sources) have been used to probe the Galactic disk (see Figure 5), while radio sources across the entire sky have been used to probe the Galactic halo (see Figure 6 for extragalactic point sources and Figure 7 for Galactic pulsars).  [25]. Positive (negative) RMs, wich correspond to a magnetic field pointing on average toward (away from) the observer, are plotted in red (blue). The symbol size is proportional to |RM| 0.5 . The background yellow pattern is an artist's impression of the Galactic structure.
The regular magnetic field, B reg , has a strength B reg 1.5 μG in the Galactic vicinity of the Sun, compared to B fluct ∼ 5 μG for the fluctuating magnetic field [29]. B reg increases toward the Galactic center, to 3 μG at Galactocentric radius r = 3 kpc [30], i.e., with an exponential scale length 7.2 kpc. Moreover, B reg decreases away from the Galactic midplane, with an exponential scale height estimated at ≈ 2 kpc, on average over Galactic quadrants Q1 and Q2, above and below the midplane [27].
In the Galactic disk, B reg is nearly horizontal and generally dominated by its azimuthal component. In the Galactic vicinity of the Sun, B reg points toward (l, b) (82 • , 0 • ) [31], in very good agreement with the orientation of B ord inferred from starlight polarimetry (see Sect. 2.1).    9)) reconstructed from the RMs of extragalactic sources [28]. Positive (negative) RMs are plotted in red (blue). B reg reverses direction at least a couple of times with decreasing Galactocentric radius, but the exact number and radial locations of the field reversals are still controversial. These field reversals have often been interpreted as evidence that B reg is bisymmetric (azimuthal wavenumber m = 1), while an axisymmetric (m = 0) field would be expected from dynamo theory. In reality, [32] showed that neither the axisymmetric nor the bisymmetric picture is consistent with the existing pulsar rotation measures, and they concluded that B reg must have a more complex pattern. In general, B reg is described as a spiral magnetic field with a small pitch angle. A possible model of B reg in the Galactic disk, derived by [33], is sketched in Figure 8.
In the Galactic halo, B reg probably has a significant vertical component, (B reg ) z . Near the horizontal position of the Sun, [34] obtained (B reg ) z −0.14 μG above the Galactic midplane (z > 0) and (B reg ) z +0.30 μG below the midplane (z < 0), whereas [35] obtained (B reg ) z 0.00 μG toward the north Galactic pole and (B reg ) z +0.31 μG toward the south Galactic pole. In contrast to the situation prevailing in the Galactic disk, B reg shows no sign of reversal with decreasing Galactocentric radius. However, the horizontal component of B reg clearly reverses direction between the northern and southern Galactic hemispheres, which suggests that B reg is antisymmetric (odd symmetry) with respect to the midplane. [36] found that B reg is slightly more likely to be bisymmetric than axisymmetric. They also showed that B reg can be described as an upward/downward spiraling magnetic field (in the northern/southern hemisphere), formed by an azimuthal field plus an X-shape poloidal field (as observed in the halos of external spiral galaxies; see Sect. 3.1). A field line from a possible model of B reg in the Galactic halo, derived by [36], is plotted in Figure 9.

Faraday tomography
An important limitation of the observational methods described in Sects. 2.1-2.3 is that they provide only LoSintegrated quantities, with no details on how the integrants vary along the LoS. For instance, the synchrotron intensity (Eq. 5) measured in a given direction tells us only about the total amount of synchrotron emission produced along the entire LoS through the Galaxy, with no information on the local value of E ν (Eq. 4). Similarly, the rotation measure of a given radio source (Eq. 7) tells us only about the total amount of Faraday rotation incurred along the LoS between the source and the observer, with no information on the local value of n e B .
A powerful and promising approach to probe the 3D structure of the interstellar magnetic field is now being increasingly utilized. This approach is also based on Faraday rotation, but instead of considering the Faraday rotation of the linearly polarized radiation from a background radio source (as explained in Sect. 2.3), the idea is to exploit the Faraday rotation of the synchrotron radiation from the Galaxy itself (discussed in Sect. 2.2).
In the case of a background radio source, i.e., when the regions of synchrotron emission and Faraday rotation are spatially separated, the Faraday rotation angle, Δψ, varies linearly with λ 2 , and the rotation measure, RM, is defined as the slope of the linear relation between Δψ and λ 2 (see Eq. 6). Hence, RM is a purely observational quantity, which can be meaningfully measured only for a background radio source and which can then be related to the physical properties (n e and B ) of the foreground Faradayrotating medium through Eq. (7).
In contrast, when the radio source is the Galaxy itself, the regions of synchrotron emission and Faraday rotation are spatially mixed. In that case, Δψ no longer varies linearly with λ 2 and the very concept of rotation measure becomes meaningless. However, one may resort to the more general concept of Faraday depth, defined as where all symbols have the same meaning as in Eq. (7) and z is the LoS distance from the observer 5 [37,38]. Φ(z) has basically the same formal expression as RM (Eq. 7), but it differs from RM in the sense that it is a truly physical quantity, which can be defined at any point of the ISM, independent of any background radio source. Φ(z) simply corresponds to the LoS depth, z, measured in terms of Faraday rotation -in much the same way as optical depth corresponds to LoS depth measured in terms of opacity. When synchrotron emission and Faraday rotation are mixed along the LoS, the polarized intensity measured at a given wavelength λ, is the superposition of the polarized emission produced at every LoS distance z, i.e., at every Faraday depth Φ, and Faraday-rotated by an angle Δψ = Φ λ 2 (from Eq. (6) with RM replaced by Φ). Since the Faraday rotation angle, Δψ, varies with wavelength, the polarized intensities measured at different wavelengths correspond to different combinations of all the LoS contributions and, therefore, provide different pieces of information. Thus, the idea is to measure the polarized intensity at a large number of different wavelengths and to convert its variation with λ 2 into a variation with Φ. Mathematically, this can be done through a Fourier transform.
By applying this rotation measure synthesis to all the pixels of a given area in the sky, one obtains a so-called Faraday cube, i.e., a 3D map of the synchrotron polarized emission in Faraday space, (α, δ, Φ) or (l, b, Φ). An example is shown in Figure 10. In practice, Faraday tomography can be used to separate synchrotron-emitting regions located at different Faraday depths along the LoS and to estimate their respective polarized synchrotron intensities, which in turn can lead to the strength and the orientation of their B ⊥ (see Sect. 2.2). Faraday tomography can also be used to uncover intervening Faraday screens and to estimate their Faraday thicknesses, which in turn can lead to their B . The method is particularly interesting when the uncovered Faraday screens can be identified with known gaseous structures, because it then offers a new way of probing their magnetic fields.

Interstellar magnetic fields in external galaxies
Interstellar magnetic fields in external galaxies are detected and measured with the same tools as those employed for our own Galaxy, namely, synchrotron emission, Faraday rotation, and, more recently, dust polarized emission. Observations of external galaxies are complementary to observations of our Galaxy, because they directly provide a bird's eye view of their large-scale magnetic fields, whereas our position within our Galaxy makes it difficult to disentagle the contributions from the large-scale Galactic magnetic field and from small-scale nearby magnetic fluctuations.
Radio observations of external galaxies have systematically detected synchrotron emission from spiral, barred, flocculent (with disks, but no spiral arms), and irregular galaxies [see, e.g., 40, for a detailed review]. Measurements of the synchrotron total intensity, interpreted with the equipartition assumption (see Sect. 2.2), indicate that these galaxies host interstellar magnetic fields with total field strengths B ∼ a few μG. The total fields tend to be strongest in spiral arms and in bars, with B ∼ (20 − 30) μG, and in central starburst regions, with B ∼ (50 − 100) μG. Measurements of the synchrotron polarized intensity reveal the existence of ordered magnetic fields in spiral, barred, and flocculent galaxies. The ordered fields are generally strongest in interarm regions, with B ord ∼ (10 − 15) μG. In face-on galaxies, B ord describes a spiral pattern, with B ord approximately parallel to the gaseous spiral arms (when present). The prototype example, displayed in Figure 11, is the whirlpool galaxy, M 51. In edge-on galaxies, B ord appears to be horizontal in the disk and X-shaped in the halo. This is illustrated in Figure 12, with the galaxy NGC 891. Figure 11. Total intensity contours of the λ 6 cm radio continuum emission from the face-on spiral galaxy M 51 observed with the VLA and the Effelsberg 100 m radio telescope. The background is an optical image from the HST. The small bars show the polarization half-vectors rotated by 90 • to trace the orientation of B ⊥ , with no correction for Faraday rotation [41].
It is very likely that elliptical galaxies also possess μG interstellar magnetic fields. However, these fields are generally much more difficult (or even impossible) to detect through synchrotron emission, because of a lack of relativistic electrons in the absence of active star formation [43]. Nevertheless, one can hold the following theoretical reasoning: since elliptical galaxies have strong interstellar turbulence, but a very low rotation rate, they must be subject to a fluctuating dynamo -rather than the mean-field αω dynamo that operates in spiral galaxies -and this dynamo must produce purely fluctuating magnetic fields, i.e., magnetic fields without an ordered component [44,45].
As explained in Sect. 2.2, synchrotron emission is sensitive to the orientation, but not the direction, of the magnetic field. This is why synchrotron observations carry information on the ordered magnetic field, B ord , but not on the regular magnetic field, B reg . The only way to separate out the contribution from B reg is to resort to Faraday rota- tion measures. In the case of external galaxies, the rotation measures of interest are those of background radio sources or those of the galaxies themselves.
Large-scale patterns in the RM maps of external galaxies reveal the presence of regular magnetic fields. The azimuthal structure of B reg in galactic disks, inferred from the large-scale azimuthal variation of RM, displays a variety of behaviors: in some cases, B reg is dominated by one azimuthal (generally axisymmetric) mode; in other cases, a superposition of 2 or 3 azimuthal modes are needed to describe B reg [see, e.g., Table 2 in 40]. The vertical structure of B reg and its potential (even or odd) symmetry with respect to the midplane are more difficult to establish. Indications of even symmetry have been found for a handful of nearby galaxies [40].
The CHANG-ES (Continuum HAlos in Nearby Galaxies -an EVLA Survey) project to observe 35 nearby edgeon galaxies at 6 GHz and 1.6 GHz [46] has provided the most comprehensive data set to date on magnetic fields in galactic halos. The polarization maps of the observed galaxies confirm and generalize the earlier finding that B ord has an X-shape pattern in the halos of spiral galaxies [47]. In addition, the sensitivity and broad bandwidth of the observations have made it possible to perform Faraday tomography. The resulting RM maps unambiguously show that the ordered magnetic field, B ord , is partly (perhaps mostly) a regular field, B reg (see footnote 2), which extends over several kpc and has a typical scale 1 kpc [47].
Interstellar magnetic fields in external galaxies are now also being observed through the polarization of the far-infrared (FIR) dust thermal emission. For instance, the magnetic fields of the face-on galaxy M 51  [48]. For M 51, the FIR polarization map ( Figure 13) is in very good agreement with its synchrotron counterpart (Figure 11): here, too, the inferred B ord follows approximately the material spiral arms. The FIR polarization fraction is much lower in the FIR-bright central region, possibly as a result of turbulent depolarization (across the beam and along the LoS). For NGC 891, the FIR polarization map (Figure 14) is also consistent with its synchrotron counterpart (Figure 12), especially in the disk where the inferred B ord is again nearly horizontal. There is tentative evidence for a vertical B ord off the disk, but the FIR polarized emission from the halo is too weak to reveal a possible X-shape B ord . The FIR polarization fraction is very low in a few places, probably where one is looking down spiral arms and viewing the magnetic field almost head-on. New FIR polarimetric mapping observations of nearby galaxies, including M 51 [49], were recently carried out as part of the SALSA (Survey on extragALactic magnetiSm with SOFIA) Legacy Program. The first data release, for a set of 14 nearby (< 20 Mpc) galaxies, observed with SOFIA/HAWC+ from 53 μm to 214 μm, was presented by [50]. The results of SALSA are complementary to those of radio polarimetric observations. Both sets of results will eventually be combined to produce a comprehensive empirical picture of the kpc-scale structure and strength of magnetic fields in external galaxies.

Extragalactic magnetic fields
Magnetic fields have also been detected outside galaxiescertainly in the intergalactic medium of clusters of galaxies, probably in filaments of the cosmic web, and tentatively in cosmic voids. Intergalactic magnetic fields in clusters of galaxies are mostly detected through diffuse radio synchrotron emission from the intergalactic medium (IGM) and through Faraday rotation of background or embedded radio galaxies [see, e.g., [51] for a comprehensive review of early results and [52] for a review of more recent results]. A small fraction of the clusters (about 50 clusters according to [52]) display extended diffuse synchrotron emission, which shows no correlation with the individual galaxies, but appears to be associated with the IGM. It is likely that the other clusters also emit synchrotron radiation, but their surface brightnesses are probably too low to enable detection with present-day radio telescopes.
Clusters observed in radio synchrotron emission have led to a classification into radio halos, radio relics, and mini-halos according to the morphology and location of their radio emission. Radio halos are roundish structures extending over 1 Mpc in the centers of certain clusters undergoing violent merger events. Their measured synchrotron total intensities, together with the assumption that the intergalactic magnetic field is homogeneous and in equipartition with cosmic rays (see Sect. 2.2), lead to magnetic field strengths ∼ (0.1 − 1) μG. The non-detection of polarization in most cases indicates either beam depolarization in the absence of an ordered magnetic field or Faraday depolarization due to mixing of thermal and relativistic electrons (see Sect. 2.4). Radio relics are elongated structures with sizes 1 Mpc near the outskirts of certain clusters, where they are probably produced by shock compression during merger events. Their equipartition magnetic field strengths are typically ∼ (0.5 − 2) μG. In contrast to radio halos, they are strongly and coherently polarized, and the inferred magnetic field orientations are generally along their long axes. Mini-halos extend over 0.5 Mpc around dominant radio galaxies in the centers of relaxed, cooling-core clus- ters. Their equipartition magnetic field strengths can reach ∼ 10 μG.
To illustrate, Figure 15 shows an image of the radio halo in the galaxy cluster A 665, while Figure 16 shows an image of the pair of radio relics in the merging galaxy cluster ZwCl 2341.1+0000.  Rotation measures of background or embedded radio galaxies, combined with estimates of both the thermalelectron density in the IGM and the dominant scales of magnetic fluctuations, provide useful complementary information on intergalactic magnetic fields. The thermalelectron density is generally inferred from the measured X-ray surface brightnesses of clusters or taken from a generic model. The dominant magnetic fluctuation scales are estimated from the patchiness of the observed RM distributions. The resulting magnetic field strengths are ∼ (1 − 10) μG, with values as high as ∼ 30 μG in cooling cores.
At scales even larger than galaxy clusters, there have been detections of extended diffuse synchrotron emission from filaments of the cosmic web [55,56], indicating the likely existence of extracluster magnetic fields. [55] compared their observations to MHD simulations and found that their detected radio sources were similar to the brightest patches of diffuse synchrotron emission, which correspond to the densest and hottest portions of cosmic filaments, in the simulations. From this, they concluded that the underlying magnetic fields must be on average ∼ (20 − 50) nG strong. For illustration, an image of the radio synchrotron ridge connecting the merging galaxy clusters A 399 and A 401 within a cosmic filament [56] is displayed in Figure 17. Finally, voids of the cosmic web have been suggested to host extremely weak magnetic fields. The evidence is indirect and based on an interpretation of the measured γ-ray emission from blazars. From the non-detection of GeV echos in the long-term GeV-TeV light curves of the MRK 421 blazar, [57] derived a lower limit to the magnetic field strength in cosmic voids of B 10 −20.5 G. A more constraining estimate was later derived by [58], who relied on the sizes of the GeV halos around stacked lowredshift blazars to find B ∼ (10 −17 − 10 −15 ) G.