ON THE SOURCE OF FARADAY ROTATION IN THE JET OF THE RADIO GALAXY 3C 120

We present VLBA observations of the jet in the radio galaxy 3C 120 corresponding to two different observing programs carried out in 2001 and 2007. Partial analysis of these data revealed gradients in Faraday rotation and polarization (Gómez et al. 2008), and unusually high brightness temperature 140 pc from the core (Roca-Sogorb et al. 2010).

Observations during 2001 were made in dual polarization at the standard frequencies of 15, 22, and 43 GHz, covering a total of 12 epochs: 2000 December 30 (hereafter epoch A), 2001 February 1 (B), 2001 March 5 (C), 2001 April 1 (D), 2001 May 7 (E), 2001 June 8 (F), 2001 July 7 (G), 2001 August 9 (H), 2001 September 9 (I), 2001 October 11 (J), 2001 November 10 (K), and 2001 December 13 (L). The data were recorded in 2 bit sampling VLBA format with 32 MHz bandwidth per circular polarization at 256 Mbits s⁻¹, except for epochs B, C, D, F, and G, for which 1 bit sampling and 128 Mbits s⁻¹ were used. One of the Very Large Array (VLA) antennas was added to the array at epochs A and E. Bad weather conditions and/or hardware problems, resulting in the loss of data, occurred at: HN during epochs A, C, and D; OV for epoch H; and KP, MK, and BR at epoch L.

The 2007 observations were performed on November 3 (at 86 GHz), November 7 (at 43, 22, and 15 GHz), and November 30 (at 12, 8, 5, 2, and 1.7 GHz) with all available VLBA antennas except Saint Croix, which was down for maintenance. The data were recorded in 2 bit sampling VLBA format with 32 MHz bandwidth per circular polarization at a recording rate of 256 Mbits s⁻¹. Observations at 12 GHz were split into two 16 MHz bandwidths centered at 12.59 and 12.12 GHz to maximize the possible detection of small Faraday rotation on relatively small angular scales.

Reduction of the data was performed with the AIPS software in the usual manner (e.g., Leppanen et al. 1995). Opacity corrections at 22, 43, and 86 GHz were introduced by solving for receiver temperature and zenith opacity at each antenna. The feed D-terms (instrumental polarization) were found to be very consistent over all observed sources and to remain stable across epochs during the 2001 observations.

The absolute phase offset between the right- and left-circularly polarized data, which determines the electric vector position angle (EVPA), was obtained by comparison of the integrated polarization of the VLBA images of several calibrators (0420 − 014, OJ 287, BL Lac, 3C 454.3, DA193, 3C 279, and 4C 39.25) with VLA observations at epochs 2000 December 31, 2001 February 3, 2001 March 4, 2001 April 6, 2001 May 11, 2001 June 10, 2001 August 12, 2001 September 10, 2001 October 12, 2001 November 6, 2001 December 15, and 2007 November 19, as well as archival data from the UMRAO, MOJAVE, and NRAO long-term monitoring programs. Estimated errors in the orientation of the EVPAs vary from epoch to epoch and with frequency, but usually lie in the range of 5°–10°. After the initial reduction, the data were edited, self-calibrated, and imaged both in total and polarized intensity with a combination of AIPS and DIFMAP (Shepherd 1997). Comparison of the D-terms across epochs provides an alternative calibration of the EVPAs (Gómez et al. 2002), which was found to be consistent with that obtained by comparison with the VLA data.

Figure 1 shows the total and linearly polarized intensity images corresponding to the 2001 monitoring program. These were used to obtain the sequence and mean value of the RM maps shown in Figures 1 and 2 of Gómez et al. (2008), respectively, which requires careful alignment of the images across epochs and frequencies. A detailed description of the procedure used and accuracy achieved is presented in the Appendix.

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VLBA observations of 3C 120 taken during 2007 November are shown in Figures 2–4, which provide a 50-fold range in angular resolution. In Roca-Sogorb et al. (2010), a partial analysis of these data was carried out that revealed a brightness temperature for the component located 80 mas from the core about 600 times higher than expected at such distances. Roca-Sogorb et al. (2010) concluded that, although a helical shocked jet model may explain this unusually high brightness temperature, it appears that some other intrinsic process capable of producing a local burst in particle and/or magnetic energy may be needed to also explain the sudden appearance and apparent stationarity of this component.

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The 1.7 GHz total intensity image in Figure 2 shows a continuous jet that extends approximately 300 mas, with a bulge of emission between 200 and 280 mas. Although the complex structure of the bulge prevents us from obtaining an accurate measure of its position, comparison by eye between our image and those by Walker et al. (2001)—covering in total a time span of almost 30 years—confirms the proper motion of 1.7 ± 0.4 mas yr⁻¹ for the bulge reported by Walker et al. (2001). This is similar to the proper motions measured at parsec scales (e.g., Gómez et al. 2001b) and indicates that relativistic bulk velocities are sustained in the jet over at least hundreds of parsecs from the core.

The progressively higher frequency images in Figures 2 and 3 reveal a rich structure in both total and linearly polarized intensity even at the shortest wavelengths, being the emission at 80 mas particularly remarkable, as reported by Roca-Sogorb et al. (2010). The component 12 mas from the core (hereafter C12) is also especially bright. Roca-Sogorb et al. (2010) estimated a compression factor⁴ η ∼ 0.35 assuming that the feature corresponds to a moving shock wave. This allows the detection of this component even at 86 GHz (Figure 4), at which some emission from the innermost 2 mas is also visible in the image. No polarization is detected at 86 GHz though. Comparison of the core flux density among frequencies yields a flat spectrum at 43 GHz and frequencies below, but optically thin at 86 GHz; we should note, however, that this may be affected by the relatively large uncertainties involved in the flux calibration at this frequency. Previous 86 GHz observations of 3C 120 established an upper limit to the overall core size of 54 μas (Gómez et al. 1999a), followed by a measurement of the FWHM size of the core along the axial direction of 22 ± 2 μas, as well as an estimation of the number density of the combined electron–positron population in the core (Marscher et al. 2007).

The first indications of the presence of the localized Faraday rotation region between 3 and 4 mas from the core were obtained through monthly polarimetric VLBA observations at 22 and 43 GHz carried out between 1997 November and 1999 March (Gómez et al. 2000, 2001b). The EVPAs of several components were observed to rotate while they passed through this region by an amount which followed a quadratic dependence with observing wavelength—as expected for Faraday rotation. This is more clearly seen in the RM map for epoch 1999 January 10 shown in Figure 5, obtained from observations at 22 and 43 GHz. To solve for the ±π ambiguities in the EVPAs when obtaining the RM image we have considered those values that result in the smallest RM values and yield the best agreement (both in RM and RM-corrected EVPAs) with the image obtained for observations in 2001 (see Figure 2 of Gómez et al. 2008), also plotted in Figure 5 for comparison. The 2001 RM image reveals the presence of an RM screen in 3C 120 whose properties remain constant over one year, during which most of the jet shows RM and RM-corrected EVPAs values with standard deviations smaller than 1000 rad m⁻² and 20°, respectively. The Faraday screen displays a localized region of enhanced RM between approximately 3 and 4 mas from the core, with a peak of ∼6000 rad m⁻², as well as gradients across and along the jet.

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RM images for observations in 2007 combining the high-, intermediate-, and low-frequency intervals are shown in Figures 6–8, respectively.

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To quantify any possible variation in the Faraday screen, we have subtracted the RM values of 1999 January from those of the mean RM map for 2001 and computed the mean value of the difference in the components (jet areas in the mean 2001 map) labeled in Figure 5 (following the nomenclature of Gómez et al. 2000, 2001b). Component L is located at the localized region of high Faraday rotation, which is found to remain in the same jet area as in 2001, with very similar values of the RM (mean difference of −660 ± 770 rad m⁻²). However, the RM-corrected EVPAs show significant rotation, with a mean difference between both epochs of −64° ±  9°. A similar situation is found for component H, with a mean variation in the RM of 1030 ± 1010 rad m⁻² and a rotation of the RM-corrected EVPAs of −72° ± 19°. On the other hand, component K shows no significant changes in either the RM-corrected EVPAs or RM, with variations of −3° ± 19° and 810 ± 930 rad m⁻², respectively. For component O, we also find very similar RM-corrected EVPAs, with a variation of 8° ± 28°. However, the RM in component O is observed to have changed significantly, with a difference between both epochs of 2730 ± 910 rad m⁻².

Therefore, we find uncorrelated changes in the linear polarization of the underlying jet emission and the Faraday rotation screen: while the RM remains constant in the outer jet—including the localized region of high RM—the RM-corrected EVPAs of two particular components (L and H) rotate by almost 90°; on the other hand, in the innermost 2 mas the RM changes significantly but without variations in the RM-corrected EVPAs. These uncorrelated changes suggest that the emitting jet and source of RM are not closely connected physically.

Components L and H have RM-corrected EVPAs closely aligned with the jet, in agreement with observations by Jorstad et al. (2005). This is in contrast to what we find during 2001, where the RM-corrected EVPAs are observed to be approximately perpendicular to the jet direction. This suggests an aligned magnetic field, in agreement with that observed on larger scales (Walker et al. 1987). If these components correspond to strong plane–perpendicular shock waves, compression of the magnetic field parallel to the shock front can result in a dominant magnetic field perpendicular to the components' motion (e.g., Marscher & Gear 1985; Hughes et al. 1989; Gómez et al. 1994), as observed in knots L and H. However, no similar orientation of the EVPAs is found for component O—which is probably also associated with an even stronger shock—or in any of the other components that have traveled along the same jet regions as that of L and H during the 2001 observations (see also Jorstad et al. 2005). On the other hand, if components L and H are not particularly strong shocks—which finds support in the fact that their degrees of polarization are similar to those observed for other components at similar jet locations—we can consider the possibility that these components either have an intrinsically different magnetic field (mainly perpendicular to the jet axis), or that they have a different velocity and/or orientation with respect to the observer. In this latter case, the Lorentz transformation of the magnetic field—which amplifies the components transverse to the motion—would generally result in an observed dominant toroidal field for an assumed helical magnetic field (e.g., Blandford & Königl 1979; Lyutikov et al. 2005). The clear stratification in polarization observed between the northern and southern jet regions (see Figure 3 of Gómez et al. 2008) and the fact that both components L and H move along the southern side may support this idea of stratification across the jet of the magnetic field and/or kinematics.

The middle- and low-frequency range RM maps (Figures 7 and 8) reveal no indication of localized regions of high RM at these scales similar to that found at parsec scales in previous observations (Gómez et al. 2008; see also Figure 5), as may have been expected given the wealth of evidence for interaction between the jet and ambient medium (e.g., Axon et al. 1989; Sánchez et al. 2004; Gómez et al. 2000, 2008). The high-frequency range RM map in Figure 6 does not show the localized region of high RM that was found in previous observations. This can be understood by examining Figure 9, which shows the superposition of the 15 GHz total intensity images at the 2001.00 and 2007.85 epochs, revealing a significant change in the jet geometry with time. The position angle of the innermost 3 mas structure has changed from −126° ± 2° in 2001.00 to −114° ± 2° in 2007.85, that is, the jet direction of ejection rotated to the north by 12° between these two epochs. As a consequence of this rotation, the components in the 2007 jet do not travel across the localized region of enhanced RM. They thus fail to reveal it, since it is only through the motion of superluminal components that we are able to map the jet polarization owing to the increase in energy density and magnetic field ordering that they produce.

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The rotation of the direction of ejection is in agreement with the helical structure suggested by Gómez et al. (2001b), and the proposed precessing/helical models of Caproni & Abraham (2004) and Hardee et al. (2005). In particular, Caproni & Abraham (2004) estimated a precession period of 12.3 years, predicting a swing to the north of the direction of ejection in the jet between our 2001 and 2007 epochs, as is indeed observed.

There is evidence for non-ballistic trajectories of the superluminal components for observations between 1997 November and 1999 March (Gómez et al. 2000, 2001b), resulting in the gentle bend toward the north observed in the 2001 epoch in Figure 9. This contrasts with the rectilinear structure observed at the 2007.85 epoch. Component C12 is one of the brightest ever observed at parsec scales in 3C 120, so it is possible that it contains an unusually large energy density, with enough momentum to move ballistically and "break through" the bent jet funnel inferred in the 2001 epoch. This may have left behind a funnel through which upstream components move ballistically, resulting in the almost rectilinear jet observed in 2007.85.

Similar changes in the geometry of the innermost structure of the jet have also been found in the BL Lac object PKS 0735+178. In this case, they are related to changes in the overall activity of the source: quasi-stationary or subluminal components moving through a twisted structure are observed during periods of low activity, while superluminal components moving along a straight jet are found during periods of high activity (Gómez et al. 1999b, 2001a; Gabuzda et al. 2001; Agudo et al. 2006; Britzen et al. 2010).

If component C12 is interacting with the external medium, it does not result in enhanced RM. Figures 6 and 7 show that the RM of C12 is approximately −45 rad m⁻² (−66 ± 1 rad m⁻² at the lower frequency interval in Figure 8), significantly smaller than the ∼6000 rad m⁻² found in the region between 3 and 4 mas from the core (Gómez et al. 2008; see also Figure 5), presumably produced by the interaction of the jet with the external medium. However, there is a sign reversal in the RM of C12 when compared with the remainder of the jet.

A progressive decrease in the RM along the jet in 3C 120 is visible in the 2007 observations (Figures 6–8), as well as in the 1999 January image in Figure 5. The relatively high RM close to the core may be responsible for the dramatic decrease in the degree of polarization toward the core, as previously suggested by Gómez et al. (2008). Similar decreases in the RM along the jet have been previously observed in other sources (e.g., Taylor 1998; Gabuzda & Chernetskii 2003; Jorstad et al. 2007; O'Sullivan & Gabuzda 2009). This can be explained as the result of the decrease in the density of the external ionized gas and magnetic field strength with distance from the core (e.g., Guidetti et al. 2010).

Component C12 departs from this monotonic decrease in RM with core distance, undergoing a change in the sign of the RM, which implies a double sign reversal when analyzing the RM along the remainder of the jet. We note, however, that our RM images—and therefore the existence of sign reversals—may be affected by a source of RM in the direction of 3C 120 that is unrelated to the jet, which recent observations estimate to be ∼23 rad m⁻², with a 1σ error of ∼10 rad m⁻² (Taylor et al. 2009).

RM sign reversals have been previously reported along (Zavala & Taylor 2001; O'Sullivan & Gabuzda 2009) and across (Gabuzda et al. 2004; Asada et al. 2008b; Mahmud et al. 2009) jets, but to our knowledge, no similar double sign reversal at parsec scales as reported here has been found previously (see also Guidetti et al. 2010). Sign reversals in the RM across a jet can be readily explained by a sheath threaded by a helical magnetic field. To account for the reversals along a jet, different alternative explanations have been proposed. One is based on "magnetic tower" models, in which the magnetic field lines are wound up in two nested helices with opposite poloidal polarities, with the inner helix less tightly wound than the outer helix. Such magnetic towers are expected to arise by the Pointing–Robertson effect (Contopoulos & Kazanas 1998), caused by the differential rotation of the accretion disk. A change in the relative contributions to the observed RM of the inner and outer helical fields has been considered by Mahmud et al. (2009) to explain changes in the direction of transverse RM gradients, which can eventually also lead to a sign reversal. Similar magnetic tower models have also been considered to explain the different helical pitch angles derived for the emitting jet and the sheath in NRAO 140 (Asada et al. 2008b) and S5 0836+710 (Asada et al. 2010). It is also possible to explain a sign reversal in the RM along the jet by assuming that the sheath responsible for the Faraday rotation is at least moderately relativistic, so that light aberration can lead to a change in the line-of-sight-dominant component of the magnetic field through a small change in the direction or velocity of the flow, as considered previously by O'Sullivan & Gabuzda (2009).

It would be difficult to explain the double RM sign reversal along the jet of 3C 120 through magnetic tower models, since this would consequently require an unlikely double change in the relative contributions to the RM of the inner and outer helical fields. However, the change in the RM sign in C12, when compared with the RM of the remaining jet, can be explained within the moderately relativistic sheath model as produced by a local change in the velocity or orientation, as would be expected in the case of precession in 3C 120. Note that this could also explain its unusually bright emission through differential Doppler boosting.

It is interesting to note that, although the RM of C12 undergoes a sign reversal, the RM-corrected EVPAs have the same orientation as for the remainder of the optically thin jet, i.e., perpendicular to the jet. (Note that component C80 contains RM-corrected EVPAs aligned with the jet, but as reported by Roca-Sogorb et al. 2010, this is probably due to its peculiar nature.) Therefore, in order to explain the RM sign reversal in C12 through any of the different proposed models without producing a change in the RM-corrected EVPAs, we need to assume that the emitting jet and the sheath responsible for the Faraday screen have different kinematical properties and/or magnetic field configurations. Alternatively, a much simpler interpretation for the different RM sign in C12 can be obtained by considering that the Faraday rotation is produced in a foreground cloud with a different magnetic field than that of the remaining jet.

A sign reversal in the RM along the jet is also observed in the 1999 January image (Figure 5), as well as between the innermost 2 mas of the jet in this image and those obtained in 2001 (Figure 1 in Gómez et al. 2008) and 2007.85 (Figure 6). If we assume that the sheath is at least moderately relativistic, a change in the direction of ejection in the jet—as expected for precession—could explain the differences in the RM between 1999 and 2007 through the different projections of the field along the line of sight. To explain the RM sign reversal between 1999 and 2001, an unlikely large change in the bulk velocity of the sheath would be needed (given the similar directions of ejection for the jet at both epochs), so that a change in the line-of-sight component of the field could be obtained through light aberration. Note however that, as mentioned for C12, different kinematical properties and/or magnetic field configurations would be needed for the sheath and emitting jet, so that the RM can change without producing a rotation of the RM-corrected EVPAs.

Broderick & Loeb (2009) have considered the possibility of having relativistic helical motions in the Faraday rotating sheath, showing that sign reversal in the RM can naturally arise in this case, especially for observations at high frequencies that probe the innermost regions where there is a transition between ultra-relativistic and moderately relativistic helical motion. This could explain the RM sign reversals along the jet in the 1999 January image, but it would require a—a priori unlikely—considerable change in the kinematical properties of the sheath to account for the RM time variability observed between 1999 January and later epochs.

The relativistic helical sheath model of Broderick & Loeb (2009) might also account for the sign reversal of component C12, which could also explain the variation in the RM with changing frequency intervals.