© ESO, 2015

1. Introduction

A large number of superbubbles and supershells have been found and discussed within our own Galaxy (e.g. Heiles 1979; Hu 1981; Heiles 1984; Koo et al. 1992; Maciejewski et al. 1996; Uyanıker et al. 2001; McClure-Griffiths et al. 2000, 2006; Pidopryhora et al. 2007) and in external galaxies (e.g. Meaburn 1980; Graham & Lawrie 1982; Brinks & Bajaja 1986; Deul & den Hartog 1990; Kim et al. 1998). They are created either by energetic stellar winds from OB star associations, by multiple supernova explosions, or by a combination. Besides their identification by shell-like H i emission, superbubbles and supershells were also traced by soft X-ray (e.g. Cash et al. 1980) and Hα emission (e.g. Reynolds & Ogden 1979). Superbubbles powered by sufficient energy will break out of the Galactic plane (Tomisaka & Ikeuchi 1986; Mac Low & McCray 1988; Mac Low et al. 1989) and form vertical “chimneys” in the interstellar medium (e.g. the Stockert chimney, Müller et al. 1987). A general scenario was proposed by Norman & Ikeuchi (1989) that chimneys play an important role in the interaction between the Galactic disk and halo by carrying up mass, energy, momentum, and magnetic flux. Therefore it is of interest to understand the properties of the superbubbles and their evolution processes. However, so far only a few superbubbles and chimneys have been resolved well and the magnetic field strengths measured (e.g. Vallée 1993).

The W4 superbubble in the Perseus arm is one of the few superbubbles that extend over several degrees and that have been also previously resolved well in observations. It was first identified by Normandeau et al. (1996) from H i observations with the synthesis telescope of the Dominion Radio Astrophysical Observatory (DRAO; Landecker et al. 2000). A cone-shaped cavity was revealed to open upwards from its powering source, the young open star cluster OCl 352, which includes nine O-type stars. The lower part of the cavity is bounded by the well-known Galactic H ii region W4. Evidence was found for an energetic outflow towards high positive latitudes, because H i streams were seen to point away from OCl 352. Because of the open conical shape viewed in the neutral gas, the entire structure was first named “W4 chimney”. Follow-up Hα observations (Dennison et al. 1997) showed that the ionized gas is detected in the periphery of the H i cavity and revealed an enclosed superbubble rather than a chimney, which is sealed at about b = 7°. As shown by West et al. (2007), the appearance of this huge structure seen from the 1.4 GHz radio continuum emission also resembles a closed bubble. We therefore refer to it as “W4 superbubble” in this work. Basu et al. (1999) explained the morphological difference between a chimney and a superbubble by the penetration of UV photons to the higher latitude regions. Based on the study of infrared and radio continuum data, Terebey et al. (2003) find a large leakage of UV photons from OCl 352. This leakage was indirectly confirmed by the discovery of an even larger high-latitude Hα loop on top of the W4 superbubble extending up to b = 30° (Reynolds et al. 2001).

The distance to the W4 superbubble was taken as 2.2 kpc in the work of Normandeau et al. (1996), Dennison et al. (1997), Reynolds et al. (2001), and Terebey et al. (2003), while 2.35 kpc was used by Basu et al. (1999) and West et al. (2007). Through measuring the trigonometric parallax of the methanol maser, Xu et al. (2006) got 1.95 kpc for the distance of the W3 OH region. Considering a probable association between the H ii regions W3 and W4 that gives another constraint on the distance of the W4 superbubble, we adopt the median value of 2.2 kpc in the following analysis.

The age of the W4 superbubble has not been determined with high precision. Dennison et al. (1997) estimated an age between 6.4 and 9.6 Myr, while Basu et al. (1999) derived a lower value of about 2.5 Myr. According to the formation of the large high-latitude Hα loop found on top of the W4 superbubble, Reynolds et al. (2001) argue that the formation of the W4 superbubble is not a single event, but rather caused by sequential star formation. Age estimates, however, are inevitably affected by the presence and strength of the magnetic fields. Numerical simulations have indicated that the magnetic field has a significant impact on the evolution of superbubbles (e.g. Tomisaka 1990; Ferrière et al. 1991; Tomisaka 1998). The expansion of superbubbles differs along and perpendicular to the field lines and results in an elongated shape (de Avillez & Breitschwerdt 2005; Stil et al. 2009). Komljenovic et al. (1999) have suggested that magnetic fields of a few μG must exist in the shells of the W4 superbubble to maintain its highly collimated shape and prevent its fragmentation from Rayleigh-Taylor instability. The strength of the line-of-sight component of the magnetic fields within the shells of the W4 superbubble was first estimated by West et al. (2007) based on the polarization data collected by the DRAO synthesis telescope. They determined a field strength between 3 μG and 5 μG by analysing lines through the W4 supperbubble shell separated by 5′. No short-spacing information was included in their data, which is, however, required to correctly interpret polarization structures resulting from Faraday rotation in the interstellar medium (e.g. Reich 2006; Sun et al. 2007; Landecker et al. 2010). We discuss the influence of polarized large-scale emission on this result in Sect. 4.2.

This work presents a study of the radio spectrum and the magnetic fields within the shells of the W4 superbubble based on new sensitive multi-frequency radio continuum and polarization observations including zero spacings. We describe the data sets we used in Sect. 2 and present all observational results and their analysis in Sect. 3. In Sect. 4, we use a Faraday screen model to derive the magnetic field strengths in the W4 superbubble. We discuss and summarize the results in Sect. 5.

Fig. 1 Total intensity I, polarization intensity PI, and polarization angle PA images of the W4 superbubble at λ6 cm (upper panels a), b), c)), λ11 cm (middle panels d), e), f)), and λ21 cm (bottom panels g), h), i)). The angular resolutions are 95 for λ6 cm images in panels a) and b), 43 for λ11 cm images in panels d) and e), and 935 for λ21 cm images in panels g), h), and i). The PA images at λ6 cm (panel c)) and λ11 cm (panel f)) have angular resolutions of 12′ and 6′, respectively. The total intensity contours for I and PI images run from 1.8 mK Tb in steps of 2.4 mK Tb for λ6 cm, from 10.0 mK Tb in steps of 12.0 mK Tb for λ11 cm (after subtracting strong point-like sources), and from 2000 mK Tb in steps of 50 mK Tb for λ21 cm. The PI contours on the PA images start from 5.0 mK Tb in steps of 1.0 mK Tb for λ6 cm, and from 50.0 mK Tb in steps of 8.0 mK Tb for λ11 cm. PI contours are not overlaid on the λ21 cm PA image, because no clear correlations can be found. The rectangles in panel a) are the regions for TT-plots study, while the rectangles in panels b), c), and e), f) indicate the regions used for the Faraday screen model fitting.

2. Data

New sensitive radio continuum and linear polarization observations of the W4 superbubble have been made at λ6 cm with the Urumqi 25-m radio telescope of Xinjiang Astronomical Observatories, Chinese Academy of Sciences, and at λ11 cm with the Effelsberg 100-m radio telescope of the Max-Planck-Institut für Radioastronomie, Germany. Total intensity and polarization data at λ21 cm were taken from an unpublished section of the Effelsberg Medium Latitude Survey (EMLS; Uyanıker et al. 1998, 1999; Reich et al. 2004). The Stockert λ21 cm total intensity northern sky survey (Reich 1982; Reich & Reich 1986) and the DRAO 26-m single-dish polarization survey (Wolleben et al. 2006) provided the missing large-scale intensities and the absolute zero levels. We also added high-resolution λ21 cm data observed with the DRAO synthesis telescope by West et al. (2007) and Landecker et al. (2010) to the large-scale corrected EMLS maps.

Technical details of each observation, such as the central frequency, angular resolution, and sensitivity, are listed in Table 1. The bandwidth depolarization (e.g. Crawford & Tiffany 2007) for the single-channel observations by the Urumqi and Effelsberg telescopes was found to be negligible (<1%) for all the three wavelengths, even for a rotation measure (RM) as large as 300 rad m^-2.

2.1. Urumqi λ6 cm data

The λ6 cm total intensity and linear polarization data were obtained between 2007 and 2009 during the conduction of the Sino-German λ6 cm polarization survey of the Galactic plane (Sun et al. 2007; Gao et al. 2010; Sun et al. 2011; Xiao et al. 2011), using the same observational and reduction methods. The λ6 cm observations had two modes – the broad-band mode with a central frequency of 4800 MHz and a bandwidth of 600 MHz – and a narrow-band mode with a central frequency shifted to 4963 MHz and a reduced bandwidth of 295 MHz. Raster scans with a speed of 4°/min were made along the Galactic longitude (L) and latitude (B) directions. A single observation mostly lasted for about two hours, so that only a portion of the large target field was covered. Elevations were always high enough that ground radiation fluctuations can be largely avoided. Ten full coverages were processed and then calibrated by 3C 286 and 3C 295, the main polarized and un-polarized calibrators. Finally, individual maps were combined following the procedures described by Gao et al. (2010). The final image of the W4 superbubble (see Fig. 1) is centred at , covering an area of ×.

2.2. Effelsberg λ11 cm data

The λ11 cm observations were done in the summer of 2008 with the Effelsberg 100-m telescope. The receiving system was described by Uyanıker (2004), but was upgraded in 2005 with lower noise amplifiers and an eight-channel polarimeter. Here we made use of its broad-band channel with 80 MHz bandwidth. Data processing and calibration follow the same procedures as for the λ6 cm observations.

2.3. Combined λ21 cm data

The λ21 cm data were extracted from the EMLS (Reich et al., in prep.) with a central frequency of 1400 MHz and a bandwidth of 20 MHz. The missing large-scale structures were added by the Stockert λ21 cm survey data (Reich 1982; Reich & Reich 1986) for total intensities, and the DRAO 26-m single-dish data (Wolleben et al. 2006) for polarization intensities.

We also added the available λ21 cm total intensity data from the Canadian Galactic plane survey (Taylor et al. 2003), the polarization data from Landecker et al. (2010), and the synthesis data from West et al. (2007), convolved to a 15 circular beam to the zero-level restored EMLS maps. A detailed description of the merging process of polarization data from the DRAO synthesis telescope, the Effelsberg 100-m and the DRAO 26-m telescopes was given by Landecker et al. (2010), whose procedure we followed. The resulting λ21 cm map does not fully cover the area of the λ6 cm, λ11 cm, and EMLS λ21 cm maps.

2.4. Absolute zero-level restoration for the λ6 cm and λ11 cm polarization data

Interferometric data miss short-spacings and single-dish maps are generally set on arbitrary zero levels. As emphasized by Reich (2006), missing large-scale structure means that diffuse polarized emission originating in the magnetized interstellar medium cannot be properly interpreted.

The observed polarization U and Q maps at λ6 cm and λ11 cm were set to zero at their boundaries and thus miss polarized emission from larger-scale components. The zero-level problem was solved for the λ6 cm polarization data of the Urumqi survey (e.g. Sun et al. 2007; Gao et al. 2010) by adding the missing large-scale component by extrapolation of the WMAP K-band (22.8 GHz) polarization data (Page et al. 2007; Hinshaw et al. 2009), which are on absolute levels. This is based on the assumption that Faraday rotation of the Galactic diffuse interstellar medium is negligible for frequencies as high as 4.8 GHz, which is valid except for the inner Galaxy (Sun et al. 2011). For the outer region within a few degrees away from the Galactic plane, such as the W4 superbubble, Faraday rotation effects can certainly be neglected between λ6 cm and the WMAP K-band.

For the W4 superbubble, we followed the same polarization zero-level restoration scheme as described by Gao et al. (2010), but using the most recent WMAP K-band 9-yr data (Bennett et al. 2013). First, the Urumqi λ6 cm polarization U and Q maps and the corresponding WMAP K-band polarization maps were convolved to a common angular resolution of 2°. The convolved WMAP U and Q maps needed to be scaled to λ6 cm by a factor of $\mathrm{(}\frac{\mathrm{4800}}{\mathrm{22}\hspace{0.17em}\mathrm{800}}{\mathrm{)}}^{\mathit{\beta }}$, where β is the brightness temperature spectral index (T_b ~ ν^β) for diffuse polarized emission. Spectral index maps for polarization intensities at 75′ resolution were derived from the combined λ21 cm (Effelsberg 100-m and DRAO 26-m) and the WMAP K-band data, and also for control for the WMAP K- and Ka-band (33 GHz) data for the entire W4 superbubble area. In both cases, the mean of β was close to −3, i.e. for λ21 cm versus K-band, β = −2.97 ± 0.04, and for K-band versus Ka-band, β = −2.98 ± 0.31, indicating that depolarization at λ21 cm is not important for large-scale emission. Finally, the β-scaled WMAP U and Q data at 2° angular resolution were compared with the convolved λ6 cm U and Q data, respectively. The differences were taken as the missing large-scale components and added to the observed λ6 cm data at their original angular resolution. The λ6 cm polarization intensity (PI) was then calculated from the restored U and Q as $\mathrm{PI}\mathrm{=}\sqrt{{\mathit{U}}^{\mathrm{2}}\mathrm{+}{\mathit{Q}}^{\mathrm{2}}}$, and the polarization angle (PA) was obtained by $\mathrm{PA}\mathrm{=}\frac{\mathrm{1}}{\mathrm{2}}$atan(U/Q).

The Faraday rotation effect at λ11 cm is about 3.4 times that of λ6 cm (λ² dependence), so a successful zero-level recovery using high-frequency WMAP K-band data requires a careful check on the rotation measure (RM) in the area of interest. For the W4 superbubble area, we calculated a RM map between λ21 cm (Effelsberg + DRAO) and λ1.3 cm (WMAP K-band) from the polarization angle data: RM = (PA_1.3cm − PA_21cm)/(0.013² − 0.214²) at an angular resolution of 75′. The RMs are found to be small in general and the mean is 0.74 ± 1.01 rad m^-2, which causes only small deviations in PA of −1° to 33 between the Effelsberg λ11 cm and the WMAP λ1.3 cm data. Therefore, we restored the missing large-scale polarized emission for the Effelsberg λ11 cm data by the same procedures as for the Urumqi λ6 cm data.

Fig. 2 Combined λ21 cm polarized emission of the W4 superbubble with data from the DRAO interferometer, the Effelsberg 100-m, and the DRAO 26-m single-dish telescopes at an angular resolution of 3′. Overlaid λ21 cm contours are from the source subtracted and spatially filtered total intensity map (see text). Contour lines run from 2000 mK Tb in steps of 50 mK Tb.

Fig. 3 Depolarization along the western shell of the W4 superbubble at λ6 cm (panel a)), where total intensity contours start at 4.9 mK Tb and run in steps of 3.0 mK Tb, and at λ11 cm (panel b)) where total intensity contours start from 9.0 mK Tb in steps of 13.5 mK Tb, and at λ21 cm (panel c)) where the total intensity (DRAO interferometer + Effelsberg + DRAO 26-m) contours run from 2000 + (n − 1) × 50 mK Tb (n = 1, 2, 3, 4), and 2500 + (n − 5) × 800 mK Tb (n = 5, 6, 7, 8). The angular resolutions for the λ6 cm, λ11 cm, and λ21 cm images are 95, 43, and 3′, respectively.

3. Results

We present the total intensity I, the polarization intensity PI of the W4 superbubble at λ6 cm, λ11 cm, and λ21 cm at angular resolutions of 95, 43, and 935 in Fig. 1, where the λ21 cm images are from the combined EMLS and DRAO 26-m single dish map. The angular resolutions of the λ6 cm and λ11 cm PA images are convolved to 12′ and 6′, respectively, to increase the signal-to-noise ratio. The λ21 cm PA image is shown at its original resolution of 935. A higher angular resolution λ21 cm PI map combined from the DRAO synthesis telescope (West et al. 2007), the EMLS, and the DRAO 26-m telescope convolved to a 3′ circular beam is displayed in Fig. 2. This map is overlaid with contours of a source-subtracted and unsharp-masked λ21 cm total intensity map, which was combined from DRAO synthesis telescope, EMLS, and Stockert survey data. The singled-out PI images for the western¹ shell of the W4 superbubble at λ6 cm, λ11 cm, and λ21 cm are shown in Fig. 3. For all the images, the λ6 cm and λ11 cm total intensity images are the observed ones on relative zero levels, while all the others are restored to absolute zero levels.

3.1. Total intensity emission and spectral information

In all total intensity images, the W4 superbubble shows up by two bright ridges emerging from the H ii region complex W4 at about ℓ ~ 133° and ℓ ~ 136°, extending towards high latitudes. These two ridges form a loop structure, since they close at about b = 6°. From the λ6 cm and λ11 cm images, a faint high-latitude extension of the western shell can be traced to more than b = 7°. Another partial shell-like structure can be distinguished above the major eastern shell of the W4 superbubble and merges with the western extension at about b = 8°. According to the apparent size determined by the maximum lengths on the Galactic longitude and latitude dimensions, (Δb is calculated with respect to the position of OCl 352 at 9), the physical size of the W4 superbubble is about 150 pc in width and 270 pc in height for a distance of 2.2 kpc. These results are consistent with previous estimates (e.g. Dennison et al. 1997).

Based on the tight correlation between radio continuum and Hα emission and the flat radio spectrum derived between 408 MHz and 1420 MHz, West et al. (2007) conclude that the radio continuum emission from the shells of the W4 superbubble is optically thin thermal emission. We confirmed this by deriving the spectral index from the present data using TT-plots (Turtle et al. 1962) between 1.4 GHz and 4.8 GHz. After subtracting the NVSS sources (Condon et al. 1998), the brightness temperature spectral index between λ6 cm and λ11 cm was found to be β = −1.98 ± 0.16 for the western shell and β = −2.04 ± 0.26 for the eastern shell (Fig. 4, left panels). Between λ6 cm and λ21 cm, we obtained β = −2.12 ± 0.39 for region “A”, β = −2.19 ± 0.38 for region “B”, and β = −2.16 ± 0.33 and β = −2.16 ± 0.10 for the regions “C” and “D”, respectively for the marked regions in Fig. 1. These results agree with optical-thin thermal emission, which we use for the passive Faraday screen model to derive the magnetic fields within the shells of the W4 superbubble in Sect. 4.2.

Fig. 4 TT-plot results for the western shell (upper panels) and the eastern shell (lower panels) of the W4 superbubble between λ6 cm and λ11 cm (left panels) and for the four regions (A, B, C, and D) in the shells (see Fig. 1) between λ6 cm and λ21 cm.

3.2. Polarization

Unlike the resemblance in the total intensity images shown for the three different wavelengths, polarization behaves much differently. At λ6 cm, the most pronounced feature related to the W4 superbubble is the strong depolarization that nicely follows the western shell and the PA deviation across the shell. No other prominent and closely related PI and PA features are seen along any other shell structures.

The λ11 cm polarization image discloses more structural details owing to its higher angular resolution. The polarization intensities and angles vary strongly in the western shell area of the W4 superbubble (see Fig. 3). Other than at λ6 cm, depolarization is also seen for some sections of the eastern shell and the high-latitude filament centred approximately at ℓ = 136°,b = 7°. This, in conjunction with the λ6 cm PI image, implies that RM varies in values and regularity over the W4 superbubble and is smaller in the eastern shell than in the western shell. Polarization structures are also visible in the bubble’s interior. A notable feature is the arc-like structure running from longitude 133° to 134° and latitude to , which is also visible but fainter at λ6 cm.

At λ21 cm, no strong structural coincidence can be identified between total intensity and polarization at first glance. West et al. (2007) saw the western and eastern shells of the W4 superbubble in depolarization in their λ21 cm map using DRAO synthesis data alone. When averaging their data for a 10′ wide latitude stripe centred at , the polarization intensity for the eastern shell drops from a surrounding level of about 65 mK T_b to 40 mK T_b, and for the western shell it decreases from 50 mK T_b to about 40 mK T_b. When combining the DRAO synthesis telescope data with the Effelsberg and DRAO single-dish data (Fig. 2), we found that this depolarization is much less pronounced than the pure DRAO synthesis telescope data. The reason is the much higher absolute polarization level of about 500 mK T_b for the eastern and 350 mK T_b for the western shell. Fluctuations of the Galactic polarized emission seem to mask the depolarization along the W4 superbubble shells. For a zoomed view of the western shell at 3′ resolution (Fig. 3), there is, however, a morphological coincidence between total and polarization intensity, indicating that related depolarization exists.

On larger scales, an inclined broad stripe of strong polarized emission runs across the image from the lower left (south-east) to the upper right (north-west) corner, while depolarization patches are seen in the orthogonal areas of the image. Both the Effelsberg and the DRAO single-dish data independently show this feature at λ21 cm. This general distribution is also seen in the λ6 cm and λ11 cm polarization data that are corrected by large-scale emission based on the WMAP K-band data (see Fig. 1).

4. The magnetic field strength in the W4 superbubble shell

Regular changes in sign or values of RMs of extragalactic sources across a finite area often indicate the existence of a Galactic Faraday screen. Sufficient RM sources in a sky area can be used to determine the line-of-sight component of the magnetic fields within such foreground screens (e.g. Harvey-Smith et al. 2011). There are 40 sources with determined RMs within the W4 superbubble area in the catalogue of Xu & Han (2014)² supplemented by the NVSS RM catalogue (Taylor et al. 2009). Most of these RMs show negative signs, resulting from the orientation of the Galactic magnetic field running clockwise (viewed from the north Galactic pole) in this part of the Perseus arm (Han et al. 2006). Five RMs are positive, which might indicate small-scale variations or source-intrinsic properties. However, the present RM number density is too sparse to estimate the magnetic field for shell regions of the W4 superbubble.

4.1. The Faraday screen model

A passive Faraday screen is a magneto-ionized bubble, filament, or sheet that does not emit polarized emission, but modulates background polarized emission passing through it via the Faraday effect. A successful model for deriving the physical parameters of these Faraday screens was developed by Sun et al. (2007) for screens detected in the Urumqi λ6 cm survey. It was also applied in several follow-up studies (e.g. Gao et al. 2010; Xiao et al. 2011). In its simplest form, the model takes the observational fact that the foreground and background Galactic magnetic field of the screens have the same orientation and PA ~ 0°, i.e. parallel to the Galactic plane at high enough frequencies. We have verified in Sect. 3.1 that the W4 superbubble exclusively emits optically thin thermal emission. We now check whether foreground and background PAs around the W4 superbubble area meet the condition of PA ~ 0°. Starlight polarization observations of the W4 superbubble area (Heiles 2000) support the idea that the Galactic magnetic fields are aligned to the Galactic plane (PA = −1° ± 7°) for a distance range from 30 pc to 2.85 kpc. This is further supported by the low-frequency polarization measurements for the large excessive “Fan” region (Spoelstra 1984), covering the W4 superbubble area, and also by the WMAP K- and Ka-band polarization data, where Galactic RMs in this part of the Galaxy are small, and the large-scale Galactic magnetic fields (Han et al. 2006) will only marginally change PAs from their intrinsic values. In addition, we also carried out λ6 cm simulations in the direction of the W4 superbubble using the Sun et al. (2008) and Sun & Reich (2010) Galactic 3D-emission model, which is based on all-sky surveys, RMs, and thermal emission data and also includes realistic magnetic field turbulence (Sun & Reich 2009). The simulation result is shown in Fig. 5. Foreground PA of the W4 superbubble at 2.2 kpc is close to zero and differs by just about 1° from the PA of the background emission at distances of 8 kpc or more. We repeated the simulation for various directions within the W4 superbubble area at λ6 cm, and obtained very similar results. Simulations at λ11 cm and λ21 cm show very small PA differences as well. We concluded that the Galactic 3D-emission simulations also support that the assumptions required for the passive Faraday screen model are satisfied.

The passive Faraday screen model uses three parameters: a depolarization factor f, which describes the reduction of the background polarization by the Faraday screen; the Faraday screen foreground polarized emission fraction c with respect to the observed polarized emission at an off-position away from the screen; and the polarization rotation angle within the screen ψ_s, which is the parameter for calculating RM (RM = ψ_s/λ²), and the line-of-sight component of the magnetic field (see Eq. (6)). These three parameters fit two observables: (1) the ratio PI_on/ PI_off and (2) the angle difference PA_on − PA_off, where “on” and “off” denote that the line of sight passes through (on) or not (off) the screen. The Faraday screen model equation is given in Eq. (1) (see Sun et al. 2007, for a detailed derivation): $\{\begin{array}{c}\\ \frac{{\mathrm{PI}}_{\mathrm{on}}}{{\mathrm{PI}}_{\mathrm{off}}}\mathrm{=}\sqrt{{\mathit{f}}^{\mathrm{2}}\mathrm{(}\mathrm{1}\mathrm{-}\mathit{c}{\mathrm{)}}^{\mathrm{2}}\mathrm{+}{\mathit{c}}^{\mathrm{2}}\mathrm{+}\mathrm{2}\mathit{fc}\mathrm{(}\mathrm{1}\mathrm{-}\mathit{c}\mathrm{)}\cos \mathrm{2}{\mathit{\psi }}_{\mathrm{s}}}\mathit{,}\\ {\mathrm{PA}}_{\mathrm{on}}\mathrm{-}{\mathrm{PA}}_{\mathrm{off}}\mathrm{=}\frac{\mathrm{1}}{\mathrm{2}}\arctan \left(\frac{\mathit{f}\mathrm{(}\mathrm{1}\mathrm{-}\mathit{c}\mathrm{)}\sin \mathrm{2}{\mathit{\psi }}_{\mathrm{s}}}{\mathit{c}\mathrm{+}\mathit{f}\mathrm{(}\mathrm{1}\mathrm{-}\mathit{c}\mathrm{)}\cos \mathrm{2}{\mathit{\psi }}_{\mathrm{s}}}\right)\mathrm{·}& \end{array}$(1)In the following we allow f to be in the range [0.00, 1.00] and c between 0.6 to 1.0, when taking the simulation result (Fig. 5) into account. These two parameters vary in steps of 0.01. ψ_s is searched for in the range [−90°, 90°] in steps of 1°.

Fig. 5 Simulations in the direction ℓ = 135°,b = 6° showing accumulated and spatial averaged RM (including one σ errors), PA, PI, and I values at λ6 cm as a function of distance from the Sun.

Fig. 6 Upper panel: profiles of the λ6 cm I (relative zero level), PI (absolute zero level), and PA (absolute zero level) averaged perpendicular to the western shell of the W4 superbubble within the area marked by the large white rectangular region in Fig. 1. The pixel size is 3′. The vertical dashed lines indicate the “on – off” boundaries of the Faraday screen. Lower panel: the same as the upper panel, but for the Effelsberg λ11 cm data.

4.2. Analysis of the western shell

The clearest Faraday effect for the W4 superbubble is the depolarized western shell seen at λ6 cm and λ11 cm. With the measurements at these two wavelengths, we estimated the line-of-sight component of the magnetic field B_// based on the Faraday screen model described above for a section as indicated by the large white rectangle in Fig. 1. Averaged λ6 cm and λ11 cm I, PI, and PA profiles perpendicular to the western shell were calculated and shown in Fig. 6. The shell direction is inclined, and the averaged stripes or columns run parallel to it. We labelled the result by the column number from east to west across the western shell (see Fig. 6). The typical character of a passive Faraday screen is seen at λ6 cm; i.e., an apparent PI depression is identified with its minimum close to the peak position of the total intensity I. The very small PA difference between “on” and “off” positions implies a large foreground fraction c of the polarized emission.

To calculate the two observables, PI_on/ PI_off and PA_on − PA_off, the “on” and “off” positions of the Faraday screen must be determined first. Combining the profiles of the λ6 cm and λ11 cm data, we set the boundary of “on” and “off” positions of the Faraday screen as marked in Fig. 6. The column size of 3′ corresponds to 1.9 pc for a distance of 2.2 kpc of the W4 superbubble. The λ6 cm PI_off and PA_off were calculated as the average values of PIs and PAs on the “off” positions (Cols. 1−8 and 17−25, see Fig. 6 upper panel). The central eight (9th to 16th, Fig. 6 and Table 2) columns represent the interior of the Faraday screen and were used for model fitting.

We assumed 1σ observational uncertainty for the λ6 cm observations and used Eq. (1) for the Faraday screen model fitting. A series of (f, c, ψ_s) results were obtained, which are consistent with the λ6 cm observables PI_on/ PI_off and PA_on − PA_off. We then used these qualified (f, c, ψ_s) to predict λ11 cm PI_on ($\mathrm{PI}\mathrm{=}\sqrt{{\mathit{U}}^{\mathrm{2}}\mathrm{+}{\mathit{Q}}^{\mathrm{2}}}$) and PA_on ($\mathrm{PA}\mathrm{=}\frac{\mathrm{1}}{\mathrm{2}}\mathrm{atan}\frac{\mathit{U}}{\mathit{Q}}$) based on the following equation (for details see Sun et al. 2007): $\{\begin{array}{c}\\ {\mathit{U}}_{\mathrm{on}}\mathrm{=}\mathit{f}{\mathrm{PI}}_{\mathrm{bg}}\hspace{0.17em}\sin \hspace{0.17em}\mathrm{2}{\mathit{\psi }}_{\mathrm{s}}\mathit{,}\\ {\mathit{Q}}_{\mathrm{on}}\mathrm{=}{\mathrm{PI}}_{\mathrm{fg}}\mathrm{+}\mathit{f}{\mathrm{PI}}_{\mathrm{bg}}\cos \hspace{0.17em}\mathrm{2}{\mathit{\psi }}_{\mathrm{s}}\mathit{.}& \end{array}$(2)Here, PI_fg,11cm = PI_{off,11 cm} × c and PI_{bg,11 cm} = PI_{off,11 cm} × (1 − c), where λ11 cm PI_{off,11 cm} was calculated as ${\mathrm{PI}}_{\mathrm{off}\mathit{,}\mathrm{11}\mathrm{cm}}\mathrm{=}{\mathrm{PI}}_{\mathrm{off}\mathit{,}\mathrm{6}\mathrm{cm}}\mathrm{(}\frac{\mathrm{2639}\mathrm{MHz}}{\mathrm{4800}\mathrm{MHz}}{\mathrm{)}}^{\mathit{\beta }}\mathrm{=}\mathrm{65.8}\mathrm{mK}{\mathit{T}}_{\mathrm{b}}$, with a spectral index β = −3 as obtained in Sect. 2.4. This agrees with the measured values at the edges of the λ11 cm PI profile in Fig. 6. The rotation angles at λ11 cm were calculated as ${\mathit{\psi }}_{\mathrm{11}\mathrm{cm}}\mathrm{=}{\mathit{\psi }}_{\mathrm{6}\mathrm{cm}}\mathrm{(}\frac{\mathrm{0.114}}{\mathrm{0.0625}}{\mathrm{)}}^{\mathrm{2}}$. We compared the predicted values with the λ11 cm observational results within 1σ errors, which further filtered the (f, c, ψ_s) data to agree with both λ6 cm and λ11 cm observations. From all the remaining results, we found the parameter c to be rather well constrained within 0.8 to 0.9 (see Table 2) and largely independent of f variations. This is consistent with the dominant foreground contribution towards the W4 superbubble. The reduction of the polarized background emission is mathematically possible in various ways. Here, ψ_s is the most interesting parameter and is also well constrained, which enables us to make a reasonable estimate of the magnetic field and assess its errors. In Table 2, we listed the average values of f, c, and ψ_s for each column in the Faraday screen, including standard deviation. We searched for the best fit (f, c, ψ_s) for each column by the least χ² method. The difference between the average and the best fit value (f, c, ψ_s) is small, with the maximum of 1.9σ. In the following, we used the averaged ψ_s and its standard deviation to derive the magnetic field within the western shell of the W4 superbubble.

The λ21 cm observations cannot be used for the model fitting since depolarization occurs at λ21 cm even by smaller RMs within the shell. However, it can be examined to verify the fit result. Considering the small-scale RM structures as shown by the λ11 cm data, total depolarization could be expected for the background PI at λ21 cm passing through the bubble’s shell. In fact, the interferometric λ21 cm image by West et al. (2007) shows the depolarization along the W4 superbubble shells, which is almost masked in the single-dish polarization image as discussed in Sect. 3.2. In the West et al. (2007) interferometric map, the depolarization averaged for a 10′ wide latitude stripe is about 25 mK T_b along the eastern and about 10 mK T_b along the western shell. The single-dish map polarization level of about 500 mK T_b in the eastern and about 350 mK T_b in the western shell area imply an upper limit of about 0.97 for c in the western shell and about 0.95 in the eastern shell. The large difference in the polarization emission levels in the interferometric and in the single-dish maps means that a quantitative analysis of the interferometric polarization data without large-scale correction cannot be made to estimate the field strength. We concluded that the λ21 cm polarization data agree with the parameters of the Faraday screen model along the western shell based on the λ6 cm and λ11 cm observations.

For an estimate of B_// within the western shell, the thermal electron density n_e, its filling factor f_ne, and the path length l within the bubble’s shell are needed. Emission measure (EM), which is the integral of f_ne and ${\mathit{n}}_{\mathrm{e}}^{\mathrm{2}}$ over the path length dl can be calculated, because it is related to optically-thin thermal radio continuum emission by the following equation (Wilson et al. 2013): $\left(\frac{{\mathit{T}}_{\mathrm{b}}}{\mathrm{K}}\right)\mathrm{=}\mathrm{8.235}\mathrm{\times }{\mathrm{10}}^{-2}{\left(\frac{{\mathit{T}}_{\mathrm{e}}}{\mathrm{K}}\right)}^{-0.35}{\left(\frac{\mathit{\nu }}{\mathrm{GHz}}\right)}^{-2.1}\left(\frac{\mathit{EM}}{{\mathrm{pc}\mathrm{cm}}^{-6}}\right)\mathit{a}\mathrm{\left(}\mathit{\nu ,T}\mathrm{\right)}\mathit{,}$(3)where, T_b is the radio continuum brightness temperature measured at frequency ν, a(ν,T) is a factor close to 1. We assumed T_e = 8000 K for the ionized Galactic interstellar medium in general. Based on the λ6 cm observation, we deduced the EMs within the western shell of the W4 superbubble. However, from Fig. 6 we saw a large-scale emission component of about 1.9 mK T_b at λ6 cm besides thermal emission I from the western shell. After subtracting this large-scale component, EMs of the central eight columns within the screen area were calculated based on Eq. (3), as listed in Table 2.

Fig. 7 Left panel: electron density ne across the western shell of the W4 superbubble for filling factors fne = 0.1 (green triangle), 0.4 (blue square), 0.7 (cyan diamond), and 1.0 (magenta circle). Right panel: the strength of the line-of-sight component of the B-field across the western shell for different filling factors fne.

To verify the EM results that we obtained from the radio continuum data, Hα measurements were used to estimate the EMs independently following Haffner et al. (1998) and Finkbeiner (2003) by using $\mathit{EM}\mathrm{=}\mathrm{2.75}{\mathit{T}}_{\mathrm{4}}^{\mathrm{0.9}}{\mathit{I}}_{\mathrm{H}\mathit{\alpha }}\exp \mathrm{\left[}\mathrm{2.44}\mathit{E}\mathrm{\right(}\mathit{B}\mathrm{-}\mathit{V}\mathrm{\left)}\mathrm{\right]}\mathit{.}$(4)Dennison et al. (1997) measured Hα emission for several positions towards the W4 superbubble. At their position K (, ), they observed an intensity of 5.8 Rayleigh. Reynolds et al. (2001) measured 6.9 ± 0.5 Rayleigh at the position . Both directions are within the western shell region of the W4 superbubble. The extinction parameter E(B − V), which must be taken into account, is in general difficult to obtain and often ignored for regions outside the Galactic plane. Two stars, Hilt 266 () and Hilt 338 (), were found near the W4 superbubble with distances of 2.5 kpc and 2.3 kpc, respectively. They have a measured extinction value of E(B − V) = 0.66 (Hiltner 1956). Based on Eq. (4) and assuming T = 8000 K, we derived the EMs for the two positions as 65 pc cm^-6 and 77.7 ± 5.6pc cm^-6, which are consistent with those based on radio continuum data in Table 2.

The path lengths for the central eight columns (9th−16th) across the western shell of the W4 superbubble are related to the geometry, where we assume a uniform shell. The largest RM corresponds to the longest path length (Vallée 1982), which is corresponding to the 13th column in our case (see Fig. 6 and Table 2), and defines the inner radius of the shell. We also considered the case of a thermal shell, where the strongest total intensity emission is at the 12th column, and included the results in Table 2. The angle between the central axis of the W4 superbubble and the 13th column is about 17, and the angle between the 13th column and the outer edge of the western shell is 105. Then for a distance of 2.2 kpc, we calculated the inner and outer radii of the shell as 65 pc and 72 pc, respectively. With a column size of 3′, the path lengths of the central eight columns were deduced. The electron densities and the strength of the line-of-sight component of the magnetic field B_// can be obtained following the equations given by Harvey-Smith et al. (2011), where the filling factor f_ne is the only unknown parameter: $\begin{array}{ccc}{\mathit{n}}_{\mathrm{e}}& \mathrm{=}& \\ {\mathit{B}}_{\mathit{/}\mathit{/}}& \mathrm{=}& \end{array}$The filling factor is often assumed to be 1.0, as in West et al. (2007), while Harvey-Smith et al. (2011) used f_ne = 0.1 for the sample of H ii regions they studied. Since no well-determined value has been reported for superbubbles so far, we calculated n_e and B_// based on Eqs. (5) and (6), for f_ne = 0.1, 0.4, 0.7, and 1.0. We used the standard error propagation to estimate the errors in n_e and B_//. The uncertainty of n_e results from the error of EM, which stems from the λ6 cm total intensity measurements. Sun et al. (2007) quote the maximum uncertainty of 10% for the λ6 cm survey data. Besides the uncertainty of EM, the errors in B_// also depend on the uncertainties in RM. The standard deviations used for this purpose were listed in Table 2.

We showed the n_e and B_// profiles across the western shell of the W4 superbubble in Fig. 7. Owing to the $\mathrm{1}\mathit{/}\sqrt{{\mathit{f}}_{{\mathit{n}}_{\mathrm{e}}}}$ dependence, f_ne = 0.1 results in high electron density and a large B field, while the values for f_ne = 0.4, 0.7, and 1.0 are much smaller. To distinguish which case is more realistic, we made a simple estimate according to the magnetic flux conservation. For the W4 superbubble, the swept-up magnetic field should be a factor of about 5 higher than the undisturbed Galactic B field when we consider a ring with an inner radius of 65 pc and an outer radius of 72 pc. Using RM data from pulsars, Han et al. (2006) find that the strength of the large-scale regular radial B field of the Galaxy decreases from the inner Galaxy (4 μG) to the solar neighbourhood (2 μG). If a turbulent field of the same order is considered, the field strength in the W4 superbubble area is about 3 μG. The 3-D simulation of Sun et al. (2008) and Sun & Reich (2009) where both regular and turbulent B fields were included gave a similar value of B_tot of around 2.4 μG. Thus the enhanced line-of-sight B-field strength in the western shell should not exceed 15 μG by much, otherwise an amplification mechanism is needed to explain a larger B field for f_ne = 0.1. If a B-field amplification can be excluded, the filling factor f_ne in the western shell of the W4 superbubble is likely within the range of 0.4 to 1.0. We limit the following discussion to the case that the filling factor f_ne is 0.4, 0.7, and 1.0, where f_ne = 1.0 gives the lower limit of the electron density n_e and the strength of the line-of-sight component of the magnetic field B_//. When considering that the line-of-sight passes solely through the western shell (13th to 16th column), we obtained the average B_// to be −5.0(±10%) μG (f_ne = 1.0) to −8.0(±10%) μG (f_ne = 0.4), and the electron density n_e is between 1.0(±5%) cm^-3 (f_ne = 1.0) and 1.5(±5%) cm^-3 (f_ne = 0.4).

West et al. (2007) used a different analysis method to derive the line-of-sight component of the magnetic field strength in the shell of the W4 supperbubble. Based on the observed depolarization amount, they estimated the PA difference from adjacent lines passing through the shell. From the Faraday screen model, we found the RMs within the shell for the 13th to 16th column between −70 rad m^-2 and −300 rad m^-2, which causes one to four full rotations of PAs at λ21 cm. West et al. (2007) quote the λ21 cm differential angle of 60° and calculated a line-of-sight B-field strength between 3.4 μG and 9.1 μG from the different path lengths through the shell. The polarization intensity, polarization angles, and their differences are, however, influenced by the large-scale polarized emission, which is incompletely observed by the DRAO interferometer. Sun et al. (2007) quote the observed Stokes parameter U, Q from a passive Faraday screen as U = PI_fgsin2ψ_fg + fPI_bgsin(2ψ_bg + 2ψ_s), Q = PI_fgcos2ψ_fg + fPI_bgcos(2ψ_bg + 2ψ_s), where fg and bg denote foreground and background components of PI and PA. Here, f is the depolarization factor and ψ_s is the Faraday rotation angle within the screen. For the W4 superbubble, the foreground and background PA angles are close to zero (see Sect. 4.1.), then U and Q were calculated as U = fPI_bgsin2ψ_s and Q = PI_fg + fPI_bgcos2ψ_s (Eq. (2)). Therefore, the observed depolarization amount in PI and the PA differences for neighbouring lines through the shell depend not only on the difference in ψ_s, which is needed for a B-field calculation, but also on PI_fg and PI_bg. Without taking this into account, the B-field result depends in some way on the large-scale polarization fraction included in the data. Only if the Faraday screen is very local and PI_fg = 0 mK T_b does this method give the correct results. However, this is not the case for the W4 superbubble.

4.3. The north-eastern extension

Fig. 8 λ11 cm PI (left panel) and PA (right panel) of the north-eastern shell extension overlaid by total intensity contours. The contour levels and the angular resolution of the images are the same as in Fig. 1.

For better understanding of the magnetic field configuration and the strength of the W4 superbubble, we searched for more parts of shells and arcs, where Faraday effects could be studied in terms of the described Faraday screen model. We note that it is difficult to find unconfused areas with good quality “on” and “off” data. However, a section of the north-eastern extension located above the major eastern shell is noted in the λ11 cm polarization image (see Fig. 8), which we found to be suitable for modelling. The λ6 cm data show no evidence of depolarization in this region, indicating that the RM is smaller than in the western part of the W4 superbubble. We again applied the Faraday screen model and obtained f ~ 0.87, c ~ 0.86 and a positive RM of about 55 rad m^-2 in this area. The fitted parameters predict PI_on/ PI_off = 0.97 and for the λ6 cm, and PI_on/ PI_off = 0.89 and for the λ21 cm observations, which generally agrees with the non-detection of noticeable Faraday rotated structures in both maps. Following the procedures introduced above, we obtained a lower electron density of n_e = 0.5 (f_ne = 1.0) − 0.9 cm^-3 (f_ne = 0.4) with 1σ error of 15%, and a weaker line-of-sight component of the magnetic field B_// = 3.1 (f_ne = 1.0) − 4.9 μG (f_ne = 0.4) with 1σ error of 30% within the upper north-eastern shell extension.

5. Discussion and summary

We have shown that strong regular magnetic fields exist in the W4 superbubble’s shells. A study of the process of creating this magnetic field configuration is beyond the scope of this paper, while numerical simulations (e.g. Tomisaka 1998; de Avillez & Breitschwerdt 2005) provide hints of an evolutionary scenario. To explain the observations, it seems most likely that the originally plane-parallel magnetic fields were lifted up and compressed during the expansion of the W4 superbubble.

The calculation of the total magnetic field strength in the W4 superbubble shell depends on its orientation relative to the line of sight. From the discovery of atomic hydrogen associated to the W4 superbubble, Normandeau et al. (1996) concluded that the W4 superbubble is inclined towards the observer. Lagrois & Joncas (2009) studied this inclination in detail and found that the inclination angle is between 9° and 27°. In addition, we measured an inclination angle of 18° with respect to the Galactic north pole for the western shell (see Fig. 1). If the magnetic field in the W4 superbubble is directed along its shell and if taking its geometry into account, the deprojected regular B_tot field in the western shell can be deduced as ${\mathit{B}}_{\mathrm{tot}}\mathrm{=}{\mathit{B}}_{\mathit{/}\mathit{/}}\sqrt{\mathrm{1}\mathrm{+}\mathrm{(}\frac{\mathrm{1}}{\tan \mathit{\theta }\cos \mathrm{18}°}{\mathrm{)}}^{\mathrm{2}}}\mathrm{=}\mathrm{(}\mathrm{2.3}\mathrm{-}\mathrm{6.7}\mathrm{)}{\mathit{B}}_{\mathit{/}\mathit{/}}$, where θ is the inclination angle between 9° and 27°.

Thermal and magnetic pressure, besides gravity, ram pressure, and turbulence are key input parameters for superbubble evolution simulations. Thermal pressure is defined as P_ther = 2n₀kT_e, where n₀ = n_e for total ionization, k is the Boltzmann constant, and T_e is 8000 K as assumed above. Magnetic pressure is calculated as ${\mathit{P}}_{\mathrm{mag}}\mathrm{=}{\mathit{B}}_{\mathrm{tot}}^{\mathrm{2}}\mathit{/}\mathrm{8}\mathit{\pi }$. For each column within the western shell of the W4 superbubble shell (13th, 14th, and 16th columns, the 15th column is excluded because of the poor constraints on the B-field), we calculated the thermal and magnetic pressure based on the results shown in Fig. 7 and made a comparison in Table 3. For the inclination angle of θ = 27°, the magnetic pressure P_mag is generally several times of the thermal pressure P_ther, and P_mag becomes overwhelming when the inclination angle θ approaches to 9°.

For the north-eastern extension in the higher latitude region, P_mag and P_ther are comparable when θ ~ 27°, regardless of f_ne = 0.4 or 1.0. P_mag dominates P_ther if θ approaches 9°, even for f_ne = 1.0. A more precise inclination angle would help to better constrain the physical properties of the W4 superbubble.

We found a positive RM on the eastern side and a negative RM on the western side of the W4 superbubble. This is expected for the scenario described above, where the W4 superbubble expands and breaks out of the Galactic plane and lifts up the magnetic field, which runs clockwise (viewed from the north Galactic pole) in the Perseus arm (Han et al. 2006). Then, for the eastern shell, the field lines will go up and for the western shell downwards. Because the W4 superbubble tilts towards us (Normandeau et al. 1996; Lagrois & Joncas 2009), the line-of-sight component of the magnetic field points away in the western shell of the W4 superbubble, resulting in a negative RM, and towards us in the eastern shell, where a positive RM is observed.

Radio continuum and polarization observations at λ6 cm, λ11 cm, and λ21 cm have been made to study the radio emission properties and to estimate the magnetic fields of the W4 superbubble. With the flat radio continuum spectrum found between λ6 cm, λ11 cm, and λ21 cm, we confirm the thermal origin of the radio continuum emission of the W4 superbubble. Polarized emission shows dramatically morphological differences from wavelength to wavelength. With the advantage of being less affected by Faraday rotation, the λ6 cm and λ11 cm polarization data were used for the estimates of the line-of-sight component of the magnetic field within the western shell of the W4 superbubble by a passive Faraday screen model. Considering the thermal electron filling factor f_ne, the radio continuum observations and a simple geometric assumption result in an electron density of ${\mathit{n}}_{\mathrm{e}}\mathrm{~}\mathrm{1.0}\mathrm{\times }\mathrm{1}\mathit{/}\sqrt{{\mathit{f}}_{{\mathit{n}}_{\mathrm{e}}}}$ cm^-3, and the line-of-sight component of the magnetic field B_// ~$\mathrm{-}\mathrm{5.0}\mathrm{\times }\mathrm{1}\mathit{/}\sqrt{{\mathit{f}}_{{\mathit{n}}_{\mathrm{e}}}}$μG (pointing away from us) for the western shell of the W4 superbubble, where the typical error is about 5% for n_e and 10% for B_//. Based on a simple estimate, we found that f_ne likely has a value greater than 0.1 assumed for H ii regions (Harvey-Smith et al. 2011). Being related to the inclination angle of the superbubble with respect to the plane of the sky, a total magnetic field is found above 12 μG. This results in a magnetic pressure, which is one or two orders of magnitude higher than the thermal pressure in the western shell of the W4 superbubble. The λ11 cm polarization data allow a model fit of the weaker RM in the high-latitude north-eastern shell, where we find a lower electron density of n_e = 0.5 to 0.9 cm^-3 and B_// of 3.1−4.9 μG for filling factors f_ne of 1.0 or 0.4, respectively. This means that the magnetic and thermal pressure might be comparable in the upper parts of the superbubble. The RM sign reverses as expected for a scenario where the Galactic magnetic field is pushed out of the plane by the expanding W4 superbubble, which is tilted towards us. These results are expected to constrain magneto-hydrodynamical simulations of the W4 superbubble and superbubbles in general.

Acknowledgments

X.Y.G. and J.L.H. are supported by the National Natural Science foundation of China (11303035, 11473034) and the Partner group of the MPIfR at NAOC in the framework of the exchange programme between MPG and CAS for many bilateral visits. X.Y.G. acknowledges financial support by the MPG, by Michael Kramer during his stay at the MPIfR, Bonn, and the Young Researcher Grant of National Astronomical Observatories, Chinese Academy of Sciences. This research is based in part on observations with the Effelsberg 100-m telescope of the MPIfR. We would like to thank the anonymous referee for helpful comments and suggestions.

References

All Tables

All Figures

Fig. 1 Total intensity I, polarization intensity PI, and polarization angle PA images of the W4 superbubble at λ6 cm (upper panels a), b), c)), λ11 cm (middle panels d), e), f)), and λ21 cm (bottom panels g), h), i)). The angular resolutions are 95 for λ6 cm images in panels a) and b), 43 for λ11 cm images in panels d) and e), and 935 for λ21 cm images in panels g), h), and i). The PA images at λ6 cm (panel c)) and λ11 cm (panel f)) have angular resolutions of 12′ and 6′, respectively. The total intensity contours for I and PI images run from 1.8 mK Tb in steps of 2.4 mK Tb for λ6 cm, from 10.0 mK Tb in steps of 12.0 mK Tb for λ11 cm (after subtracting strong point-like sources), and from 2000 mK Tb in steps of 50 mK Tb for λ21 cm. The PI contours on the PA images start from 5.0 mK Tb in steps of 1.0 mK Tb for λ6 cm, and from 50.0 mK Tb in steps of 8.0 mK Tb for λ11 cm. PI contours are not overlaid on the λ21 cm PA image, because no clear correlations can be found. The rectangles in panel a) are the regions for TT-plots study, while the rectangles in panels b), c), and e), f) indicate the regions used for the Faraday screen model fitting.

In the text

	Fig. 2 Combined λ21 cm polarized emission of the W4 superbubble with data from the DRAO interferometer, the Effelsberg 100-m, and the DRAO 26-m single-dish telescopes at an angular resolution of 3′. Overlaid λ21 cm contours are from the source subtracted and spatially filtered total intensity map (see text). Contour lines run from 2000 mK Tb in steps of 50 mK Tb.
In the text

Fig. 3 Depolarization along the western shell of the W4 superbubble at λ6 cm (panel a)), where total intensity contours start at 4.9 mK Tb and run in steps of 3.0 mK Tb, and at λ11 cm (panel b)) where total intensity contours start from 9.0 mK Tb in steps of 13.5 mK Tb, and at λ21 cm (panel c)) where the total intensity (DRAO interferometer + Effelsberg + DRAO 26-m) contours run from 2000 + (n − 1) × 50 mK Tb (n = 1, 2, 3, 4), and 2500 + (n − 5) × 800 mK Tb (n = 5, 6, 7, 8). The angular resolutions for the λ6 cm, λ11 cm, and λ21 cm images are 95, 43, and 3′, respectively.

In the text

	Fig. 4 TT-plot results for the western shell (upper panels) and the eastern shell (lower panels) of the W4 superbubble between λ6 cm and λ11 cm (left panels) and for the four regions (A, B, C, and D) in the shells (see Fig. 1) between λ6 cm and λ21 cm.
In the text

	Fig. 5 Simulations in the direction ℓ = 135°,b = 6° showing accumulated and spatial averaged RM (including one σ errors), PA, PI, and I values at λ6 cm as a function of distance from the Sun.
In the text

Fig. 6 Upper panel: profiles of the λ6 cm I (relative zero level), PI (absolute zero level), and PA (absolute zero level) averaged perpendicular to the western shell of the W4 superbubble within the area marked by the large white rectangular region in Fig. 1. The pixel size is 3′. The vertical dashed lines indicate the “on – off” boundaries of the Faraday screen. Lower panel: the same as the upper panel, but for the Effelsberg λ11 cm data.

In the text

	Fig. 7 Left panel: electron density ne across the western shell of the W4 superbubble for filling factors fne = 0.1 (green triangle), 0.4 (blue square), 0.7 (cyan diamond), and 1.0 (magenta circle). Right panel: the strength of the line-of-sight component of the B-field across the western shell for different filling factors fne.
In the text

	Fig. 8 λ11 cm PI (left panel) and PA (right panel) of the north-eastern shell extension overlaid by total intensity contours. The contour levels and the angular resolution of the images are the same as in Fig. 1.
In the text