An oversized magnetic sheath wrapping around the parsec-scale jet in 3C 273
M. M. Lisakov, E. V. Kravchenko, A. B. Pushkarev, Y. Y. Kovalev, T. K. Savolainen, M. L. Lister
DDraft version February 10, 2021
Typeset using L A TEX twocolumn style in AASTeX63
An oversized magnetic sheath wrapping around the parsec-scale jet in 3C 273
M. M. Lisakov ,
1, 2
E. V. Kravchenko ,
3, 2, 4
A. B. Pushkarev ,
5, 2, 3
Y. Y. Kovalev ,
2, 3, 1
T. K. Savolainen ,
6, 7, 1 and M. L. Lister Max-Planck-Institut f¨ur Radioastronomie, Auf dem H¨ugel 69, Bonn 53121, Germany Astro Space Center, Lebedev Physical Institute, Russian Academy of Sciences, Profsoyuznaya st., 84/32, Moscow, 117997, Russia Moscow Institute of Physics and Technology, Institutsky per. 9, Moscow region, Dolgoprudny, 141700, Russia INAF Istituto di Radioastronomia, Via P. Gobetti, 101, Bologna, 40129, Italy Crimean Astrophysical Observatory, Nauchny 298688, Crimea, Russia Aalto University Department of Electronics and Nanoengineering, PL 15500, FI-00076 Aalto, Finland Aalto University Mets¨ahovi Radio Observatory, Mets¨ahovintie 114, FI-02540 Kylm¨al¨a, Finland Department of Physics and Astronomy, Purdue University, 525 Northwestern Avenue, West Lafayette, IN 47907, USA (Received 2 December 2020; Revised 27 January 2021; Accepted 29 January 2021)
Accepted to ApJABSTRACTIn recent studies, several AGN have exhibited gradients of the Faraday Rotation Measure (RM)transverse to their parsec-scale jet direction. Faraday rotation likely occurs as a result of a magnetizedsheath wrapped around the jet. In the case of 3C 273, using Very Long Baseline Array multi-epochobservations at 5, 8 and 15 GHz in 2009–2010, we observe that the jet RM has changed significantlytowards negative values compared with that previously observed. These changes could be explainedby a swing of the parsec-scale jet direction which causes synchrotron emission to pass through differentportions of the Faraday screen. We develop a model for the jet–sheath system in 3C 273 where thesheath is wider than the single-epoch narrow relativistic jet. We present our oversized sheath modeltogether with a derived wide jet full intrinsic opening angle α int = 2 . ◦ and magnetic field strength B || = 3 µ G and thermal particle density N e = 125 cm − at the wide jet–sheath boundary 230 pc down-stream (deprojected) from its beginning. Most of the Faraday rotation occurs within the innermostlayers of the sheath. The model brings together the jet direction swing and long-term RM evolutionand may be applicable to other AGN jets that exhibit changes of their apparent jet direction. Keywords: galaxies: active — galaxies: radio jets — galaxies: quasars: individual (3C 273) — tech-niques: interferometric — INTRODUCTIONGeneral relativistic magnetohydrodynamic(GRMHD) simulations illustrate the key role of mag-netic fields in the formation of relativistic jets in ActiveGalactic Nuclei (AGN; e.g. Meier et al. 2001; Vlahakis& K¨onigl 2004; Tchekhovskoy et al. 2011; Zamaninasabet al. 2014). The topology and structure of these mag-netic fields remains an active area of research. Therotation of the central supermassive black hole twists
Corresponding author: Mikhail [email protected] magnetic field lines into a helical shape that can berevealed by observations of transverse Faraday rotationgradients. GRMHD simulations also show that accret-ing supermassive black hole systems naturally form aspine–sheath structure of the relativistic jets as a resultof transverse velocity stratification in the outflows (e.g.McKinney 2006; Nakamura et al. 2018). The sheath,which may be a magnetized screen surrounding the jetor the jet boundary layer, has been suggested as a plau-sible source of the Faraday rotation (e.g. Asada et al.2008).Very Long Baseline Interferometry (VLBI) observa-tions of parsec-scale AGN jets (e.g., Zavala & Taylor2003, 2004; O’Sullivan & Gabuzda 2009) reveal Fara- a r X i v : . [ a s t r o - ph . H E ] F e b Lisakov et al. day rotations greater than 45 ◦ and a linear dependenceof the polarization angle with the wavelength squared.This implies that most of Faraday rotation occurs withinthe thermal magnetized media located in close proximityto the jet (e.g., Zavala & Taylor 2004). The detection ofa Rotation Measure (RM) gradient across the jet (Asadaet al. 2002) in the quasar 3C 273 (z=0.158; Strauss et al.1992), and subsequently in other AGN (e.g., Gabuzdaet al. 2014; Kravchenko et al. 2017), support the sce-nario that the sheath is threaded by a helical magneticfield.A number of studies have revealed that AGN jetschange their direction on parsec-scales over time (e.g.,Savolainen et al. 2006; Lister et al. 2013), including3C 273 (Fig. 1). As different components are ejectedin different directions into the jet, they fill in the fulljet cross-section. Therefore, the true jet width appearswider after stacking together observations performedover many years (Pushkarev et al. 2017; Kovalev et al.2020). Hereafter we call the latter a wide jet, while asingle-epoch jet is called a narrow jet.3C 273 (1226+023) has been extensively studied withpolarimetric VLBI observations, and it remains the best-established case of a transverse RM gradient in AGNjets. In this paper, we present a new multi-epoch high-resolution polarimetric study of 3C 273, and Faraday ro-tation measure analysis, focusing on its long-term evolu-tion, in order to find a connection between the apparentjet orientation and the values of the Rotation Measure.In Section 2, we describe our observations and data re-duction steps. In Section 3, we collect several trans-verse slice measurements from published research andcompare them with our measurements. In Section 4, wepresent a model of an oversized sheath wrapping aroundthe parsec-scale jet in 3C 273 and discuss the geometryof the jet and physical parameters of the plasma in thesheath.One milliarcsecond corresponds to a projected linearscale of 2.71 pc at the redshift z = 0 .
158 of 3C 273,assuming H = 71 km s − Mpc − , Ω m = 0 .
27 , andΩ Λ = 0 .
73. For our calculations we use the viewing an-gle θ = 6 ◦ and the corresponding intrinsic full openingangle of the narrow single-epoch jet of 3C 273 α int = 1 ◦ (Lisakov et al. 2017). OBSERVATIONS AND DATA REDUCTIONThe observations were performed with the 10-elementVery Long Baseline Array (VLBA, project codesS2087A, B, C, E) on 2009 August 28, 2009 October 25,2009 December 5, and 2010 January 26 at seven fre-quencies: 4.6, 5.0, 8.1, 8.4, 15.4, 23.8, 43.2 GHz with abandwidth of 16 MHz for frequencies below 15.4 GHz
Figure 1.
15 GHz total intensity contours of 3C 273 forepochs 1998 Mar 07 (red, taken from the MOJAVE database)and 2009 Oct 25 (blue, from present study). Both imageswere restored with the same, average equal-area circularGaussian FWHM beam size of 0.8 mas (shown in the bottom-left corner) for easier comparison. The images are aligned atthe position of the Stokes I peaks. Solid and dashed linesmark the fitted jet ridge lines at the two epochs. Figure 2.
The plot of EVPA vs. λ at locations in the jetshown in Figure 3, with the linear fits and the resultant RMvalues given in rad m − . Colours correspond to those usedin Fig. 3. and 32 MHz for 15.4 GHz and above. For the aims ofthis study, we consider only the 4.6–15.4 GHz frequencyrange, while detailed polarization analysis of the quasarin the full frequency range will be presented in a sepa-rate publication (Lisakov et al. in prep.). Data reduc-tion and calibration, as well as other techniques used forthe analysis were discussed by Lisakov et al. (2017).The polarization calibration was performed in thesame manner as described in Kravchenko et al. (2017)and Kravchenko & Kovalev (2017), including instrumen-tal polarization of the antennas that was determinedwith the task LPCAL in AIPS using 1308+326 as a agnetic sheath around the 3C 273 jet with estimated uncertainty of 5 ◦ and 4 ◦ at 4.6–8.4 and15.4 GHz, respectively.Frequency-dependent map offsets were determined us-ing 2D cross-correlation on optically thin portions of thejet (Lisakov et al. 2017) and were used to align imagesat the different frequencies. Average map offsets in thejet direction are 0.8 mas between 4.6 and 8.1 GHz and0.6 mas between 8.1 and 15.4 GHz. The Faraday rota-tion analysis was performed separately in two frequencyranges: low (4.6 – 8.4 GHz) and middle (8.1 – 15.4 GHz)in order to avoid smearing, which results from a convolu-tion with larger beam sizes. Images at different frequen-cies were tapered to approximate the resolution of thelower frequency in the corresponding range. All mapswere convolved with the restoring beam averaged overfour observations at 4.6 and 8.1 GHz in correspondingfrequency ranges. We calculated the polarization er-rors according to Hovatta et al. (2012a), and blanked allpixels whose polarized flux density did not exceed threetimes the polarization error. The RM is defined as alinear slope of the EVPA( λ ) dependence. Examplesof EVPA( λ ) fits for different parts of the jet are givenin Fig. 2. The solution of the n π -ambiguity problemand goodness of the λ -fit were determined by minimiz-ing the reduced χ . Accordingly, the pixels that had χ > .
99 (which in our case of four data points andtwo degrees of freedom corresponds to the 95 per centconfidence level) were blanked. RM IMAGES AND SLICESFaraday Rotation Measure images are presented inFig. 3 for the observations at 4.6–8.4 GHz and in Fig. 4for the 8.1–15.4 GHz range. Only a single-epoch imageis presented, since the RM distribution throughout thejet is consistent over four epochs and does not changedramatically in regions downstream from the core. Bythe ‘core’ or ‘apparent core’, we mean the most north-eastern region of the jet in the VLBI images. We asso-ciate it with the apparent base of the jet and a surfacewith an optical depth τ ≈ the whole jet length, at least up to 57 pc in projectionalong the jet.The absence of detected Rotation Measure close tothe apparent core of 3C 273 is usually attributed todepolarization that happens in this region (e.g. Asadaet al. 2002; Hovatta et al. 2012b). We note that duringour observations in 2009–2010 there was a major γ -rayflare detected in 3C 273 and a subsequent flare at radio-wavelengths (Lisakov et al. 2017). This is also supportedby RadioAstron observations performed in 2012–2014(Kovalev et al. 2016; Bruni et al. 2017) that show severevariability in the finest-scale structure of 3C 273 whichis associated with the apparent core region. This vari-ability together with the low level of polarized emissionlead to blanking of the RM values close to the apparentjet base according to our criteria described in Section 2.To study the long-term evolution of the Rotation Mea-sure and its gradient across the jet, we have collectedpreviously published results on 3C 273. Asada et al.(2002) and Asada et al. (2008) reported a gradient ofRM values taken across the jet at 4.6–8.6 GHz 9 masdownstream from the apparent core. In their observa-tions performed on 1995 December 9, 1995 November22, and 2002 December 15, RM values across the jetfrom south to north have ranges [130 , − and[170 , − , which correspond to a gradient of ≈
50 rad m − mas − . Zavala & Taylor (2005) reporteda much larger transverse gradient of 500 rad m − mas − taken slightly closer to the apparent core at 12 −
22 GHz.Their observations were performed in 2000 January 27and 2000 August 11, and also exhibit mostly posi-tive RM values along the slice, [150 , − and[ − , − at the two epochs, respectively.Wardle (2018) compiled most of the RM measure-ments including those of Chen (2005) performed in1999–2000 at 8 −
22 GHz. All RM values trans-verse to the 3C 273 jet are positive, ranging within[200 , − at the same location as in the pre-vious works. RM gradients in these observations were ≈
200 rad m − mas − .A notable new result came from the research of Ho-vatta et al. (2012a) based on 8–15 GHz observationson 2006 March 9 and 2006 June 15, where the authorsfor the first time observed significant negative RM val-ues, in contrast to earlier observations. Hovatta et al.(2012a) report RM values across the jet ranging within[ − , − , yielding a RM gradient of the samesign ≈
180 rad m − mas − .To compare with previous studies, we have analyzedtransverse slices from our data taken at 9 mas (as inAsada et al. 2008) and 16 mas (control slice) from theapparent jet base at 4.6–8.4 GHz and 5.5 mas (as in Lisakov et al.
Figure 3.
Left: 4.6–8.4 GHz Rotation Measure image (color) overlaid on the 4.6 GHz total intensity contours for 3C 273 atepoch 2009 December 05. The FWHM beam size is indicated in the bottom left corner. Points indicate locations where theEVPA( λ ) data were extracted as shown in Fig. 2. The location of the slices are displayed by arrows. The first slice (center) istaken at a distance 9 mas from the image center, as in Asada et al. (2008). Right: a reference slice taken at 16 mas from theimage center in the region that should not be affected by the jet direction change by 2009. In both slices, color lines representmeasured RM values at each of the individual observations, while the thick black line is the average. The shaded area showsthe average RM uncertainty. The beam projection FWHM on each slice is shown as a bar. Figure 4.
The same as in Fig. 3, but for the 8.1–15.4 GHz range, with the total contours from 8.1 GHz at epoch 2009 Dec 05. agnetic sheath around the 3C 273 jet − , − at 4.6–8.4 GHz and[ − , − at 8.1–15.4 GHz. The latter agreeswell with the measurements of Hovatta et al. (2012a).On the other hand, at 4.6–8.4 GHz, farther from the jetbeginning, the RM values are positive throughout thewhole cross-section of the jet, see Fig. 3 (slice 2). Thesepositive RM profiles are more similar to the 4.6–8.6 GHzresults of Asada et al. (2008).At middle frequencies, transverse RM variations arepresent at every separation from the core, showing neg-ative values at the southern edge and positive at thenorthern edge. We note, that due to our higher band-width and longer integration times we detect a broaderRM distribution across the jet with respect to previousstudies, hence more negative RM values are detected atthe southern edge of the jet. DISCUSSION4.1.
RM variability
With a large set of observations that span over 14years and probe variability timescales down to severalmonths, we can study both long-term and short-termevolution of the Rotation Measure values in the jet. Wefocus here on comparing transverse slices.Fig. 3 and Fig. 4 clearly show that within the 5 monthscovered by our observations, the RM values across thejet at different distances from the apparent core do notchange significantly. For the whole jet, net RM valueschange by no more than by 40 rad m − at 4.6–8.4 GHzand by no more than 120 rad m − at 8.1–15.4 GHz.These values do not exceed the uncertainty associatedwith the absolute EVPA calibration. Within the 5-month period covered by our observations in 2009–2010the RM pattern in the jet of 3C 273 has remained largelyconstant, consistent with the measurements of Zavala &Taylor (2005) over 6 months and three years. This isin contrast to the short timescale variability over threemonths as reported by Hovatta et al. (2012a).When considering variability on timescales of years,there are notable changes in the RM distribution in thejet of 3C 273. Asada et al. (2008) reported on the smallchanges in the RM over 7 years. But a major changeappears to have occurred some time between 2003 and2006. Namely, at 7 mas downstream the jet, there arenow negative values at the southern edge of the jet. This was first discovered by Hovatta et al. (2012a) andis fully confirmed with our observations at both 4.6–8.4 GHz and 8.1–15.4 GHz, see e.g. Fig. 3 (slice 1) andFig. 4 (slice 1).Although there are alternative explanations of thelong-term evolution of the RM values, we argue thatanything outside the immediate jet vicinity fails to ex-plain variability on the timescale of several years andlarge changes in RM, considering the high Galactic lat-itude b = 64 . ◦ of 3C 273 (Taylor et al. 2009).4.2. Geometry of the jet of 3C 273
According to Lister et al. (2013), the narrow jet of3C 273 had abruptly changed its apparent direction by20 ◦ in 2003. Fig. 1 shows these structural variationsin the quasar jet in application to the observations of1998 March 7 and 2009 October 25 at 15 GHz. As-suming a constant viewing angle of the overall quasarjet axis of θ = 6 ◦ (Lisakov et al. 2017), this translatesinto an intrinsic jet direction change of 2 ◦ , larger thanthe intrinsic opening angle measured at a single epoch α int = 1 . ◦ (Lisakov et al. 2017).With a median apparent jet speed of 0 . − (Lister et al. 2019), structural changes should affect thejet by 2010 within about 7 mas from its apparent be-ginning, consistent with Fig. 1. We also note that somemoving features in the jet of 3C 273 have larger appar-ent speeds, up to 1 . − , which could potentiallydouble the affected jet region (Savolainen et al. 2006).4.3. Wide Faraday sheath in 3C 273
We suggest that the Faraday rotating medium consistsof an oversized sheath wrapped around the wide jet in-stead of being tightly connected with the narrow, single-epoch jet as shown in Fig. 5. The inner opening angle ofthe sheath is therefore larger than the opening angle ofthe narrow single-epoch jet that wiggles within the inneropening angle of the oversized sheath. In this scenario,there is a misalignment between the visible narrow rel-ativistic jet axis and the symmetry axis of a broaderconical sheath which is threaded with toroidal magneticfield. Therefore, due to the swing in the parsec-scalejet direction occurring in 2003, synchrotron radiationpassed through different regions of the Faraday screenand different RM values were observed before and afterthis change. This possibility was previously consideredto explain some RM changes in 3C 273 (Hovatta et al.2012b) and 3C 120 (G´omez et al. 2011).There are several possible ways to verify this sce-nario. Firstly, the screen is detached from the rela-tivistic jet and most probably has a much slower ve-locity. Therefore, it should evolve relatively slowly. In-deed, for our data, we have measured the jet net RM
Lisakov et al.
Figure 5.
Sketch of a sheath wrapped around the wide jet.Subject to the single-epoch relativistic jet orientation, syn-chrotron emission of the jet passes through different parts ofthe sheath. RM values are all positive before 2003 (rightmostjet position) and cross zero after 2003 (middle jet position).If the jet of 3C 273 turns more to the south (to the leftmostposition in this sketch), only negative RM values will be ob-served. changes between observations in 2009–2010 as: − − −
25 rad m − at 4.6–8.4 GHz and 114, −
34, 63 rad m − at 8.1–15.4 GHz. These values are within the uncertain-ties associated with the EVPA calibration. Secondly,should the rotating medium constitute a sheath aroundthe narrow relativistic jet with thickness comparable tothe jet cross-section, it will inevitably be destroyed bythe relativistic jet once it changes direction. However,we do not detect any traces of such an interaction.We note that Park et al. (2019) present RM imagesof the jet in the radio galaxy M87 within the Bondi ra-dius and conclude that the dominant source of the ob-served significantly high RMs are hot winds. The latterare non-relativistic, moderately magnetized gas outflowsthat surround the highly magnetized jet of M87 and arethreaded by toroidally-dominated magnetic fields. ButM87 shows no RM gradients across its jet. Park et al.(2019) suggest that this is due to a misalignment be-tween the jet axis and the symmetry axis of the toroidalfield loops in the Faraday screen, therefore the RM gra-dients are not observed in M87 since only a portion of the sheath is illuminated. Although the matter whichforms the sheath in M87 and in 3C 273 may have a dif-ferent origin, observational properties for both sourcesare well explained within the presented model.Our model of an oversized sheath explains the long-term RM variability in the inner parts of the jet withdifferent apparent directions of the relativistic jet beforeand after 2003 and hence the jet synchrotron emissionpassing through different parts of the Faraday screen.We can also predict that if the jet direction changesfarther to the south, mostly negative RM values will beobserved. 4.4. Screen parameters
To estimate parameters of the Faraday screen we havedeveloped a simple model. The wide jet with a radius r jet is wrapped by a hollow conical sheath with inner ra-dius r jet and outer radius r screen , see Fig. 5. The toroidalcomponent of the magnetic field in the sheath decayswith perpendicular distance from the wide jet axis as B || = B r − and the thermal particle density declines as N e = N r − where B and N are taken at 1 pc from thewide jet axis. After integrating RM ∝ (cid:82) B || N e dl overdifferent lines of sight perpendicular to the apparent jetdirection, we obtained the distribution of the RM val-ues across the jet width. We then convolved these witha Gaussian restoring beam assuming five beams acrossthe jet to resemble the data at 4.6–8.4 GHz. This simplemodel is designed to account only for smooth and mono-tonic distribution of RM across the jet and give a hintof typical parameters of the medium in the real sheath.For any r screen , the inner layers of the screen, up to r screen = 3 × r jet , contribute 75% of the observed RM asexpected from the model, see Fig. 6. This supports ourinitial assumption that the sheath would be disruptedby the jet changing its direction if this sheath is locatedin the immediate vicinity of the narrow relativistic jet.Moreover, the predicted RM distribution across the jetis well described by a straight line.One may assume that the maximum value of theRM across the jet at 9 mas from the apparent coremeasured by Asada et al. (2002) was 500 rad m − andthat the minimum value, not observed yet, would be −
500 rad m − . Then with our measurements of RMvalues across the jet at 4.6–8.4 GHz taken at the samedistance, we estimate a total wide jet intrinsic openingangle of α int = 2 . ◦ , twice as large as single-epoch esti-mates (Lisakov et al. 2017). To perform this, we combinetransverse RM distributions, taken at different epochs,with the narrow jet position angle changes taken into ac-count, as is shown in Fig. 7. The apparent angular widthof the RM distribution at a single epoch is estimated as agnetic sheath around the 3C 273 jet Figure 6.
Model RM values across the jet for the 4.6–8.4 GHz range at 9 mas from the core. B = 12 µG and N = 2000 cm − were chosen to obtain the total range[ − , − of observed RM values for r screen =3 r jet . The family of black curves represents r screen valuesranging from 5 r jet to 100 r jet . Figure 7.
The RM values at 4.6–8.4 GHz taken at 9 masfrom the apparent jet beginning transverse to its direction.Blue and orange points represent two epochs, 1997 and 2002,reported by Asada et al. (2008), while green points are takenfrom our observation on Dec 05, 2009. The two verticaldashed lines show the average narrow jet position angle be-fore (at − ◦ ) the major jet swing in 2003, and after (at − ◦ ). The black diagonal line represent a linear fit to thecombined data set. the width of the transverse jet intensity profile taken atthe 1% level. Afterwards, the combined transverse RMdistribution was fitted with a linear function, in accor-dance with the model. The total range of jet positionangles, required to obtain a [ − , − rangeof the RM, is 55 ◦ which corresponds to the intrinsicopening angle of the wide jet α int = 2 . ◦ .With this estimate, at 9 mas from the apparent core,the total width of the wide jet is 8 pc, r jet = 4 pc. As we found for an arbitrary large r screen , the inner layersof the sheath up to r = 3 r jet are responsible for 75%of the rotation. Hence we assumed r screen = 3 r jet . Therange of RM values [ − , B × N =24000 µ G cm − for a path length 2 r jet = 8 pc throughthe sheath. Clearly, B and N can not be calculatedindependently within this analysis. At the same time,the line-of-sight path length through the screen couldnot change the estimates of B × N by more than afactor of two within our model, for any reasonable screenwidth. With r jet = 4 pc, B || × N e = 375 µ G cm − at thewide jet – wide sheath boundary. For assumed magneticfield component parallel to the line of sight B || = 3 µ Gat the inner edge of the sheath, the thermal particledensity is N e = 125 cm − .With the same logic applied to the 8.1–15.4 GHz,a range of RM values [ − , B × N =37500 µG cm − , as obtained from the model with pathlength of 2 r jet = 5 pc. B × N is 25% higher than thatat 9 mas, what is expected given the lower distance tothe jet beginning. As is apparent from Fig. 4, trans-verse RM distributions observed at higher frequenciesin general show more complex shape and thus require amore elaborate model to describe them. This is a scopeof future work that will allow a better estimate of theFaraday screen parameters.It is important to note that using the core shift anal-ysis (Lobanov 1998) and estimates of the magnetic field B = 0 .
47 G and relativistic electron density N =1500 cm − at the jet beginning (Lisakov et al. 2017),the estimated values in the jet are B = 3 µ G, N =8 × − cm − at 5.5 mas (corresponding to 140 pc, de-projected) and B = 2 µ G, N = 3 × − cm − at9 mas(230 pc, deprojected) from the apparent jet base.4.5. The jet opening angle derived from stacked images
We produced a stacked map of 3C 273 in total in-tensity at 15 GHz (Fig. 8) using public data from theMOJAVE database (Lister et al. 2019). According todiscussion in Section 4.3, this map represents the widejet in 3C 273. In total, 105 epochs ranging from 1995July 28 to 2019 April 15 were stacked together. Eachsingle-epoch image was convolved with the same mediancircular beam and shifted such that the 15 GHz VLBIcore is placed in the phase center. The core position(Lister et al. 2019) was determined from source struc-ture modeling performed in the Fourier plane with theprocedure modelfit from the Caltech
Difmap package(Shepherd 1997). We fitted a ridge line to the imageand measured the apparent wide jet opening angle α app following the procedure described in Pushkarev et al. Lisakov et al.
Figure 8.
15 GHz naturally weighted stacked clean imageof 3C 273 based on 105 VLBA epochs from the MOJAVEprogram (Lister et al. 2019). The contours are shown at in-creasing powers of √ − . The restoring beam dimensions are plotted asa shaded circle in the lower left corner. The constructedtotal intensity ridge line is depicted in red. A wedge indicat-ing observing epochs (vertical ticks) used for producing thestacked image is shown on top. (2017). The intrinsic wide jet opening angle, calculatedas tan( α int /
2) = tan( α app /
2) sin θ , is shown in Fig. 9.The intrinsic opening angle of the wide jet is α int ≈ ◦ up to the distances of about 9 mas from the core alongthe ridge line, in noticeable agreement with the estimatemade above under the assumption on the minimum Ro-tation Measure −
500 rad m − .We also note that high resolution space VLBI imagesof 3C 273 obtained with RadioAstron at both 1.6 GHzand 4.8 GHz and presented recently by Bruni et al.(2021) show a clear evidence for the new establisheddirection of the jet in 3C 273. SUMMARYWe present new high-resolution images of the FaradayRotation Measure in the parsec-scale jet of 3C 273, seeSection 3, based on multifrequency VLBA polarimetricobservations at 4.6–15.4 GHz. From the comparison ofour results with the previous studies, we confirm the ex-istence of transverse RM gradients in the jet of 3C 273out to at least 57 pc projected distance (500 pc depro-jected), and detect a change of RM towards negative val-ues compared with observations performed before 2003.
Figure 9.
Intrinsic opening angle of the jet derived fromstacked image in Fig. 8 as a function of the core separationmeasured along the ridge line.
In order to coherently explain the change of the jet po-sition angle together with the change of the Faraday Ro-tation Measure across the jet, in Section 4.3 we develop amodel of an oversized sheath that is wrapped around thewide jet in 3C 273. The sheath does not show any rapidvariability and most likely is disconnected from the rel-ativistic jet. Single-epoch images of 3C 273 reveal onlya portion of the wider jet. After the parsec-scale jet di-rection swing in 2003, different lines-of-sight through thesheath are sampled, resulting in different observed Fara-day Rotation Measure values. We predict that mostlynegative RM values will be observed if the jet turns evenmore southward. Within our model we estimate the to-tal wide jet intrinsic opening angle α int = 2 . ◦ , basedsolely on the RM measurements across the jet. Most ofthe rotation occurs within a layer of 3 × r jet width, seeSection 4.4. In this scenario, we estimate B = 3 µ Gand N = 125 cm − ◦ at thejet region near the 15 GHz core. The outflow quickly col-limates to α int ≈ ◦ . This regime holds within distancesfrom about 1 to 9 mas from the core, further supportingour model. agnetic sheath around the 3C 273 jet Facilities:
VLBA
Software:
AIPS (van Moorsel et al. 1996),Difmap (Shepherd 1997), astropy (Astropy Collabora-tion et al. 2013), WebPlotDigitizer https://automeris.io/WebPlotDigitizer REFERENCES