A polarization study of the supernova remnant CTB 80

We checked the total-intensity spectra by applying the TT-plot method (Turtle et al. 1962), namely plotting and linearly fitting brightness temperature at one frequency against that at the other frequency to obtain the spectral index β as T ∝ ν^β . The spectral index α for flux density S, defined as S ∝ ν^α , can be obtained as α = β + 2. TT-plots are immune to the influence of constant large-scale background emission, which is critical for weak structures such as shell A. From Figure 1, it can be clearly seen that CTB 80 sits on a plateau of diffuse emission whose influence on the total-intensity spectra can also be eliminated by utilizing TT-plots.

The TT-plot results between 408 MHz and 4800 MHz, and between 1420 MHz and 4800 MHz are featured in Figure 2 for all the three areas. Both shell B and shell C have a brightness temperature spectral index of β ∼ −2.4 corresponding to a flux density spectral index of α ∼ −0.4, consistent with previous results (Kothes et al. 2006; Gao et al. 2011). For shell structure A, the spectrum is flatter with a brightness temperature spectral index of β ∼ −2.3 between 408 MHz and 4800 MHz, and β ∼ −2.2 between 1420 MHz and 4800 MHz.

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The emission encoded in the maps in Figure 1 consists of contributions from CTB 80 and the Milky Way background. The latter is irrelevant and shall be removed for further analysis. For Q and U maps, we removed the background emission by subtracting a plane fitted with the values surrounding CTB 80. From these reprocessed Q and U maps, we obtained polarized intensity PI (Fig. 3) and polarization angle as $\psi =\displaystyle \frac{1}{2}{\rm{\arctan }}\displaystyle \frac{U}{Q}$.

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For the total-intensity maps, it is very difficult to exclude the background emission. As a consequence, the polarization percentage defined as PC = PI/I would have large uncertainties. In order to circumvent this problem, we compare the polarization at different frequencies by considering the relative polarization percentage or the depolarization factor defined as $D{P}_{\nu }=\displaystyle \frac{P{I}_{\nu }}{P{I}_{{\nu }_{0}}}{(\displaystyle \frac{{\nu }_{0}}{\nu })}^{\beta }$, where ν = 1420 MHz or 2695 MHz, and ν₀ = 4800 MHz. Here we assume that depolarization is the least at 4800 MHz and use PI₄₈₀₀ as the reference. If there is no depolarization, both DP₁₄₂₀ and DP₂₆₉₅ would be around 1.

We calculated DP₁₄₂₀ and DP₂₆₉₅ by using the brightness temperature spectral index from the TT-plots between 1420 MHz and 4800 MHz (Fig. 2), namely β = −2.24 for area A, β = −2.40 for area B and β = −2.37 for area C. The results are depicted in the lower panels of Figure 3.

There is strong depolarization at 1420 MHz. The general morphology of the polarized intensity at 1420 MHz before smoothing resembles that at 4800 MHz (Fig. 1). However, the polarized intensity is largely reduced and the morphology dramatically changes after smoothing because of fluctuation in the polarization angles. There are clear offsets between positions of strong polarized emission at 1420 MHz and that at 4800 MHz, as can be seen from Figure 3. This implies that the polarized emission at 1420 MHz and at 4800 MHz probably originates from different regions. We therefore did not include the polarization data at 1420 MHz for RM calculations.

The polarized intensity at 2695 MHz corresponds well to that at 4800 MHz. Thus, the depolarization factor is around 1 for all areas except for the region near PSR B1951+32 where DP₂₆₉₅ varies from about 0.1 to about 0.7, indicating depolarization towards this region. A detailed discussion on the depolarization mechanisms was provided by Sokoloff et al. (1998). If the depolarization is caused by thermal gas that co-exists with the synchrotron-emitting medium, which is referred to as depth depolarization, the depolarization factor can be expressed as $D{P}_{\nu }=\displaystyle \frac{\sin ({\rm{RM}}{\lambda }^{2})}{\sin ({\rm{RM}}{\lambda }_{0}^{2})}\displaystyle \frac{{\lambda }_{0}^{2}}{{\lambda }^{2}}$. Here the wavelengths λ and λ₀ correspond to the frequencies 2695 MHz and 4800 MHz, respectively; and RM is the rotation measure contributed by the whole medium. Given the DP₂₆₉₅ values above for the area near PSR B1951+32, the absolute values of RM fall in the range of ∼ 120 – ∼ 240 rad m⁻². If the depolarization is caused by RM fluctuations σ_RM within the beam, which is referred to as beam depolarization, the depolarization factor can be written as $D{P}_{\nu }=\exp [-2{\sigma }_{{\rm{RM}}}^{2}({\lambda }^{4}-{\lambda }_{0}^{4})]$. The values of DP₂₆₉₅ yield the RM fluctuations from ∼ 35 rad m⁻² to ∼ 85 rad m⁻². However, the RM fluctuations at these levels will cause virtually complete depolarization at 1420 MHz even before smoothing, which contradicts the observations. Therefore, we attribute the observed depolarization around the pulsar area to depth depolarization.

The polarization angle varies with wavelength λ because of Faraday rotation, and can be expressed as ψ = ψ₀ + RM λ². RM is equal to the Faraday depth and thus is calculated as ${\rm{RM}}=0.81\displaystyle {\int }_{{\rm{source}}}^{{\rm{observer}}}{n}_{e}{B}_{\parallel }{\rm{d}}l$, where n_e is the thermal electron density in cm⁻³, B_∥ is the line-of-sight component of the magnetic field in μG, dl is the path length segment along the line of sight in pc and the resultant RM is in rad m⁻². Positive RMs mean that the magnetic field points towards the observer. The intrinsic polarization angle ψ₀ is perpendicular to the orientation of the transverse magnetic fields in the source.

We used data at 4800 MHz and 2695 MHz to estimate the rotation measure as ${\rm{RM}}=\displaystyle \frac{{\psi }_{2}-{\psi }_{1}}{{\lambda }_{2}^{2}-{\lambda }_{1}^{2}}$, where the subscripts 1 and 2 stand for quantities at these two wavelengths, respectively. Because of the nπ ambiguity of polarization angles, the resultant RM can differ by an integer multiple of ${\mathcal R} =\pi /({\lambda }_{1}^{2}-{\lambda }_{2}^{2})\sim 370$ rad m⁻². We assume RMs with the minimal absolute values as relevant. RMs calculated that way are displayed in Figure 4 (top panel). All pixels with polarized intensity smaller than the 3 × σ-level, which is about 36 mK at 2695 MHz and 1.5 mK at 4800 MHz, were not included for the RM calculation. The intrinsic polarization angles ψ₀ were then determined based on RM. The orientation of magnetic fields perpendicular to the line of sight, or transverse magnetic fields, is also shown in Figure 4. The transverse magnetic fields nearly follow shell C and are almost perpendicular to shell B, which is consistent with the results by Mantovani et al. (1985).

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The RM map exhibits clear patterns as can be seen from Figure 4. For shell structure C, RM changes from positive values towards the southeast to negative values towards the northwest, where the transition is around Galactic latitude b = 2.7°, which confirms the results by Mantovani et al. (1985). The RM distribution is fairly smooth for the positive RM-area with an average of about +60 rad m⁻². For the higher latitude area, the part encompassing the pulsar and its PWN has an average RM of about −150 rad m⁻², which is close to the RM of the pulsar PSR B1951+32. The remaining part further northwest has an average RM of about −60 rad m⁻².

The RM distribution towards CTB 80 consists of contributions from the Galactic medium in front of the SNR (RM_fg) and the medium local to the SNR (RM_snr), which can be written as ${{\rm{RM}}={\rm{RM}}}_{{\rm{fg}}}+\displaystyle \frac{1}{2}{{\rm{RM}}}_{{\rm{snr}}}$. Here RM_snr represents the integral of the line-of-sight magnetic field weighted by the thermal electron density over the whole SNR, and the factor $\displaystyle \frac{1}{2}$ comes from the assumption that the thermal gas and emitting medium are uniformly mixed (e.g. Sokoloff et al. 1998). In contrast, the RM of PSR B1951+32 can be expressed as RM_psr = RM_fg + f RM_snr, where the factor f depends on the relative location of the pulsar inside the SNR along the line of sight. If the pulsar sits in the middle of the emitting area, we would expect f to be $\displaystyle \frac{1}{2}$.

The foreground RM can be estimated from pulsars and simulations. We retrieved pulsars within 10° of PSR B1951+32 from the ATNF pulsar catalog ⁴ (Manchester et al. 2005), and plotted RM and DM against distance in Figure 5. The distances were calculated from DM according to the electron density model by Yao et al. (2017). For pulsar PSR B1951+32, we applied a distance of 2 kpc, the same as for CTB 80. DM is defined as the integral of electron density along the line of sight from the source to the observer. Assuming a uniform distribution of electron density and magnetic field, both DM and RM are expected to have a linear relation with distance. This is roughly the case for DM, which can be seen from Figure 5. However, RM is complicated by a large scatter. For the four pulsars with distances less than 2 kpc, their RM values are: −18 rad m⁻², −35 rad m⁻², −75 rad m⁻² and +26 rad m⁻² in the order of increasing distances. The average RM for the four pulsars is about −26 rad m⁻² with a large standard deviation of about 36 rad m⁻². We also run simulations of 3D Galactic RM towards (l, b) = (69°, 2.7°) with the models of Galactic magnetic fields developed by Sun & Reich (2010), and obtained a profile of RM versus distance from the average within a radius of 2°. The profile shows that the foreground RM is about −40 rad m⁻² at a distance of 2 kpc. Below, we use a value of −30 rad m⁻² for RM_fg, which is roughly the average of the estimates from the pulsars and the simulations. It should be emphasized here that RM_fg is uncertain though.

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Based on the RM of CTB 80 (Fig. 4) and RM_fg, we obtain a value of about −240 rad m⁻² for RM_snr of the area near PSR B1951+32, falling in the range estimated from depolarization analysis. For PSR B1951+32, we can derive the f value of about $\displaystyle \frac{5}{8}$, slightly larger than $\displaystyle \frac{1}{2}$, meaning that the pulsar is located further than the middle of the emitting medium along the line of sight. For the lower part of shell C, the resulting RM_snr is about +180 rad m⁻². This value is expected to cause large depolarization at 2695 MHz, which is not seen from the depolarization map in Fig 3. Thus, synchrotron emission and thermal gas cannot be mixed. A Faraday screen with an RM of about +90 rad m⁻² in front of the synchrotron emission of the lower part of C can explain the observations.

The change of RM signs for SNRs was reported previously for the SNR CTA 1 (Sun et al. 2011) and SNR G296.5+10.0 (Harvey-Smith et al. 2010). The former was interpreted by the influence of a foreground cloud in accordance with RMs of extragalactic sources, and the latter was attributed to the toroidal field generated by stellar wind from the progenitor star. In the case of CTB 80, the foreground RM is small. However, the large positive RMs in the lower part of shell C could be attributed to the thermal gas inside the SNR but in front of the emitting medium, which acts as a Faraday screen. There are no anomalies from RMs of extragalactic sources towards this area when investigating the Galactic foreground RM map by Oppermann et al. (2015). The reason could be that this foreground map was constructed mainly from the RM catalog by Taylor et al. (2009) with a source density of about 1 per square degree, and is therefore not sensitive to RM variations over smaller scales as in shell C. For CTB 80, the sign change occurs within one shell, and the second scenario thus cannot work. Kothes & Brown (2009) demonstrated that the sign of RM changes along the shell of an SNR, in particular when the angle between the magnetic field and the line of sight is small. This seems possible because the location of CTB 80 is close to the strong Cygnus X region, which results from the tangential view along the local arm with the magnetic field aligned.

The partial shell structure A (Fig. 1) is very intriguing. We overlaid the contours of the polarized intensity at 4800 MHz onto the high resolution total intensity image at 1420 MHz in Figure 6. CTB 80 has an unusual and complex morphology compared to other SNRs and its full extent is not very clear. Whether the faint but highly polarized structure A is part of CTB 80 or not is difficult to decide. With regard to total intensity, it seems that shell B bends towards longitudes larger than about 69.4° to form a quasi-circular shell, whereas shell A is roughly perpendicular to shell B. The non-smooth transition of emission from shell A to shell B suggests that shell A might not be related with shell B and thus CTB 80. The polarized emission from structure A (Fig. 6) appears to be separated from CTB 80. However, the end of the total-intensity shell B is seen in superposition with shell A in the unpolarized area that may indicate depolarization. In fact, Mavromatakis et al. (2001) found faint emission in Hα + [N II] and [S II] in this area. This signifies the existence of ionized matter which might cause depolarization through Faraday effects. In the case that depolarization took place, shell A would be located behind shell B and might be connected to the stronger filaments or shells of CTB 80.

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Both shell B and shell C are partly fueled by receiving high-energy particles from PSR B1951+32 and its PWN (e.g. Castelletti & Dubner 2005). Since structure A is further apart, we would expect its spectrum to be similar or steeper than that of shell B or C. This contradicts our result where structure A has a flatter spectrum. The flattening of a spectrum could be caused by strong compression by interaction with the interstellar medium. The flux-density spectral index can be connected to the shock compression ratio r following α = −3/2(r – 1) (Reynolds et al. 2012). Given α = −0.2 for structure A, the corresponding ratio is about 8.5. However, there is no indication of high density clumps towards this area from high-resolution H I observations (Park et al. 2013), meaning that this scenario is unlikely. It is therefore possible that shell A is a separate SNR, or part of it, independent of CTB 80.

Mavromatakis et al. (2001) presented CCD images of CTB 80 in several optical lines and discovered a number of long and thin filaments in this area. They concluded that CTB 80 is more extended than earlier radio observations indicated. Lynds Bright Nebula (LBN, Lynds 1965) 156 and 158 are also located in the area of CTB 80, manifesting a complex filamentary structure in their surroundings, which complicates a clear identification of structure A. Mavromatakis & Strom (2002) found shock-heated filaments in the northeast of CTB 80, which they regarded as an indication for the existence of another SNR in this area, although its size and shape were not well constrained by the observed filaments. The two longest thin filaments, apparently emerging from LBN 156, run almost parallel to structure A, but at a distance of about 15'. These filaments have very faint radio counterparts. It seems thus possible that shell A is part of the SNR proposed by Mavromatakis & Strom (2002).