VLBI observations of CygnusA with sub-milliarcsecond ...aa.springer.de/papers/8329003/2300873.pdf · bent core-jet structure extending ˘ 5mas along pa = 270 − 280 (Krichbaumetal.,1993a).VLBIdetectiontestsat86GHz

Astron. Astrophys. 329, 873–894 (1998) ASTRONOMYAND

ASTROPHYSICS

VLBI observations of Cygnus A with sub-milliarcsecond resolutionT.P. Krichbaum1, W. Alef1, A. Witzel1, J.A. Zensus2,1, R.S. Booth3, A. Greve4, and A.E.E. Rogers5

1 Max-Planck-Institut fur Radioastronomie, Auf dem Hugel 69, D-53121 Bonn, Germany2 National Radio Astronomy Observatory, Charlottesville, VA 22903, USA3 Onsala Space Observatory, Chalmers University of Technology, S-43992 Onsala, Sweden4 Institut de Radioastronomie Millimetrique, F-38406 St. Martin d’Heres, France5 MIT-NEROC Haystack Observatory, Westford, MA 01886, USA

Received 3 July 1997 / Accepted 5 September 1997

Abstract. We present new images of the two-sided VLBI-structure of the radio galaxy Cygnus A at 1.6 GHz, 22 GHz and43 GHz. The maps show the jet and counter-jet of Cygnus Aon scales from ∼ 400 to 0.1 milliarcseconds, corresponding toprojected sizes of ∼ 300 pc to 0.07 pc. Our best 22 GHz im-age shows a small (few degree) misalignment of the VLBI-jetswith the kpc-jets, longitudinal oscillations of the jet’s ridge linewith amplitudes of ≤ 0.6 mas, and transverse oscillations ofthe jet’s width with amplitudes of 0.2 − 0.3 mas. At distancesof < 15 mas from the core, both jets expand at an openingangle of ∼ 5 ◦ . Between 22 and 43 GHz the core has an in-verted spectrum. The spectrum of the jet appears steep, that ofthe counter-jet relatively flat. From two 22 GHz observationswe find evidence for apparent acceleration (from 0.1 c to 0.7 c)along the jet. The acceleration could be jet-intrinsic or relatedto phase velocities. In the counter-jet structural variations seemalso to be present, but cannot accurately be determined. Between1.6 GHz and 43 GHz the jet-to-counter-jet ratio R is frequencydependent with a maximum of R' 5 near 5 GHz and a smallerratio of R = 1−2 at 1.6 GHz and 43 GHz. This can be interpretedas an effect of absorption by a partially opaque inclined absorber(e.g. a disk or a torus) obscuring the counter-jet but not the jet.With an absorption corrected intrinsically small jet-to-counter-jet ratio, Cygnus A could be oriented at a relatively large angleto the line of sight (θ > 80 ◦ , for R < 2) with jet velocities inthe range 0.2h ≤ β < 1 (H0 = 100 · h−1km sec−1Mpc−1).

Key words: galaxies: active; Cygnus A; jets – radio continuum:galaxies – techniques: interferometric

1. Introduction

The double lobed FR II class radio galaxy Cygnus A (3C 405,1957+405) – one of the first radio sources discovered in the sky(Bolton & Stanley 1948) – resembles in luminosity (radio- toX-ray) and morphology (parsec- to kilo-parsec) typical radio

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loud quasars at z ∼ 1. VLBI-imaging at high frequencies al-lows imaging of the sub-parsec scale regions. This may help tosolve the problem of the still poorly understood process of en-ergy release and jet generation at the centres of such luminousobjects.

In the optical, Cygnus A is identified with a giant ellipticalcD galaxy (Smith 1951, Baade & Minkowski 1954, Kronberget al. , 1977) at a redshift z = 0.0562 (Simkin 1977, Spinrad &Stauffer 1982, Stockton et al. , 1994), which lies within a lumi-nous X-ray cluster (Fabbiano et al. , 1979). The centre of thegalaxy shows a prominent extended double morphology (Jen-nisson & Das Gupta 1953, Baade & Minkowski 1954, van denBergh 1976) of∼ 2” size with its rotational symmetry axis ori-ented along pa ∼ 285 ◦ . Optical and infrared imaging showa very complex line and continuum emitting central region onsub-arcsecond scales (cf. Carilli & Barthel, 1996). The embed-ded core component is not yet clearly identified, but seems tobe small (≤ 300 pc). It is affected by strong foreground absorp-tion (Ward et al. , 1991, Vestergaard & Barthel 1993, Stocktonet al. , 1994, Jackson et al. , 1994). The strong extinction, theoptical spectra (e.g. Osterbrock & Miller 1975, Pierce & Stock-ton 1986), the polarization properties of the continuum (e.g.Goodrich & Miller 1989, Tadhunter et al. , 1990) and of the lines(Jackson & Tadhunter 1993), and the recent detection of a broademission line (Mg II) probably scattered from a hidden quasarnucleus (Antonucci et al. , 1994), consistently indicate that thecore of Cygnus A is not directly visible in the optical/IR, butresembles a Seyfert-2 nucleus whose radiation is blocked fromdirect view by an obscuring torus (Antonnucci & Miller 1985,Barthel 1989).

In the radio, Cygnus A is dominated by two extended andcomplex radio-lobes of ∼ 130” separation, and two highly col-limated jets (spectral index α1.5/15 GHz ' −0.5), leading fromthe core component located at the centre of the optical galaxy(Hargrave & Ryle 1974, Wade et al. , 1971) to the two outerlobes (Perley et al. , 1984, Dreher et al. , 1987a, Carilli et al. ,1991). Near the core (<∼ 30”), the western 50” long VLA jet isoriented along pa = 285 ◦ , however changes to pa = 289 ◦ after

874 T.P. Krichbaum et al.: VLBI observations of Cygnus A with sub-milliarcsecond resolution

entering the NW-lobe. The fainter counter-jet is 10” long andextends towards the SE-lobe along pa = 107 ◦ . It appears mis-aligned with the jet by ∼ 2 ◦ . A detailed description of thearcsecond structure of Cygnus A is given in Carilli & Harris(1996) and Carilli & Barthel (1996).

Between 1–300 GHz the radio spectrum of the central com-ponent of Cygnus A is fairly flat (Kafatos et al. , 1980, Ealeset al. , 1989, Salter et al. , 1989). At 86 – 100 GHz, interfero-metric observations with arcsecond resolution show a compactunresolved core component of ∼ 1 Jy, which seems to vary inintensity by ∼ 30 % on time scale of years (Wright & Birkin-shaw, 1984, Wright & Sault, 1993). Early VLBI observations at5-10.7 GHz, (Kellermann et al. , 1975, Kellermann et al. , 1981,Linfield 1981, Linfield 1985) show a one sided core-jet structureof∼ 5 mas length which is aligned within a few degrees with thehot spot of the NW lobe. Subluminal motion in the jet was de-tected from two follow up observations at 5 GHz (Carilli et al. ,1991b and 1994). The early 5 GHz images showed no counter-jet. This limited the jet to counter-jet ratio toR ≤ 12−15 (Lin-field 1985, Carilli et al. , 1991b). The detection of a counter-jetwas recently claimed by Carilli et al. , (1994), who averagedtwo 5 GHz VLBI-maps separated in time by ∼ 5 yrs (epochs1986.9 and 1991.4). The third and most recent 5 GHz observa-tion (epoch 1995.2; Bartel et al. , 1995, Sorathia et al. , 1996)confirms this detection and constrains the jet-to-counter-jet ra-tio to 3 ≤ R ≤ 7. These observations also reveal subluminalmotion in two outer jet components (βapp = 0.4 and 0.6).

VLBI observations at higher frequencies are required toimage directly the central sub-parsec scale regions, whichare self-absorbed at longer wavelengths (e.g. Krichbaum &Witzel, 1992). A first and relatively crude 43 GHz-map (3 sta-tions only, resolution ∼ 0.4 mas) showed a knotty and slightlybent core-jet structure extending ∼ 5 mas along pa = 270 −280 ◦ (Krichbaum et al. , 1993a). VLBI detection tests at 86 GHz(Standke et al. , 1994, Krichbaum et al. , 1994c), however, indi-cate that the jet remains compact even at these frequencies.

In this paper we present and discuss new VLBI imagesfrom two 22 GHz VLBI observations of Cygnus A (1992.4 and1994.2), a 43 GHz VLBI observation performed nearly simul-taneously to the first 22 GHz experiment, and an image of thelarge scale structure obtained at 1.6 GHz (1986.7). Preliminaryreports of this project were given in Krichbaum et al. (1996 aand b).

Throughout the paper we will assume a Hubble constant ofH0 = 100 · h−1km sec−1Mpc−1 (h being the Hubble param-eter), a deceleration parameter q0 = 0.5, and a spectral indexdefined as S ∝ να. At the redshift of z = 0.0562 an angleof 1 mas corresponds to a projected scale of 0.74 pc. Angu-lar motion with 1 mas/yr corresponds to an apparent speed ofβapp = v/c = 2.56.

Fig. 1. The uv-coverage of the high frequency experiments: 43 GHzMay 1992 (top), 22 GHz June 1992 (centre) and March 1994 (bottom).

2. Observations and data analysis

2.1. The experiments

Cygnus A was observed at 1.6 GHz in 1986.74 (5 stations), at22.2 GHz in 1992.44 (8 stations) and 1994.17 (13 stations), andat 43.2 GHz in 1992.40 (8 stations). Details of the observationalsetup and the participating stations are summarized in Table1. At 22 and 43 GHz the quasar 2005+403 was repeatedly ob-

T.P. Krichbaum et al.: VLBI observations of Cygnus A with sub-milliarcsecond resolution 875

Table 1. The upper table summarizes station names (col.2) and their abbreviations (col.1), antenna diameters (col.3), name of institution (col.4)and location (col.5). The lower table lists the observing date (col.1), the start and stop time of the VLBI observations (col.2), the mean referenceepoch (col.3), the observed band (col.4), the bandwidth and the recording mode of the data acquisition (col.5), the abbreviated names of theparticipating antennas (col.6), and the sky polarization (col.7) (IEEE convention).

Station Locations

Abbr. Station Diameter Institution Country[m]

Antennas in Europe

B: Effelsberg 100 Max-Planck-Institut fur Radioastronomie GermanyJ: Jodrell Bank 76 Nuffield Radio Astronomy Laboratories EnglandL: Medicina 32 Istituto di Radioastronomia ItalyN: Noto 32 Istituto di Radioastronomia ItalyZ: Pico Veleta 30 Institut de Radioastronomie Millimetrique SpainW: Westerbork 5×25 Netherlands Foundation for Research in Astronomy NetherlandsD: Onsala 25 Onsala Space Observatory SwedenS: Onsala 20 Onsala Space Observatory Sweden

Antennas in USA

K: Haystack 37 Northeast Radio Observatory Corporation Massachusetts, USAY27: Phased VLA 27×25 National Radio Astronomy Observatory New Mexico, USA

VLBA antennas

F: Fort Davis 25 National Radio Astronomy Observatory Texas, USAI: North Liberty 25 National Radio Astronomy Observatory Iowa, USAO: Ovro 25 National Radio Astronomy Observatory California, USAP: Pie Town 25 National Radio Astronomy Observatory New Mexico, USAR: Brewster 25 National Radio Astronomy Observatory Washington, USAT: Kitt Peak 25 National Radio Astronomy Observatory Arizona, USAU: Mauna Kea 25 National Radio Astronomy Observatory Hawaii, USAV: St. Croix 25 National Radio Astronomy Observatory Virgin Islands, USAX: Los Alamos 25 National Radio Astronomy Observatory New Mexico, USA

The Experiments

date UT epoch frequency range observing mode stations Polarization[hrs] [yrs] [MHz] [MHz]

Sep 27 11- 4 1986.74 1636.99- 1692.99 56 (Mk III, A) B,L,J,D,W LCPMay 26 0-12 1992.40 43192.99-43248.99 56 (Mk III, B) B,K,S,Z,I,P,T,X RCP:IPTXZ, LCP:BKSJun 10 19-14 1992.44 22222.99-22250.99 28 (Mk III, B) B,L,K,F,I,O,T,Y27 LCPMar 4 3-23 1994.17 22206.99-22262.99 56 (Mk III, B) B,L,N,S,F,I,O,R,T,U,V,X,Y27 LCP

served at 2–3 hour intervals to facilitate easier fringe detectionand calibration. At 43 GHz Cygnus A was observed within alarger global observing campaign (see also Krichbaum et al. ,1993b, 1994a and b, Alberdi et al. , 1997), including for thefirst time at this frequency 4 antennas of the VLBA1 and theIRAM 30 m Millimeter-Radiotelescope (MRT) on Pico Veleta(cf. Krichbaum et al. , 1993a). Unfortunately, a polarization mis-match between the 30 m MRT and the VLBA antennas, whichrecorded in right circular polarization (RCP), and the antennasat Effelsberg, Haystack and Onsala, which recorded left circu-lar polarization (LCP), limited the uv-coverage (Table 1). For

1 The Very Long Baseline Array (VLBA) is operated by the NRAO.

the imaging at 43 GHz we therefore used only visibilities frombaselines with parallel handed polarization (LCP: 3 baselines,RCP: 10 baselines).

2.2. Fringe fitting and calibration

The data were correlated at the Max-Planck-Institut fur Radioas-tronomie in Bonn, Germany.

The 1.6 GHz data were fringe fitted and calibrated in AIPS inthe standard manner. The 22 and 43 GHz data were fringe fittedwith the software of the MK III VLBI system (Rogers et al. ,1993, Alef 1989). The global fringe fitting algorithm (Alef &Porcas, 1986) was used to improve the phase noise and to further


Fig. 2. Maps of Cygnus A at 43 GHz (top)and 22 GHz (middle and bottom). Contourlevels are -0.3, -0.1, 0.1, 0.3, 0.7, 2, 4, 8, 16,32, and 64 % of the peak flux density (fromtop to bottom: 0.18, 0.21, and 0.24 Jy/beam).The 0.1 % level is omitted in the 43 GHzmap. The maps are restored with a beamof (from top to bottom): 0.30 × 0.13 mas,pa = −2 ◦ , 0.49 × 0.15 mas, pa = −21 ◦ ,and 0.45× 0.15 mas, pa = −13 ◦ .

lower the detection threshold to SNR ≥ 5 at 43 GHz and SNR ≥3− 4 at 22 GHz. A brief description of this iterative procedureis given for example, in Krichbaum et al. (1992). After fringe-fitting the data were segmented into smaller time intervals (∼60 sec at 22 GHz, 25 sec at 43 GHz) to avoid coherence losseslarger than 10 %.

The data were then exported into the MPIfR data format(Alef 1989) where the ‘a priori’ amplitude calibration was ap-plied. After this, the editing, the phase and amplitude self-calibration, and the imaging and model fitting was performed

within the CalTech VLBI package (Pearson 1991). The ‘a priori’amplitude calibration was based on system-temperature mea-surements and elevation dependent antenna gain curves. In ad-dition a correction for atmospheric opacity effects was appliedat 22 and 43 GHz (see Krichbaum et al. , 1993a and b for details).The accuracy of the amplitude calibration was determined fromcomparison of the raw-calibrated data with the self-calibrateddata sets obtained for the program and the calibrator sourcesduring the imaging and model fitting. On this basis we can con-


C3 C2 C1 J6 J7

J0 J1 J2 J3 J4 J5

C3 C2 C1 J6 J7 J8

J0 J2 J3 J4 J5

C3 C2 C1 J6 J7 J8 J9

J0 J1 J2 J3 J4 J5a J5b

Fig. 3. The sub-mas to mas structure ofCygnus A at 43 GHz at epoch 1992.40 (top),at 22 GHz at epoch 1992.44 (middle) and atepoch 1994.17 (bottom). For all 3 maps a com-mon observing beam of 0.40 × 0.15 mas ori-ented along pa = 0 ◦ was used. Contour levelsare 0.25, 0.5, 1, 2, 5, 10, 20, 30, 50, 70, and90 % of the peak flux density (top: 0.21 Jy/beam,middle: 0.18 Jy/beam, bottom: 0.24 Jy/beam).The 22 GHz maps are rotated clockwise by10 ◦ (R.A. axis along pa = −80 ◦ ), the 43 GHzmap by 16 ◦ (R.A. axis along pa = −74 ◦ ). Thealignment of the images is based on the mostlikely component cross-identification with com-ponent J0 located at the map centre (see text for adiscussion). Labels denote for modelfit compo-nents (see Tables 2 and 3). The bar in the bottommap gives the spatial scale.

fidently assign an uncertainty in the amplitude calibration of∼ 10− 15 % at 1.6 and 22 GHz and ∼ 20− 25 % at 43 GHz.

2.3. Imaging

The imaging was done using the hybrid-mapping technique(Cornwell & Wilkinson 1981) implemented in the CalTechVLBI-package and the difference mapping program DIFMAP(Shepherd et al. , 1994). Starting from a point source model, wefirst derived the basic source structure. This and simple modelfits with only a few Gaussian components fitted to the data al-lowed the application of station dependent second order correc-tions to the antenna gains and removal of smaller systematic ef-fects. In the next step the image quality was iteratively improved

with amplitude self-calibration on successively shortened cal-ibration time-scales and consecutively improved starting mod-els. In amplitude self-calibration, the lack of data at short uv-spacings can lead to the loss of extended emission. To preventthis, we down-weighted the data at long uv-spacings, using arelatively strong uv-taper (5-30 %) and restarted the amplitudeself-calibration several times from the raw-calibrated data. Toavoid drifts of the flux density scale and to better constrain time-dependent antenna gain solutions, the amplitude self-calibrationwas in the beginning not applied to the VLBI array as a whole,but first to single stations and later to antenna sub-arrays. Tocheck the reality and stability of components seen in the finalmap (particularly on the counter-jet side), such features weretemporarily removed and the effect of the fit to the data was in-


spected. Similar to the method described in Carilli et al. (1994)we produced ‘biased’ maps and Gaussian model fits, in whichthese features were removed. We then self-calibrated the visi-bility amplitudes using time scales of 30-90 min and checked ifthe features removed were reappearing. By this means, we areconfident that the emission at larger core-separations and on thecounter-jet side is real.

3. Results

3.1. The maps at 22 and 43 GHz

In Fig. 2 we show the overall brightness distribution of Cygnus Aat 22 and 43 GHz in CLEAN-maps of 40 × 16 mas size. Lim-itations of the data quality and the uv-coverage (see Fig. 1)are reflected in the dynamic range of the 3 maps, which in-creases from top to bottom. Above the 0.5 % contour level all3 images consistently show a complex and knotty appearingjet of ∼ 3 − 4 mas length, oriented in the direction towardsthe outer VLA-structure. At lower levels, faint and partially re-solved two-sided jet emission becomes visible. Limitations ofthe data quality at 43 GHz allow only a marginal detection ofthe extended emission at separations beyond±(3−4) mas. Theuv-coverage of the 22 GHz data set of 1994 is much better thanthe corresponding coverage in 1992 (see Fig. 1). This probablyexplains the differences seen in the outer jet emission (beyond|r| > 4 mas) between the map of 1992 and 1994 (Fig. 2, bot-tom).

In Fig. 3 we show enlargements of the central regionof Cygnus A at 43 GHz (top: 1992.40) and 22 GHz (middle:1992.44, bottom: 1994.17). The maps are rotated as indicatedin the figure caption. The high degree of complexity of the jetstructure makes a cross-identification of the individual featuresin the three maps difficult. Following the most plausible (butnot unique) identification scheme described in Sect. 4.2, themaps are aligned on component J0 located at the map centre.Comparison of the two 22 GHz images of 1992.44 and 1994.17immediately reveals evidence for structural variations on sub-parsec scales, although the overall jet length (as measured e.g.at the 0.5 % level) seems not to have changed very much.

3.2. The large scale structure at 1.6 and 22 GHz

In Fig. 4 we show an 18 cm EVN-map of Cygnus A obtainedfrom data of 1986. The source structure is clearly two-sided.Using the brightest component at the map centre as reference,the western jet extends up to r ' 440 mas along pa = 288±1 ◦ .The eastern counter-jet appears to be shorter and extends alongpa = 105 ± 2 ◦ up to r ' 150 mas. The jet emission appearswell collimated and continuous, making a description by distinctGaussian modelfit components difficult. Simple modelfits yieldcomponents at relative separations of r = −119,−31, 0, 34, 92,and 155 mas (from east to west).

The good uv-coverage of the 22 GHz data of 1994 leads tothe detection of faint two sided jet emission at up to 40−50 masseparation from the brightness peak. In Fig. 5 we show thisbi-directional structure in a tapered ‘low’ angular resolution

map convolved with a circular beam of 0.7 mas size. In theregion 0 ≤ r ≤ 5 − 10 mas, the (western) jet extends alongpa = 278.5± 1 ◦ . At larger separations the jet is oriented alongpa = 284.5 ± 1 ◦ , more in the direction towards the arcsecondjet (pa = 285 ◦ ). A slightly larger position angle of the jetmeasured at 18 cm (pa = 288 ◦ , see above) indicates jet bendingby ∆pa ' 5 ◦ .

At 22 GHz the counter-jet extends up to ∼ 30 − 40 maseast, but it becomes faint and less well defined beyond ∼ 10−15 mas. In the central and better defined region, the counter-jet is oriented along pa = 105 ± 1 ◦ , misaligned by ∼ 7.5 ±2 ◦ with the corresponding region at the jet side. No significantmisalignment of the outer counter-jet with the outer (≥ 5 mas)jet is seen (∆pa = 0.5± 2 ◦ ). Visual inspection of the 22 GHzmaps (see Fig. 2 and Fig. 5) indicates a weak S-shape symmetryof the overall jet structure, with the inner jet and counter-jet(|r| ≤ (6 − 8) mas) rotated by a few degrees compared to theouter structure.

3.3. The model fits for 22 and 43 GHz

A fit of Gaussian component models to quasi continuous, jet-like brightness distributions is difficult and does not alwaysyield unique results. However, model fits provide a very usefulparametrization of the basic source structure and complementthe information directly extracted from the maps, particularlyin the search for structural variability.

Relatively simple model fits with (N < 7) components didnot fitted all details of the visibilities and resulted in relativelylarge formal agreement factors (reduced χ2) of χ2 > 3 − 4 at22 GHz and χ2 > 1.5 − 2 at 43 GHz. We used these fits for afirst and at this point tentative cross-identification of the mostprominent features (C1, J0, J2, J3, J4 and J6) seen in each dataset. We then fixed the presumed core component J0 at the originof the coordinate system (r = 0 mas, θ = 0 ◦ ) and fitted morecomplex models (N = 10− 15 components) to the data. Thesefits were much better (χ2 < 1.5) and also appeared more similarto the hybrid maps (compare Fig. 6 with Fig. 3).

If the measurement errors of the modelfit parameters arederived formally from Gaussian error statistics, they often ap-pear unrealistically small. In order to obtain better estimates ofthese uncertainties, we selected the 10− 20 ‘best fitting’ mod-els (χ2 < 1.5) from each observation. Since these models wereobtained from slightly different calibrated and edited data sets,the scatter of the parameters could be used as a measure for thetypical ‘internal’ uncertainty of each parameter, also taking intoaccount amplitude calibration errors and correlated variationsof the fit parameters caused by changes of the number of fit-ted components. An ‘average model’ for each observation wasobtained from a weighted average of the corresponding param-eters of the ‘best models’. This average model was then usedas a starting model for the final model fit iteration cycle, nowusing the same data set as for the final map. The resulting finalmodel parameters are summarized in Tables 2 and 3. In Fig. 6we show maps of the models with labels denoting the individualcomponents.


Fig. 4. EVN-VLBI map of Cygnus A at18 cm. Contour levels are -0.5, -0.25, 0.25,0.5, 1, 2, 4, 8, 16, 32, 64 % of the peakflux density of 0.27 Jy/beam. The size ofthe restoring beam is 23.6 × 20.7 mas,pa = 54 ◦ . The overall source extendsover about 550 mas corresponding to 440 pcprojected length. The jet is oriented alongpa ' 287 ◦ .

Fig. 5. Jet- and counter-jet of Cygnus A in a tapered low angular resolution map. The figure shows the largest field of view (∼ 100× 30 mas),which could be reliably imaged using the 22 GHz data of 1994.17. The map is displayed with a circular restoring beam of 0.7 mas size and auv-tapering of 10 % at 800 Mλ uv-distance. The contour levels are (-0.05), 0.05, 0.15, 0.3, 0.5, 1, 2, 5, 20, 50, and 90 % of the peak flux densityof 0.73 Jy/beam. The total flux density seen in the map is 1.65± 0.05 Jy. The scale bar gives the linear scale.

4. Discussion

4.1. Identification of components

Based on the morphological similarities seen in the maps andmodels (component separations, flux densities, sizes and de-rived brightness temperatures), we tried to cross-identify thecomponents of the 22 GHz and 43 GHz maps. In column 1 ofTable 2 and 3 we assign letters to corresponding components.Within this identification scheme, faint and partially resolved jetfeatures (C3-C1) are located east of a brighter and more com-pact jet-like structure (J0-J6). This structure has a length of about∼ 1.2 mas and consists of the main components J0 (r = 0 mas),J2 (r = 0.36 mas), J3 (r = 0.57 mas), J4 (r = 0.77 mas), J5(r = 0.97 mas), and J6 (r = 1.10 mas) (distances r are takenfrom the 22 GHz data set of 1994.17). These components (seeTables 2 and 3) have typical sizes of 0.1−0.3 mas and brightnesstemperaturesTB of a few 1010−1011 K (at 22 GHz). Fainter and

more elongated components of larger extent are located west ofJ6. These features (components J7–J10) are less well definedand cover a region from about r = 1.4 − 8 mas. The compo-nents J7–J10 represent obviously only a crude and simplifiedparametrization of the outer jet structure, which is too faint tobe adequately represented by Gaussian components.

With the present data, alternative identification schemes can-not be completely excluded. However, the kinematical (Sects.4.4, 4.2, 4.4.2) and spectral properties (Sect. 4.3) of the pro-posed identification are consistent with the general propertiesobserved in many other extragalactic radio jets (e.g. Zensuset al. , 1995) and therefore appear most plausible. Future (e.g.phase-reference) VLBI-observations will be required to checkthe correctness of the proposed component registration.


C3 C2 C1 J5 J6 J7

J0 J1 J2 J3 J4

C3 C2 C1 J6 J7 J8

J0 J2 J3 J4 J5

C3 C2 C1 J6 J7 J8 J9

J0 J1 J2 J3 J4 J5

Fig. 6. Maps of Gaussian model fits at 43 GHz,1992.40 (top), and at 22 GHz, 1992.44 (middle)and 1994.17 (bottom). Labels indicate compo-nents as given in Tables 2 and 3. Each of the 3maps is rotated clockwise by 10 ◦ . ComponentJ0 was chosen as the reference point located atthe map centre in all 3 cases. Contour levels ofthe 3 images are 0.2, 0.4, 0.8, 1.6, 3.2, 6.4, 12.8,25.6, and 51.2 % of the peak flux density of 0.22(top), 0.21 (middle), and 0.20 (bottom) Jy/beam.A common restoring beam of 0.40 × 0.15 mas,pa = 0 ◦ was used.

4.2. Identification of the VLBI core

The obvious component to be identified with the VLBI-coreof Cygnus A is the brightest and most compact component J0seen in the 43 GHz map (TB ' 1010 K, see Fig. 3, top). Inorder to find the corresponding feature in the 22 GHz imagewe aligned both maps (and the corresponding model fits) indifferent ways, we calculated intensity profiles along the jetaxis from the CLEAN-maps, and determined the spectral indexvariations along the jet (note: the 22 and 43 GHz maps weremade at nearly simultaneous epochs).

In Fig. 7 we show the brightness distribution of the central jetat 43 GHz and 22 GHz plotted along the jet ridgeline. The upperfigure shows both profiles aligned in a similar way as the maps

(see Fig. 3, top and middle). The relative positions of the com-ponents C1 (r = −0.6 mas), J2 (r = 0.3 mas), J3 (r = 0.55 mas),J4 (r = 0.70 mas) and J5 (r = 0.90 mas) match in both data setsvery well and give a consistent and another corresponding com-ponent identification with only minor differences of the relativeseparations between adjacent components.

In this identification scheme, it appears that at 22 GHz theposition of the inverted spectrum VLBI-core J0 is located (in1992.4) at the eastern flank of the brighter component J2 (at r =0.3 mas). However, after the emergence of a new component J1in 1994.17 (see Figs. 3 and 6, and paragraphs 4.4.2 and 4.4.3) J0appeared more distinct. The pronounced flux density variabilityof J0 at 22 GHz further supports its identification as VLBI-core:between 1992.44 and 1994.17 J0 brightened by ∆S/S ' 40 %,


Table 2. The Gaussian Component Models: Column 1 gives the com-ponent identification, column 2 its flux density (S), columns 3 and 4the relative position (separation r and position angle θ) with respectto J0, columns 5, 6, and 7 the size (FWHM), the axial ratio (AR) andthe geometric mean of the component size (MSIZE), respectively. Thesecond row for a component gives the formal errors for each quantity.Components below the separation indicated by a horizontal line arefaint, extended and represent the jet structure, already partly resolvedby the beam.

The Gaussian Component Model: 1992.40, 43 GHzId. S r θ FWHM AR PA MSIZE

[Jy] [mas] [◦] [mas] [◦] [mas]C3 .010 2.272 100.603 .123 1.000 .000 .123

.006 .280 9.961 .112 .000 .000 .112C2 .019 1.254 108.255 .183 .300 158.203 .100

.006 .483 8.162 .132 .218 77.001 .094C1 .124 .581 102.337 .382 .373 168.122 .233

.016 .026 4.029 .133 .074 3.597 .065J0 .228 .000 .000 .151 .688 23.030 .125

.041 .000 .000 .010 .190 23.904 .026J1 .097 .096 -92.056 .100 .461 111.894 .068

.013 .009 24.994 .038 .251 48.865 .031J2 .272 .320 -68.701 .291 .583 150.728 .222

.024 .015 2.674 .042 .135 52.631 .031J3 .054 .617 -65.236 .225 .387 166.100 .140

.027 .036 1.829 .067 .032 72.528 .042J4 .127 .754 -71.249 .386 .290 144.037 .208

.012 .057 2.045 .055 .102 43.929 .026J5 .057 .917 -70.923 .293 .453 167.797 .197

.013 .059 1.027 .113 .156 13.946 .121J6 .024 1.424 -67.929 .201 .100 153.428 .063

.016 .081 6.072 .230 .186 80.369 .145J7 .042 1.859 -76.636 1.143 .100 106.872 .361

.008 .117 4.286 .181 .365 58.027 .148The Gaussian Component Model: 1992.44, 22 GHz

Id. S r θ FWHM AR PA MSIZE[Jy] [mas] [◦] [mas] [◦] [mas]

C3 .008 2.562 106.066 .534 .300 20.029 .292.002 .166 1.263 .129 .360 36.429 .044

C2 .026 1.301 106.769 1.051 .463 103.747 .715.003 .039 .992 .159 .311 32.992 .106

C1 .089 .630 103.029 .252 .508 129.632 .180.006 .015 .939 .055 .054 11.221 .036

J0 .165 .000 .000 .272 .874 142.677 .255.049 .000 .000 .024 .248 34.015 .052

J2 .374 .300 -62.663 .213 .837 94.676 .195.018 .011 2.085 .009 .196 22.362 .029

J3 .188 .554 -68.152 .250 .366 138.721 .151.009 .014 .739 .036 .108 19.178 .030

J4 .169 .714 -76.356 .255 .577 160.943 .194.024 .021 1.818 .046 .071 18.466 .034

J5 .078 .859 -78.627 .194 .709 171.017 .163.018 .015 9.310 .055 .190 55.158 .045

J6 .102 1.152 -79.764 .402 .802 147.813 .360.029 .052 .990 .093 .232 37.153 .087

J7 .031 1.750 -73.083 .334 .100 85.148 .106.007 .047 1.835 .064 .217 45.932 .087

J8 .044 2.289 -79.089 1.066 .179 100.463 .451.009 .136 .286 .300 .049 11.010 .117

J10 .029 6.113 -72.492 2.959 .538 85.285 2.170.004 .267 .791 .532 .181 30.322 .206

Table 3. Annotation as in Table 2.

The Gaussian Component Model: 1994.17, 22 GHzId. S r θ FWHM AR PA MSIZE

[Jy] [mas] [◦] [mas] [◦] [mas]C3 .005 2.730 103.748 .840 .346 6.214 .494

.001 .056 1.874 .205 .078 8.166 .051C2 .012 1.272 107.357 .706 .482 98.151 .490

.002 .060 1.204 .114 .240 63.411 .039C1 .055 .606 104.567 .231 .823 107.625 .210

.003 .019 .703 .016 .062 52.295 .011J0 .251 .000 .000 .259 .409 112.739 .165

.028 .000 .000 .021 .111 6.803 .027J1 .080 .129 -103.506 .182 .340 121.368 .106

.003 .020 4.087 .024 .131 17.120 .035J2 .353 .355 -75.979 .233 .864 169.250 .217

.028 .020 .900 .010 .029 64.258 .011J3 .179 .566 -74.996 .209 .882 1.847 .196

.008 .021 2.065 .013 .037 65.506 .011J4 .175 .772 -78.902 .354 .385 41.960 .220

.033 .037 .787 .026 .186 12.914 .040J5a .080 .972 -78.322 .347 .207 48.721 .158

.006 .020 .427 .006 .113 2.220 .033J5b .195 1.100 -75.259 .377 .688 76.319 .313

.016 .022 .493 .037 .117 6.224 .012J6 .044 1.360 -81.369 .404 .200 98.668 .180

.010 .034 .483 .055 .131 3.982 .075J7 .025 1.761 -78.656 .556 .394 138.614 .349

.007 .094 1.454 .102 .076 15.189 .072J8 .065 2.414 -79.407 .835 .370 100.494 .508

.014 .100 .378 .145 .052 14.253 .067J9 .013 3.969 -81.944 2.255 .357 82.134 1.348

.004 .373 1.187 .778 .176 13.192 .459J10 .033 7.854 -77.748 6.086 .129 105.729 2.188

.015 .551 .230 1.496 .019 .655 .401

whereas the flux density variations of the other componentsremained < 5− 10 %.

A second possibility is the identification of the componentC1, located r ' 0.6 mas east of J0, as VLBI-core. C1, however,has a less inverted spectrum than J0 and also has a lower bright-ness temperature. Using C1 as reference, the jet-to-counter-jetratio becomes unrealistically high (see Sect. 4.5 and Fig. 13).At 22 GHz, C1 is also less variable in flux density than J0. Wetherefore regard C1 a less plausible candidate for the VLBI-core.

A third alternative would be the identification of the bright-est jet component in the 22 and 43 GHz maps of 1992 withthe VLBI-core. In Fig. 7 (bottom frame) we aligned the 22 and43 GHz profiles on their brightness peaks. The tentative identi-fication of the component J0 at 43 GHz (located at r = 0 mas,S43GHz = 0.23 ± 0.04 Jy) with the component J2 at 22 GHz(located at r = 0.3 mas, S22GHz = 0.37±0.02 Jy) yields a verysteep spectrum of the core (α22/43GHz = −0.72± 0.27). This,the mismatch of the positions, and relative separations of adja-cent components in both images of 1992 – in particular on thecounter-jet side (see Figs. 3 and 6 and Tables 2 and 3) – makesuch an identification unlikely. We note, however, that opacityeffects could cause frequency dependent position shifts affect-


ing the cross-identification of components. Since we failed toverify the expected systematic trends in such shifts, we considerin the following the position shift between 22 and 43 GHz assmall (≤ 0.1 mas).

4.3. Spectral indices

We determined the spectral index along the jet, using the Gaus-sian models and the intensity profiles of the 22 and 43 GHzmaps of 1992. We calculated the spectral index and its error forthe components C3 to J9 from a weighted average of the twospectral indices derived (i) from the modelfits and (ii) from theintensity profiles. In Fig. 8 we plot the spectral indexα22/43GHz

(Sν ∝ να) versus relative separation from J0 in 1992.4 (Table2). As seen in the figure, the component J0 has the most in-verted spectrum (α22/43GHz = 0.95 ± 0.30), and therefore isregarded as the synchrotron self-absorbed base of the jet: theVLBI-core. The components C1 (α22/43GHz = 0.28 ± 0.11)and J1 (α22/43GHz = 0.50 ± 0.50) show less inverted spectra.J2 (α22/43GHz = −0.38 ± 0.10) and subsequent componentsappear relatively steep (optically thin emission). We note thatthe spectral index of the components east of J0 is systematicallyflatter than on the western side. Averaging over a larger re-gion yields a mean spectral index of α22/43GHz = 0.18± 0.10for −3 ≤ r < 0 mas on the eastern (counter-jet) side, andα22/43GHz = −0.55 ± 0.07 for 0 < r ≤ 3 mas on the western(jet) side. We further note that at r = 0.8−1.0 mas the spectrumof the jet flattens, perhaps indicating the presence of jet internalprocesses (shocks, acceleration, recollimation, etc.). This spec-tral flattening is also seen in Fig. 7 (top frame) and in spectralindex maps derived directly from the CLEAN-maps.

4.4. Structural variability and motion

The presence of structural variability in the jet of Cygnus A isindicated by variations seen in the visibilities at both epochs,and more directly, from inspection of the two 22 GHz mapsof 1992 and 1994 (Fig. 3). The complexity of the structures inboth images makes an unambiguous measurement of the motiondifficult. The exact determination of the velocity depends on therelative alignment of the two 22 GHz images. Phase referencingVLBI observations would be required to determine the absoluteposition and motion of the jet components. In the followingwe used three methods to investigate source expansion and tomeasure motions.

In a first attempt we convolved the 22 GHz images with arelatively large beam and looked for overall expansion of thesource structure (Sect. 4.4.1). In a second step we convolvedthe maps with a slightly super-resolving beam and measuredthe position variations of the most prominent distinct features(Sect. 4.4.2). Finally we used the results from the Gaussianmodel fits to determine the motion of the model fit components(Sect. 4.4.3).

-1.0 0.0 1.0 2.0relative separation [mas]

0.0

50.0

100.0

150.0

rel

ativ

e br

ight

ness

[mJy

/bea

m]

0.0

50.0

100.0

150.0

43 GHz, 1992.4022 GHz, 1992.44

Fig. 7. Intensity profiles along the jet’s ridgeline at 43 GHz (solid line)and 22 GHz (dashed line) in 1992. Profiles were calculated after con-volution of the maps with a circular beam of 0.15 mas size. Case 1(top): alignment on core position as suggested from overall morphol-ogy seen in the maps and from model fits. The presumed core positionis at r = 0 mas. Positive distances are measured towards the west. Case2 (bottom): an alternative alignment using the brightness maxima at43 GHz and 22 GHz (see text).

4.4.1. Overall source expansion

In Fig. 9 we plot the jet profiles obtained from both 22 GHz mapsafter convolution with a circular beam of the size of 0.4 mas (=corresponding to the major axis of the true elliptical beam).The profiles were arbitrarily aligned on their intensity peaks, bywhich the information whether expansion takes place on jet- orcounter-jet side, is lost. From this figure it is obvious that thewidth of the profile increased between 1992 and 1994. We obtainan increase of the full width at half maximum of ∆FWHM =FWHM (1994.17) − FWHM (1992.44) = 0.28 ± 0.14 mas.This corresponds to an expansion rate ofµ = 0.16±0.08 mas/yr(βapp = 0.4±0.2). Larger expansion rates are obtained, if the in-crease of the width is measured at quarter maximum. This yields∆FWQM = 0.34 ± 0.14 mas, and µ = 0.20 ± 0.08 mas/yr(βapp = 0.51±0.20). At larger distances, a weak feature seemsto have moved from r = 1.42 ± 0.20 mas (in 1992.44) tor = 1.92 ± 0.20 mas (in 1994.17). This corresponds to motionwith µ = 0.29± 0.16 mas/yr, respectively βapp = 0.74± 0.41.

It therefore appears that the angular expansion rate and theapparent jet velocity increase along the jet. This result also holdsif the alignment of the two profiles is done not on the intensitypeaks, but on the eastern component located at r ' −1.0 mas(see Fig. 9). In this case a shift of the brightness maximumof ∆r = −0.15 mas (µ = −0.09 mas/yr, βapp = −0.22) isobtained. We note, however, that the actual speed in the jet isreduced by a factor of ≤ 2 if the jet expands in both directions.


-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0relative separation [mas]

-2.0

-1.0

0.0

1.0

2.0sp

ectr

al in

dex

alph

a (2

2/43

GH

z)

Fig. 8. Spectral index α22/43GHz (Sν ∝ να) between 22 and 43 GHzfor epoch 1992.4 plotted versus relative core separation. Symbols de-note for the spectral indices of the modelfit components (from leftto right) C3, C2, C1, J0, J1, J2, J3, J4, J5, J6, J7 and the concate-nated component J89 (=J8+J9). Based on its strongly inverted spec-trum, J0 is adopted as VLBI-core and is therefore arbitrarily centeredat r = 0 mas. Note that on average the counter-jet components C3-C1(r < 0 mas) exhibit flatter spectra than the components J1-J9 on thejet side (r > 0mas).

-2.0 -1.0 0.0 1.0 2.0 3.0relative separation [mas]

0.0

100.0

200.0

300.0

400.0

500.0

inte

nsity

[mJy

/bea

m]

22 GHz 1992.4422 GHz 1994.17

Fig. 9. Intensity profile of the jet plotted versus relative separation fromthe brightness maximum at 22 GHz for epoch 1992.44 (solid line) and1994.17 (dashed line). The profiles were calculated after convolutionof the maps with a circular beam of 0.4 mas size.

4.4.2. Motion derived from maps

In Fig. 10 we show jet profiles derived from the two 22 GHzmaps after convolution with a beam size of 0.12 mas, reflectingthe full angular resolution (minor axis of the true beam). Weconsider three alternative cases:

In Fig. 10 a (top frame), both 22 GHz profiles are alignedfollowing the morphological similarities seen in the maps andthe component identification suggested from the model fits. Inthis – we think most plausible – identification scheme, a new

Table 4. Motion of jet components derived from the 22 GHz mapsof 1992.44 and 1994.17. Column 1 gives the component identifica-tion as in the model fits, column 2 gives the relative separation withrespect to J0 (r1994.17 determined from the 22 GHz map of 1994.17).Column 3 shows the displacement ∆r = r(1994.17)− r(1992.44) be-tween the two epochs. Column 4 shows the derived apparent velocityβapp = vapp/c (using H0 = 100 km s−1 Mpc−1, q0 = 0.5). Belowthe horizontal line, the results for the fainter, extended and less welldefined features J5–J8 are given.

Id r1994.17 ∆r βapp[mas] [mas]

C1 -0.60 ± 0.08 0.10 ± 0.11 0.15 ± 0.16J0 0 – –J1 0.16 ± 0.02 0.07 ± 0.03 0.10 ± 0.04J2 0.36 ± 0.02 0.06 ± 0.03 0.09 ± 0.04J3 0.55 ± 0.02 0.06 ± 0.03 0.09 ± 0.04J4 0.80 ± 0.02 0.15 ± 0.03 0.22 ± 0.04J5 1.10 ± 0.03 0.22 ± 0.04 0.33 ± 0.06J6 1.29 ± 0.05 0.19 ± 0.07 0.28 ± 0.10J7a 1.61 ± 0.10 0.36 ± 0.14 0.53 ± 0.21J7b 1.84 ± 0.10 0.21 ± 0.14 0.31 ± 0.21J8 2.24 ± 0.20 0.38 ± 0.28 0.56 ± 0.41

component J1 emerged west of J0 in 1994.17. Probably due tolimitations of angular resolution, J1 is not visible in the 22 GHzmap of 1992.40, however is clearly seen in the 43 GHz mapof higher angular resolution. Table 4 summarizes the relativeposition shifts (∆r = r(1994.17) − r(1992.44)) for each com-ponent with respect to the adopted stationary position of J0.Column 3 of the table gives the corresponding apparent veloc-ity (βapp = ∆r/∆t ∗ 2.556, with ∆t = 1.73 yrs and a factorof 2.556 c/(mas/yr) converting angular rate to apparent veloc-ity). For J1 we estimated ∆r using its relative core separationr43GHz = 0.09± 0.02 mas from the 43 GHz profile of 1992.40(see Fig. 7), and neglecting a possible small frequency depen-dence of r.

The data of Table 4 show evidence for jet expansion withexpansion rates in the range of µ ' 0.035...0.22 mas/yr(βapp ' 0.09...0.56), and a systematic trend of increasing ex-pansion rates with increasing r. Dynamic range limitations inthe 22 GHz maps allow no reliable measurement of the mo-tion of the faint and extended components C3 and C2. Forthis reason we suspect that the somewhat unexpected appar-ent position shift of C1 towards J0 is not significant. Weightedaveraging of the relative displacements for the componentsJ1-J8 yields a mean displacement of ∆r = 0.11 ± 0.07 mas(χ2 = 22.60 for N = 9 components; 99 % probability for a sig-nificant correlation), corresponding to a mean expansion rate ofµ = d(∆r)/dt = 0.06± 0.04 mas/yr (βapp = 0.16± 0.10).

In this identification scheme all jet components separatefrom J0 (with the possible exception for C1). This in turn indi-rectly supports the identification of J0 as the stationary VLBI-core.

As a second possibility (case 2) we aligned the 22 GHzprofiles on their brightness peaks, arbitrarily centered at r =0 mas (Fig. 10 b, central frame). We emphasize however, that


the identification of the intensity maximum with the VLBI-core is not supported from the structure seen in the 43 GHzmap, unless large frequency dependent position shifts (e.g.r43GHz − r22GHz = −0.3 mas for C1) and rapidly changingspectral indices between adjacent components are allowed (cf.Fig. 7, bottom frame). With the present alignment we derivednegative angular separation rates for the eastern components lo-cated at 0 < r < 1 mas (µ ≥ −0.06 mas/yr, apparent stationar-ity for the component at r = −1 mas) and a positive expansionrate of µ = 0.06 ± 0.04 mas/yr (βapp = 0.16 ± 0.10) for thewestern components located at 0 < r < 2 mas. As in case 1,subluminal motion in the jet with similar velocities is obtained.Since the motion pattern is more complicated than in case 1, weconsider it less likely.

In a third approach (case 3) the alignment of the profiles waschosen in such a way that the widths and the slopes of the innerjet structure (−0.1 ≤ r ≤ 0.6 mas) were matched (Fig. 10 c,bottom frame). In this scheme, the main jet components, whichare mutually visible in both profiles, remained stationary, butchanged their relative brightness. In the western region (at r ≥0.6 mas), apparent overall jet expansion (with similar speedsas in case 2) is caused by an increase of the jet brightness inthis region. A ‘somehow conspired’ brightness change thereforeonly simulates true motion. Since ‘true’ motion of individualcomponents is seen at larger core separations (Carilli et al. ,1994, Sorathia et al. , 1996) and also in many other radio sources(e.g. Zensus et al. , 1995), we do not consider this case anyfurther.

4.4.3. Motion derived from model fits

The apparent motion of individual Gaussian jet componentscan also be determined from the model fits. We measured thechanges of the relative core separations for corresponding com-ponents, using simple and also more complex model fits to the22 GHz data of 1992 and 1994. For all cases a small but sys-tematic trend of an increase of the relative separations r fromJ0 is obtained. In Table 5 (col. 3) we summarize the relativedisplacements ∆r = r(1994.17)− r(1992.44) of the individualcomponents from the models of Tables 2 and 3. The compar-ison of two simpler model fits, which were restricted to thecomponents C1–J8, yielded the apparent position shifts shownin column 4 of Table 5.

The velocities derived from complex and simple model fitsare very similar and rule out large systematic errors caused byblending of jet components. No significant motion is detectedfor components C3, C2, C1 and J3. In 1992, J1 is seen with thehigher angular resolution at 43 GHz, but not at 22 GHz. Com-bination with the data of 1994 places upper and lower limits toits motion. For J2 and J4 position shifts of the order of half abeam size (22 GHz beam: 0.12 − 0.15 mas) are seen. For J5,J6 and J9 the displacements and therefore their velocities seemto be larger. The model fits do not give conclusive results forthe motion of J7. Inspection of the maps and the correspond-ing brightness profiles, however, give the impression of fadingjet brightness in this region. This might affect the accuracy of

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0relative separation [mas]

0.0

50.0

100.0

150.0

0.0

50.0

100.0

150.0

rela

tive

brig

htne

ss [m

Jy/b

eam

]

0.0

50.0

100.0

150.0

1992.441994.17

C1 J0 J1 J2 J3 J4

Fig. 10. Plot of the intensity profiles along the jet ridgeline at 22 GHz.The profiles were obtained after convolution of the maps with a circularbeam of 0.12 mas size. Three alternative alignments of the profile of1992 (solid line) and 1994 (dashed line) are shown (see text). Themost likely alignment uses profiles centered on J0 and is shown ontop. Labels denote the most prominent Gaussian model fit components(see Tables 2 and 3). In the frame below, the profiles are centered onthe brightest component. In the bottom frame the alignment was doneusing the widths of the profiles. In all 3 cases structural variations andmotion with βapp ' 0.1− 0.2 are evident.

the measurement. In column 5 of Table 5 we summarize theapparent velocities βapp for the individual components. Theyare consistent and in good agreement with the results obtaineddirectly from the maps (see Table 4).

4.4.4. Apparent acceleration

Summarizing the results of the previous paragraphs, we con-clude that the mas-jet of Cygnus A contains moving and station-ary features. Although structural variability seems to be presentin the region of the counter-jet components C3-C1 (in particularfor C1) as well, the present data do not allow to determine thismotion with sufficient accuracy.

In Fig. 11 we plot the apparent velocities βapp of the jetcomponents J1–J9 versus their separation r1994.17 from J0 in1994.17. The filled symbols denote results obtained from theanalysis of the maps (circles) and the model fits (squares). Bothmatch very well. We further added velocity measurements at5 GHz from Carilli et al. , (1994) and Sorathia et al. , (1996) fortwo components located at larger separations (open diamonds).It appears that for core separations r < 1 mas the apparentjet velocity is typically βapp ' 0.1, whereas the componentsfurther out (J5–J10) seem to move at a 2–3 times faster velocityof βapp ' 0.2 − 0.3. This and the high velocity of βapp =0.35± 0.15 and βapp = 0.55± 0.15 of the 5 GHz components(located at extrapolated positions: r1994.17 = 5.18±0.08 mas and


Table 5. Relative motion of components derived from Gaussian model fits. Column 1 summarizes the component label, column 2 its relative sepa-ration r1994.17 in 1994.17 with respect to the stationary assumed core component J0, and column 3 the position shift ∆r = r(1994.17)−r(1992.44)between both epochs. Column 4 summarizes position shifts derived from an alternative, but simpler model. Column 5 shows the apparent velocityβapp derived from a weighted average of columns 3 and 4. For faint and extended outer jet components shown below the horizontal line, theresults are less certain.

Id r1994.17 ∆r ∆r βapp[mas] [mas] [mas]

C3 -2.73 ± 0.06 -0.17 ± 0.18 -0.12 ± 0.27C2 -1.27 ± 0.06 -0.03 ± 0.07 -0.04 ± 0.10C1 -0.61 ± 0.02 -0.02 ± 0.03 -0.01 ± 0.04 -0.03 ± 0.03J0 0 – – –J1 0.13 ± 0.02 0.00 ≤ ∆r ≤0.15 0.01 ≤ ∆r ≤ 0.16 0 ≤ βapp ≤ 0.24J2 0.36 ± 0.02 0.06 ± 0.03 0.06 ± 0.03 0.09 ± 0.04J3 0.57 ± 0.02 0.02 ± 0.03 0.01 ± 0.03 0 ≤ βapp ≤ 0.07J4 0.77 ± 0.04 0.06 ± 0.04 0.06 ± 0.03 0.09 ± 0.03J5 1.07 ± 0.02 0.21 ± 0.03 0.15 ± 0.05 0.28 ± 0.04J6 1.36 ± 0.03 0.21 ± 0.06 0.01 ≤ ∆r ≤ 0.40 0.31 ± 0.09J7 1.76 ± 0.09 0.01 ± 0.10 -0.20 ≤ ∆r ≤ 0.40 ≤ 0.59J8 2.41 ± 0.10 0.12 ± 0.17 0.16 ± 0.14 0.21 ± 0.16J9 3.97 ± 0.37 0.25 ± 0.45 0.38 ± 0.66 (?)J10 7.85 ± 0.55 1.74 ± 0.61 2.57 ± 0.90 (?)

0 1 10relative separation along jet axis [mas]

0.00

0.20

0.40

0.60

0.80

1.00

appa

rent

vel

ocity

[v/c

]

22 GHz, maps22 GHz, modelfits5 GHz

Fig. 11. Apparent velocity βapp plotted versus separation from J0 atepoch 1994.14. Filled symbols denote velocities derived from the maps(circles) and from the model fits (squares) at 22 GHz. Measurementsat 5 GHz (open diamonds) are from Carilli et al. , (1994), and Sorathiaet al. , (1996), with r extrapolated to epoch 1994.14.

r1994.17 = 16.0±0.3 mas) indicates acceleration along the jet anda possible transition from slow to fast motion near r ' 1 mas.We note that in this region the jet intensity drops by a large factor(see Fig. 9), that the spectrum flattens (see Fig. 8), and that the jetwidth has a local maximum (see Fig. 17). We therefore suspectthat changes in the physical conditions in the jet or in the externalmedium are responsible for the observed acceleration.

Table 6. The jet-to-counter-jet ratio R as measured from integratedintensity profiles (see text).

ν epoch beam Rmin Rmax R Rcombined

[GHz] [mas]1.64 1986.74 10 − 3.1 1.31.64 1986.74 25 − 3.5 1.11.64 1.2 ± 0.1

22.2 1992.44 0.15 1.4 16 5.222.2 1992.44 0.40 1.0 17 2.722.2 4.0 ± 1.022.2 1994.17 0.15 1.2 40 5.122.2 1994.17 0.40 1.3 28 4.1

43.2 1992.40 0.15 − 19 2.343.2 1992.40 0.40 − 12 1.543.2 2.3 ± 0.6

4.5. The jet-to-counter-jet ratio

The clear detection of a counter-jet in the maps at 18 cm, 1.3 cmand 7 mm allows the determination of the jet-to-counter-jet ratioR = Sjet/Scjet over a wide range of wavelengths. The measure-ment ofR, however, requires knowledge of the exact position ofthe VLBI core, which is not always identical with the brightestcomponent. In fact, the 22 and 43 GHz data indicate that opacityeffects might alter the brightness distribution at the jet base (seeFig. 8). This could lead to frequency dependent shifts of thecore position, which in our data is located somewhere betweenC1 and J2.

To overcome the lack of an absolute core position, we de-termined the jet-to-counter-jet ratio in the following way: wenumerically integrated the profiles and determined the jet-to-counter-jet ratio R(r) as a function of separation r from the


-200.0 -100.0 0.0 100.0 200.0relative separation [mas]

1

10

100

Inte

nsity

I / J

et-t

o-co

unte

rjet r

atio

R

Intensity Ijet-to-counterjet ratio R

-80.0 0.0 80.0relative separation [mas]

1

10

100

Inte

nsity

I / J

et-t

o-co

unte

rjet r

atio

R

Intensity Ijet-to-counterjet ratio R

Fig. 12. Intensity profile (I) plotted along the jet’s ridgeline at 18cm.The profile was calculated after convolution with a circular beam of25 mas size (top) and 10 mas size (bottom). The dashed line gives thenumerically integrated jet-to-counter-jet ratio R(r) (see text). At thepresumed core position (r = 0) the jet-to-counter-jet ratio is R ' 1.3(top) and R ' 1.1 (bottom).

brightness maximum (located at r = 0). This has the advantagethat the jet-to-counter-jet ratio can be determined graphically, ifthe position rc of the core relative to the brightness maximumis known (note that the function R(r) does not depend on thecomponent identification nor the location of the VLBI-core).To obtain a better estimate of the uncertainties we used profilesresulting from maps convolved with a large and a small beamsize.

In Figs. 12, 13 and 14 we show the intensity profiles I(r) andjet-to-counter-jet function R(r) for the 1.6 GHz, 22 GHz, and43 GHz data, respectively. In Table 6 we summarize the resultsobtained from these figures. In columns 1, 2, and 3 we give theobserving frequency, epoch, and convolution beam size of theintensity profiles. A lower (Rmin, col. 4) and an upper (Rmax,col. 5) limit to the jet-to-counter-jet ratio is derived under the

-4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0relative separation [mas]

10-1

100

101

102

103

Inte

nsity

I / J

et-t

o-co

unte

rjet r

atio

R

I: 1992.44I: 1994.17R: 1992.44R: 1994.17

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0relative separation [mas]

100

101

102

Inte

nsity

I / J

et-t

o-co

unte

rjet r

atio

R

I: 1992.44I: 1994.17R: 1992.44R: 1994.17

Fig. 13. Intensity profiles (I) and jet-to-counter-jet ratios (R) at 22 GHzplotted versus relative separation from brightness maximum for epochs1992.44 (solid line) and 1994.17 (dashed line). The intensity profileswere calculated after convolution with a circular beam of 0.4 mas (top)and 0.15 mas (bottom). Both profiles are arbitrarily aligned to theirpeak at r = 0 mas. Lines with symbols denote the jet-to-counter-jetratio at different epochs: triangles for 1992.44, squares for 1994.17.At the tentative core position east of the maximum (relative separationr = −(0.3 − 0.4) mas, see text) the jet-to-counter-jet ratio is R ' 3(top) and R ' 5 (bottom).

assumption that at 22 GHz the true core is located somewherebetween C1 and J2. ForRmin we used the position of the intensitymaximum, and assumed that the ‘true core’ is self-absorbed andtherefore located east of this peak; for Rmax we used the jet-to-counter-jet ratio at the position of the first prominent counter-jet component C1. Column 6 summarizes the estimate for R,assuming that component J0 is the VLBI core. At 1.6 GHz, wemeasured the jet-to-counter-jet ratio at the brightness peak (R)and at the eastern half-beam width point (Rmax).

Column 7 of Table 6 summarizes our ‘best’ estimate of R,combining the results:At 1.6 GHz the jet-to-counter-jet ratio is R = 1.2 ± 0.1, at


-1.0 0.0 1.0 2.0relative separation [mas]

100

101

102

Inte

nsity

I / J

et-t

o-co

unte

rjet r

atio

R

I: 0.15masI: 0.40masR: 0.15masR: 0.40mas

Fig. 14. Jet-to-counter-jet ratio (R) and intensity profiles (I) plottedversus relative separation from brightness maximum at 43 GHz. Thesolid line denotes for convolution with a circular beam of 0.4 mas, thedashed line for a beam size of 0.15 mas. At the position of the brightestcomponent (r = 0 mas) the jet-to-counter-jet ratio is R ' 2.

22 GHz R = 4± 1, and at 43 GHz R = 2.3± 0.6. In Fig. 15 wesummarize this result in a plot ofR versus frequency, where wealso included a measurement R = 5±2 at 5 GHz from Sorathiaet al. , (1996).

A firm lower limit of the jet-to-counter-jet ratio comes fromthe 18 cm data, where the counter-jet appears most pronounced:Rmin = 1.1. It is more difficult to obtain an upper limit since itdepends on the correctness of the core identification at 1.3 cmand 7 mm. With the assumption of a correct core identificationat 43 GHz (smallest opacity effects), an upper limit of Rmax =14 appears more realistic than the higher value of Rmax = 40obtained at 22 GHz, if C1 were to be adopted as the core.

Given the different quality of the images and remaining un-certainties in the determination ofR, the frequency dependenceof R (Fig. 15) must be regarded with some caution. We note,however, that such a frequency dependence is expected if jet andcounter-jet are not symmetric (intrinsically asymmetric bright-ness, different spectral properties) or if absorption effects nearthe nucleus (e.g. partial obscuration of one of the jets by someforeground material) alter the intensity ratios.

4.6. Evidence for an inclined free-free absorbing disc ?

Evidence for partial foreground absorption comes from ob-served spectral differences between the jet and counter-jet: thecounter-jet components, although not compact, have a flat toinverted spectrum α22/43GHz ≥ 0 (see Fig. 8), whereas thespectrum of the jet appears steep with a canonical value for op-tically thin synchrotron emission ofα22/43GHz = −0.5 to−0.7.A similar behaviour recently observed in 3C 84 (Vermeulen etal. , 1994, Walker et al. , 1994) and Cen A (Jones et al. , 1996) hasled to the suggestion of optically thick free-free absorption inan inclined disc, partly obscuring the counter-jet but not the jet.

1 10 100frequency [GHz]

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Jet-

to-c

ount

erje

t rat

io R

Fig. 15. The frequency dependence of the jet-to-counter-jet ratio R(see text).

In Cygnus A, evidence for foreground absorption and a possiblecircum-nuclear disk comes from optical and infrared observa-tions (e.g. Ward et al. , 1991, Vestergard & Barthel 1993, Stock-ton et al. , 1994), and from recent HST-images (e.g. Jackson etal. , 1994, see also Carilli & Barthel, 1996 for a comprehensivesummary).

If such an absorbing disk has a diameter of less than afew parsecs (corresponding to a few mas in Cyg A), the jet-to-counter-jet ratio at long cm-wavelengths remains unaffectedas long as the observing beam is much larger than the disksize. With decreasing wavelength and increasing angular res-olution (approaching the disk size), the regions shadowed bythe disk will be resolved and become visible in the maps. Thusthe brightness of the counter-jet will be reduced, leading to anapparent increase of R. At even shorter wavelengths one mayexpect a decrease of the disk opacity, which then will cause anincrease of the apparent brightness of the counter-jet. Thus thefrequency dependent functionR(ν) should exhibit a maximum,followed by a decrease of R towards the mm-bands. Exactlythis behaviour is seen in Fig. 15.

In the following we assume that the frequency dependenceofR is caused by free-free absorption of a circum-nuclear torusseen nearly edge on. X-ray observations yield a column den-sity of NH ∼ 3 − 4 · 1023 cm−2 (Ueno et al. , 1994), whichwe fully attribute to an obscuring torus. The presence of suchforeground absorption with a similar column density is inde-pendently suggested from recent HI absorption measurementsof Cygnus A with the VLA (Conway & Blanco, 1995). Thesymmetric jet-to-counter-jet ratio at 18 cm (R ' 1) restricts thesize of the absorbing region to be of the order or less than theobserving beam at 18 cm. Otherwise a more asymmetric ratioR would have been measured. From the angular resolution of∼ 20 mas at 18 cm we obtain an upper limit of the path length


through the torus of L ≤ 20 mas = 15 pc, see 2. Together withNH from above this gives an electron density in the torus ofne = NH/L ≥ 7−9 ·103 cm−3. Similar densities are estimatedfor other radio galaxies (e.g. 3C 84, O’Dea et al. , 1984) and areassumed to be typical. The turnover frequency for free-free ab-sorption is νff = 0.3·(T−1.35

e n2eL)1/2, whereTe is the (electron)

temperature in K. Below this frequency the absorber becomesoptically thick (τff = 1). In Cygnus A the jet-to-counter-jet ra-tio decreases towards higher frequencies, indicative of a loweropacity in the mm-bands. For a turnover near νff ' 43 GHz,an electron temperature of the torus of Te ≥ 3 · 103 K is de-rived, close to the values determined from optical spectroscopy(Te ' 1.5·104 K, Tadhunter, 1996) and theoretical expectations(cf. Maloney, 1996).

Partial obscuration and absorption of the counter-jet emis-sion by an inclined hot molecular or atomic disc or torus(Te > 103−4 K, ne >∼ 104 cm−3) of several parsec size(L < 15 pc) therefore provides a natural explanation of theobserved frequency dependence of R.

4.7. Oscillations of the jet axis

In Fig. 16 we plot the path of the mean jet axis at 22 GHz(1994.17) in an (α, δ)-coordinate system centered on the bright-ness maximum of the jet. In order to minimize spurious effectscaused by individual convolutions, the ridgeline profile shownwas determined from an average of four ridgelines, which wereobtained from maps convolved with circular beams of size 0.4,0.7, 1.0, and 1.5 mas, respectively. A straight line fitted to themean ridgeline is oriented along pa = 284.4 ± 1.0 ◦ (solid linein Fig. 16). It shows the mean jet orientation in the region−15 ≤ r ≤ 20 mas, which agrees very well with the jet orienta-tion seen at kpc-scales (e.g. Perley et al. , 1984). Perpendicularto its mean orientation (the straight line), the ridgeline profileoscillates transversely with amplitudes of up to ≤ 0.6 mas. Inthe region 3 ≤ r ≤ 10 mas the jet is systematically displacedsouth from the straight line. This displacement is also seen di-rectly in the tapered low angular resolution map (Fig. 5) andcoincides with an increase of the jet width by a factor of ∼ 2 inthis region (see below and Fig. 17). Note that the oscillations ofthe counter-jet beyond r ≤ −10 mas result from faint, not welldefined emission in this region, and probably are not real.

On scales of up to several tens of milli-arcseconds, the ob-served transverse oscillations of the mean jet axis seem to begoverned by (at least) two modes: a fast mode with wavelengthλ/D ' 4− 8 and a slower mode with λ/D ' 20− 40 (with λbeing the wavelength of the oscillation, and D the deconvolvedtransverse width of the jet of D = 0.5 − 1.0 mas determinedfrom Fig. 17, top).

An analysis of the unaveraged profiles and profiles withhigher angular resolution (0.1 − 0.2 mas) gives evidence forridgeline oscillations also on sub-mas to mas-scales. The am-plitudes of these displacements are typically 0.1−0.2 mas. The

2 A new HI absorption VLBI map of Cygnus A from Conway (1997)shows foreground absorption on the counter-jet side and nicely con-firms this size estimate.

-15.0 -10.0 -5.0 0.0 5.0 10.0 15.0 20.0relative R.A. [mas]

-5.0

0.0

5.0

rela

tive

Dec

l. [m

as]

mean ridgelinelinear fitresidual

Fig. 16. Plot of the mean ridgeline of the jet at 22 GHz (1994.17). Thesolid line shows a linear fit to the data (y = a ·x+b, a = 0.257±0.002,b = −0.123± 0.014), the dashed line shows the data after subtractionof the fit.

wavelength of these oscillations are of order λ ' 0.8−1.0 mas,or in units of the jet width λ/D ' 3− 7. This indicates that theamplitude and the wavelength of the transverse oscillations ofthe jet axis probably increase with core separation.

4.8. Oscillations of the jet width

To determine the transverse width of the jet, we convolvedthe 22 GHz maps with various circular beams ranging from0.12 mas to 0.7 mas size, determined the mean ridgeline of thejet and fitted Gaussian profiles perpendicular to it. In Fig. 17we show the resulting deconvolved full transverse widths D(at FWHM) plotted versus separation r from the brightnesspeak. The figure shows two main effects: the jet width is os-cillating and – on average – increases with r. In the region0 ≤ r ≤ 5 mas the oscillations are particularly pronouncedand make it difficult to determine a single overall expansionrate dD/dr. The opening angle of the jet cone can be deter-mined from the slope dD/dr. Formal fits of a straight line tothe width-profile yield an opening angle of (2± 1) ◦ for the in-nermost part of the jet (0 ≤ r ≤ 3 mas), indicative of strongercollimation and confinement in this region than further out. Theoverall jet opening can be approximately determined from astraight line fit to the whole structure. In the region of the bestdefined jet width (0 < r < 15 mas), this gives an (full) openingangle of the jet cone of Φjet = 4.8 ± 0.5 ◦ (see Fig. 17 a, top).For the counter-jet an opening angle of Φcjet = 3.5 ± 0.5 ◦ isobtained in the region −10 ≤ r ≤ 0 mas. The ratio of thetwo opening angles is Φjet/Φcjet = 1.37 ± 0.24, which is con-sistent with the expected relativistic length contraction of thecounter-jet and the armlength ratio (see Sect. 4.10). At 18 cmwe derived in a similar way opening angles of jet and counter-jetof Φjet ' Φcjet = 5±2 ◦ , respectively. Between 1.6 and 22 GHzthe opening angles for the jets thus agree remarkably well.

In a freely expanding relativistic jet, the full opening an-gle Φ of the jet is related to the Mach angle by Φ/2 =(arctan (γ ·M ))−1, where γ is the Lorentz factor and M theMach number. Since Cygnus A is oriented close to the planeof the sky (Sect. 4.9), a correction for projection effects can be


neglected. Using Φ ≤ 5 ◦ , we obtain γM ≥ 23 (inequalitydenotes jet expansion at a lower than adiabatic rate, e.g. pos-sible confinement). Perley et al. (1984) and Carilli & Barthel(1996) pointed out that the transverse expansion of the jet ofCygnus A varies and depends on jet location. In the expandingregions on kpc-scales they find Mach numbers in the range ofγM ' 8−70. Our data are consistent with this and furthermoresupport the hypothesis that the jet width is oscillating.

In Fig. 17 b (bottom) we plot the width of the inner jet at22 GHz (2 epochs: 1992 and 1994) with higher angular resolu-tion. In the region −2 ≤ r ≤ 2 mas the profiles of 1992 and1994 are remarkably similar. In the regions beyond±2 mas andin the region −0.5 ≤ r ≤ −1.0 mas, where the counter-jet isfaint, the 1994 profile yields a more reliable result (better uv-coverage). We think that the similarity of the profiles in the re-gion −2 ≤ r ≤ 2 mas excludes systematic measurement errorscaused by the mapping or convolution processes and thereforedemonstrates the reliability of the result. The jet width oscillateswith peak-to-peak amplitudes of ∼ 0.15 − 0.2 mas on angularscales of∼ 0.8−1.4 mas, ie. on similar scales to the oscillationsof the jet axis.

In summary, the analysis of the oscillations of the jet axisand the jet width indicates the following trends:(i) at larger separations from the centre (at r = 0), the trans-verse width of jet and counter-jet increases with r (jet opening).If interpreted as free jet expansion, a relativistic Mach numberγM ≥ 20 is derived.(ii) on sub-mas to mas-scales the jet width oscillates systemat-ically; the amplitude of these variations seems to increase withr. The oscillations of the width appear to be correlated withsimilarly oscillating transverse displacements of the mean jetaxis, at least in some regions. The wavelengths of these oscilla-tions are of order of a few (≥ 3) to several tens of (≤ 40− 50)units of the jet width D, with some indication that the shorterwavelengths dominate in the inner jet (r ≤ 2 − 3 mas) and thelonger wavelengths dominate further out (3 ≤ r ≤ 20 mas).

Oscillations of the jet axis and the jet width are not un-expected and may be interpreted within scenarios of rela-tivistic plasma flows which are governed by hydrodynamical(or magneto-hydrodynamical) instabilities (e.g. Hardee et al. ,1995, Appl 1996), and/or by jet recollimation (e.g. Daly &Marscher, 1988). Note that these models also predict systematicvariations of the component velocities, which might be used toexplain the observed acceleration of the motion (see Sect. 4.4.4).

4.9. Jet velocity and orientation

In the symmetric relativistic twin jet model (Scheuer and Read-head, 1979), the jet velocityβ and inclination θ of the jet towardsthe observer are determined from the apparent jet velocity βappand the jet-to-counter-jet ratio R :

β =βapp

sin θ + βapp cos θ(1)

β =ρ

cos θ(2)

-15.0 -10.0 -5.0 0.0 5.0 10.0 15.0relative separation [mas]

0.0

0.5

1.0

deco

nvol

ved

tran

sver

se w

idth

[mas

]

jetcounter jet

-4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0relative separation [mas]

0.0

0.2

0.4

0.6

0.8

1.0

jet w

idth

[mas

] / r

el. i

nten

sity

width 1994width 1992intensity 1994intensity 1992

Fig. 17. Deconvolved transverse width D of the jet (FWHM [mas])at 22 GHz plotted versus relative separation. Top: The increase of thetransverse width of jet (solid line) and counter-jet (dashed line) mea-sured from the map of 1994.17. The straight lines indicate linear fitsto the jet width. For the jet a full opening angle of the jet cone ofΦjet = 4.8 ± 0.5 ◦ is derived. The corresponding opening angle of thecounter-jet is Φcjet = 3.5 ± 0.5 ◦ . Bottom: Oscillations of the decon-volved transverse width in the central region of the jet at 22 GHz. Thesolid line with filled circles denotes for epoch 1994.17, the dashed linewith filled squares for epoch 1992.44. The typical error bar for themeasured width is shown separately (bottom left). For clarity the nor-malized intensity profiles (solid line: 1994.17, dashed line: 1992.44)are shown on top.

where ρ = (Rn − 1)/(Rn + 1), n = 1/(2 − α). This model as-sumes that jet and counter-jet are intrinsically symmetric (per-fectly aligned, identical βjet = βcjet) and that the apparent ve-locity βapp is directly related to the intrinsic speed β (no phasevelocities).

The high degree of symmetry seen on kpc-scales and in the18 cm map and the very small misalignment between the jet andcounter-jet at 1.3 cm support the hypothesis of an intrinsicallyquite symmetric structure of the jets. Without violating the re-quirement of intrinsic symmetry, the observed asymmetry in the


brightness distribution of jet and counter-jet could be explainedgeometrically, e.g. by partial obscuration of the counter-jet froman inclined torus. The presence of different apparent velocitiesand a possible acceleration, however, complicate the situation,because it is not clear if and how the observed velocities arerelated to the bulk relativistic flow, which is responsible for therelativistic intensity enhancement. Since the observed acceler-ation from 0.1 c to 0.7 c cannot be explained geometrically byjet bending (the jet certainly is oriented at a large angle to theline of sight) nor by foreground absorption, intrinsic accelera-tion processes and/or phase velocity effects must be taken intoaccount.

With these complications in mind, we apply the twin jetmodel for Cygnus A. Fig. 15 suggests that the jet-to-counter-jet ratio is R ≤ 7, with the lowest ratios measured at 18 cm(R = 1.2± 0.1) and at 7 mm (R = 2.3± 0.6) (see Table 6). Theobserved apparent velocities lie in the interval (0.1 ≤ βapp ≤0.7) · h, with the Hubble parameter h defined by H0 = 100 ·h−1km sec−1Mpc−1.

In Fig. 18, we plot the intrinsic jet speed β versus jet in-clination θ. From known βapp and R, the intersection points Pbetween the two functionsβ(βapp, θ) andβ(R, θ) give a solutionfor β and θ (assuming α = −0.7). The area P1-P2-P3-P4 delin-eates the allowed range of β and θ. The large range of apparentvelocitiesβapp = 0.1−0.7 causes this area to be relatively large.

P5 marks a solution from the 22 GHz observations alone,usingR = 4 andβapp = 0.2·h. It is obvious that this solution andthe solutions with low apparent velocities (βapp ≤ 0.2 · h) andrelatively large jet-to-counter-jet ratios (R ≥ 4) (point P1) yieldjet inclinations θ ≤ 50 ◦ , which are too low to be consideredrealistic for Cygnus A. The true velocity of the jet therefore mustbe larger. This has the important consequence that the observedslow velocity can not be directly coupled to the bulk flow, thusnecessitates additional assumptions, e.g. internal accelerationor phase velocity effects. Moreover, a larger velocity β > 0.2 ·h would be more consistent with theoretical expectations, inparticular with regard to the high degree of jet collimation, thesignificant jet length, and the existence of well developed largescale radio lobes (Muxlow et al. , 1988, Roland et al. , 1988,Williams 1991).

If the jet-to-counter-jet ratio is affected by opacity effects,the intrinsic brightness of the counter-jet would become largerand the intrinsic jet-to-counter-jet ratio therefore would becomemuch smaller than its peak value of R = 5 ± 2 (Sorathia etal. , 1996). The 1.6 and 22 GHz data delineate the most plau-sible range for the absorption-free (true) jet-to-counter-jet ra-tio: 1.1 ≤ R ≤ 4. For (0.2 ≤ βapp ≤ 0.6) · h and theequations above, the allowed ranges for jet velocity and in-clination are (see shaded area in Fig. 18): 0.19 ≤ β ≤ 0.59and 31◦ ≤ θ ≤ 88◦ for h = 1, and 0.39 ≤ β ≤ 1 and50◦ ≤ θ ≤ 89◦ for h = 2. The demand for the larger velocities(β ≥ 0.4, cf. Carilli & Barthel 1996) would give preference forthe solution with h = 2, ruling out H0 = 100 km sec−1Mpc−1.Note that Fig. 18 reveals only a very weak dependence of θon βapp (θ = arccos (r/β) = arctan (βapp(1− r)/r)), if the jetand counter-jet are very symmetric. Such symmetry, however, is

suggested from the 1.6 and 43 GHz data (1.1 ≤ R ≤ 2.3). Thisgives – even for a large range of apparent velocities – a betterpossibility for Cygnus A to be oriented as close as 80− 89 ◦ tothe plane of the sky.

4.10. Armlength ratio of the jets

Relativity theory predicts an apparent length contraction or ex-pansionL0/(1±β cos θ) of a relativistic jet with intrinsic lengthL0 and speed ±β (+/− : receding, approaching). From the 1.6and 22 GHz maps and the corresponding intensity profiles wemeasured the length of the jet and counter-jet and determinedthe armlength ratio x = (1 + β cos θ)/(1− β cos θ) = 1.4± 0.3(x = 1.5±0.2 at 22 GHz, x = 1.3±0.2 at 1.6 GHz). At 22 GHza similar ratio is obtained from the ratio of the opening angleof the jet and counter-jet Φjet/Φcjet = 1.37 ± 0.24, (see Sect.4.8). From the relation R = x(2−α) we obtain R = 2.5± 1.4 ingood agreement with the jet-to-counter-jet ratios found at 1.6and 43 GHz (where absorption effects are minimal). This canbe regarded as an independent and alternative measure for theintrinsic (from absorption unaffected) jet-to-counter-jet ratio.With an assumed intrinsic jet-to-counter-jet ratio of the order ofR ' 2 and a typical velocity of βapp > 0.4, the jet would beinclined at θ ≥ 70◦ (for h = 2).

4.11. Application of jet models

4.11.1. Hydrodynamical oscillations of the jet width

In a collimated relativistic hydrodynamical gas flow, ie. ajet, a decrease of the pressure P leads via Bernouilli’s equa-tion γP 1/4 =constant to an increase of the flow speed γ =1/√

1− β2. An apparent acceleration fromβ1 = 0.1 toβ2 = 0.7thus requires a drop of the internal jet pressure or a drop of thepressure of the external gas by a factor P1/P2 = ((1−β2

1 )/(1−β2

2 )2 = 3.8.The model of Daly & Marscher 1988 (hereafter DM88) re-

lates pressure and velocity changes along a relativistic jet withoscillations of the jet width and formation of shocks. In the jetof Cygnus A, the apparent acceleration of components seemsto be correlated with an intensity drop (Fig. 9) and a spectralflattening (Fig. 8) in the region at r ' 1 − 2 mas, and with anincrease of the jet width (Fig. 17). We therefore apply the modelof DM88 and use their notation.

From Fig. 17 we determined the maximum relative ampli-tude of the oscillation of the jet width in the region r ' 1−2 masto be of orderDmax/D0 ' 2. The pressure ratio ζ = (Px/P0)1/2

between the external medium (Px) and reconfinement region(P0) then follows from equation (24) of DM88 giving ζ '0.55. This, and equation (25a) from DM88, yield a velocityin the reconfinement region γ0 = 0.19(2

√ζ − 1)(zmax/D0) =

0.094(zmax/D0) ≥ 1.9, where we determined from Fig. 17 theratio (zmax/D0) between the recollimation scale of the oscilla-tion zmax and the minimal jet widthD0 to be (zmax/D0) ≥ 20.Transformed into intrinsic jet speed, γ0 ≥ 1.9 is equivalent toβ = 1/(1− γ−2)1/2 ≥ 0.85 or (for a jet orientation close to theplane of sky) βapp ' β/γ ≥ 0.45. This velocity agrees well


P1

P2

P3

P4

P5

R=7 R=4 R=1.1

100806040200

1.0

0.8

0.6

0.4

0.2

0

INCLINATION ANGLE [degrees]

JET

VE

LO

CIT

Y[v

/c]

=0.6app

app

app=0.2=0.1

100806040200

1.0

0.8

0.6

0.4

0.2

0

INCLINATION ANGLE [degrees]

JET

VE

LO

CIT

Y[v

/c]

P2

P1

P4

P3

R=7 R=4 R=1.1

=1.2app

app

app

=0.4

=0.2

P5

Fig. 18. The parameter space for the jet velocity β and inclination an-gle θ of the symmetric relativistic twin jet model, using the knownjet-to-counter-jet ratio R and the apparent velocity βapp. The area de-lineated by the points P1-P2-P3-P4 gives the allowed range of solutionsfor all possible combinations of R and βapp. P5 markes a solution ob-tained at 22 GHz (R = 4, βapp = 0.2 · h). The shaded area above P5and limited by the lines R = 1.1 and R = 4 gives our best estimatefor β and R. Note that for intrinsically symmetric jets (R ' 1), theinclination angle is > 80 ◦ and depends only weakly on the jet ve-locity. The upper figure is for h = 1, the lower figure is for h = 2(H0 = 100 · h−1km sec−1Mpc−1, and q0 = 0).

with the observed speed at larger core separations and also withthe velocity constraints obtained from the jet-to-counter-jet ratio(Sect. 4.5).

The highest jet velocity occurs in the rarefraction regionwhere the internal pressure is minimal. Using Pmin/P0 =(2√ζ−1)1/4 ' 0.8 and Bernouilli’s equation, velocity changes

of several 10 % (γmax/γ0 = (P0/Pmin)1/4 ' 1.1) can be ob-tained. This is much too low to explain the observed accelera-tion. If, on the other hand, a pressure drop of Pmin/P0 = 1/3.8(see above) is assumed in order to explain the accelerationby pressure gradients, we obtain ζ = 0.252. With equation(24) of DM88 this yields an amplitude of the oscillations ofDmax/D0 ' 250. Such strong variations are not seen in thepresent data sets.

Although the model of a relativistic hydrodynamical jet flow(DM88) provides a qualitative explanation of the observed re-

lation between jet speed and jet width, it cannot quantitativelyreproduce the observed properties; either the amount of acceler-ation is too large or the oscillations of the jet width are too small.To reduce the strength of the oscillations for a given and fixedvelocity gradient, additional jet confinement (e.g. by a magneticfield) is required. If, however, the strength of the oscillations iskept fixed, a decoupling of the observed velocity from the bulkvelocity seems probable.

The fact that the jet opens conically on small core sepa-rations (r ≤ 15 mas), but then becomes recollimated furtherout (5 GHz maps, cf. Carilli & Barthel, 1996), indicates theexistence of relatively slow oscillations of the width. This re-quires (from equations 25a and b of DM88) a high relativisticjet speed of γ ' 10− 20. Such a high γ is also suggested fromthe Mach number (M =

√2(γ2 − 1) ' 20), and is not im-

plausible with regard to the unified scheme for AGN (Barthel,1989). It is therefore very likely that the observed slow motionis related to pattern velocities, which are caused by instabilitiesand/or shocks. Both phenomena are expected to develop in thepresence of pressure gradients. If this is the case, the observed(pattern) velocity (0.1-0.7 c) could be considerably slower thanthe velocity of the bulk flow.

4.11.2. Kelvin Helmholtz instabilities

The relatively rapid oscillations of the jet ridgeline and the jetwidth may be better explained with (helical) Kelvin-Helmholtzinstabilities in a magnetized relativistic jet (e.g. Hardee, 1990).In this model, moving jet components are identified with surfaceand/or body waves generated by these instabilities. The phasevelocity of such waves is always lower than the bulk velocityof the jet. In the following we apply the model of Hardee etal. , 1995 (see also Hardee, 1996), which – based on numeri-cal simulations – relates the jet speed and wavelength of theinstabilities by the following basic equations.

The wave speed βw of a Kelvin-Helmholtz instability (ofmode n, m) is:

βwβ

=γη1/2

γη1/2 + 1(3)

The wavelength of the instability is:

λ/D = fnmγM

γη1/2 + 1(4)

were D is the jet radius, fnm = 16/(2n + 4m + 1) describesthe instability mode, γ is the Lorentz factor, β the speed of therelativistic jet flow, and η = ρj/ρx the density contrast betweenthe jet and the external medium.

If we identify the observed apparent speed with the patternspeed of the instability (βapp = βw), it is obvious that spa-tial variations of the density contrast η and/or of the intrinsicjet speed γ could produce the observed apparent accelerationfrom βw,1 = 0.1 (at separation r1 ' 1 mas) to βw,2 = 0.7 (atr2 ' 10 mas). For 0.1 ≤ βw ≤ 0.7 we obtain a jet densitycontrast in the range 0.1 ≤ γη1/2 ≤ 2.3, in good agreement


with the expectation that the jet of Cygnus A is light and su-personic (γM ≥ 20). To increase the apparent speed βw by afactor of about 7, the density contrast η must drop by about afactor of η2/η1 ' 500 · (γ1/γ2)2 (indices denote the positionsr1 and r2, respectively). The demand of less steep density gra-dients requires an intrinsic jet acceleration of no more than afactor γ2/γ1 ≤ 22. In our opinnion, a mixture of both, increas-ing density contrast (e.g. due to a decreasing external densityρx) and intrinsic acceleration, would set a plausible scenario forreconciling the observations with the model. The model predictsfurthermore the wavelengths of the jet oscillations. With a Machnumber γM ≥ 20 and a density contrast γη1/2 ' 2.3 in theouter regions (near r2), the typical wavelength of the instabili-ties of mode (n,m) are λ/D ≥ 6.1 · fnm. For the basic modesn = 1, m = 0 this yields fnm = 5.3 and λ/D = 32, in goodagreement with the slow variations of the jet axis seen in thisregion (Fig. 16, Sect. 4.7). At smaller core separations (near r1)the observed wavelengths are shorter, requiring modes of higherorder (n,m ≥ 2) and a lower Mach number γM ≤ 8. Thus theobserved increase of the wavelength of the jet oscillations withr requires – if interpreted within this model – an increase ofthe relativistic Mach number, and therefore an increase of thejet speed (acceleration). We furthermore note that close to theorigin, modes of higher order – which are attenuated at largercore separations – are not unexpected.

In summary we conclude that the model is able to explain theexistence and the basic shape (the wavelength) of the jet oscilla-tions observed in two different regions (r1 and r2), if jet intrinsicacceleration and/or density gradients along the jet are added tothe model. In a simple manner it explains the observed range ofvelocities, relating them to mode dependent wave speeds of he-lical Kelvin-Helmholtz instabilities in a magnetized relativisticjet.

4.12. The unified scheme and a two fluid model

The unified scheme of radio-galaxies and quasars tries to ex-plain the observed differences between both classes as geo-metrical effect, using different source orientations with respectto the observer (e.g. Barthel, 1989). Cygnus A is generally re-garded as the prototype of a FR II-radio-galaxy, which, if ro-tated towards the line of sight should change into a superluminalquasar. The observed properties of quasars, however, require abulk jet velocity very close to c (β ' 1), in contrast to the ob-served slow motion in Cygnus A of βapp = (0.1 − 0.7) · h. Incombination with the jet inclination nearly in the plane of thesky, this gives only room for a moderately low Lorentz-factorγ ≤ max(

√(1 + (βapp · h)2)) < 1.6, for h ≤ 2.

Eq. (1) and θ > 45 ◦ exclude the possibility that the fast(0.7h c) and the slow (0.1h c) part of the motion results from thesame relativistic flow of constant velocity β. This furthermoreexcludes that the different velocities can be explained geomet-rically by jet bending. In the following we discuss a generalizedversion of the two-fluid model (e.g. Sol et al. , 1989, Pelletier& Roland, 1989). Similarly to a hydrodynamical flow (e.g. ariver) we assume that the velocity γ in a jet of an AGN varies

0.0 20.0 40.0 60.0 80.0 100.0inclination [deg]

10-5

10-4

10-3

10-2

10-1

100

101

flux

dens

ity [J

y]

fast component (10 c)slow component (0.5 c)

Fig. 19. Flux density of a fast (γ2 = 10.5, βapp = 10, solid line) andslow (γ1 = 1.08, βapp = 0.5, dashed line) relativistic flow plotted ver-sus jet inclination. For the fast component an intrinsic flux S2 = 10−3

Jy is adopted, for the slow flow S1 = 10−1 Jy. This approximately re-flects the typical brightness of superluminal components in a prominentquasar (S ∼ 1 Jy) and of the subluminal components in a prominentradio galaxy like Cygnus A (S ∼ 0.1− 0.4 Jy).

perpendicular to the jet axis. For simplicity we regard only theslowest (γ1) and the fastest (γ2) component of the flow.

The relativistically enhanced intensity of a jet with Lorentz-factor γ1 = 1/

√(1− β2

1 ) is Sobs1 (γ1) = S1 · D(2−α)1 , with the

Doppler-factorD1 = 1/γ1·1/(1−β1 cos(θ)) andS1 being the in-trinsic and unboosted flux density of the jet. If oriented at a largeangle to the line of sight, a second relativistic flow with Lorentz-factor γ2 > γ1 will be Doppler diminished, whenever D2 < 1.This happens at all angles θ2 ≥ arccos((1 −

√(1− β2

2 ))/β2).With γ2 > γ1 it follows that θ2 < θ1. An increase of the incli-nation angle θ therefore leads to a much more rapid decreaseof the brightness of the faster γ2-flow, than of the slower γ1-flow (see Fig. 19). Depending on the source orientation, theobserver thus will see only the part of the jet flow which hasa Doppler-boosted brightness larger than his (limited) imagingsensitivity. The Doppler-bias therefore will lead to a preferentialdetection of low-velocity flows in sources, which are oriented atlarge inclination angles, and to detection of high-velocity flowsin sources, which are inclined at smaller angles. Consequentlyit is possible to explain in this way the apparent discrepancybetween the relative low velocities observed in Cygnus A andsimilar radio-galaxies (e.g. M87, 3C 84, Cen A, 3C 338) and thehigher velocities seen in the superluminal quasars. We also notethat the intrinsic brightness S2 of the fast component of the flowshould be 2-3 orders of magnitude lower than the brightness ofthe slow component S1 (see Fig. 19).

5. Summary

We present VLBI-maps of Cygnus A at 1.6, 22, and 43 GHz.These images show a two-sided core-jet structure with a west-


ern jet and an eastern counter-jet oriented within 5 degreestowards the kpc-jets seen with the VLA. The data allow thejets to be traced from 0.1 mas up to ∼ 400 mas. At 22 GHzwe find systematic oscillations of the mean jet ridgeline (twomodes: λ/D ≤ 8 and λ/D ≥ 20) and oscillations of the trans-verse width of the jet (∆D/D ' 2). Between a few and sev-eral 100 mas core separation, the opening angle of the jet andthe counter-jet is ∼ 5 ◦ . The armlength ratio between jet andcounter-jet is 1.4 ± 0.3. A weak S-shape symmetry of jet andcounter-jet seen at 22 GHz needs further confirmation.

From 22 GHz and 43 GHz images obtained in 1992.4 wedetermined the spectrum of the jets of Cygnus A on mas-scales.East of an inverted spectrum compact component, which weidentify as the VLBI-core (α22/43GHz ' 1), the componentson the counter-jet side exhibit flat spectra (α22/43GHz ' 0). Onthe jet side the spectrum is considerably steeper (α22/43GHz '−0.6), however showing a local flattening near 1 mas core-separation. In this region a drop of the jet brightness and ap-parent acceleration of the motion is also observed.

22 GHz observations at two epochs (1992.44 and 1994.17)give strong evidence for subluminal motion with βapp = (0.1−0.2)h at small separations (r ≤ 1 mas) and βapp = (0.3− 0.7)hin the region 1 < r ≤ 3 mas. In the inner jet all features moveaway from the VLBI-core, which we assumed to be stationary.On the counter-jet side we were not able to determine any sys-tematic motion and future VLBI monitoring is needed to extendthe time base.

From the maps we determined the jet-to-counter-jet ratio Rat 1.6, 22, and 43 GHz. Adding data from the literature, we finda pronounced frequency dependence of this ratio: R=1.2, 5.0,4.0, and 2.3 at 1.6, 5, 22, and 43 GHz, respectively. If the jets arenot intrinsically asymmetric, this frequency dependence can beexplained quite naturally by partial obscuration of the counter-jet from a circum-nuclear disk or torus (free-free absorption).

The jet-to-counter-jet ratio and the measured apparent ve-locity allow the determination of the jet orientation and theintrinsic jet velocity (adopting assumptions of the relativistictwin-jet model). Using the presumed absorption-free low jet-to-counter-jet ratio at 1.6 GHz, we find that the jet is orientedat a large angle to the line of sight (θ > 80 ◦ , for R < 2). Thejet velocity then is in the range 0.19h ≤ β < 1. We argue thatthe measured apparent velocities are probably related to patternspeeds and that the intrinsic jet velocity is relativistic (≥ 0.4 c).In this case the Hubble parameter is more likely to be close toh = 2 rather than h = 1 (H0 = 100 · h−1km sec−1Mpc−1).

From the discussion of jet models invoking Kelvin-Helmholtz instabilities and not only a single jet flow with asingle velocity (generalization of the two fluid model) it appearsthat the observed velocities in Cygnus A (at least partially) arerelated to pattern velocities, which are slower than the intrinsicjet flow. We note that velocity measurements in jets which areoriented close to the plane of the sky are biased towards slowvelocities, whereas the brightness of the faster jet componentis diminished below the detection sensitivity by the relativisticDoppler-effect.

Acknowledgements. VLBI observations at high frequencies are techni-cally difficult. For their efforts we thank the technical staff and the op-erators at the observatories. D. Graham provided invaluable support forthe VLBI observations at Pico Veleta. For their help during the observa-tions or with the antenna calibration we thank A. Alberdi, W. Altenhoff,S. Britzen, F. Colomer, A. Kraus, I. Pauliny-Toth, C. Schalinski andK. Standke. We profited from scientific discussions with A. Bridle, A.Lobanov, R.W. Porcas, S.J. Qian, J. Roland, and S. Wagner and thankR. Schilizzi for his comments. Special thanks are given to the operatorsat the MK III correlator U. Stursberg and H. Blaschke. The NationalRadio Astronomy Observatory is operated by Associated UniversitiesInc., under cooperative agreement with the National Science Founda-tion. VLBI at the MIT-NEROC Haystack Observatory is supported bythe National Science Foundation. The VLBI equipment at Pico Veletawas financed by the Stiftung Volkswagenwerk. The work of T.P.K. wassupported in part by a grant from the BMBF (Verbundforschung).

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VLBI observations of CygnusA with sub-milliarcsecond ...aa.springer.de/papers/8329003/2300873.pdf · bent core-jet structure extending ˘ 5mas along pa = 270 − 280 (Krichbaumetal.,1993a).VLBIdetectiontestsat86GHz