Multiwaveband Polarimetric Observations of 15 Active Galactic Nuclei at High Frequencies: Correlated Polarization Behavior
Svetlana G. Jorstad, Alan P. Marscher, Jason A. Stevens, Paul S. Smith, James R. Forster, Walter K. Gear, Timothy V. Cawthorne, Matthew L. Lister, Alastair M. Stirling, José L. Gómez, Jane S. Greaves, E. Ian Robson
aa r X i v : . [ a s t r o - ph ] M a y Multiwaveband Polarimetric Observations of 15 Active GalacticNuclei at High Frequencies: Correlated Polarization Behavior
Svetlana G. Jorstad , , Alan P. Marscher , Jason A. Stevens , Paul S. Smith , James R.Forster , Walter K. Gear , Timothy V. Cawthorne , Matthew L. Lister , Alastair M.Stirling , Jos´e L. G´omez , Jane S. Greaves , and E. Ian Robson ABSTRACT
We report on multi-frequency linear polarization monitoring of 15 activegalactic nuclei containing highly relativistic jets with apparent speeds from ∼ c to > c . The measurements were obtained at optical, 1 mm, and 3 mm wave-lengths, and at 7 mm with the Very Long Baseline Array. The data show a wide Institute for Astrophysical Research, Boston University, 725 Commonwealth Ave., Boston, MA 02215-1401; [email protected], [email protected] Sobolev Astronomical Institute, St. Petersburg State University, Universitetskij pr. 28, 198504 St.Petersburg, Russia Centre for Astrophysics Research, Science and Technology Centre, University of Hertfordshire, CollegeLane, Herts AL10 9AB, UK; [email protected] Steward Observatory, The University of Arizona, Tucson, AZ 85721; [email protected] Hat Creek Observatory, University of California, Berkeley, 42231 Bidwell Rd. Hatcreek, CA 96040;[email protected] School of Physics and Astronomy, Cardiff University, 5, The Parade Cardiff CF2 3YB, Wales, UK;[email protected] Center for Astrophysics, University of Central Lancashire, Preston, PR1 2HE, UK; [email protected] Department of Physics, Purdue University, 525 Northwestern Ave., West Lafayette, IN 47907-2036;[email protected] University of Manchester, Jodrell Bank Observatory, Macclesfield, Cheshire, SK11 9DL, UK (currentaddress); [email protected] Insituto de Astrof´ısica de Andaluc´ıa (CSIC), Apartado 3004, Granada 18080, Spain; [email protected] School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS,UK; [email protected] Astronomy Technology Centre, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK;[email protected] <
1% to > Subject headings: galaxies: active — galaxies: quasars: individual (0420-014,0528+134, 3C 273, 3C 279, PKS1510-089, 3C 345, CTA102, 3C 454.3) — galaxies:BL Lacertae objects: individual (3C 66A, OJ 287, 1803+784, 1823+568, BLLac)— galaxies: individual(3C 111, 3C 120) — galaxies: jet — polarization
1. Introduction
Magnetic fields play a prominent role in the physical processes that occur in the jetsof active galactic nuclei (AGN). The leading model for jet production, acceleration, andcollimation involves poloidal magnetic fields that are wound up by the differential rotation ofa rotating disk or ergosphere surrounding a central supermassive black hole (e.g., McKinney2006; Meier, Koide, & Uchida 2000). The twisted field propagates outward as Poynting fluxin the polar directions, with eventual conversion into a well-focused relativistic plasma flow(e.g., Vlahakis & K¨onigl 2004; Meier & Nakamura 2006). Within this zone, the magneticfield should maintain a tight helical pattern.Beyond the jet acceleration region—which may extend over hundreds or thousands ofgravitational radii from the black hole (Vlahakis & K¨onigl 2004; Marscher 2006)—the jetmay become turbulent or subject to velocity shear. In the former case, the magnetic field 3 –should be chaotic, with any line of sight passing through many turbulent cells and significantdifferences in both strength and direction of the field in adjacent cells. In contrast, velocityshear stretches and orders the field lines along the flow (e.g., Laing 1980). Shock wavespassing through the flow (or vice versa) will compress the component of the field that isparallel to the shock front, which imposes order even on a magnetic field that is completelychaotic in front of the shock.The geometry and degree of order of the magnetic field are therefore key indicatorsof the physical conditions in a jet. Because the primary emission mechanism at radio tooptical wavelengths is synchrotron radiation, the linear polarization of the continuum canbe used as a probe of the magnetic field. We can also use the fractional polarization anddirection of the electric vector position angle (EVPA) to identify distinct features in the jetthat are observed at different wavelengths. The most prominent features on VLBI imagesof jets in radio-loud AGN are (1) the core, which is the bright, very compact section at thenarrow end of a one-sided jet, and (2) condensations in the flow that appear as bright knots,often called “components” of the jet. The core likely lies some distance from the centralengine of the AGN, probably either near the end or beyond the zone of acceleration andcollimation of the jet (Marscher 2006). The knots usually separate from the core at apparentsuperluminal speeds, but roughly stationary knots are also present in many jets, perhapsrepresenting standing shocks (e.g., Jorstad et al. 2001; Kellermann et al. 2004; Lister 2006;Jorstad et al. 2005, hereafter J05). The apparent speeds of the components can exceed β app ∼ c (J05) that requires the Lorentz factor of the flow exceeds β app . The leadingmodel identifies the moving knots as propagating shocks, either transverse to the jet axis(e.g., Hughes, Aller, & Aller 1985, 1989; Marscher & Gear 1985) or at an oblique angle(Hughes 2005). Polarization studies can help to determine whether this model is viable.The standard paradigm of transverse shocks propagating down a relativistic jet canexplain many aspects of the time variability of the brightness, polarization, and structureat radio wavelengths (e.g., Hughes, Aller, & Aller 1985, 1989; Cawthorne & Wardle 1988;Wardle et al. 1995). However, this model makes predictions—e.g., that the magnetic fieldof a knot should be transverse to jet axis—that often do not match observations. Anotherpossibility is that there is a systematically ordered component of the magnetic field, forexample one with a helical geometry (e.g., Lyutikov, Pariev, & Gabuzda 2005), in the jetthat modulates its brightness and polarization variability. In fact, a helical magnetic field isrequired in the magnetohydrodynamical jet launching models (Meier, Koide, & Uchida 2000;Vlahakis & K¨onigl 2004). Gabuzda (2006) provides some support for such a geometry inrecent low frequency VLBI observations of Faraday rotation in AGN jets. However, thisstructure can be related to the magnetic field in the Faraday screen surrounding the jet sincehigh frequency radio polarization mapping reveals aspects that are difficult to explain by a 4 –helical field (Hughes 2005; Zavala & Taylor 2005).The situation is even more confusing in the optical and near-IR regions, where varia-tions in flux and polarization are often extremely rapid, and sub-milliarcsecond resolutionis not available (e.g., Hagen-Thorn 1980; Moore, Schmidt, & West 1987; Smith et al. 1987;Mead et al. 1990). Furthermore, existing optical data indicate that the connection betweenvariations in brightness and polarization is tenuous (e.g., Smith 1996). These factors com-plicate interpretation of the optical/near-IR emission, since detailed models are needed butthe data are not extensive enough to guide them. An alternative approach is to inves-tigate the global polarization behavior across a sizable range of the electromagnetic spec-trum. Such studies (Wills et al. 1992; Gabuzda, Sitko, & Smith 1996; Lister & Smith 2000;Gabuzda et al. 2006) have produced convincing evidence for a connection between the ra-dio and optical polarization properties of AGN, suggestive of a common, probably cospatial,origin for the emission at these two wavebands. However, such studies have been based onsingle-epoch measurements, whereas the investigation we present here involves multi-epochobservations of fifteen objects. This allows us to use both the time and frequency domainsto explore the geometry and degree of ordering of the magnetic field and other properties ofthe emission regions in relativistic jets.Bright jets with high apparent superluminal motion are a prevalent feature of blazars, aclassification that includes BL Lac objects and optically violently variable quasars (OVVs)that are quite rare in the general AGN population (Kellermann et al. 2004; Lister 2006).The prominence of the jets from radio to optical wavelengths and the pronounced variabilityof their polarized emission makes blazars and radio galaxies with blazar-like behavior idealobjects for probing the magnetic fields in jets through multi-epoch polarization studies.We have carried out a 3-yr monitoring program of fifteen radio-loud, highly variableAGN. The program combines roughly bimonthly, high resolution polarized and total inten-sity radio images with optical, submillimeter-wave (sub-mm), and millimeter-wave (mm)polarization observations performed at many of the same epochs. The sample includes ob-jects that are usually brighter than about 2 Jy at 7 mm and 1 Jy at 1 mm, with a mixture ofquasars (0420 − −
2. Observations and Data Reduction
We have measured the total flux densities and polarization of the objects in our samplein four spectral regions: at 7 mm (43 GHz), 3 mm (86 GHz), 0.85/1.3 mm (350/230 GHz),and optical wavelengths (an effective wavelength of ∼ We carried out optical polarization and photometric measurements at several epochsusing the Two-Holer Polarimeter/Photometer (Sitko, Schmidt, & Stein 1985) with the Stew-ard Observatory 1.5 m telescope located on Mt. Lemmon, Arizona, and 1.55 m telescopeon Mt. Bigelow, Arizona. This instrument uses a semi-achromatic half-waveplate spinningat 20.65 Hz to modulate incident polarization, and a Wollaston prism to direct orthogonallypolarized beams to two RCA C31034 GaAs photomultiplier tubes. For all polarization mea-surements we used either a 4 . ′′ . ′′ ∼
320 and 890 nm, with an effectivecentral wavelength of ∼ R filter ( λ eff ∼
640 nm ) was employed to avoid majorunpolarized emission-line features (Smith, Schmidt, & Allen 1993). We accomplished skysubtraction by nodding the telescope to a nearby ( < V -band photometry ( R -band photometry in the case of 3C 273) of several objects, employing either an 8 . ′′ . ′′ V magnitudes of 3C 111 and 3C 120 on 1999 February 13 from the photometric solutionprovided by observations of equatorial standard stars (Landolt 1992).Table 1 lists the results of the optical observations. The columns correspond to (1) 6 –source, (2) epoch of observation, (3) filter bandpass of the photometry, (4) apparent magni-tude, (5) flux density I opt , (6) filter bandpass of the polarimetry, where W denotes unfiltered,or “white-light” measurements, (7) degree of linear polarization m opt , and (8) polarizationposition angle χ opt . We have corrected the degree of linear polarization for the statisticalbias inherent in this positive-definite quantity by using the method of Wardle & Kronberg(1974). Usually this correction is negligible because of the high signal-to-noise (S/N) ratioof most measurements.Because of the high observed optical polarization levels and high galactic latitudes ofthe majority of the sources, interstellar polarization (ISP) is not a significant concern in mostcases. Interstellar polarization from dust within the Milky Way Galaxy does appear to bea major component of the observed optical polarization for 3C 111 ( b = − . ◦ ) and 3C 120( b = − . ◦ ). A star ∼ ′′ west of 3C 111 shows very high polarization ( m = 3 . ± . χ = 123 ◦ ± ◦ ); this was used to correct the polarimetry for ISP in the line of sight to theradio galaxy. The corrected measurements suggest that the intrinsic polarization of 3C 111was typically <
3% throughout the monitoring campaign. The average polarization for fivestars within 8 arcmin of 3C 120 yields m = 1 . ± .
06% and χ = 98 ◦ ± ◦ . We have usedthis ISP estimate to correct the observed polarization of 3C 120 for interstellar polarizationand, as for 3C 111, list the corrected measurements in Table 1. The corrected values indicatethat 3C 120 had very low polarization ( m opt < . R -band measurements. Table1 lists the corrected polarization for 3C 273. We performed observations at 1.35 and 0.85 mm with the James Clerk Maxwell Tele-scope (JCMT) located on Mauna Kea, Hawaii using the Submillimetre Common User Bolome-ter Array (SCUBA, Holland et al. 1999) and its polarimeter (Greaves et al. 2003). Theinitial plan was to observe exclusively at 1.35 mm because the sources are almost alwaysbrighter, the atmospheric opacity is lower, and the sky is more stable than at 0.85 mm.However, failure of the SCUBA filter drum in November 1999 forced a switch to 0.85 mmthereafter. The polarization properties of blazars tend to be very similar at millimeter andsubmillimeter wavelengths (Nartallo et al. 1998), so the modest change in wavelength shouldnot affect our analysis. For convenience we will refer to the data obtained with the JCMTas “1 mm” data. 7 –The SCUBA polarimeter consists of a rotating quartz half-waveplate and a fixed ana-lyzer. During an observation, the waveplate is stepped through 16 positions, and photometricdata are taken at each position. One rotation takes ∼
360 s to complete, and the procedureresults in a sinusoidally modulated signal from which the Stokes parameters are extracted.A typical observation consists of 5–10 complete rotations of the waveplate. We achievedflux calibration in the standard manner with observations of planets or JCMT secondarycalibrators. We measured the instrumental polarization ( ∼ SU RF and
SIT . The Stokes parameters wereextracted by fitting sinusoids to the data, either half-cycle (8 points) resulting in two esti-mates, or full-cycle (16 points) yielding only one estimate but generally giving better resultswith noisy data. We removed spurious measurements by performing a Kolmogorov-Smirnovtest on the collated data and then calculated the degree and position angle of the polariza-tion, corrected for instrumental polarization and parallactic angle. Table 2 lists the datawith the columns corresponding to (1) source, (2) epoch of observation, (3) wavelength λ ,(4) flux density I , (5) degree of linear polarization m , and (6) polarization positionangle χ . As with the optical measurements, the values of m have been corrected forstatistical bias. From April 2000 to April 2001 we monitored the sources at 86 GHz using the linearpolarization system on the the Berkeley-Illinois-Maryland Array (BIMA) in Hat Creek, Cal-ifornia during unsubscribed telescope time. The data quality was quite variable, and typicaltotal integration times were about 10 minutes per source. We omit from our analysis datataken during extremely high atmospheric phase variations or bad opacity conditions. Weobserved planets (Mars, Uranus, and Venus), H II regions (W3OH and MWC349), and 3C 84as quality checks and for flux calibration.We analyzed the data by mapping all four Stokes parameters for each sideband sepa-rately, producing images of total intensity, linearly polarized flux density, degree of polar-ization, and polarization position angle for each source at each epoch. Data having S/N < I , (4) degree of linear polarization m , and (5)polarization position angle χ . We performed total and polarized intensity imaging at 43 GHz with the Very LongBaseline Array (VLBA) at 17 epochs from 25 March 1998 to 14 April 2001. We describethe observations and data reduction in detail in J05, where the total and polarized intensityimages are presented. Table 4 gives the results of fitting the VLBI core seen in the total andpolarized intensity images by components with circular Gaussian brightness distributions(see J05). Columns of the table are as follows: (1) source, (2) epoch of observation, (3)flux density in the core I , (4) projected inner jet direction Θ jet , (5) degree of linearpolarization in the core m , and (6) polarization position angle in the core χ . Wedetermine the projected inner jet direction from the position of the brightest jet componentclosest to, but at least one synthesized beam width from, the core.Table 5 gives the polarization of jet components downstream of the VLBI core that areeither (i) brighter than or comparable to the core at least at one epoch ( I comp ≥ I )or (ii) have detectable polarization at three or more epochs. These data allow us to probethe physics of the strongest disturbances that propagate down the jet. Table 5 contains: (1)source, (2) epoch of observation, (3) designation of the component, which follows that ofJ05, (4) flux density in the component I comp7mm , (5) distance from the core R , (6) position anglerelative to the core Θ, (7) degree of linear polarization m comp7mm , and polarization position angle χ comp7mm , in the component. Values of the degree of polarization in both tables are correctedfor statistical bias.
3. Observed Characteristics of Polarization
Tables 1-4 show that the linear polarization for all objects at most wavelengths variessignificantly both in degree and position angle. Figure 1 represents the relationship betweenthe degree of polarization at optical, 1 mm, and 3 mm wavelengths from the whole sourcewith respect to the degree of polarization measured in the VLBI core at 7 mm. The data 9 –plotted in Figure 1 correspond to the closest observations obtained at opt-7 mm, 1-7 mm,and 3-7 mm wavelengths for each source. These measurements are simultaneous within 1-3days. There is a statistically significant correlation at a significance level ǫ =0.05 betweenfractional polarization in the VLBI core and degree of polarization at short wavelengths.The optical polarization maintains the strongest connection to the polarization in the VLBIcore ( r =0.87, where r is the linear coefficient of correlation). This result confirms the strongcorrelation between the polarization level of the radio core at 7 mm and overall opticalpolarization found by Lister & Smith (2000). Their sample included quasars with both highand low optical polarization. However, it raises the question of why the optical polarizationshows a better connection to the polarization in the VLBI core than does the polarizationat 1 mm. We have computed the fractional polarization variability index V p λ at each frequencyusing the definition employed by Aller, Aller, & Hughes (2003a): V pλ = ( m max λ − σ m max λ ) − ( m min λ + σ m min λ )( m max λ − σ m max λ ) + ( m min λ + σ m min λ ) , (1)where m max λ and m min λ are, respectively, the maximum and minimum fractional polarizationmeasured over all epochs at wavelength λ , and σ m max and σ m min are the corresponding uncer-tainties. This approach is especially justified in our case, since all objects were observed overthe same period of time, although the time intervals are different at different wavelengths( ∼ ∼ ∼ V p =0. We introduce the polarization positionangle variability index, V a λ : V a λ = | ∆ χ λ | − q σ χ λ + σ χ λ , (2) Throughout the paper we calculate coefficients of linear correlation and use the method ofBowker & Lieberman 1972 for testing the significance of these coefficients. The hypothesis that there is nocorrelation between two variables, r =0, can be rejected at a significance level ǫ if t = | r/ √ − r |√ N − ≥ t ǫ/ N − , where t ǫ/ N − is the percentage point of the t -distribution for N − N isthe number of observations.
10 –where ∆ χ λ is the observed range of polarization direction and σ χ λ , σ χ λ are the uncertaintiesin the two values of EVPAs that define the range. We treat the 180 ◦ ambiguities in EVPAssuch that ∆ χ λ can not exceed 90 ◦ . As in the case of V p , if V a ≤ V a = 0and conclude that the observations were unable to measure variability in the polarizationposition angle.Figure 2 shows the relationship between the polarization and position angle variabilityindices in the VLBI core and at short wavelengths. A statistically significant correlationoccurs both between V popt and V p7mm and between V aopt and V a7mm ( r =0.62 and r =0.78, respec-tively). This result indicates that changes in the ordering of magnetic fields in the opticalregion and VLBI core are correlated, which suggests that the polarization variability hasthe same origin at the two wavebands. The correlation between the values at 3 mm and inthe VLBI core might be affected by the region of the jet lying somewhat outside the VLBIcore that contributes significantly to the 3 mm polarized emission. There is no correlationbetween variability indices at 1 mm and in the VLBI core. We use the polarization variability indices to classify the sources in our sample withrespect to their polarization properties. This classification scheme differs somewhat fromthe classical separation of AGN into radio galaxies, quasars, and BL Lac objects, which wehave used to discuss kinematics in the parsec-scale jets (J05). The new categorization revealssignificant differences in the polarization properties (see §
7) among the introduced groupsthat would be diluted in the traditional scheme.Figure 3 shows that the fractional polarization and polarization position angle variabilityindices in the 7 mm core are strongly correlated ( r =0.83) in a way that produces a clearseparation of the sources into three groups: LVP – low variability of polarization in the radiocore, V p7mm ≤ V a7mm ≤ . < V p7mm ≤ . < V a7mm ≤ V p7mm > V a7mm > m >
10% if dilution from essentiallyunpolarized non-synchrotron components such as the big blue bump is taken into account 11 –(Impey, Malkan, & Tapia 1989). All three LVP sources are highly polarized and variable at1 mm, and the fractional polarization of 3C 273 at 3 mm might be as high as 4%.The IVP group consists of four (out of five) BL Lac objects and two highly opticallypolarized quasars, 3C 279 and 3C 345. This group, therefore, includes extremely highly po-larized blazars, whose polarization in the optical and at 1 mm can exceed 30% and whose po-larization at 3 mm and in the VLBI core does not drop below 2-3%. Note that Nartallo et al.(1998) have found no differences in polarization properties of BL Lac objects and compactflat-spectrum quasars at short mm and sub-mm wavelengths.The majority of the quasars (five out of eight) and one BL Lac object, OJ 287, form theHVP group. The linear polarization of the VLBI core in these sources can be very low—atthe noise level—or as high as ≥ V p at 3 mm, 1 mm,and optical wavelengths are similar to those for the IVP group, although V a indices indicatemore dramatic polarization position angle variability at all wavelengths. We did not observehigh polarization at short mm wavelengths ( m ≥
10% and m ≥ m opt ≥
4. Total and Polarized Flux Density Spectra
We have constructed single-epoch total and polarized flux density spectra based on mea-surements at different wavelengths obtained within 2 weeks of each other (except 1803+784and 1823+568, where, at best, there is nearly a month between observations at differentwavelengths). We have corrected the optical flux densities shown in Table 1 for galacticextinction using values of A λ compiled by the NASA Extragalactic Database. The total fluxdensities at 7 mm are corrected for possible missing flux density in the VLBA images usingsingle-dish observations as described in J05. The measurements at 7 mm include the coreand components within the 1% contours of the peak total intensity at a given epoch (J05), I jet = I core + P i I comp i . The polarized flux density at 7 mm is integrated over the same VLBA 12 –image. Therefore, I p jet = q Q + U , Q jet = Q core + P i Q comp i , U jet = U core + P i U comp i ,m jet = I p jet /I jet , and χ jet = 0 . − ( U jet /Q jet ), where I core , Q core , and U core are the Stokesparameters of the core, and I comp i , Q comp i , and U comp i are the Stokes parameters of a givenpolarized jet component. Figure 5 presents the total and polarized spectral energy distri-butions (SED), while Table 6 lists the spectral indices α mm (based on total flux densities atthe three mm wavelengths) and α opt / , where S ν ∝ ν − α . We calculate the spectral indices α pmm and α popt / using the corresponding polarized flux densities, S p ν ∝ ν − α p .Table 6 shows that the total flux density spectra at mm-wavelengths are flat, indepen-dent of the type of source, with the majority of spectral indices having | α mm | < α opt / ∼
1, while the LVP sources possess much flatteroptical to 1 mm spectra. In the IVP group α opt / depends on whether the source is aquasar ( α opt / ∼
1) or BL Lac object ( α opt / ∼ α popt / and α opt / ( r =0.92). However, two sources from the LVP group (3C 120 and 3C 273) deviategreatly from the dependence α popt / = α opt / (solid line in Fig. 6), with a significantlysteeper polarized flux density spectral index than for the total flux density. This suggeststhat at least two emission components are present in the optical region, one of which is un-polarized. Impey, Malkan, & Tapia (1989) find an increase in the degree of polarization andhigher variability of the Stokes parameters in 3C 273 at longer optical wavelengths. Suchbehavior is expected if the optical emission consists of a variable synchrotron componentplus a relatively static blue unpolarized continuum source, such as the big blue bump. Thedecomposition of the optical synchrotron spectrum from other optical emission sources isreadily seen in the spectropolarimetry of 3C 273 (Smith, Schmidt, & Allen 1993). In thecase of 3C 120, the strong dilution of the optical synchrotron polarization is likely caused byhost galaxy starlight included within the measurement aperture.In the majority of the HVP and IVP sources, the spectral indices α popt / and α opt / are similar to each other. This suggests that a single synchrotron component is responsiblefor the total flux and polarized continuum from millimeter to optical wavelengths. How-ever, three of the HVP sources (0420 − − .
10% relative to the synchrotron emission. A flatter polarizedspectrum likely rules out any significant contribution by a non-synchrotron component, al- 13 –though two (or more) synchrotron components might coexist in the IVP sources. For BL Lac,contribution to the optical flux from the host galaxy might help to explain thr slightly steeper α popt / than the total flux spectral index.
5. Faraday Rotation in the Inner Jet
Figure 5 presents measurements of the polarization angle χ at different frequenciesobtained within 2 weeks of each other and shows that the direction of mm-wave polarizationrotates with wavelength. In the HVP and IVP sources the EVPA at 7 mm displayed in thefigure corresponds to that of the VLBI core only, while in the LVP sources it correspondsto χ jet , as described in §
4. We attribute this rotation to Faraday rotation by a foregroundscreen close to the VLBI core (Zavala & Taylor 2004; Attridge, Wardle, & Homan 2005).We define the rotation measure RM by assuming that at 1 mm we see the unrotated directionof the polarization and that the emission from 1 mm to 7 mm propagates through the samescreen. Figure 7 shows the result of fitting the dependence of the polarization position angleon wavelength by a Faraday rotation law: χ = χ + RM λ . For 0420 −
014 our programdoes not contain simultaneous observations at three mm wavelengths necessary to estimate RM . We have supplemented our data by observations obtained with the VLBA at 7 mm and1.3 cm in the program BG073 (see G´omez et al. 2000), for which 0420 −
014 and 3C 454.3were used as calibrators. For 0420 −
014 we use our polarization measurement at 1 mm on1998 December 13 and EVPAs in the 7 mm and 1.3 cm core on 1998 December 3 fromBG073. The EVPA at 7 mm is consistent with χ at epoch 1998 December 11 from ourprogram. For 3C 454.3 and BL Lac we use observations different from those plotted in Fig.5. For 3C 454.3 we use observations at 1 mm and 3 mm from our program (2000 June 6 and8, respectively) and 7 mm VLBA observations on 2000 June 9 (BG073). These observationsare closer to each other than the measurements presented in Figure 5 (2000, November 29– December 11) and less affected by the variability of bright component B B RM ◦ = RM (1+ z ) . Some of the RM values have largeuncertainties that might be attributed to several problems which our observations possess.First, the observations are not completely simultaneous, whereas the polarization positionangle can sometimes have short timescales of variability even at 7 mm (D’Arcangelo et al.2007). Second, the polarization position angles at 7 mm correspond to those of the VLBIcore only, while the EVPAs at 1 mm and at 3 mm are from the whole source. Althoughwe have tested that, at epochs used for estimates of the rotation measure, jet componentscontribute little to the polarization of the core (except 3C 454.3), their contribution to thepolarized flux at 1 mm and 3 mm is unknown. Third, the structure of the magnetic field inthe 7 mm core and in the regions emitting at shorter mm wavelength,- especially at 1 mm,-might be different. Therefore, the observed rotation could be an intrinsic property of themagnetic field structure.To test that the derived rotation measures are reliable, we construct the distributions of∆ χ = | χ − χ | for all pairs of observations simultaneous within 2 weeks for χ λ beforeand after RM correction (Fig. 8). Note that the distributions do not include the observationsused to calculate the rotation measures. This avoids the bias that these observations wouldintroduce to the distributions. Ideally, the EVPAs after RM correction should align within10 ◦ -20 ◦ , which corresponds to the uncertainties of our measurements. This is a feature ofboth distributions (uncorrected and corrected) for the IVP sources, reflecting the fact thatin the IVP sources the uncertanties of EVPAs are comparable to the RM correction values.However, EVPAs corrected for RM exhibit a slightly better alignment than ∆ χ before thecorrection, as expected if the EVPA rotation is caused by a Faraday screen. In the HVPsources the RM correction significantly improves alignment between χ and χ : 69% ofuncorrected values of ∆ χ exceed 20 ◦ while only 44% of corrected EVPAs have ∆ χ > ◦ .The existence of a few large misalingments between EVPAs after the RM correction can beattributed to variability of RM in the VLBI core of quasars (Zavala & Taylor 2004). Thispartially affects the analysis performed in § h| RM ◦ |i = (1 . ± . × rad m − , than the HVP sources, h| RM ◦ |i = (8 . ± . × rad m − . Two ofthe HVP blazars, 0528+128 and CTA 102, have EVPA corrections at 7 mm close to 90 ◦ . A90 ◦ flip in EVPA can be caused by the spectral properties of the source – optically thin at1 mm but optically thick at 7 mm. However, according to Pacholczyk (1970) the degreeof polarization should decrease significantly (by a factor of ∼
7) when the optical depth tosynchrotron self-absorption exceeds unity, while both quasars show only a moderate decreaseof polarization from 1 mm to 7 mm at the epochs used to calculate RM ( m = 4 . ± . m = 1 . ± .
5% for 0528+134; m = 6 . ± .
9% and m = 4 . ± .
7% for 15 –CTA 102).In a sample of 40 AGN Zavala & Taylor (2004) have determined rotation measuresusing VLBI images at 8-15 GHz that are lower than we derive at mm wavelengths. Theauthors suggest that an external screen “in close proximity to the jet” is the most promisingcandidate for the source of the Faraday rotation. In this context, lower rotation measuresobtained in the VLBI core at longer wavelengths might reflect a strong decrease in thicknessof the screen with distance from the central engine. This is expected because the locationof the core shifts with wavelength owing to optical depth effects. We assume a decreasinggradient in electron density of the screen, described by a power law: N e ∝ d − a , where d is the distance from the central engine. The rotation measure depends on the density andmagnetic field parallel to the line of sight, B k , integrated along the path through the screento the observer: RM ∝ R N e B k dl . In the absence of a velocity gradient across the jet, themagnetic field along the jet scales as B z ∝ d − and the magnetic field transverse to the jetscales as B φ ∝ d − (Begelman, Blandford, & Rees 1984). If the Faraday screen is at leastmildly relativistic and has a helical field (Gabuzda 2006), B φ provides the main contributionto the magnetic field component along the line of sight, therefore, B k ∝ d − . This leads to | RM | ∝ d − a under the approximation that l ∝ d . The location of the core from the centralengine depends on the frequency of the observation ν as derived, for example, in Lobanov(1998): d core ,ν = ( B k b F/ν ) /k r , where B is the magnetic field at distance 1 pc from the centralengine, F is a function of the redshift and parameters depending on the jet geometry andrelativistic electron energy distribution, and the equipartion value k r = 1. For a source witha flat mm-wave spectrum d core ,ν ∝ ν − , which yeilds the dependence of the rotation measureobserved in the core on the frequency of observation as | RM core ,ν | ∝ ν a . Therefore, valuesof rotation measure obtained with different sets of frequencies should produce an estimateof the parameter a . We assume that the RM ◦ derived from polarization observations of thecore at frequencies ν , ν , and ν , where ν is the lowest one, yields the intrinsic rotationmeasure at the location d core ,ν .Table 7 contains the published rotation measures obtained in the VLBI core at wave-lengths longer than 7 mm, RM ◦ and RM ◦ , and derived values of a . For sourceswith RM ◦ available at more than two wavelengths, a is calculated using a least-squaresmethod. Table 7 does not show any difference in the values of a between the HVP andIVP sources. The average h a i = 1 . ± . a = 2 expected for out-flow in a spherical or conical wind. This implies that an outflowing sheath wrapped arounda conically expanding jet is a reasonable model for the foreground screen, consistent withthe finding of Zavala & Taylor (2004). The sheath can result from a mildly relativisticouter wind that emanates from the accretion disk and confines the inner relativistic jet(Gracia, Tsinganos, & Bogovalov 2005). According to the RM ◦ values in 7, the thickness 16 –of the sheath is higher in the HVP sources with respect to the IVP sources, a situationthat should assist in stronger confinement of the jet of HVP blazars. The latter may helpto explain the finding by J05 that the jet opening angles for quasars are smaller than forBL Lac objects.We have corrected the values of χ and χ in the HVP and IVP sources for Faradayrotation by applying the corrections listed in Table 7 to the EVPAs given in Tables 3 and 4.The adjusted values of the EVPAs are used in the subsequent analysis. In the LVP sources, the core at 7 mm is unpolarized, hence the polarization positionangle of the inner jet is defined by the polarization of VLBI components within a few masof the core. For the epochs shown in Figure 5 these are components C c ∼ t and u at 1-2 mas in 3C 120, and component B λ dependence of χ in 3C 273, which yields a high rotation measure, RM = (1 . ± . × rad m − . The value is consistent with the high rotation measureobtained for component Q /W RM = 2 . × rad m − . However, a significant decrease in the density of theFaraday screen with distance from the core discussed above explains the good alignmentbetween the EVPA at 1 mm and χ jet when components are seen farther downstream. Thisoccurs for 3C 111 and 3C 120: in 3C 111 χ = − ◦ ± ◦ and χ jet = − ◦ ± ◦ ; in3C 120 χ = − ◦ ± ◦ and χ jet = − ◦ ± ◦ . The implication is that the magneticfield in the 1 mm emission region have the same orientation as that in the jet features afew milliarcseconds from the core. Very low polarization in the VLBI core at 7 mm, thehigh rotation measure obtained close to the core in 3C 273, and consistency between thedirection of polarization in the inner jet and at 1 mm in 3C 111 and 3C 120, all suggestthat in the LVP sources the 1 mm and 3 mm cores have low polarization as well. The lowpolarization of the core could be the result of either fine-scale turbulence or depolarizationby a very thick, inhomogeneous foreground screen with RM > × rad m − , as suggestedby Attridge, Wardle, & Homan (2005).The EVPAs of the LVP sources are not corrected for RM owing to the complexitiesdiscussed above. We use simplification that, when strong polarized components are detected,they have left already the high RM zone. 17 –
6. Correlation Analysis6.1. Comparison of Polarization at Different Wavelengths
We have calculated linear coefficients of correlation f p between the polarized flux densi-ties in the core at 7 mm and overall polarized flux density measurements at (1) optical, f po ,(2) 1 mm, f p , and (3) 3 mm, f p . These apply to sources having data from at least threeessentially simultaneous observations at two wavelengths. (Here we consider the observationat two wavelengths “simultaneous” if they are obtained within 2 weeks of each other.) Wedo the same for the correlation coefficients r m of the the degree of polarization in the coreat 7 mm and the overall fractional polarization in each of the other wavebands, using thesame subscript designations. For some sources several measurements have been carried outat high frequencies within two weeks of a few VLBA epochs. In these cases, we use only theobservation that is nearest to the corresponding VLBA epoch. Table 8 contains coefficientsof correlation f po , f p , and f p (columns 2-4) and r mo , r m , and r m (columns 5-7). The numberof points participating in the computation is indicated in parentheses. The coefficients ofcorrelation that are significant at a level ǫ = 0 . § < −
014 or 1510 − §
4) changes the significanceof the correlation. Table 9 shows that including highly polarized components within afew milliarcseconds from the core dramatically improves the correlation in 1) all the LVPsources, 2) two of the HVP sources (CTA 102 and 3C 454.3), and 3) none of the IVP sources.For 3C 279 the correlation coefficient between the 7 mm and 1 mm polarization increases 18 –( r m = 0 . We have computed coefficients of correlation between the degree of polarization andtotal flux density, r λ (listed in Table 10), and between the polarized and total flux densities, f λ (given in Table 11). The coefficients are calculated for each source that has three ormore simultaneous measurements of the two quantities at wavelength λ (in this case theobservations are completely simultaneous). Since the JCMT observations were performed at1.35 mm and 0.85 mm, we have adjusted flux densities and fractional polarization at 0.85 mmto 1.35 mm using the spectral indices α mm and α p mm provided in Table 6. The data at 1 mmare supplemented by the measurements obtained by Nartallo et al. (1998) at 1.1 mm forsources common to both samples: 0420 − r and f correspond tothe VLBI core only.Table 10 reveals that, in general, the total flux density and percentage polarizationare not well correlated. However, at 1 mm the one statistically significant coefficient (forBL Lac) indicates a decrease of fractional polarization when the source brightens, while atoptical, 3 mm, and 7 mm wavelengths the few correlation coefficients that are meaningfulcorrespond to a positive correlation between the total flux density and degree of polarization.An increase of the total flux at mm wavelengths is usually connected with the emergence anew superluminal component from the VLBI core (Savolainen et al. 2002). The componentmight have a different direction of polarization than the core and partially cancel the ob-served polarization, thus leading to a poor correlation between the total flux and degree ofpolarization. Table 11, which lists correlation coefficients between the total and polarizedflux densities, yields a qualitatively different result. Significant coefficients of correlationindicate that the polarized flux density increases as the total flux density rises at all wave-lengths. The correlation occurs for 44%, 47%, 46%, and 77% of sources at optical, 1 mm,3 mm, and 7 mm wavelengths, respectively.Figure 10 shows the dependence between the percentage polarization and total fluxdensity at 1 mm and in the core at 7 mm for HVP and IVP sources. For all 12 sources,the fractional polarization at maximum flux density in the VLBI core exceeds the averagedegree of polarization (dotted line) while at 1 mm eight sources show the inverse relation: thefractional polarization at maximum flux density is lower than the average. The exceptionsare 3C 279, CTA 102, and 3C 454.3, with all having jet components different from the corethat appear to contribute to the emission at 1 mm. 1803+784 is another exception - it has 19 –the smallest range of flux variability at 1 mm.Despite poor correlation between the total flux density and percent polarization, - whichpartially can be affected by complex polarization structure of the mm-wave core region duringejection of a new VLBI component - the data support the inference that the fractionalpolarization at 1 mm tends to decrease when a source brightens. In contrast, in the core at7 mm the degree of polarization rises along with the total flux density. An increase of boththe degree of polarization and polarized flux density as the VLBI core brightens implies thatthe flux increase is accompanied by ordering of the magnetic field in the emission region. Thetwo opposing tendencies seen at 1 mm—lower fractional polarization but higher polarizedflux as the total flux becomes higher—indicate that the flux increases as emission with weaker(but non-zero) polarization becomes prominent.
7. Polarization Position Angle Behavior7.1. Comparison of Polarization Position Angle at Different Wavelengths
For the IVP and HVP sources we have computed values of deviation between opticaland mm-wave EVPAs, ∆ χ λ λ = | χ λ − χ λ | , where λ is the optical wavelength and λ is1 mm, 3 mm, or 7 mm, for measurements obtained within 2 weeks of each other (recall that χ corresponds to the EVPA in the VLBI core). Figure 11 presents the distributions of∆ χ λ λ .Figure 11 shows that the IVP sources possess excellent agreement between polariza-tion position angle at different wavelengths: 87% of ∆ χ o1 (8), 92% of ∆ χ o3 (12), and 90%of ∆ χ o7 (21) fall into the range 0 ◦ –20 ◦ (the number in parentheses indicates the numberof observations). The distribution of ∆ χ o7 for the IVP sources agrees very well with thedistribution of | χ opt − χ core , | obtained by Gabuzda et al. (2006) for 11 BL Lac objectsand 3C 279. This suggests that in the majority of BL Lac objects (i) alignment betweenthe optical polarization position angle and EVPA in the VLBI core at 7 mm is a commonfeature, and (ii) good agreement of the EVPA at different wavelengths from optical to mmwavelengths is expected.For the HVP sources, the result is qualitatively different: 31% of ∆ χ o1 (13), 55% of ∆ χ o3 (11), and 64% of ∆ χ o7 (22) are located within 20 ◦ . The best agreement is observed betweenoptical EVPA and polarization position angle in the core at 7 mm, and between opticaland 3 mm EVPA, while the distribution of ∆ χ o1 indicates significantly larger misalignmentsbetween polarization position angles. 20 –In the LVP sources the EVPA at 7 mm corresponds to χ jet , defined by jet componentswithin a few milliarcseconds of the core. Since the EVPAs are not corrected for rotationmeasure, distributions of ∆ χ λ λ are constructed for all possible pairs of wavelengths (Fig.12). Figure 12 shows that for the LVP sources the best agreement in direction of polarizationoccurs between 1 mm and 7 mm as well as between 3 mm and 7 mm. This result, plus agood correlation between the fractional polarization light curves at these wavelengths foundin § > § We have compared the polarization position angle, χ λ , for each polarization measure-ment with the position angle of the jet projected on the sky, Θ jet (Table 4). Θ jet correspondsto the nearest VLBA epoch to a given polarization measurement. Figure 13 gives the distri-butions of the offsets between direction of polarization and jet axis, | χ λ − Θ jet | , for polarizationmeasured at the different wavelengths, λ , and for the different groups of objects. In the caseof the IVP and HVP sources, χ corresponds to the EVPA in the core; in the LVP group χ is equal to χ jet as defined in §
4. The EVPAs at 3 mm and 7 mm for the HVP and IVPsources are corrected for RM and the distributions at these wavelengths should be similarto that at 1 mm if the RM variability is not significant. It is possible though that the differ-ence in the number of observations at the mm wavelengths can introduce some discrepancybetween the distributions.Figure 13 shows obvious alignment of the electric vector with the jet direction in theIVP sources: 75% of χ opt (36), 59% of χ (56), 76% of χ (29), and 64% of χ (102)lie within 20 ◦ of the inner jet direction (the numbers in parentheses indicate the number ofobservations at each wavelength), although the widest range of offsets is observed at 1 mm. 21 –In contrast, the HVP sources do not show any significant relation between EVPA and jetdirection, and the values of χ λ are distributed almost uniformly from 0 ◦ to 90 ◦ with respect tothe jet direction at all wavelengths. An exception is the distribution at 1 mm, which containstwo peaks at intervals 0 ◦ –20 ◦ and 80 ◦ –90 ◦ , suggesting that there is a preference for the electricvector to lie along or perpendicular to the jet. The difference between the distributions of theIVP and HVP sources is similar to the difference between the distributions of core electricvector offsets from the jet direction found by Lister & Homan (2005) for BL Lac objects andquasars, respectively, in the MOJAVE survey at 2 cm (Monitoring of Jets in AGN with VLBAExperiments). Although our dichotomy is not based simply on the optical classification of anobject, we conclude that this difference persists from cm to optical wavelengths and impliesdifferences in the magnetic fields and/or processes responsible for the polarized emission inthese objects.In the LVP sources the distributions of | χ λ − Θ jet | at optical and 1 mm wavelengths donot support a connection of the EVPA with the jet direction, although the polarization at1 mm seems to avoid being parallel to the jet. The polarization position angle at 3 mm andin the inner jet at 7 mm clearly reveals a preferential direction perpendicular to the jet: 89%of χ (9) and 62% of χ (47) values lie within 70 ◦ –90 ◦ of the jet axis. Although thedistribution at 3 mm is dominated by the observations of 3C 273, all three sources make asignificant contribution in the pronounced peak of the distribution at 7 mm.The properties of polarization position angle with respect to the jet direction are distinctfor each group: good alignment of the electric vector with the jet direction at all wavelengthsin the IVP sources, chaotic behavior of the electric vector in the HVP blazars independentof frequency, and electric vector preferentially transverse to the jet direction in the LVPobjects at 3 mm and in the inner jet at 7 mm. It is noteworthy that the dichotomy at highfrequencies is similar to that found for regions farther out in the jet at lower frequencies(Cawthorne et al. 1993; Lister & Homan 2005).
8. Interpretation8.1. Magnetic Turbulence
Our data are consistent with the assumption that we observe incoherent synchrotronradiation across the wavelength range from optical to mm wavelengths. A uniform magneticfield throughout the emission region yields the maximum possible degree of polarization, m max = ( α + 1) / ( α + 5 /
3) (e.g., Pacholczyk 1970), which is ∼
70% at mm wavelengths( α ∼ .
5, Table 6) and ∼
78% in the optical band ( α ∼ .
4; Impey & Neugebauer 1988). 22 –Such a high degree of polarization has never been observed in a blazar. The polarization canbe significantly reduced if the emission region is turbulent so that it is composed of manycells, each containing a roughly uniform magnetic field that is randomly oriented relativeto that in other cells (Burn 1966; Burch 1979). For N cells within a telescope beam, thefractional polarization is given by the equation (Hughes & Miller 1991): m ≈ m max / √ N ± m max / √ N . (3)The results obtained in §§ h m max λ i ± σ max λ , as well as similar values, h m min λ i ± σ min λ , for the minimumdegree of polarization. The values, given in Table 12, show that both the maximum andminimum degree of polarization increase with frequency except for the LVP group, withinwhich the optical polarization is similar to the polarization in the VLBI core. At a givenfrequency, the fractional polarization is lowest for the LVP objects and highest for the IVPsources, independent of whether the polarization is near the minimum or maximum. We usethe means and standard deviations given in Table 12 and equation (3) to determine whetherthe observed parameters can be derived within a cellular model. Table 12 lists the numberof cells, N maxcell and N mincell , that result in the observed degree of polarization under this model.We can calculate the number of turbulent cells for any degree of polarization; how-ever, the same number should account for the standard deviation as well. We find that thisrequirement is not satisfied at high-polarization states, where the standard deviation is sig-nificantly lower than the model predicts. In low-polarization states, the requirement holds atall wavelengths except 1 mm, where the standard deviations for the LVP and HVP sourcesare slightly lower than expected according to the derived number of cells. This suggests thatthe high-polarization states involve an additional process that provides some order to themagnetic field, while the low-polarization states can be explained within the cellular model.Three interesting consequences follow from analysis of Table 12. First, the observeddifference in degree of polarization among the groups of objects suggests that the emissionregions of the LVP and HVP sources contain more turbulent cells than is the case for IVPobjects – either the cells are finer in the LVP and HVP sources, or the emission regionis smaller in the IVP blazars. Second, the fact that sources within a group have similarfractional polarization at different wavelengths implies that the emitting regions partiallyoverlap. Third, the fact that fractional polarization decreases with wavelength suggests thatthe emitting region is larger at longer wavelengths. 23 –Faraday rotation by a foreground screen can produce depolarization across a beam thatalso results in frequency dependence of the polarization (Burn 1966). However, Faradaydepolarization can not account for the frequency dependence among the groups at opticaland 1 mm wavelengths since the effect is negligible at such short wavelengths. We assumethat turbulence and difference in volume of emission is responsible for the frequency depen-dence at optical and 1 mm wavelengths but the decrease of polarization at longer mm-wavescould be caused by Faraday depolarization. To calculate the frequency dependence of thepolarization we apply a model proposed by Burn (1966), with the simplifications suggestedby Zavala & Taylor (2004): m (%) = m RM=0 | sinc(RM λ ) | , (4)where RM values are rotation measures derived in § RM esti-mates. In this case m RM=0 corresponds to m and is different for each source. Figure14 shows the frequency dependence of the polarization according to the observations andeq. (4). Figure 14 demonstrates that although for some sources (3C 279 and 1803+784)the dependence of the polarization on frequency can be caused by Faraday depolarization,for the majority of the objects the fractional polarization decreases with wavelength muchfaster than eq. (4) predicts. It appears that depolarization from a gradient across the beamin a Faraday screen alone is unable to explain the observed frequency dependence of thepolarization. A difference in the size of the emitting regions and/or in turbulence scale ofthe magnetic field is needed to account for the dependence. A commonly occurring structure that leads to ordering of magnetic fields is a shock,which compresses the component of the magnetic field that lies parallel to the shock front.The significant dichotomy in degree of polarization at high-polarization states among thegroups might then be explained by differences in shock strengths. Lister & Smith (2000)proposed a similar explanation to account for differences in polarization properties of low andhigh optically polarized radio-loud quasars (LPRQs and HPQs, respectively), suggesting thatLPRQs have weaker shocks than do HPQs. We use the Hughes & Miller (1991) approachto estimate the shock strength for the sources in our sample: m ≈ α + 1 α + 5 / × (1 − η − ) sin Θ ′ − (1 − η − ) sin Θ ′ , (5)where η = n shocked /n unshocked and n is the number density of the plasma; Θ ′ is the viewing an-gle of the jet corrected for relativistic aberration: Θ ′ = tan − [sin Θ ◦ / (Γ(cos Θ ◦ −√ − Γ − ))], 24 –where Γ is the bulk Lorentz factor and Θ ◦ is the viewing angle of the jet in the observer’sframe. The use of the viewing angle with respect to the jet axis in the formula applies toa transverse plane-wave shock, and the formula is valid for a shock propagating through aplasma with a completely chaotic magnetic field. The maximum possible polarization shouldbe seen when the shock is viewed along the plane of compression in the frame of the shock(i.e., Θ ′ ≈ ◦ ). Columns 3, 5, 7, and 9 of Table 13 list the values of the estimated shockstrength η based on the maximum observed degree of polarization (columns 2, 4, 6, and 8)at each wavelength. The last column of the table contains the viewing angle Θ ′ in the shockframe, as derived from the values of h Θ ◦ i and h Γ i obtained for each object in J05. Becausewe do not have multi-color data in the optical region, the computation of η adopts α opt / for the value of α opt , while at 1 mm, 3 mm, and 7 mm we use the three-point spectral index α mm derived from all three mm wavelengths (see Table 6).The shock strengths listed in Table 13 are similar among the sources and rather low, η ∼ . − .
2, and hence cannot be the primary reason behind the diversity in degree ofpolarization. Instead, we can explain this by differences in viewing angle relative to theplane of compression, although a very high level of polarization ( m & η ∼ −
3. Note that for 3C 66A J05 find a significant range ofapparent speeds of superluminal components, from 1.5 c to 27 c . We use the Lorentz factor andviewing angle that corresponds to the average of Γ and Θ ◦ derived for the fast componentsonly (Γ=27.8 and Θ ◦ =3.3 ◦ ), because h Γ i and h Θ ◦ i averaged over all components (J05) failsto produce polarization as large as that observed for any given value of η . The latter isthe case for 1823+568 as well. However, for 1823+568 moving components within 1 mas ofthe core were not observed (J05) and the jet parameters are obtained using kinematics oftwo components at ∼ ◦ in the VLBI core of1823+568 might be different from those derived in J05.Figure 15 shows the dependence between bulk Lorentz factor and polarization variabil-ity index. There is a correlation between Γ and V popt ( r =0.53, ǫ = 0 .
1) and between Γ and V p7mm ( r =0.72, ǫ = 0 . V p3mm correlates with Γ ( r =0.42), this correlation is sig-nificant only at a level ǫ > r = − N maxcell at 1 mm is much smaller than at 3 mm and7 mm, in keeping with the model. The partial discrepancy suggests that another emissioncomponent in addition to transverse shocks is prominent at 1 mm. A primary candidate isthe “true” core, i.e., the bright, narrow end of the jet when observed at a wavelength wherethe emission is completely optically thin (Fig. 16). At wavelengths of 3 mm and longer,what appears to be the core is most likely a location at or outside the point where the opticaldepth τ ( ν ) ∼
1. The fact that the optical polarization does show the correlation, as well asthe best alignment of position angle with the electric vector in the core at 7 mm, implies thatmost of the nonthermal optical emission arises in shocks close to the 7 mm core rather thanin the“true” core. This suggests that the “true” core does not possess relativistic electronsenergetic enough to produce the optical synchrotron emission.
In the shock-in-jet model (e.g., Marscher & Gear 1985; Hughes, Aller, & Aller 1985),we expect a correlation between total flux and polarization owing to ordering of the magneticfield in the shocked region if the quiescent jet has a completely chaotic magnetic field.However, if the magnetic field in the unshocked region possesses a component parallel to thejet axis, a transverse shock will enhance the total flux but partially cancel the polarization asit compresses the turbulent component. In this case the polarized flux will at first decreaseas the total flux rises. If the shocked emission grows strong enough that its polarized fluxbecomes greater than the initial polarized flux of the ambient jet, the EVPA will flip by 90 ◦ after a minimum in polarized flux, and the polarized flux will subsequently grow with thetotal flux until the shocked emission weakens. The initial phase of decline in polarized fluxmay easily be missed in observations spaced such as ours. If an oblique shock is responsiblefor an outburst, its effect on the polarization will depend on the angle of the shock frontrelative to the ordered component of the ambient magnetic field, the viewing angle, andthe bulk Lorentz factor of the jet. It is possible, in some cases, for the net polarization toincrease, with the EVPA becoming closer to the position angle of the jet axis on the sky(Hughes 2005).Figure 10 shows that the maximum of degree of polarization in the core at 7 mm tendsto occur when the total flux rises, while at 1 mm the opposite relation is more probable. 26 –An increase of the total flux in the VLBI core is usually connected with the emergence ofa new superluminal component from the optically thick part of the core (see J05). If thesecomponents represent transverse shock formation in the jet, they should display electricvectors aligned with the jet axis. On the other hand, χ at minimum flux might reflectthe magnetic field direction in the unshocked region. Figure 17 ( left panel ) displays thedistributions of misalignment angles between the polarization and inner jet directions attimes of minimum observed flux at 1 mm. Figure 17 ( middle panel ) shows the distributionsof offsets between χ and the local jet direction for each superluminal component listedin Table 5 at the point when we can first separate the knot unambiguously from the coreon the image (i.e., farther downstream than 0.1 mas). Figure 17 ( right panel ) presents thedistribution of degree of polarization in the superluminal knots at their maximum total fluxwhen the separation from the core > < χ with respect to the jet axis is that,despite the high resolution of the 7 mm images, the jet direction at the position where theemission occurs might be different from the direction inferred from the images. The latterimplies that HVP sources possess higher bending of the jets on milliarcsecond scales than doIVP sources. Conical shocks might explain the appearance of stationary features in the jet(G´omez et al. 1997; Daly & Marscher 1988), which are common in the HVP sources (J05).This model suggests that the core at 7 mm does not always represent the emission from thesurface where the optical depth τ is of order unity. Rather, at any given frequency below theturnover in the spectrum, it would be either the τ ∼ τ < B B z , where a degree of polarization p will be obtained as the result of velocity shearin the jet flow. We assume that the magnetic field starts out in a turbulent state with cellsize ∆ x : ∆ z/ ∆ R ≈ Γ N ∆ R p/ (∆ xβ rel ), where Γ N is the bulk Lorentz factor at the northernside of the jet, ∆ R is the half-width of the jet, and β rel is the relative speed between thenorthern and southern sides. In the plasma frame on the northern side (subscript “N”), β rel = ( β S − β N ) / (1 − β N β S ), where β = √ − Γ − . We assume that the Lorentz factorof knot B N = 8 .
3) and the Lorentzfactor of knot B S = 13 . p B1 =4.0%, p B2 =6.2%) whenthe direction of the electric vector is transverse to the jet axis, so we approximate p ∼ ∼ θ = 1 . ◦ andΘ ◦ = 6 . ◦ , respectively). This exercise gives a ratio ∆ R/ ∆ x ∼
40 and size of a turbulent cell∆ x ∼ .
001 pc. For the quasar 3C 273 we have obtained several groups of closely spacedobservations at 3 mm near some VLBA epochs (see Table 3). The data reveal a very shorttimescale (computed according to the definition of Burbidge, Jones, & O’Dell 1974) of thefractional polarization variability at 3 mm, ∆ t var ∼ . x var ∼ .
001 pc, which is consistent with the scale ofturbulence in the magnetic field.In summary, the sources in our sample show significant variety in the distributions ofoffsets between polarization position angle and jet direction. The observed behavior can beexplained within the context of shock waves compressing highly turbulent magnetic fields andvelocity shear stretching field lines along a direction parallel to the axis if the jet structureand kinematics on milliarcsecond scales are taken into account. 29 –
The polarized emission at 1 mm possesses properties distinguished from the other wave-lengths: 1) there is no correlation between fractional polarization variability index andLorentz factor of the jet; 2) the maximum degree of polarization tends to occur when the to-tal flux is lower than average; 3) the standard deviation of the mean of the minimum degreesof polarization over sources in a variability group is lower than expected in the cellular modelof magnetic field structure. An inverse relationship between the degree of polarization andtotal flux is expected in electromagnetically dominated (ED) jets (Lovelace & Romanova2003) if the plasma responsible for a rise in the total flux has a more chaotic magnetic fieldthan that of the ED section. This can be the case even if a shock orders an underlyingturbulent field in the same sense as does the mostly toroidal field in the ED portion of thejet, since the polarization of the ED region should be quite high.The upstream ED model of the jet is a promising scenario since it explains the highLorentz factors of the flow needed to produce the high apparent speeds seen in some blazars.Acceleration of the jet to such high values of Γ is accomplished by conversion of Poyntingflux to flow energy through the Lorentz force that occurs on scales that are much largerthan the gravitational radius of the central black hole (e.g., Vlahakis 2006). The tentativeanticorrelation between total flux and degree of polarization at 1 mm and rather positivecorrelation between the values at 3 mm and in the core at 7 mm suggest that the accel-eration might end between the VLBI cores at 1 mm and 3 mm. In this case the 1 mmemission region should possess a large scale, mostly toroidal, magnetic field component,which in the plane of the sky should lie either transverse or longitudinal to the jet direction(Lyutikov, Pariev, & Gabuzda 2005). This is consistent with the distributions of EVPAs at1 mm with respect to the jet direction in the IVP and HVP sources, in which emission fromthe VLBI core at 1 mm seems to dominate the overall source emission at 1 mm (Fig. 13).If the section of the jet seen at 3 mm and 7 mm is beyond the transition point where thejet becomes mainly hydrodynamical and turbulent, then the polarization behavior at thesewavelengths will be similar to that discussed in §§
9. Summary
We have performed multi-frequency, multi-epoch, quasi-simultaneous linear polarizationobservations of a sample of AGN that possess highly relativistic jets and high levels ofpolarization at 1 mm. We separate the sample into three groups according to the pattern ofvariability of the polarization in the VLBI core at 7 mm. This classification appears to beconnected with physical differences between the objects. However, the sample is small andfuture observations of a larger sample are needed to confirm the findings. The properties ofthe groups are as follows:1) The objects with low variability of polarization (LVP) in the VLBI core unite tworadio galaxies with superluminal speeds on parsec scales and a quasar with low observed op-tical polarization. The LVP sources have measured optical polarization <
2% and radio corepolarization < RM > × rad m − , that cause depolarization of thecore region at mm wavelengths. The optical nonthermal emission is greatly diluted by non-synchrotron components, probably associated with the Big Blue Bump. The parsec-scale jetsare characterized by moderate Lorentz factors, near the low end of the blazar range, and byviewing and opening angles that are larger than those of a typical blazar. The distributionsof EVPAs at 3 mm and in the inner jet at 7 mm with respect to the jet axis reveal a preferredlongitudinal component of the magnetic field that can be explained by velocity shear.2) The sources with intermediate variability of polarization (IVP) in the VLBI coreinclude BL Lac objects and quasars with preferred direction of the electric vector at allwavelengths close to the direction of the inner jet. They possess very high optical polarization( & > α ∼ RM . × rad m − , in the corethat is consistent with the lack of emission lines in the spectra of BL Lac objects owing to arelatively low column density of gas. The radio jets of the IVP sources are highly relativistic,with Γ ≥
10. The alignment of the polarization with the jet at all wavelengths indicates thedominance of a transverse or (in the plasma frame) oblique component of the magnetic field.3) The category of objects with highly variable polarization (HVP) in the VLBI coreconsists of the OVV quasars and the BL Lac object OJ 287. These display strong variationsin both degree and polarization position angle. The very high optical polarization seen inthe IVP sources occurs in the HVP sources, but, in contrast with the IVP blazars, lowpolarization ( < α ∼ RM ∼ × rad m − , implying that the coreis surrounded by dense thermal plasma. The radio jets of the HVP sources have Lorentzfactors at the high-end tail of the blazar distribution. The general misalignment between thepolarization position angle and jet direction indicates that there is little, if any, connectionbetween the two.The diversity of polarization properties of the sources in the sample allows us to estab-lish connections between parameters at different wavelengths. (i) There is good agreementbetween the optical EVPA and that in the VLBI core at 7 mm for the IVP and HVP blazars.(ii) The overall polarization of a source at 1 mm and 3 mm strongly correlates with the de-gree of polarization in the inner jet of the LVP sources. (iii) The EVPA at 1 mm and 3 mmcorresponds to that in the inner jet for the LVP sources. (iv) There is a strong correlationbetween the level of polarization variability in the optical region and in the VLBI core at7 mm. (v) The optical and 7 mm polarization variability indices correlate with the bulkLorentz factor of the radio jets. (vi) The degree of polarization decreases with wavelength.(vii) The distributions of electric vector offsets with respect to the inner jet direction at op-tical and mm wavelengths are similar within each variability group, with distinct differencesamong the three groups.In general, the time variability across the various wavelengths follows the expectationsof models in which rather weak shock waves propagate down a jet containing a turbulentmagnetic field. After taking into account relativistic aberration, we find that the shock frontsgenerally lie at oblique angles to the jet axis.The correlations that we have uncovered tightly link the emission at optical and 3 mmwavelengths to the VLBI core at 7 mm. At 1 mm there is a possible anticorrelation betweentotal flux density and degree of polarization, but not at 7 mm or 3 mm. This suggests thepresence of a well-ordered magnetic field in a region that is optically thick at λ & REFERENCES
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37 –Table 1.
Optical Polarization Data
Source Epoch
F ilt S M ag I opt [mJy]
F ilt m m opt [%] χ opt [ ◦ ](1) (2) (3) (4) (5) (6) (7) (8)3C 66A 1999/02/12 · · · · · · W ± ± V ± ± W ± ± V ± ± W ± ± V ± ± W ± ± V ± ± W ± ± · · · · · · W ± ± V ± ± W ± ± · · · · · · W ± ± V ± ± W ± ± ± ± W ± ± · · · · · · W ± ± · · · · · · W ± ± · · · · · · W ± ± · · · · · · W ± ± · · · · · · W ± ±
38 –Table 2.
JCMT Polarization Data
Source Epoch λ [mm] I [Jy] m [%] χ [ ◦ ](1) (2) (3) (4) (5) (6)3C 66A 1998/05/15 1.35 0.38 ± ± ± ± ± ± ± ± ± ± ±
5) (172 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
53C 111 1998/07/17 1.35 1.03 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
39 –Table 3.
BIMA Polarization Data
Source Epoch I [Jy] m [%] χ [ ◦ ](1) (2) (3) (4) (5)3C 66A 2000/04/21 0.82 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
43C 111 2000/04/04 2.63 ± ± ± ± ± ± ± ± ±
40 –Table 4.
VLBA Polarization Data for the Core
Source Epoch I [Jy] Θ jet [ ◦ ] m [%] χ [ ◦ ](1) (2) (3) (4) (5) (6)3C 66A 1998/03/25 0.52 ± − ± ± ± ± − ± ± ± ± − ± ± ± ± − ± ± ± ± − ± ± ± ± − ± ± ± ± − ± ± − ± ± − ± ± ± ± − ± ± ± ± − ± ± ± ± − ± ± ± ± − ± ± ± ± − ± ± ± ± − ± ± ± ± − ± ± ± ± − ± ± ± ± − ± ± ±
41 –Table 5.
VLBA Polarization Data for the Jet Component
Source Epoch Comp. I comp7mm [Jy] R [mas] Θ[ ◦ ] m comp7mm [%] χ comp7mm [ ◦ ](1) (2) (3) (4) (5) (6) (7) (8)3C 111 1998/03/25 C ± ± ± ± − ± c ± ± ± ± − ± C ± ± ± ± − ± c ± ± ± ± − ± C ± ± ± ± − ± c ± ± ± ± − ± C ± ± ± ± − ± c ± ± ± ± − ± C ± ± ± ± − ± c ± ± ± ± − ± C ± ± ± ± − ± c ± ± ± ± − ± C ± ± ± ± − ± c ± ± ± ± − ± C ± ± ± ± − ± c ± ± ± ± − ± c ± ± ± ± − ± C ± ± ± ± − ± c ± ± ± ± − ± c ± ± ± ± − ± C ± ± ± ± − ± c ± ± ± ± − ± c ± ± ± ± − ± c ± ± ± ± − ± c ± ± ± ± − ± c ± ± ± ± − ± c ± ± ± ± − ±
42 –Table 6.
Total and Polarized Flux Spectral Indices
Source Group α opt / α popt / α mm α pmm (1) (2) (3) (4) (5) (6)3C 111 LVP 0.55 ± ± ± ± ± ± ± − ± ± ± ± ± ± ± ± − ± ± ± ± − ± ± ± ± ± · · · · · · ± ± · · · · · · ± ± ± ± ± ± −
014 HVP 1.00 ± ± ± ± ± ± ± − ± ± ± ± − ± −
089 HVP 0.90 ± ± ± − ± ± ± ± ± ± ± ± − ± α opt / are determined from uncertainties of flux measurements; uncertaintiesfor α mm are based on consistency between different wavelengths
43 –Table 7.
Rotation Measures
Source z Group ∆ χ ∆ χ RM ◦ RM ◦ RM ◦ a deg. deg. 10 rad m − rad m − rad m − − −
16 12 ± · · · · · · · · ·
3C 279 0.538 IVP − −
16 14 ± − ± − − ± · · · − ∗ (3) 1.61803+784 0.68 IVP − −
16 12 ± · · · − ± ± − −
16 6.7 ± ± −
014 0.915 HVP 4 19 − ± · · · · · · · · · − −
87 280 ± · · · − ± · · · · · · · · · −
089 0.361 HVP − −
38 26 ± · · · · · · · · · CTA 102 1.037 HVP 18 97 − ± · · · − ∗ (4) 1.63C 454.3 0.859 HVP − −
19 24 ± · · · RM correction at 3 mm; (5)- RM correction at 7 mm, (6) - intrinsic rotation measure obtainedin the 43 GHz core; (7) - intrinsic rotation measure obtained in the 15 GHz core; (8) - intrinsic rotationmeasure obtained in the 8 GHz core; ∗ - intrinsic rotation measure obtained in the core at 5 GHz instead of8 GHz; numbers in parentheses denote references for RM ◦ measured at low frequencies: 1 - Zavala & Taylor(2003), 2 - Gabuzda et al. (2006), 3 - Taylor (1998), 4 - Taylor (2000); (9) - the exponent in the relation RM ∝ d − a .
44 –Table 8.
Correlation Coefficients between Polarization in the Core at 7 mmand Overall Polarization at Optical, 1 mm, and 3 mm Wavelengths
Source f po f p f p r mo r m r m (1) (2) (3) (4) (5) (6) (7)3C 66A · · · (1) · · · (0) · · · (2) · · · (0) · · · ( 0) · · · (0)0420 −
014 0.67 (4) · · · (1) 0.72 (5) 0.55 ( 4) · · · (1)3C 120 · · · (1) · · · ( 2) · · · (1) · · · (1) · · · ( 2) · · · (1)0528+134 · · · (1) − − · · · (1) − − · · · (1) · · · ( 2) · · · (2) · · · (1) · · · ( 2) · · · (2)3C 279 0.31 (5) 0.34 ( 9) − · · · (1) 0.79 ( 5)
3C 345 − − · · · (0) − − · · · (0) − · · · (0) 0.29 ( 5) 0.76 (4) − BL Lac − − CTA 102 − − · · · (2) − − − − − ǫ =0.1; integers in parentheses indicate number of observations. Table 9.
Correlation Coefficients between Polarization in the Inner Jet at7 mm and Overall Polarization at 1 mm and 3 mm
Source f p ′ f p ′ r m ′ r m ′ (1) (2) (3) (4) (5)3C 111 0.25 ( 7) · · · (2) · · · (2)3C 120 · · · (1) · · · (1)3C 273 CTA 102
3C 454.3 0.36 (13) 0.22 (3)
45 –Table 10.
Correlation Coefficients between Degree of Polarization and TotalFlux Density
Source r opt r r r (1) (2) (3) (4) (5)3C 66A 0.08 (6) −
3C 111 · · · (1) − · · · ( 0)0420 − − · · · ( 1)
3C 120 · · · (2) − · · · ( 2) · · · ( 2)0528+134 · · · (1) − − − − − − − − − · · · (2) − − − − · · · (0) 0.11 ( 6) − · · · (0) 0.00 ( 8) − − − − − − Table 11.
Correlation Coefficients between Polarized and Total Flux Density
Source f opt f f f (1) (2) (3) (4) (5)3C 66A 0.61 (6) 0.12 (11)
3C 111 · · · (1) 0.24 (10) 0.15 ( 3) · · · ( 0)0420 − · · · ( 1)
3C 120 · · · (2) 0.05 ( 8) · · · ( 2) · · · ( 2)0528+134 · · · (1) 0.32 (11) − OJ 287
3C 273 0.21 (6) − · · · (2) 0.03 ( 5) · · · (0) 0.26 ( 6) − · · · (0) BL Lac − CTA 102 −
3C 454.3 0.63 (3)
46 –Table 12.
Average Values of Fractional Polarization
Group Opt 1 mm 3 mm 7 mmLVP h m max i [%] 1.4 ± ± ± ± N maxcell h m max i [%] 11.4 ± ± ± ± N maxcell
47 66 510 136IVP h m max i [%] 29.0 ± ± ± ± N maxcell h m min i [%] 0.4 ± ± ± ± N mincell h m min i [%] 1.7 ± ± ± ± N mincell h m min i [%] 10.6 ± ± ± ± N mincell
54 306 480 1225Note. — Values in parentheses indicate standard deviations expected from the cellular model with numberof cells derived from the fractional polarization; see text
Table 13.
Derived Shock Strength
Source m maxopt [%] η opt m max1mm [%] η m max3mm [%] η m max7mm [%] η Θ ′ [ ◦ ](1) (2) (3) (4) (5) (6) (7) (8) (9) (10)3C 66A 29.7 1.94 36.4 3.20 9.3 1.21 7.7 1.17 116.03C 111 3.1 1.05 12.2 1.22 2.3 1.04 0.5 1.01 108.30420 −
014 26.2 1.81 7.5 1.18 0.5 1.01 3.3 1.07 59.83C 120 0.5 1.01 11.1 1.30 2.1 1.05 1.1 1.02 124.50528+134 7.0 1.15 12.1 1.32 1.4 1.03 5.4 1.12 57.0OJ 287 15.6 1.24 6.9 1.11 4.0 1.06 5.0 1.08 85.33C 273 0.5 1.01 7.2 1.11 4.0 1.06 1.6 1.02 96.83C 279 39.2 3.49 10.9 1.30 13.7 1.40 6.9 1.17 59.21510 −
089 4.1 1.06 9.7 1.15 4.8 1.07 9.7 1.15 83.63C 345 38.3 1.78 11.4 1.18 8.1 1.13 9.6 1.15 82.71803+784 · · · · · · −− −−
47 –Fig. 1.— Degree of polarization at optical, 1 mm, and 3 mm wavelengths from the wholesource vs. degree of polarization measured in the VLBI core at 7 mm for the most nearlysimultaneous pair of observations for each source. The linear coefficient of correlation, r ,is given in each panel. Symbols denote the quasars (open circles), BL Lac objects (filledcircles), and radio galaxies (triangles). 48 –Fig. 2.— Left panel:
Dependence between polarization variability index at optical, 1 mm,and 3 mm wavelengths and polarization variability index in the VLBI core at 7 mm.
Rightpanel:
Dependence between polarization position angle variability index at optical, 1 mm,and 3 mm wavelengths and polarization position angle variability index in the VLBI core at7 mm. The symbols are the same as in Fig. 1. 49 –Fig. 3.— Connection between polarization and position angle variability indices in the VLBIcore at 7 mm. Symbols denote the quasars (open circles), BL Lac objects (filled circles), andradio galaxies (triangles) . 50 –Fig. 4.— Distributions of degree of linear polarization in the IVP ( left ), HVP ( middle ), andLVP ( right ) variability groups at optical, 1 mm, and 3 mm wavelengths and in the VLBIcore at 7 mm. 51 –Fig. 5.— Total (filled circles) and polarized (filled triangles) flux density spectra and polar-ization position angle (crosses) measurements from optical to 7 mm wavelengths. 52 –Fig. 6.— Dependence between polarized and total flux spectral indices calculated betweenthe optical and 1 mm wavelengths (open circles - HVP sources, filled circles - IVP sources,triangles - LVP sources). 53 –Fig. 7.— Dependence of polarization position angle on square of wavelength in the IVPand HVP sources. Solid line represents approximation of the dependence by a λ Faradayrotation law. 54 –Fig. 8.— Distributions of offsets between EVPAs at 3 mm and in the 7mm core before the RM correction ( left panel ) and after the RM correction ( right panel ). The distributions donot include the observations used to calculate the RM . 55 –Fig. 9.— Dependence of polarization position angle on square of wavelength in 3C 273. Solidline represents approximation of the dependence by a λ Faraday rotation law. 56 –Fig. 10.— Fractional polarization vs. total flux density at 1 mm from the whole source andin the core at 7 mm. Filled circles correspond to our observations and triangles repesent thedata at 1.1 mm from Nartallo et al. (1998). 57 –Fig. 11.— Distributions of offsets between EVPAs for simultaneous observations at differentwavelengths in the IVP and HVP sources. 58 –Fig. 12.— Distributions of offsets between EVPAs for simultaneous observations at differentwavelengths in the LVP. The polarization position angle at 7 mm corresponds to the EVPAin the inner jet. 59 –Fig. 13.— Distributions of offsets between polarization position angle and jet direction. 60 –Fig. 14.— Dependence of degree of polarization on wavelength in the IVP (left panel)and HVP (right panel) sources. Solid lines represent the expected Faraday depolarizationaccording to eq. 4 and RM derived in § Left panel:
Distributions of offsets between polarization position angle at 1 mmand inner jet at minimum flux observed at 1 mm in each source.
Middle panel:
Distributionsof offsets between polarization position angle at 7 mm and local jet direction for superlu-minal knots listed in Table 5.