Parsec-scale Faraday rotation and polarization of 20 active galactic nuclei jets
aa r X i v : . [ a s t r o - ph . H E ] M a r MNRAS , 1–19 (2017) Preprint 27 August 2018 Compiled using MNRAS L A TEX style file v3.0
Parsec-scale Faraday rotation and polarization of 20 active galacticnuclei jets
E. V. Kravchenko , ⋆ , Y. Y. Kovalev , and K. V. Sokolovsky , , Lebedev Physical Institute, Astro Space Center, Profsoyuznaya 84 /
32, Moscow 117997, Russia Pushchino Radio Astronomy Observatory ASC Lebedev, Pushchino 142290, Moscow region, Russia Max-Planck-Institut f¨ur Radioastronomie, Auf dem H¨ugel 69, Bonn D-53121, Germany IAASARS, National Observatory of Athens, 15236 Penteli, Greece Sternberg Astronomical Institute, Moscow State University, Universitetsky pr. 13, Moscow 119991, Russia
Accepted 2017 January 4. Received 2017 January 1; in original form 2016 October 28
ABSTRACT
We perform polarimetry analysis of 20 active galactic nuclei (AGN) jets using the Very LongBaseline Array (VLBA) at 1.4, 1.6, 2.2, 2.4, 4.6, 5.0, 8.1, 8.4, and 15.4 GHz. The study al-lowed us to investigate linearly polarized properties of the jets at parsec-scales: distribution ofthe Faraday rotation measure (RM) and fractional polarization along the jets, Faraday e ff ectsand structure of Faraday-corrected polarization images. Wavelength–dependence of the frac-tional polarization and polarization angle is consistent with external Faraday rotation, whilesome sources show internal rotation. The RM changes along the jets, systematically increas-ing its value towards synchrotron self-absorbed cores at shorter wavelengths. The highest coreRM reaches 16,900 rad m − in the source rest frame for the quasar 0952 + − . Significant transverse rotation mea-sure gradients are observed in seven sources. The magnetic field in the Faraday screen hasno preferred orientation, and is observed to be random or regular from source to source. Halfof the sources show evidence for the helical magnetic fields in their rotating magnetoionicmedia. At the same time jets themselves contain large–scale, ordered magnetic fields and tendto align its direction with the jet flow. The observed variety of polarized signatures can beexplained by a model of spine–sheath jet structure. Key words: galaxies: jets – radio continuum: galaxies – radiation mechanisms: non-thermal– polarization – magnetic fields
Magnetic fields play an important role in launching, accelera-tion and collimation of relativistic jets of active galactic nuclei(Blandford & Znajek 1977). Theoretical models and numericalsimulations suggest that a rotating accretion disk and ergospherearound a supermassive black hole will produce magnetized plasmaoutflows. Twisted magnetic fields will thread these flows (e.g.Meier et al. 2001; Vlahakis & K¨onigl 2004). While these modelspredict strong, ordered magnetic fields close to the central en-gine (e.g. Blandford & Znajek 1977; Nishikawa et al. 2005), down-stream in the jet these fields may be randomized, dissipated ortangled by di ff erent types of instabilities (e.g. Istomin & Pariev1994; Hardee 2004). Despite numerous theoretical and observa-tional studies, the exact geometry and main properties of the jetmagnetic fields are still not known. ⋆ Contact e-mail: [email protected]
Faraday rotation and depolarization at radio wave-length (e.g. Udomprasert et al. 1997; Zavala & Taylor2003; O’Sullivan & Gabuzda 2009a; Hovatta et al. 2012;O’Sullivan et al. 2012; Farnes et al. 2014; Pasetto et al. 2016),together with relativistic and opacity e ff ects complicate directanalysis of the jet properties. Multiwavelength full-Stokes verylong baseline interferometric (VLBI) observations are needed toconsider and account for these e ff ects.Complex linear polarization Π is defined as Π = Q + i U = Pe χ = mIe χ , (1)where I , Q and U are the measured Stokes parameters, P isthe modulus of Π , χ is the observed electric vector position an-gle (EVPA), and m is observed degree of polarization, m = p Q + U / I . The depolarization and Faraday rotation changethe intrinsic polarization properties of a source: the observed po-larization angle is rotated with respect to the intrinsic one ( χ )by an amount RM = d χ/ d( λ ), while the degree of polariza-tion undergoes depolarization or even repolarization and become c (cid:13) E. V. Kravchenko, Y. Y. Kovalev and K. V. Sokolovsky wavelength–dependent. Here RM denotes Faraday rotation mea-sure (Burn 1966) in radians per squared metre. RM is proportionalto the magnetic field component parallel to the line of sight (LoS), B k , and to the particle volume density n e along the path dl :RM ∝ Z LoS n e B k · dl . (2)In the simplest case, when the Faraday rotation occurs external tothe jet magneto-ionic medium, the degree of polarization does notexperience depolarization and RM can be defined as: χ = χ + RM λ . (3)Meanwhile, observed significant wavelength–dependent behaviourof the fractional polarization in the AGN jets (e.g. Conway et al.1974) suggests presence of a depolarization and various Faradaye ff ects, e.g. di ff erential Faraday rotation and Faraday dispersion(Sokolo ff et al. 1998). Thus, multiwavelength observations allowthe determination of Faraday e ff ects and RM, and hence enable oneto study intrinsic orientation of the jet magnetic field.The most likely source of Faraday rotation is the ion-ized medium, located in close proximity to the jet. It might bedense gas clouds, surrounding AGN jets and producing largeobserved RMs (Junor et al. 1999; Mantovani et al. 2010). How-ever, outer jet layers (Zavala & Taylor 2004) or the jet sheath(Asada et al. 2002; Mizuno et al. 2007) are more plausible. Manypieces of observational evidence favour this suggestions. One ofthese is the tendency for opaque VLBI cores increase their RMvalues towards shorter wavelengths (e.g. Zavala & Taylor 2004;Jorstad et al. 2007; O’Sullivan & Gabuzda 2009a; Algaba 2013).Owing to the opacity e ff ects (known as “core shift”), this be-haviour is expected, since the τ ≈ ff ects and study the magneticfield structure in 20 AGN jets at parsec-scales using full polar-ization Very Long Baseline Array (VLBA) observations conductedin the frequency range from 1.4 to 15.4 GHz. The study comple-ments the works by Farnes et al. (2014), Pasetto et al. (2016) andAnderson et al. (2016) who investigated sources at kpc–scale in acomparable frequency range of 1 GHz to 15 GHz, as well as thenumerous individual sources (e.g. Asada et al. 2008a, 2010) andsample studies (e.g. Zavala & Taylor 2003; O’Sullivan & Gabuzda2009a; Hovatta et al. 2012). Application of the VLBI technique al-lows us (i) to minimize the level of depolarization within the tele-scope beam compared to single-dish and connected-interferometer m (per cent)0 5 10 15 20N 051015 jet componentsm (per cent)0 5 10 15 20N 010203040 core components Figure 1.
Distribution of measured polarization degree for all sources in thecore and jet components. The number of appearance of each source in theFigure corresponds to the number of frequency bands, where polarized fluxwas detected, and can reach a maximum value of nine bands. The sources,with no significant polarized flux detected, are not presented. The definitionof core and jet components are given in Section 2.1. observations (e.g. O’Sullivan et al. 2012) and (ii) study separatelyjet regions with di ff erent synchrotron opacity.This paper is structured as follows: observations and data re-duction are described in Section 2. In Section 3 we give our resultsof Faraday e ff ects study and Faraday rotation measurements, thedescription of the proposed method for the reconstruction of thespatial magnetic field geometry and results of its application. Sec-tion 4 summarizes our findings. Through the paper the model of flat Λ CDM cosmology was used with H =
68 km s − , Ω M = Ω Λ = α is de-fined as S ∝ ν α , where S is the flux density, observed at frequency ν . We selected twenty sources from the geodetic VLBI database(Fey & Charlot 1997; Petrov et al. 2009), showing large frequency-dependent core shifts at cm-band and having bright jet featuressuitable as reference points for aligning images obtained at dif-ferent frequencies. Sokolovsky et al. (2011) used this sample toinvestigate the core shift e ff ect concluding that cores of all theselected sources are well described by the Blandford & K¨onigl MNRAS , 1–19 (2017) araday RM and polarization of 20 AGN jets Table 1.
Target sources and RM frequency ranges.IAU name Other Redshift Optical Observational Observational frequencies (GHz)(B1950.0) name class epoch 1.4 1.6 2.2 2.4 4.6 5.0 8.1 8.4 15.40148 +
274 1.260 QSO 2007–03–01 L L L L H H H H H0342 +
147 1.556 QSO 2007–06–01 L L L L M M MH MH H0425 +
048 OF 42 0.517 a AGN 2007–04–30 L L L L M M MH MH H0507 +
179 0.416 AGN 2007–05–03 L L L L M M MH MH H0610 +
260 3C 154 0.580 QSO 2007–03–01 - - - - - - - - -0839 +
187 1.272 QSO 2007–06–01 L L L L H H H H -0952 +
179 1.478 QSO 2007–04–30 L L L L M M MH MH H1004 +
141 2.707 QSO 2007–05–03 L L L L H H H H -1011 +
250 1.636 QSO 2007–03–01 - - - - M M M M -1049 +
215 1.300 QSO 2007–06–01 L L L L M M MH MH H1219 +
285 W Comae 0.161 b BLL 2007–04–30 L L L L H H H H H1406 −
076 1.493 QSO 2007–05–03 L L LM LM M MH H H H1458 +
718 3C 309.1 0.904 QSO 2007–03–01 L L L L M M MH MH H1642 +
690 0.751 QSO 2007–04–30 L L L L M M MH MH H1655 +
077 0.621 QSO 2007–06–01 L L L L H H H H H1803 +
784 0.680 QSO 2007–05–03 L L L L M MH MH MH H1830 +
285 0.594 QSO 2007–03–01 - - M M M M - - -1845 +
797 3C 390.3 0.056 AGN 2007–06–01 - - - - - - - - -2201 +
315 0.298 QSO 2007–04–30 L L L L - - H H H2320 +
506 1.279 QSO 2007–05–03 L L L L - H H H HThe value of RM was estimated at di ff erent frequency intervals separately due to the considered linear dependence of EVPA vs. λ , namely Low (1.4 GHzto 2.4 GHz), Middle (2.2 GHz to 5.0 GHz) and High (4.6 GHz to 15.4 GHz). Redshifts and optical classes are from V´eron-Cetty & V´eron (2010). VLBIposition can be found in Sokolovsky et al. (2011). Observational frequencies are given in GHz. a – Spectroscopic redshift obtained by Afanas’ev et al. (2003). b – Photometric redshift, see Finke et al. (2008). Table 2.
Galactic rotation measures.Source NVSS Optically Averagedthin regions over map0148 + − ± − ± − ± +
147 6 ± ± ± +
048 35 ±
11 42 ± ± + − ± − ± − ± +
260 44 ± − − +
187 38.2 ± ± ± + − ± − ± − ± +
141 12 ± ± ± + − ± − − +
215 8.8 ± − ± ± +
285 15 ± − ± ± − − ± − ± − ± +
718 63.1 ± ± ± + − ± − ± − ± +
077 14.0 ± ± ± + − ± − ± − ± +
285 30 ± − ± + − ± − − + − ± − ± − ± + − ± − ± − ± − . NVSS RM are obtained by Taylor et al.(2009). RMs given in the third column are estimated under assumption thatthe electric vector position angle maintains its direction in the optically thinregions over the whole frequency range. Values in the last column are aver-aged over the whole RM maps across 1.4 GHz to 2.4 GHz range. (1979) model with the shift being ∝ ν − . Accordingly, we definethe radio core (or simply the core) at a given frequency as the sur-face with optical depth τ ≈ u (noted as U below) fre-quency bands were used. Each band consists of four 8 MHz-widefrequency channels (IFs) per polarization. L, S, C and X bandswere split into two sub-bands (two IFs in each sub-band) centeredat 1.41, 1.66, 2.28, 2.39, 4.60, 5.00, 8.11, and 8.43 GHz respec-tively. In the following analysis these sub-bands were processedindependently. At U-band all four IFs were combined into a sin-gle sub-band centered at 15.4 GHz in order to provide sensitivitysimilar to that of individual sub-bands at lower frequencies. Thisdivision into sub-bands allows us to decrease the e ff ect of signaldepolarization over the bandwidth. The resulting width of a chan-nel is 32 MHz at 15.4 GHz and 16 MHz at other frequencies. Thetotal on-source observing time for each target was about one hourper band.The dual-polarization observations recorded data at each sta-tion with 2-bit sampling and a total rate of 256 Mbps. The data werecorrelated at Socorro (NM, USA) with averaging time of 2 s. Data calibration and imaging, as well as model fitting were donein a standard manner for each sub-band independently using theAstronomical Image Processing System (AIPS, Bridle & Greisen1994) and Difmap (Shepherd et al. 1994; Shepherd 1997). Calibra-tion steps are described by Sokolovsky et al. (2011) and the AIPSCookbook in details. The amplitude calibration accuracy in the1.4 GHz to 15 GHz frequency range is estimated to be ∼ I flux density, σ I ,and linearly polarized flux density, σ P , are calculated by consider-ing absolute calibration uncertainties and the map rms noise. MNRAS , 1–19 (2017)
E. V. Kravchenko, Y. Y. Kovalev and K. V. Sokolovsky
Polarization leakage parameters of the antennas (D-terms) were determined within AIPS with the task LPCAL(Leppanen et al. 1995). D-terms were examined for time stability(Roberts et al. 1994; G´omez et al. 2002) using the two polar-izations of each IF at all antennas. Corrections were calculatedat L- and S-bands by averaging and minimizing the R-L phaseo ff set over four epochs; at C- and X-bands by comparing the R-Lo ff set over one year time interval; and at U-band by connectingour observations with the D-term phase solutions from 10-yearMOJAVE program data (Lister et al. 2009, 2013). Thus, accuracyof leakage parameters approaches 2 ◦ (about 1 per cent) at L- andS-bands and 1 ◦ (about 0.5 per cent) at other frequencies.Absolute EVPA calibration at L- and S-bands was done us-ing the EVPAs of 3C 286 and at C-, X-, and U-bands using theEVPAs of 3C 273 and 4C + (Taylor & Myers 2000), the University of Michigan RadioAstronomy Observatory monitoring program, and from the MO-JAVE program. Absolute calibration error is assessed as the dif-ference in corrected EVPA between pairs of sub-bands, and at U-band it is assessed as the deviation of the corrected EVPA fromthe EVPA of calibrators taken from the monitoring programs. Theresulting absolute EVPA calibration error is 4 ◦ and 2 ◦ for L-, S-and C-, X-, U-bands respectively. Final calibration error of abso-lute vector position angle comprises errors from instrumental andabsolute calibrations and is estimated to be 5 ◦ at low frequencies(L- and S-bands), 2 . ◦ at middle frequencies (C- and X-bands) and2 ◦ at U-band.The uncertainties in fractional polarization, σ m , and EVPA, σ χ , are calculated from error propagation theory: σ m = I r σ + σ P I , (4)and σ χ = q σ Q + σ U Q + U ) , (5)where σ Q and σ U are the uncertainties in the Q and U Stokes fluxdensities. The contribution of the instrumental polarization leakageto the Stokes I and linear polarization maps (Roberts et al. 1994;Hovatta et al. 2012) is considered as σ Dterm = σ ∆ √ N ant N IF N scan q I + (0 . I peak ) , (6)where σ ∆ is the scatter of D-terms, N ant is the number of antennas, N IF is the number of IFs, N scan is the number of VLBA scans on po-larization calibrator with independent parallactic angles, and I peak is the peak Stokes I flux density of the map. The scatter of D-termsin our data is estimated to be 0.01, 0.005 and 0.002 for 1.4 GHzto 2.4 GHz, 4.6 GHz to 8.4 GHz and 15.4 GHz frequencies. Thenumber of antennas is 10, the number of scans on 3C 286, OJ 287and 4C + ∆ ν : ∆ χ = − RM λ ∆ νν . (7)It is noticeable at lower frequencies only, where it amounts to ≈ . ◦ for the typical RM values in AGN jets (e.g. Zavala & Taylor 2003).At higher frequencies the resulting EVPA smearing is well withincalibration errors.To model the structure of the source, a number of circularor elliptical two-dimensional Gaussian components were fitted tothe fully calibrated visibility data in the u–v plane, using the task modelfit in DIFMAP. The VLBI core was identified as the brightcomponent at the apparent jet base at each frequency and fur-ther we refer to it as “core component”. To analyse properties ofthe optically thin jet, we choose single, bright jet component, thatcould be identified through all frequencies. Hereinafter we refer toit as “jet component”. More details of model fitting are given inSokolovsky et al. (2011). The dependence of EVPA on λ was considered at ‘Low’ (1.4 GHzto 2.4 GHz), ‘Middle’ (2.2 GHz to 5.0 GHz) and ‘High’ (4.6 GHz to15.4 GHz) frequency intervals separately for all sources because ofsparse observational frequency coverage, changing opacity in coreregion, and presence of Faraday e ff ects. The RM is estimated as alinear slope of EVPA with λ at these frequency ranges, presentedin Table 1.To match the resolution of images obtained at di ff erent fre-quencies, the images were restored with the beam correspondingto uniform weighting of the data at the lowest frequency of theLow, Middle, or High range, respectively (see Table 1). The self-calibration technique used to obtain high quality images unfortu-nately loses information about absolute position of a source. There-fore, the positions of optically thin jet components were used toalign images at di ff erent frequencies. See details of this technique,tests for possible biases and comparison with other methods in, e.g.Kovalev et al. (2008); Pushkarev et al. (2012); Kutkin et al. (2014);Fuhrmann et al. (2014).We used only pixels with polarized flux density stronger thanthree times the polarization error (see Taylor & Zavala 2010 for athorough discussion and references). The resolution of the n π -wrapproblem was done by minimizing the reduced χ . Finally, we usedthe 95 per cent confidence level for the respective number of de-grees of freedom. Observed Faraday rotation occurs at three main locations: (i) thejet itself and its immediate vicinity, (ii) the intergalactic and (iii)Galactic medium. All values discussed in this work refer to the firstenvironment, while other two act as foreground Faraday screensand for further analysis their contribution must be removed.The presence of magnetic fields in the intergalactic mediumwill cause Faraday rotation (see Akahori & Ryu 2010, 2011;Bernet et al. 2012). The origin of these fields outside galaxy clus-ters, as well as their distribution in the cosmic web or redshift de-pendence is not well understood yet. Thus, the contribution of theextragalactic RM component for every source is not reliably esti-mated and we did not account it in this analysis.Estimations of RM resulting from plasma in our Galaxy havebeen performed by, e.g. Taylor et al. (2009); Mao et al. (2010);Van Eck et al. (2011); Jansson & Farrar (2012); Oppermann et al.(2012); Han (2013), focusing on reconstruction of Galactic mag-netic fields based on analysis of polarized properties of extragalac-tic radio sources, Galactic pulsars, recombination lines and ionized
MNRAS , 1–19 (2017) araday RM and polarization of 20 AGN jets Table 3.
Measured Stokes I flux density and polarization degree ( m ) of Gaussian core and jet components, peak Stokes I flux density ( I peak ) and rms noise( σ I ) in the image. The full table is available online.Source Frequency m core I core m jet I jet I peak σ I (GHz) (per cent) (mJy) (per cent) (mJy) (mJy beam − ) (mJy beam − )0148 +
274 1.4 1.62 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± < ± ± +
147 1.4 < ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± τ ∼ τ ≪ gas. Estimated values of Galactic RM agree well between theseworks. Therefore we substracted RMs obtained by Taylor et al.(2009) from the observed polarization angles, since they provideRM estimates for all sources in our sample (see Table 2). We notethat this correction is not needed for the RM gradient analysis weperform.Average uncertainties in these Galactic RMs amount to a fewto tens of rad m − (see Table 2). In Table 4 we show values ofEVPA rotation for di ff erent radio frequencies for RM = − .An error of 5 rad m − in Galactic RM a ff ects EVPA at 1.4 GHzto 2.4 GHz by 13 . ◦ to 4 . ◦ respectively. We note that these errorsmight significantly corrupt the χ values at low frequencies.Section 3.10 contains a discussion of the observed EVPA inoptically thin components in our sources, which enables us to esti-mate foreground RMs and compare them with values reported byTaylor et al. (2009). m vs. λ Faraday rotation can produce frequency-dependent depolarizationor even repolarization (e.g. Burn 1966; Sokolo ff et al. 1998). Tostudy the polarized properties of the sources, we consider a numberof e ff ects and used them to model observed m vs. λ dependencies.Meawnhile linear fit was applied to EVPA vs. λ in ranges given inTable 1.Detailed discussion of various Faraday e ff ects is given by,e.g. Sokolo ff et al. (1998) and Farnes et al. (2014). To fit the datawe follow suggestion of Farnes et al. (2014) and model m vs. λ by four functions, which reproduce the wavelength-dependence ofFaraday e ff ects quite well. Namely these are: Gaussian, Gaussianwith a constant term, two Gaussians, and polynomial, given by fol- lowing equations respectively m = a exp h − ( λ − a ) a i , (8) m = a exp h − ( λ − a ) a i + a , (9) m = a exp h − ( λ − a ) a i + a exp h − ( λ − a ) a i , (10) m = a λ a . (11)Coe ffi cients a i in the equations are to be solved for during the modelfitting.For the analysis, we consider both the core and jet compo-nents. Meanwhile, optically thick synchrotron emission could pro-duce more complex EVPA vs. λ signatures, thus can not be wellmodelled by these parametric functions (see Pacholczyk & Swihart1967; Fukui 1973; Jones & Odell 1977).The Bayesian Information Criterion (BIC, Schwarz 1978) isused to compare the goodness of fit of models with di ff erent num-ber of parameters. The BIC is given by:BIC ≈ − L + k ln( N ) , (12)where ln L is the log-likelihood of the data given the model, k isthe number of parameters of the model, and N is the sample size.Assuming Gaussian noise, the Likelihood of the model θ is definedas the joint probability to fit the data as L = max( p ( y | θ )) , p ( y | θ ) = N Y i = √ πσ i exp (cid:16) − ( y i − y Mi ( θ )) σ i (cid:17) (13) MNRAS , 1–19 (2017)
E. V. Kravchenko, Y. Y. Kovalev and K. V. Sokolovsky ) (m λ m ( % ) ) (m λ E V P A ( d e g ) − ± = -17 C1 RM 13 ± = 168 C2 RM (GHz) ν I ( m J y ) ) (m λ m ( % )
246 0148+274 Jet ) (m λ E V P A ( d e g ) ± = -7 J1 RM 14 ± = -42 J2 RM Figure 2.
Source 0148 + I levels are drawn at(-1,1,2,4...) × the lowest contour (that is 3 σ S and given in Table 3). Here and hereafter, I contours and their values are given for the lowest frequency of a givenfrequency range. The colour bar is given in rad m − .The dot and letter represent positions of the model-fitted core (”C”) and jet (”J”) components, EVPA vs. λ fits shown in the inset; the corresponding degree of polarization and spectrum are given. The EVPA value is taken from a polarization map convolved withthe beam size of the lowest frequency of the RM range that is given in Table 1. The fitted values of RM and foreground RM (“FgRM”) are shown and givenin rad m − . The spectrum is fitted by a power-law ( S ∝ ν α ) and is given for the core (black triangles and dashed line) and for the jet (blue circles and solidline) components. Upper limits on the degree of polarization correspond to 3 σ m at the position of component on the map. Fits to the m vs. λ by Gaussian(solid blue line), Gaussian with constant term (dotted green line), polynomial (dashed red line) and two Gaussians (dashed-dotted violet line) are shown, seeSect. 2.5 for details. The solid black line on RM map indicates the slice (“S”) across the RM map, taken in the clockwise direction, with the correspondingRM distribution along the slice given in the inset. Slices at di ff erent frequencies are centred at the position of jet component. The beam size along the slice isshown by line in the left corner of each plot. Grey lines surrounding black lines represent a ± σ interval on observed RM and do not include absolute EVPAcalibration error. The length of slice S1 is 2.01 beams or 15.03 mas, of slice S2 is 1.71 beams or 3.75 mas. RM gradient of the S2 slice is significant. Resultsfor other targets are presented in the electronic version of the article. MNRAS , 1–19 (2017) araday RM and polarization of 20 AGN jets Table 4.
EVPA rotation, ∆ evpa , due to rotation measure of 1 rad m − .Frequency (GHz) 1.4 1.6 2.2 2.4 4.6 5.0 8.1 8.4 15.1 λ (cm) 21.40 18.07 13.17 12.55 6.51 6.00 3.70 3.56 1.95 ∆ evpa ( ◦ ) 2.60 1.87 0.99 0.90 0.24 0.21 0.08 0.07 0.02 ) -2 log(RM) (rad m N corecomponents ) -2 log(RM) (rad m N jetcomponents Figure 3.
Distribution of the observed RM values for all sources in themodelled core (top) and jet (bottom) components. White filling correspondsto 1.4 GHz to 2.4 GHz RM frequency range, grey filling – 2.4 GHz to8.4 GHz, and oblique filling to the 4.6 GHz to 15.4 GHz. Details are givenin Table 1 and Table 6. where y = { y , ..., y N } is a set of measurement points with uncer-tainties { σ i , ..., σ N } , and θ = { θ , ..., θ k } is a set of model parameters,that predict the measurements as { y M ( θ ) , ..., y MN ( θ ) } . We favour themodel that has the lowest value of BIC. The results of the fit anddiscussion is given in Section 3.3. We first outline general results, then consider each source individ-ually.
Spectra of the core and jet components are displayed in Fig. 2 withthe power-law fit to the Stokes I : I ∝ ν α . Jet components showan optically thin synchrotron spectrum. Meanwhile, core compo-nents show flat or slightly inverted spectra over the whole fre-quency range, which is attributed to synchrotron self-absorption (e.g. Blandford & K¨onigl 1979; Konigl 1981; Sokolovsky et al.2011). No significant polarized flux density was detected from twosources, 0610 +
260 and 1845 + m – λ Dependence and Faraday E ff ects All sources posses complex polarized structure. Figure 2 presentsthe fractional polarization in the core and jet components versuswavelength squared. We model the m vs. λ dependences by a num-ber of functions, described in Section 2.5, and summarize results inTable 5 and present them in Fig. 2. The majority (12 out of 18) ofthe sources show a decrease in polarization degree with increasingwavelength. An inhomogeneous external Faraday screen is respon-sible for such behaviour, described by Burn (1966), Tribble (1991),Rossetti et al. (2008), and Mantovani et al. (2009) laws. This Fara-day screen may contain turbulent or systematically varying regularfield. Fractional polarization in both these cases possess an anal-ogous behaviour. Unfortunately, our study is not able to distin-guish between them. Six sources exhibit an increase of fractionalpolarization with wavelength, known as anomalous (Sokolo ff et al.1998) or inverse (Homan 2012) depolarization. Four sources pos-sess oscillatory polarization behaviour, expected when a few jetor rotation measure components are blended within the region(Conway et al. 1974; Goldstein & Reed 1984). Sparse frequencycoverage does not allow us to study polarized structure in moredetail or even to distinguish among di ff erent Faraday e ff ects.The listed e ff ects in the transparent jet components are accom-panied by a linear EVPA vs. λ dependence across the full fre-quency range which indicates a one-component Faraday rotatingscreen. At the same time, the majority of the opaque cores exhibitcomplex EVPA vs. λ behaviour, resulting from Faraday rotationeither in external or internal medium relative to the synchrotron MNRAS , 1–19 (2017)
E. V. Kravchenko, Y. Y. Kovalev and K. V. Sokolovsky
Table 5.
Results for the fitted depolarization models and Faraday–corrected electric field orientation.Source Core Core Jet Jet RM Helical Jetmodel physical law model physical law gradient signatures EVPA0148 +
274 peaked multiple components peaked anomalous Y aberration misaligned0342 +
147 power Tribble power Tribble N . . . misaligned0425 +
048 power Burn Gaussian low depolarization N . . . unclear0507 +
179 two Gaussians multiple components Gaussian + constant Ros. – Mantov. N . . . misaligned0610 + . . . . . . Gaussian + constant Tribble . . . . . . . . . +
187 Gaussian + constant Ros. – Mantov. Gaussian low depolarization N . . . misaligned0952 +
179 peaked multiple components Gaussian + constant Tribbe Y 90 ◦ jumps unclear1004 +
141 Gaussian + constant Ros. – Mantov. Gaussian + constant Tribble Y . . . aligned1011 + . . . . . . power Burn N . . . misaligned1049 +
215 peaked multiple components Gaussian low depolarization N . . . misaligned1219 +
285 peaked multiple components Gaussian low depolarization Y . . . unclear / anomalous1406 −
076 Gaussian Tribble Gaussian low depolarization N . . . misaligned1458 +
718 peaked multiple components peaked anomalous Y spine–sheath misaligned / anomalous1642 +
690 peaked multiple components Gaussian + constant anomalous Y spine–sheath aligned1655 +
077 two Gaussians multiple components Gaussian + constant Tribble N . . . aligned1803 +
784 power anomalous Gaussian + constant low depolarization N . . . aligned1830 + . . . . . . Gaussian Tribble N . . . misaligned1845 + . . . . . . . . . . . . . . . . . . . . . + . . . unclear Gaussian Tribble Y . . . misaligned2320 +
506 Gaussian + constant Burn / Tribble power Tribble N aberration misaligned multiple Faraday rotation measure or jet components. , , , are the fitted models given by equations from (8) to (11). Fitted parametric models are describedin Section 2.5. Physical depolarization laws, corresponding to the fitted models, are listed in Section 2.5. The observed significant RM gradients are givenin Table 7. Under “helical structure” we assume polarization structures, arising in a presence of a helical magnetic fields, e.g. spine–sheath structure. Theorientation of the jet EVPA is given relative to the local jet direction and is shown in Table 8. Discussion of each source individually is given in Section 3.11. Figure 4.
Faraday RM maps and transverse RM slices for 0952 +
179 (left, 4.6 GHz to 8.4 GHz), 1458 +
718 (middle, 1.4 GHz to 2.4 GHz) and 2201 + , 1–19 (2017) araday RM and polarization of 20 AGN jets emission region. Detailed discussion of individual sources is givenin Section 3.11. We constructed 43 maps of Faraday RM for 18 sources over two orthree frequency ranges (as shown in Table 1) following the steps de-scribed in Section 2.3. In one third of the sources no Faraday RMestimates could be obtained in the core regions since they breakthe linear λ law. The resulting RM maps with substracted Galac-tic contribution are presented in Fig. 2 together with the EVPA vs. λ fits. RM pixel values at the location of transparent jet and atopaque core components are given in Table 6, while the distribu-tion of these values over all frequencies is given in Fig. 3. One cansee from Fig. 3 that high RM values are observed at short wave-lengths in the cores only. Thus, we confirm the expected result (e.g.Trippe et al. 2012), indicating the presence of stronger magneticfields and denser medium upstream in the jet.Using the relation between the observed rotation measure(RM) and the rest frame value (RM ): RM = RM(1 + z ) , weestimate the median value of RM averaged over all sources, listedin the bottom row of Table 6. The highest measured Faraday rota-tion in the source rest frame is ( − . ± . × rad m − in the0952 +
179 core.We observed a systematic increase of the absolute RM valuesin optically thin regions with increasing frequency. Most probably,this is due to beam depolarization at long wavelengths (see simula-tions by Porth et al. 2011).
We studied the RM distribution along the cuts made perpendicularto the local jet direction defined by the jet’s ridge-line. The ridge-line (jet emission centre) was determined by fitting a Gaussian tothe image brightness distribution profile (convolved with circularbeam), taken at a given radial distance from the core (see descrip-tion of the technique in, e.g. Lobanov & Zensus 2001).During the analysis we omitted errors in the absolute EVPAcalibration since they a ff ect only the absolute rotation measurevalues, while significance of a gradient is determined by rela-tive EVPA changes (e.g. Mahmud et al. 2009; Hovatta et al. 2012).While, to analyze RM profiles at di ff erent frequency ranges, theseerrors together with the uncertainty in Galactic RM (discussed inSection 2.4) should be taken into account. Complexity of the AGNcores and opacity e ff ects may result in unreliable RM gradients (as,e.g. shown in simulations by Broderick & McKinney 2010). Thuswe analyse only regions located more than 1 beam size downstreamfrom the core, where synchrotron emission is optically thin.The criterion for a gradient to be significant comprises twosteps. At first, a line was fitted to the RM values along a slice. If thelinear slope exceeds 3 times its RMS, the second step is applied. Itconsists of fitting a constant line to the data at the level equal to theweighted average of the RM along the slice. If the χ of the secondfit is larger than the theoretical value for the appropriate degrees offreedom, the RM gradient was considered to be significant. We as-sume the degrees of freedom as the number of pixels along the RMslice minus two. The χ test, estimated in this way, carries quali-tative information and has no statistical meaning, because adjacentpixel values of the RM image are correlated and considered aver-age rms errors in the Stokes I , Q and U are not evenly distributed inthe images. Simulations (like Hovatta et al. 2012 and Pashchenko et al. in preparation) should be used for the statistical estima-tion of the gradient significance. Following Broderick & McKinney(2010) and Taylor & Zavala (2010), we also calculated the signif-icance of a gradient as the total change in RM divided by the av-erage RM error at the edges of a slice. Because it is a simplifiedapproach, it results in the smaller value of significance, than thevalue derived by our two–steps approach. Since our observationsallow us to study transverse RM profiles across a few frequencybands simultaneously, we took these slices only at the position ofmodel-fitted transparent jet components, which is identified acrossall frequencies. This enabled us to make a direct comparison ofrotation measure gradients obtained at di ff erent frequency ranges.We were able to take transverse slices on 41 RM maps. Threeout of analysed slices have width less than 1 half power beam width(HPBW), nine are . + + + + +
690 and 2201 +
315 (see Table 7). Other sources, 1458 + + + +
718 and1642 +
690 are not monotonic. We found in the literature the onlysource 3C 454.3, having similar RM gradient (Hovatta et al. 2012;Zamaninasab et al. 2013). Most likely, the helical magnetic fieldin the bending jet of 3C 454.3 gives rise to such RM profile. It isdi ffi cult to say, what causes such sharp gradients in 1458 +
718 and1642 + We see (Figure 3, Table 6) an overall tendency of the rota-tion measure to increase its value with increasing frequencyand to break the linear λ law in the cores (see also VLA re-sults by Kravchenko et al. 2015). Since the observed sources ex-hibit significant core shifts among compact extragalactic sources(Sokolovsky et al. 2011; Kovalev et al. 2008), the shift of the pho-tosphere towards central engine will result in noticeable di ff erenceof regions probed at the observed frequencies. Hence, higher val-ues of RMs at these frequencies indicate denser media and strongerline-of-sight magnetic fields (Lobanov 1998; Kovalev et al. 2008;Sokolovsky et al. 2011; Porth et al. 2011; Pushkarev et al. 2012);or more Faraday active material between the observer and thesource (Porth et al. 2011). Considering the location of the externalFaraday screen to be very close to the jet, one may assume a thin-ner Faraday screen for the VLBI core with increasing wavelength.Frequency dependence (and thus distance dependence) of the coreRM can be studied using the relation | RM core | ∼ ν a , (14)derived in Jorstad et al. (2007), where a is a power-low fall-o ff inthe electron density, n e , with distance r from the central engine, n e ∼ r − a . (15) MNRAS , 1–19 (2017) E. V. Kravchenko, Y. Y. Kovalev and K. V. Sokolovsky
Table 6.
Rotation measure results.Low frequency range Middle frequency range High frequency range PowerSource RM core RM jet RM core RM jet RM core RM jet a + − ± − ± − − ± − ±
14 1.9 ± + − ± − ±
17 0 ± − ± − ±
88 6.1 ± + − ± − − ± − − − + − ± − ± ± − ±
17 1055 ± − ±
57 2.98 ± + − − − − − − − + − − ± − − − − ± − + − ± ± − ± − ±
53 40 ±
89 2.90 ± + − ± − ± − ± − ± − − ± + − − − − ± − − − + − ± − ± − ± − ± − ± − ± + − ± − ± − − − ± − ±
15 0.0 ± −
076 30 ± ± − ± ± − ± − ±
25 1.77 ± + − ± − − ±
17 1153 ± − ± − + − ± ± − ± − ±
18 272 ±
50 106 ±
102 4.6 ± +
077 24 ± ± − − − ± − ±
13 2.54 ± + − ± ± ±
17 6 ±
18 28 ±
17 11 ±
24 0.9 ± + − − − − ± − − − + − − − − − − − + − ± − ± − − − ±
50 15 ±
253 1.40 ± +
506 44 ± ± − − − ± − ± | median |
17 8 107 22 491 29 2.5 | median(1 + z ) | − The shown RM pixel values were determined at the position of the modelled core and jet components. RM is given in rad m − and corrected for the Galacticrotation. The calculated power a of the rotation measure fall-o ff with frequency | RM core | ∼ ν a is given in the last column, see for details Sect. 3.6. All thevalues are calculated in the observer’s frame except for the last row which is given in the sources’ rest frame. The medians are calculated for absolute RMvalues. - RM at the high frequency range has not been considered in the fit. Table 7.
Detected significant transverse rotation measure gradients.Source Name Range RM RM | ∆ RM | Significance Width(GHz) ( rad m − ) ( rad m − ) ( rad m − ) (beams)Slices at position of model-fitted, transparent jet component, given in Fig. 20148 +
274 S2 4.6–15.4 1 ±
22 -62 ±
20 63 ±
30 2.1 σ +
179 S1 1.4–2.4 -8 ± ± ± σ ±
192 610 ±
177 545 ±
261 2.1 σ +
141 S2 4.6–8.4 63 ±
35 -41 ±
24 104 ±
42 2.5 σ +
285 S2 4.6–15.4 60 ±
42 -63 ±
19 123 ±
46 2.7 σ +
690 S2 4.6–8.4 -153 ±
57 -135 ±
59 17 ±
82 2.9 σ ±
258 554 ±
216 826 ±
336 2.5 σ +
315 S1 1.4–2.4 -20 ± ± ±
10 4.1 σ +
179 S1 4.6–8.4 62 ±
43 -139 ±
64 200 ±
77 2.6 σ ±
49 -92 ±
40 124 ±
63 2.0 σ +
718 S1 1.4–2.4 -17 ± ± ±
12 2.9 σ ± ± ±
10 4.5 σ ± ± ±
11 3.7 σ +
315 S1 8.1–15.4 -64 ±
195 668 ±
267 732 ±
330 2.2 σ | ∆ RM | , is characterized by RM and RM , which are either edge or extreme RM values of the monotonic or sharptransverse RM profiles accordingly. The error in | ∆ RM | is defined as the square root of σ RM and σ RM added in quadrature. The significance of a gradientis determined as the total change in RM divided by its error. We note, that we used this value as a quantitative measure for the RM gradient. Meanwhile,qualitative analysis of the gradient significance is based on two–steps approach, described in Section 3.5. – RM gradient is not monotonic. These calculations are based on a helical structure of the jet mag-netic field and the assumption that the constant toroidal componentof the field provides the main contribution to the magnetic fieldalong the line of sight for a spherical or conical outflow.Table 6 summarizes the estimated values of a . Eight of oursources show a ≈ / spherically expanding jet. Two ofour sources show flatter fall-o ff and three have higher a . These re- sults agree with other, similar measurements (Jorstad et al. 2007;O’Sullivan & Gabuzda 2009a; Trippe et al. 2012). The observeddeviations of a can naturally be explained by (i) di ff erent geom-etry of the jet, (ii) flaring activity of the source, that results in en-hancement of the poloidal magnetic field component or significantchanges of the physical conditions at the jet base; (iii) possible fila-mentary structure of the Faraday screen, which will be smeared outwithin a beam at long wavelengths. MNRAS , 1–19 (2017) araday RM and polarization of 20 AGN jets In thirteen sources we could measure the core RM at two orthree frequency ranges; seven of them show reversals of RM sign(see Fig. 2). Such behaviour may result from a complex structureof a source: the τ ∼ ff erent LoS com-ponent of the magnetic field. Such a possibility may arise withina models of helical magnetic fields (O’Sullivan & Gabuzda 2009a)or relativistic helical motion in the jet (Broderick & Loeb 2009).Changes in the jet viewing angle may originate from small changesin the jet speed (acceleration or deceleration) or jet bends, whichhave frequently been observed in AGN jets (e.g. Rani et al. 2014;Lister et al. 2016). The intrinsic direction of the electric field can be determined af-ter performing the Faraday de-rotation. Figure 5 shows Faraday-corrected maps of EVPA across the 1.4 GHz to 15.4 GHz range.The misalignment between corrected EVPA, χ , and the local jetposition angle, θ , is shown in Fig. 6 and in Table 8. These are me-dian values obtained along ridge lines through all frequencies at thepositions of model-fitted core and jet components. There is weakexcess of sources with intrinsic polarization angles inclined nearlyperpendicular to local jet direction in the transparent jet compo-nents. Partially, this can be explained by shearing of the tangledmagnetic field due to velocity gradient between the jet and the sur-rounding medium (Laing 1980, 1981). The EVPAs in the core re-gion distribute their values at any angle between 0 ◦ and 90 ◦ to thejet direction.Generally, there is no overall trend for EVPA to be either per-pendicular or parallel to the local jet direction as expected from the-oretical studies (e.g. Laing 1980; Lyutikov et al. 2005; Cawthorne2006; Nalewajko 2009). Similar results also were shown byPollack et al. (2003); Lister & Homan (2005); Hovatta et al. (2012)and Agudo et al. (2014). The absence of preferred alignment of χ with θ may be caused by a number of e ff ects, like oblique shocks,superposition of multiple components with di ff erent spectral oropacity properties within the telescope beam, residual Faraday ro-tation, asymmetric jets, and others. Further discussion is given inSection 3.11, where we consider the polarized structure of the eachsource individually. Generally, the majority of the sources show simple polarized struc-ture in the transparent jet regions, resulting from small depolariza-tion and external nature of the Faraday rotating media. This resultedin an overall tendency of the sources to maintain their E-field di-rection across the full observed bandwidth in these regions. At thesame time, optically thick jet regions show complex behaviour, nat-urally expected for our sources, since they exhibit large apparentcore shifts.The following complex polarized structures are observed: (i)peaked behaviour of the EVPA with λ , which arises within amodel of multiple rotation measure components (Goldstein & Reed1984); (ii) ∼ ◦ EVPA flips along the jet – the possible conse-quence of a change in the jet viewing angle (Lyutikov et al. 2005),interaction of the jet with ambient medium (Attridge et al. 1999),relativistic shocks in a jet (Brown et al. 1994; Wardle et al. 1994)or instabilities driven by velocity shear (Hardee 2004); (iii) “spine-sheath” structure (Laing 1996; Mizuno et al. 2007); (iv) EVPA – jet direction alignments other than 0 ◦ of 90 ◦ in the core region,which might be caused by flaring activity of the source and con-sequent emergence of a new jet component (e.g. Brown et al. 1994;Kravchenko et al. 2016). In Section 3.11 we analyze the polar-ization structure of each source individually and discuss how theabovementioned e ff ects can modify the intrinsic orientation of theelectric field.From the overall analysis one may conclude, that despite com-plex observed polarized structure, our targets can well be describedby the model of a “spine-sheath” jet (Laing 1996; Attridge et al.1999; Mizuno et al. 2007) which has previously been suggested forindividual sources (e.g. Asada et al. 2008b, 2010). Within this sug-gestion, the observed rotation measures originate in the magneto-ionic boundary layer (sheath), located external to the synchrotronemission region of the jet. Results of the Section 3.11 show thatthere is no preferred orientation of the magnetic field in the sheath:it can be both randomized and ordered. In some cases, sheath maycarries signatures of the helical field. Meanwhile jet itself (spine)contains well ordered magnetic fields, with the apparent dominanceof either poloidal or toroidal component. Unfortunately, observedB-field orientation is ambiguously connected with the real (intrinsicto the source) orientation. A number of factors are responsible forthis, like relativistic boosting and abberation (Lyutikov et al. 2005),or an origin of the observed emission within a part of a jet volume,thus only some fraction of the jet is visible over time. The bright region visible at the aparent base of the jet in all ob-served sources is referred to as the VLBI core (see Fig. 2). Themost likely physical interpretation of the core is a surface in a con-tinuous jet flow where the optical depth of synchrotron-emittingjet plasma becomes equal to unity, τ ≈
1, see also discussion byMarscher (2008). Strong support for the τ ≈ ff ect, i.e. a systematic change of aparent position of the VLBIcore as a function of observing frequency (e.g. Kovalev et al. 2008;O’Sullivan & Gabuzda 2009b; Hada et al. 2011; Sokolovsky et al.2011; Pushkarev et al. 2012). This can be naturally understood:while the jet plasma density and magnetic field strength gradu-ally decreas with increasing distance from the central engine, thejet becomes transparent at progressively lower frequencies (seeMarcaide & Shapiro 1984; Lobanov 1998; Kutkin et al. 2014).Therefore by observing the core at various frequencies we ob-tain information about the jet properties (including polarization) atvarious distances from the central engine. Combining this analysiswith the observed polarization angle, corrected for Faraday e ff ects,one may recover the spatial magnetic field geometry in this region.This technique gives only rough estimate of the intrinsic structureof the magnetic field, because of a number of factors. The mostsignificant are (i) the exact geometry of the jet must be known (e.g.jet viewing angle), otherwise only the sky projection of the fieldgeometry is available; (ii) small viewing angle with relativistic andDoppler e ff ects may dramatically distort the intrinsic direction ofpolarization; (iii) jet curvature which is changing with frequency(thus with distance), which results in frequency-dependency of thejet viewing angle; (iv) the shape of the τ ∼ ◦ EVPA flips.Because of the lack of information, which could account in-fluence of abovementioned factors, we are limited in studying thespatial magnetic field geometry for our sample. Figure 7 presents
MNRAS , 1–19 (2017) E. V. Kravchenko, Y. Y. Kovalev and K. V. Sokolovsky
Figure 5.
Faraday-corrected maps of electric vector position angle supplemented by linear polarization colour maps for 0148 +
274 in the 1.4 GHz to 15.4 GHzrange. Stokes I contour plots together with E-field ticks for 1.4, 1.6, 2.2, 2.4, 4.6, 5.0, 8.1, 8.4, and 15.5 GHz are artificially shifted along R.A. or dec. axis inthe negative direction such that optically thin jet components lay on the same horizontal or vertical line, respectively. Black and white dots mark the positionsof the modelled transparent jet and opaque core components. I contours begin at the 5 σ level and are plotted in × | (degrees) θ - χ |0 20 40 60 80N0246 coresjet components Figure 6.
Distribution of the di ff erence between the electric vector posi-tion angle, χ , and the jet direction, θ , at the jet and core components fromTable 8. The thick line represents the total distribution of all components.White filling corresponds to the core and hatched filling corresponds to thejet components. an example of application of this approach to 1004 +
141 (skyplane projection) superimposed with the 15.4 GHz Stokes I con-tours and jet ridge line. Assuming a typical jet viewing angle of6 ◦ (Savolainen et al. 2010; Pushkarev et al. 2014; Fuhrmann et al.2014), the detailed view of the 1004 +
141 core region reveals theexistence of ordered electric (and thus magnetic) field, keeping itsdirection for a few hundreds of pc.Maps of the Faraday-corrected direction of the electric field
Figure 7. +
141 spatial geometry (sky projection) of the electric vec-tors (colour sticks), reconstructed by using the technique described in Sec-tion 3.9. The frequency range is indicated by numbers and colours on thefigures. The solid blue line represents the jet ridge line. Relative 15 GHzStokes I contours are shown. Error bars at the end of the sticks representthe 1 σ total EVPA error, while 1 σ uncertainties in the position of model-fitted components are given by filled circles. over the whole source are given in Fig. 5 in the full frequency range.To apply proposed technique we (i) mark the positions of model-fitted core and jet components and (ii) align images at the positionof optically thin components in Fig. 5. Overlaying all frequencieswill give the spatial geometry of the magnetic field in the cores. MNRAS , 1–19 (2017) araday RM and polarization of 20 AGN jets Table 8.
Misalignment between EVPA in the core, χ core0 , and jet compo-nents, χ jet0 , and the jet direction, θ .Source | χ core0 − θ | | χ jet0 − θ | +
274 15 810342 +
147 18 750425 +
048 37 410507 +
179 72 610610 +
260 – –0839 +
187 82 850952 +
179 65 151004 +
141 40 131011 +
250 – 861049 +
215 48 511219 +
285 18 831406 −
076 67 871458 +
718 3 871642 +
690 71 451655 +
077 27 41803 +
784 15 151830 +
285 – 771845 +
797 – –2201 +
315 55 782302 +
506 27 55Presented are median values for measurements at all frequencies (in de-grees). A 1 σ accuracy of misalignments is 10 ◦ . A histogram representingthis table is given in Fig. 6. This approach is not applicable in the optically thin regime, wherewe see the same physical regions through all frequencies. Analy-sis of these regions is made in Sections 3.7 and 3.10. To studywhether these results can be influenced by relativistic or other ef-fects, a combined polarimetric and kinematic analysis should bedone, which is the subject of future research.
Results of Sections 3.4, 3.5 and 3.6 have shown, that observed Fara-day rotation occurs in an external screen, located in the vicinity ofAGN. Despite this, we may assume that optically thin jet emissionexperiences only rotation in the Galactic medium. Thus, we can de-termine the Galactic rotation measure. This approach also requiresthat synchrotron emission originates within the same volume in thesource to avoid frequency–dependence of the polarization angle.Under these assumptions, we did not substract Galactic rotationmeasure and applied linear fit to the observed EVPA vs. λ overthe whole frequency range. Moreover, we calculated the integratedRM value over the 1.4 GHz to 2.4 GHz RM maps. The resultingvalues are presented in Table 2 and agree well with the values ofTaylor et al. (2009).Anderson et al. (2015) recently suggest that the Galacticmedium has a complex Faraday structure. Despite our sparse fre-quency coverage in the same region, we assume that this com-plexity rather arises within the radio sources, than in the Galacticmedium. This is supported by results of Lamee et al. (2016) ob-tained with the polarization survey of the northen sky at 1.4 GHzand 2.3 GHz. + This quasar shows an rotation measure of 168 ±
13 rad m − in thecore and − ±
14 rad m − in the jet at 4.6 GHz to 15.4 GHz(Fig. 2.1). The average RM value over the 1.4 GHz to 2.4 GHzmap amounts − ± − . The jet EVPA vs. λ shows a closeto linear dependence, however the core region breaks this law. Thepolarization degree does not exceed 6 per cent anywhere in the jetand shows complex behaviour with λ both in the core and jet re-gions. Its peaked behaviour in the opaque core may be explained bysmearing of two RM components, seen in the EVPA vs. λ plot, orby superposition of two jet components with di ff erent polarizationproperties. A close view of this region in Fig 5.1 and Fig. 8 supportsthe later suggestion. Meanwhile the transparent jet posses a polar-ization signature close to the model of anomalous and inverse depo-larization (Sokolo ff et al. 1998; Homan 2012). The source exhibitsa significant RM gradient across its jet over 4.6 GHz to 15.4 GHz.Together with a peaked m − λ behaviour it may point to a helicalmagnetic field in the source. At a distance of ∼ +
274 parsec-scale jet. + The core of this quasar shows a slightly inverted spectrum and anon-linear EVPA vs. λ , resulting in an RM of − ±
51 rad m − at8.1 GHz to 15.4 GHz (Fig 2.2). The jet EVPA is consistent witha linear λ law and posses low values of RMs, consistent with0 rad m − . All of the transverse RM slices have width less then1.5 beam, and do not show any signs of a gradient. The power-lawmodel fits well with the observed degree of polarization both in thecore and jet components, implying the Faraday rotation occurs inan external screen. High m at ∼ ∼
15 per cent)might be an indication of a relativistic shock (Nalewajko 2009) atthis position (Fig. 8). Nevertheless, the overall EVPA orientation isconsistent with the magnetic field being aligned with the local jetdirection (Fig 5.2). +
048 (OF 42)
The core of this AGN shows a inverted spectrum and breaks thelinear EVPA vs. λ relation over all frequencies, as seen in Fig 2.3.Estimates of RM in this region are a few hundreds of rad m − while the RM fit in the optically thin region gives a value of a fewrad m − . The core polarization degree behaviour with wavelengthis consistent with external Faraday rotation. At the same time thejet m − λ shows a slow fall-o ff with decreasing frequency, whichmay be explained by a randomly oriented magnetic field.The Faraday-corrected EVPA is oriented perpendicularly inthe core and changes to parallel direction downstream in the jet(Fig. 8). The active state of the source or decrease in the opacitymay account for such behaviour. Downstream, the jet EVPA is ori-ented ∼ ◦ to the jet and rotates by almost 90 ◦ at the position MNRAS , 1–19 (2017) E. V. Kravchenko, Y. Y. Kovalev and K. V. Sokolovsky of model-fitted jet component (Fig. 5.3) where the jet bends. NoRM enhancement is observed at the position where the jet makesthe turn, which might indicate an interaction with the surroundingmedium or presence of instability driven structures. We were un-able to conclude about the overall direction of the magnetic field inthe quasar. It seems, that the contribution of a randomly orientedmagnetic field is significant there. + This quasar shows inverted spectrum in the core, as seen in Fig. 2.4.The fractional polarization there does not exceed 2 per cent andshows a tendency to increase its value towards longer wavelengths.Trippe et al. (2012) observed the maximum degree of polarizationof ∼
11 per cent at 80 GHz to 253 GHz, and find significant tem-poral variations in this value. The core EVPA changes non-linearlywith λ with the indication of increasing RM value towards shorterwavelengths. We estimated an RM of 1055 ±
53 rad m − in 8.1 GHzto 15.4 GHz, which is consistent with their 3 σ upper limit of14000 rad m − over 80 GHz to 253 GHz provided by Trippe et al..The polarization degree in the optically thin jet component is con-sistent with the model of an external, filamentary Faraday screen,supported by the linear EVPA behaviour with λ . Even though thewidth of the transverse RM slices is > − ◦ in thecore to ∼ − ◦ at a 2.5 mas, and 62 ◦ at 4 mas, implying poloidallydominated magnetic field in the quasar. +
260 (3C 154)
This quasar does not show strong linearly polarized flux at most ofthe frequencies. Observable orientation of the polarization anglesis presented in Fig. 5.5. + This quasar has a steep–spectrum core, as shown in Fig. 2.6. Frac-tional polarization in the core changes with frequency following themodel of an external Faraday screen. EVPA is not linear with λ andexhibits large rotation towards short wavelengths. The core RM canbe determined in a few pixels only and is of − ±
18 rad m − over4.6 GHz to 8.4 GHz. Observations of the source at higher frequen-cies may result in higher values of the rotation measure in its core.The transparent jet region shows frequency–independent fractionalpolarization, which is expected if either randomly oriented or reg-ular component of the magnetic field dominates in the Faraday ro-tating medium (e.g. Burn 1966). RM gradients are not observed,although the jet is resolved. The orientation of the polarization an-gle (Fig. 5.6 and 8) maintains to transverse direction along theextended jet, which is consistent with a poloidally dominated mag-netic field. + The flat–spectrum core of this source is weakly polarized: polariza-tion degree does not exceed 2 per cent. The fractional polarizationvs. λ shows a complex behaviour, which is close to the model ofa spectral repolarizer (Conway et al. 1974), when a two jet com-ponents with di ff erent polarization properties are blended. Assum-ing a linear fit over 8.1 GHz to 15.4 GHz, we estimated an RM of − ±
53 rad m − in the quasar’s core. This rotation measuretranslates to − ±
300 rad m − in the rest frame of the source,and thus represents the highest observed rotation measure in oursample.The optically thin jet shows a complex polarized struc-ture. While fractional polarization decreases with λ , the ob-served EVPA experiences a 40 ◦ jump between 2.4 GHz and4.6 GHz. Di ff erential Faraday rotation (Gardner & Whiteoak 1966;Sokolo ff et al. 1998) may account for such polarization signatures,implying co-spatiality of emitting and rotating regions. Faraday–corrected polarization angles oriented identically over all observedfrequencies anywhere in the transparent jet. This supports the sug-gestion about an internal Faraday rotation in this jet region, and ex-plains frequency–dependency of the RM. Significant rotation mea-sure gradients are observed over 1.4 GHz to 2.4 GHz, 4.6 GHzto 8.4 GHz and 8.1 GHz to 15.4 GHz RM maps (Fig. 2.7). RM–corrected electric vectors are consistent across frequencies andaligned with the jet in this region, meanwhile the EVPA is per-pendicular to the jet downtream and upstream of this region. Theapparent bend of the jet at the position of the jet component andchange in direction of electric vectors suggests that the jet expe-riences interaction with the ambient medium, resulting in a localenhancement of the toroidal field component and RM value (see,e.g. G´omez et al. 2008). In this context, transverse RM gradientsmay arise from the variations in magneto-ionic density and pathalong the Faraday rotating medium, rather than in changes in thedirection of the helical magnetic field. The magnetic field in thequasar 0952 +
179 jet may be dominated by poloidal component. + The core EVPA breaks the λ law and increases its slope towardsshorter wavelengths (Fig. 2.8). A fit to a λ law over 8.1 GHz to15.4 GHz is not reliable, while a fit across 4.6 GHz to 8.4 GHzagrees with a linear law and gives RM of − ±
17 rad m − . RMdecreases to − ±
17 rad m − in the transparent jet. The degree ofpolarization both in the core and jet is consistent with depolariza-tion in an external medium, which may partially cover the emittingjet region (Rossetti et al. 2008; Mantovani et al. 2009). TransverseRM slices exhibit a gradient with 2.5 σ significance and width of1.8 HPBW. The EVPAs keep their relative orientation with respectto the jet direction for the whole detected parsec-scale jet showinga very good alignment between the magnetic field and the local jetdirection (see Fig. 8 and Fig. 7). This implies dominance of thetoroidal field component. Together with the RM gradient this maypoint to a helical magnetic field in the 1004 +
141 jet. + This quasar exhibits significant linear polarization only in the re-gion located ∼ − ±
29 rad m − (see Fig. 2.9). The RM-corrected EVPAof the jet is consistent with a poloidal magnetic field. + The core RM increases from − ± − over 1.4 GHz to2.4 GHz, to − ±
17 rad m − and − ±
52 rad m − across4.6 GHz to 8.4 GHz and 8.1 GHz to 15.4 GHz respectively MNRAS , 1–19 (2017) araday RM and polarization of 20 AGN jets (Fig. 2.10). Fractional polarization is complex with λ in this re-gion, while the spectrum shows partial opaqueness. The jet RMfit across 1.4 GHz to 8.4 GHz is consistent with 0, however the15.4 GHz EVPA shows significant rotation in its value, giving riseto an RM of − ±
239 rad m − at 8.1 GHz to 15.4 GHz. Mostprobably this value is not real, resulting from the convolution ofthe 15.4 GHz map with the beam size of the 8.1 GHz map. The jetfractional polarization is frequency–independent, which is an indi-cation of tangled magnetic fields. Corrected for Faraday rotation,the polarization vectors (Fig. 5.10) are transverse to the local jet di-rection in the transparent component located 8 mas from the core.At the same time, the EVPA varies significantly near the core re-gion, as does the degree of polarization (given in Fig. 8). Kinematicstudy by Lister et al. (2016) indicates a stationary feature at a po-sition of 2 mas from the core of the source. Such behaviour of thepolarization properties resembles a relativistic shock or bend of ajet. +
285 (W Comae)
The blazar 1219 +
285 shows a typical flat-spectrum core and steep-spectrum jet (Fig. 2.11). Significant repolarization is seen in thecore towards long wavelengths. The core o ff set in the EVPA be-tween 1.4 GHz to 2.4 GHz and 4.6 GHz to 15.4 GHz is 50 ◦ , andmay arise from the opacity change. The estimated RM value doesnot change significantly through jet and is − ±
15 rad m − , whilethe transverse RM gradient ( ∼ . σ level and has a width of 2.3 HPBW. Gabuzda et al. (2015)detected a 3 σ RM gradient in the blazar across 5 GHz to 15 GHz,with an RM slice about 2.5 mas from the core. This di ff ers fromour measures in sign of the gradient though our absolute valuesare similar. Our RM-corrected orientation of linear polarization(given in Fig. 8) is coaligned and misaligned with the jet in thecore and jet ( ∼ ∼ ∼ − Small depolarization in the quasar’s core and jet at longer wave-lengths (Fig. 2.12) points to external Faraday screen with ran-domly oriented magnetic field. The core EVPA steady rotates to-wards short wavelengths, resulting in an increase of RM from30 ± − , to − ± − and − ±
17 rad m − at 1.4 GHzto 2.4 GHz, 2.2 GHz to 5.0 GHz and 5.0 GHz to 15.4 GHz re-spectively. Hovatta et al. (2012) measure a core RM of − ± − at 5.0 GHz to 15 GHz (epoch 1997–04–05)and a degree of polarization twice as high (6.1 per cent at 5 GHz).As shown in Fig. 5.12 and 8, the corrected electric vector in the Figure 8.
Faraday-corrected map of E-vectors supplemented by linear frac-tional polarization colour map for 1803 +
784 at 15.4 GHz. Black dots markthe positions of the modelled transparent jet and opaque core components.Stokes I contours begin at the 4 σ level and are plotted in × core is 67 ◦ and rotates by 90 ◦ at 0.5 mas downstream due to opacitychanges. Such complex behaviour in the core might be explainedby the emergence of a new component, which smears out the par-allel orientation of the core EVPA. Nevertheless, this complex po-larized structure of the quasar is consistent with an overall poloidalmagnetic field. +
718 (3C 309.1)
The quasar shows steep spectra both in the core and jet, as seenin Fig. 2.13. The fractional polarization has a peaked shape bothin the core and jet. Meanwhile, this behaviour in the core may beexplained by smearing of two jet components within the beam, thisis unlikely to be the cause of anomalous depolarization in the op-tically thin region. A helical field may account for this behaviour,which can be applied to the core as well. Mantovani et al. (2009)observed 3C 309.1 with 100–m E ff elsberg telescope in 2.64 GHz– 10.45 GHz range in the period 2006–01–26 – 2006–06–26.Mantovani et al. obtained the same spectral distribution of the frac-tional polarization, though they obsered with the single–dish tele-scope. Rotation measure steadly increases towards high frequen-cies, up to 1153 ±
56 rad m − across 8.1 GHz to 15.4 GHz. Theobservation of Hovatta et al. (2012) on 2006–09–06 over 8 GHz to15 GHz range gives a core RM of 628 ±
125 rad m − , and is ob-served over few pixels only. Measures of Aaron et al. (1997), madeon 1995–03–24 and 1995–12–11 with the VLBA at 5 GHz and8.4 GHz, account the core RM of ≈
450 rad m − . The jet RM is − ±
53 rad m − compared to 231 ±
103 rad m − of Hovatta et al.The jet does not exhibit RM gradient at high frequencies, thoughthe 1.4 GHz to 2.4 GHz RM map shows complex Faraday structure:three transverse RM profiles taken at di ff erent jet locations (seeFig. 4) present significant RM gradients. These gradients are sharpand may reflect changes in the density and thickness of magneto-ionic media rather than in magnetic field. RM–corrected polariza-tion angles are presented in Fig. 5.13 and Fig. 8. The core and jetEVPAs for regions up to 30 mas are well–ordered and consistentwith an apparent poloidal magnetic field in the quasar jet. Mean-while, the polarization signature 30 mas downstream resembles a‘spine-sheath’ structure, indicating dominance of the toroidal fieldcomponent in the jet spine and poloidal in its sheath. Such po-larization structure has previously been observed, e.g. in the jet MNRAS , 1–19 (2017) E. V. Kravchenko, Y. Y. Kovalev and K. V. Sokolovsky of 1652 +
398 (Mrk 501, Pushkarev et al. 2005). Moreover, both1458 +
718 and 1652 +
398 have similar kinematic picture in theirjets (Lister et al. 2016). If we assume that the jet of 1458 +
718 in-deed has a spine-sheath structure, then the transition from apparentB k to B ⊥ at 30 mas distance from the core may be explained by achange in the viewing angle. An increase in the fractional polar-ization at the model-fitted jet component support this assumption,since the sheath is expected to have a more uniform magnetic field(Lyutikov et al. 2005). + Behaviour of the EVPA and m in the core of this quasar (Fig. 2.14)is similar to that descibed by a model of multiple Faraday compo-nents. Therefore our linear RM fits may di ff er from the real values.The fractional polarization at 86 GHz is 1 . ± . ±
75 rad m − over 8 GHz to 15 GHz (epoch 2006–03–09), which is smaller thanour measure (272 ±
50 rad m − ). The jet fractional polarizationand electric vector behaviour with λ are consistent with the in-verse depolarization law taking place in a helical magnetic field(Homan 2012). Transverse RM slices are resolved and show gra-dients across the 4.6 GHz to 8.4 GHz and 8.1 GHz to 15.4 GHzbands. RM–corrected polarization structure of the jet (Fig, 5.14and Fig. 8) is complex: electric vectors are perpendicular to thejet from the jet base up to ∼ ∼
30 per cent) indicates well-ordered magnetic field.Overall, this result is consistent with a large–scale helical magneticfield in this quasar. + The core degree of polarization slightly increases towards longwavelengths, as shown in Fig. 2.15. The observations of the sourceat sub mm wavelengths (Agudo et al. 2014) provide measures of m of 9 . ± . . ± . + ± − over 1.4 GHz to 2.4 GHz to − ±
13 rad m − over 4.6 GHz to 15.4 GHz. Moreover, Agudo et al. estimate an up-per limit on the quasar’s RM of 41900 rad m − across 86 GHz to229 GHz, which agrees with the power-law increase in RM valuewith frequency. Hovatta et al. (2012) measured the core RM of -1286 ±
91 rad m − on 2006–11–10. This value significantly dif-fers from our RM, though the time di ff erence between our obser-vations is six months. Such rapid time variations of the rotationmeasure suggests a magnetized plasma associated with the jet actslike a Faraday screen and is responsible for observed RM (see,e.g. Asada et al. 2008a). Electric vectors in the core and jet arecoaligned with jet direction (see Fig. 5.15 and Fig. 8). If the toroidalcomponent of the magnetic field prevails, then the core EVPA maybe altered by ongoing activity in this region. Indeed, Lister et al.(2016) analysis shows that jet component is located within 1 masof the core at this epoch. Otherwise, the toroidal component of the Table 9.
RM measures of 1803 + ν RM Reference(GHz) rad m − − ±
64 11998–2001 43–222 4360 ± − ±
55 32002–08–24 15.3–43.1 ∼
600 42003–08–22 4.6–15.4 ∼ −
300 42006–09–06 8–15 112 ±
74 52007–05–03 5.0–15.4 28 ±
17 6References: 1 – Gabuzda & Chernetskii (2003); 2 – Jorstad et al. (2007);3 – Zavala & Taylor (2003); 4 – Mahmud et al. (2009); 5 – Hovatta et al.(2012); 6 – this work. field may lie either transverse or parallel to the jet in the plane ofthe sky (Lyutikov et al. 2005). Changes in the EVPA orientation inthe core and jet components then can be attributed to the variationsof the jet viewing angle. + This BL Lac object displays (Fig. 2.16) a flat RM through thejet (from 28 ±
17 rad m − in the core to 11 ±
24 rad m − in thejet). While synchrotron emission is significantly depolarized andwavelength–independent in the jet, the core exhibits strong repo-larization. Magnetic field in the core should be regular with a ran-dom line–of–sight component and transverse component, changingits direction. In the same time a model of random magnetic fieldis consistent with the jet region with no transverse RM gradients.Considering observations of the source made by di ff erent authors(Gabuzda & Chernetskii 2003; Jorstad et al. 2007; Zavala & Taylor2003; Mahmud et al. 2009; Hovatta et al. 2012), the core regionshows temporal RM variations in its value and sign (Table 9).Cawthorne et al. (2013) associate the 1803 +
784 core with a con-ical shock, assuming combination of random and poloidal mag-netic fields, and reproduce the observed polarization structure nu-merically. Then within this model, RM changes my arise from in-teraction of ejected material with the shock front. The kinematicstructure of the source in this region reveals (Lister et al. 2016)four persistent features within 1 mas of the core. Enhancement ofthe fractional polarization (see Fig. 8) 1 mas downstream of thecore and alignment of E-vectors with the jet also support this sug-gestion. Large-scale polarization structure of the source (Fig. 5.16)shows that the parallel orientation of the EVPA is maintained along50 mas, which is approximately 300 pc in the projection on the skyplane. We suggest that a global toroidal magnetic field threads thejet of this source. Other authors also favour this idea (e.g. Gabuzda1999; Gabuzda & Chernetskii 2003). + This quasar is weakly polarized and reliable RM fits to λ wereobtained across 2.2 GHz to 5.0 GHz only (Fig. 2.17). The coreRM is − ± − and decreases downstream along the jet to0 rad m − . Faraday-corrected electric vectors are perpendicular tothe jet (Fig. 5.17). +
797 (3C 390.3)
This object does not show strong linearly polarized flux density atthe majority of frequencies (see Fig. 5.18).
MNRAS , 1–19 (2017) araday RM and polarization of 20 AGN jets + The quasar’s core and jet are weakly polarized and both show fall-o ff in fractional polarization with λ (Fig. 2.19), being consistentwith the model of external rotation. An estimate of the core frac-tional polarization at 86 GHz ( . − ±
17 rad m − across 5.0 GHz to15.4 GHz. Two mas downstream from the core the rotation mea-sure is 602 ±
32 rad m − and decreases to 15 ±
27 rad m − furtherfrom the core. Zavala & Taylor (2004) and Hovatta et al. (2012)observed the 2201 +
315 jet across similar bandwidths on 2001–06–20 and 2006–10–06 accordingly. Zavala & Taylor measuredthe RM of 612 rad m − and 5 rad m − ±
91 rad m − and − ±
168 rad m − at the same positions in the jet. Hereby, thewhole 2201 +
315 jet shows no signs of temporal variations in RMvalue and maintains complex Faraday structure over time. Passageof jet component (as seen in Lister et al. 2016) through core regionmay be responsible for observed complex structure in all obser-vations. However absence of the temporal RM variations makesthis suggestion to be unlikely. A relativistic shock may account forthis RM enhancement, as, e.g. has been observed by G´omez et al.(2016) in BL Lac. Kinematic analysis shows a stationary featurein the 2201 +
315 jet (Lister et al. 2016) 0.5 mas downstream fromthe core, far from the region where rotation measure increases.The corrected core EVPAs (see Fig. 5.19, Fig. 8 and abovemen-tioned works) change longitudinal direction (epoch 2001–06–20)to transversal (2006–10–06 and 2007–04–30), meaning that thisregion is a ff ected by source activity. The magnetic field shows anapparent poloidal structure downstream from the core. In turn, RMgradients are observed in the 2201 +
315 jet (Table 7 and Figure 4),which is an indicator of a helical magnetic field. + Weak linear polarization in the core and jet of this quasar, given inFig. 2.20, follows the model of external Faraday rotation. The coreRM increases from 44 ± − over 1.4 GHz to 2.4 GHz to − ±
18 rad m − over 5.0 GHz to 15.4 GHz, while jet RM is19 ± − . The linear polarization (Fig.5.20) is aligned andmisaligned in the core and jet accordingly, which is a signatureof a poloidal magnetic field. At the the same time E-vectors show(Fig. 8) complex structure 1–3 mas downstream from the core: vec-tors are parallel at one side and turn to perpendicular direction atanother side of the jet, accompanied by asymmetry in fractionalpolarization across this region. Such geometry arises in a model ofhelical magnetic fields (Lyutikov et al. 2005; Porth et al. 2011). Inthis context the observed poloidal magnetic field may originate ina jet sheath, while the spine holds toroidal field. We have performed Faraday rotation measure and polarizationanalysis of 20 AGN jets through VLBI imaging at nine frequencybands across the 1.4 GHz to 15.4 GHz range. Fractional linear po-larization of opaque cores is typically found on a level of a fewper cent and can rise above 20 per cent for jet regions, similarto results of other studies. Wavelength-dependent variation of the fractional polarization in both the core and jet regions is consis-tent with the models of external Faraday rotation. Fractional polar-iation in the majority optically thin jet components decreases withincreasing wavelength. Though a few sources show low level of de-polarization in these regions, which is an indication of the presenceof either randomly oriented or regular magnetic fields. An anoma-lous depolarization is observed in a few transparent jet components,indicating presence of the internal Faraday rotation, taking placewhen emitting region is co-spatial with the rotating environment.Besides, a number of opaque cores exhibit polarized structure, pro-duced by smearing of a multiple jet or RM components within thetelescope beam, or show signatures of internal Faraday rotation.The EVPAs in jet regions with optically thin synchrotronemission follow a linear λ law, resulting in an absolute observedrotation measure in the range from 0 to 167 rad m − with a me-dian value of 22 rad m − . RMs in the opaque cores systematicallyincrease with frequency, breaking the λ law, with the maximumvalue reaching − − in the rest frame of the source0952 + ff ect is considerable. Themeasured dependence in the core region, | RM core | ∼ ν a , supportsthe hypothesis of a circum-jet location for the Faraday screen anda dominant contribution of the toroidal magnetic field component.For seven sources from our sample, RM measures are avail-able in the literature. Rotation measure values for six of the sourcesagree with our estimates (at the 3 σ level). While one source(1655 + > σ ). Simultaneous RM variability with the active state ofthe source points to a tight connection of the innermost jet regionsand Faraday screen.We detect significant transverse RM gradients in seven AGNs.The behaviour of the transverse RM profiles agrees with modelsof relativistic jets with helically-shaped magnetic fields or helicalmotion. Meanwhile, a few RM gradients across jets may arise dueto change in the density and thickness of magneto-ionic Faradaymedium, rather than in the strength and orientation of magneticfield. While 70 per cent of the considered RM slices resolve thejet (wider than 1.5 HPBW), significant RM gradients are observedin only 20 per cent of all slices. A lack of detected RM gradients,anomalous and low level of depolarization indicate the presence ofrandomly oriented magnetic fields in the Faraday medium.Faraday–corrected rotation polarization vectors in the model-fitted core and jet components are oriented at any angle between 0 ◦ and 90 ◦ relative to the jet direction. Transparent components show aweak excess of sources having transverse intrinsic EVPAs. The de-tailed analysis of individual sources shows that the direction of theelectric field in the core region may be a ff ected by ongoing flaringactivity or by di ff erent types of jet instabilities. In this considera-tion, our sources prefer to align their EVPAs with the local jet flowin the jet bases. Overall, this implies dominance of the poloidalmagnetic field component in the studied AGN jets.We proposed and applied a combined analysis of the FaradayRMs and apparent shift of the opaque cores with frequency. Thisenables study of the spatial, pc–scale magnetic field geometry, andconnects field orientation with its magnitude.Considering the large-scale EVPA maps, we see a complexstructure of the electric field orientation in half of the sources.These are, for example, spine-sheath structure or rotation of theEVPA at near side of the jet, accompanied by an increase in frac- MNRAS , 1–19 (2017) E. V. Kravchenko, Y. Y. Kovalev and K. V. Sokolovsky tional polarization. A few sources (e.g. 1458 + ACKNOWLEDGMENTS
EVK thanks Talvikki Hovatta for profound introduction in the RManalysis. We thank the anonymous referee, Eduardo Ros, and AllanRoy for comprehensive comments and suggestions which helpedto improve the manuscript. This research was supported by Rus-sian Foundation for Basic Research (projects 14-02-31789 and 17-02-00197). The VLBA is an instrument of the National Radio As-tronomy Observatory, a facility of the National Science Foundationoperated under cooperative agreement by Associated Universities,Inc. This research has made use of data from the MOJAVE databasethat is maintained by the MOJAVE team (Lister et al. 2009) and theUniversity of Michigan Radio Astronomy Observatory which hasbeen supported by the University of Michigan and by a series ofgrants from the National Science Foundation, most recently AST-0607523. This research has made use of NASA’s Astrophysics DataSystem Bibliographic Services.
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APPENDIX A: SUPPORTING INFORMATION
Additional information may be found in the online version of thearticle:(i) Table 3. Measured properties of the sources on Stokes I andlinear polarization maps(ii) Figure 2. Faraday rotation measure maps and linear polar-izaion properties for all of the sources(iii) Figure 5. Faraday-corrected maps of electric vector positionangle for all of the sources across the 1.4 GHz to 15.4 GHz range(iv) Figure 8. Faraday-corrected maps of electric vector positionangle and linear fractional polarization for the individual sources at15 GHz This paper has been typeset from a TEX / L A TEX file prepared by the author.MNRAS000