The Jets of AGN as giant co-axial cables
aa r X i v : . [ a s t r o - ph . GA ] D ec Astronomy&Astrophysicsmanuscript no. Gabuzda-AA-Dec2017 c (cid:13)
ESO 2017December 25, 2017
The jets of AGN as giant coaxial cables.
Denise C. Gabuzda, Matt Nagle and Naomi Roche Dept. of Physics, University College Cork, Cork, Ireland.Email: [email protected] ; accepted
ABSTRACT
Context.
The currents carried by the jets of active galactic nuclei (AGNs) can be probed using maps of the Faraday rotation measure(RM), since a jet current will be accompanied by a toroidal magnetic field, which will give rise to a systematic change in the RMacross the jet.
Aims.
The aim of this study is to identify new AGNs displaying statistically significant transverse RM gradients across their parsec-scale jets, in order to determine how often helical magnetic fields occur in AGN jets, and to look for overall patterns in the implieddirections for the toroidal field components and jet currents.
Methods.
We have carried out new analyses of Faraday RM maps derived from previously published 8.1, 8.4, 12.1 and 15.3 GHzdata obtained in 2006 on the NRAO Very Long Baseline Array (VLBA). In a number of key ways, our procedures were identicalto those of the original authors, but the new imaging and analysis di ff ers from the original methods in several ways: the techniqueused to match the resolutions at the di ff erent frequencies, limits on the widths spanned by the RM gradients analyzed, treatment ofcore-region RM gradients, approach to estimation of the significances of the gradients analyzed, and inclusion of a supplementaryanalysis using circular beams with areas equal to those of the corresponding elliptical naturally weighted beams. Results.
This new analysis has substantially increased the number of AGNs known to display transverse RM gradients that mayreflect the presence of a toroidal magnetic-field component. The collected data on parsec and kiloparsec scales indicate that thecurrent typically flows inward along the jet axis and outward in a more extended region surrounding the jet, typical to the currentstructure of a co-axial cable, accompanied by a self-consistent system of nested helical magnetic fields, whose toroidal componentsgive rise to the observed transverse Faraday rotation gradients.
Conclusions.
The new results presented here make it possible for the first time to conclusively demonstrate the existence of a preferreddirection for the toroidal magnetic-field components — and therefore of the currents — of AGN jets. Discerning the origin of thiscurrent–field system is of cardinal importance for understanding the physical mechanisms leading to the formation of the intrinsic jetmagnetic field, which likely plays an important role in the propagation and collimation of the jets; one possibility is the action of a“cosmic battery”.
Key words. accretion, accretion disks—galaxies: active—galaxies: jets—galaxies: magnetic fields—magnetic fields
1. Introduction
Active galactic nuclei (AGNs) release vast amounts of energy,whose ultimate source is a supermassive black hole in the galac-tic nucleus. In so-called radio-loud AGNs, two relativistic jetsof plasma emanate from the nucleus, presumably along the rota-tional axis of the black hole. The radio emission is synchrotronradiation, and can be linearly polarized up to about 75% in op-tically thin regions with uniform magnetic fields, with the polar-ization angle χ orthogonal to the projection of the magnetic field B onto the plane of the sky (Pacholczyk 1970).Very Long Baseline Interferometry (VLBI) yields radio im-ages with very high resolution, corresponding to linear sizes ofthe order of a parsec at the typical distances of AGNs. A struc-ture with a compact “core” at one end and a jet extending awayfrom it predominates for radio-loud AGNs. The VLBI jets arevirtually always one-sided, due to the relativistic aberration ofthe radiation in the forward direction of the jets’ motion: one jetapproaches the Earth and is highly boosted, while the recedingjet is highly de-boosted.A theoretical picture of the basic nature of this core–jet struc-ture was proposed by Blandford & K¨onigl (1979), in which the“core” observed with VLBI corresponds to the “photosphere” of the jet, where the optical depth is near unity, τ ≈
1, and thejet material makes a transition from optically thick to opticallythin. Although the orientation of the observed polarization an-gle rotates 90 ◦ to become parallel to the synchrotron B field insu ffi ciently optically thick regions, this transition does not occuruntil an optical depth of τ ≈
6, so that the polarized emissionobserved in all regions, including the VLBI core, is e ff ectivelyexpected to be optically thin (Cobb 1993, Wardle 2018).Multi-frequency VLBI polarization observations provide in-formation about the wavelength dependence of the parsec-scalepolarization. One example is Faraday rotation occurring alongthe line of sight between the emitting region and the observer.Faraday rotation is a rotation of the observed linear polariza-tion that arises when the associated electromagnetic wave passesthrough a region with free electrons and a non-zero B field com-ponent along the line of sight. The simplest case corresponds tothe situation when this mechanism operates in regions of “ther-mal” (non-relativistic or only mildly relativistic) plasma outsidethe emitting region, when the rotation is given by χ obs − χ o = e λ π ǫ o m c Z n e B · d l ≡ RM λ , (1) where χ obs and χ o are the observed and intrinsic polarizationangles, respectively, − e and m are the charge and mass of theparticles giving rise to the Faraday rotation, usually taken to beelectrons, c is the speed of light, n e is the density of the Faraday-rotating electrons, B is the magnetic field, d l is an element alongthe line of sight, λ is the observing wavelength, ǫ o is the permit-tivity of free space, and the coe ffi cient of λ is called the RotationMeasure, RM (e.g., Burn 1966). The action of such “external”Faraday rotation can be identified using simultaneous multifre-quency observations, through its linear λ dependence, allowingthe determination of both the RM (which reflects the electrondensity and line-of-sight B field in the region of Faraday rota-tion) and χ o (the intrinsic direction of the source’s linear polar-ization, and hence the synchrotron B field, projected onto theplane of the sky).Many theoretical studies and simulations of the relativisticjets of AGNs have predicted the development of a helical jet B field, which essentially comes about due to the combination ofthe rotation of the central black hole and its accretion disk andthe jet outflow; Tchekovskoy and Bromberg (2016) provide arecent example. Researchers have long been aware that the pres-ence of a helical jet B field could give rise to a regular gradientin the observed RM across the jet, due to the systematic changein the line-of-sight component of the helical field (Perley et al.1984, Blandford 1993). Statistically significant transverse RMgradients across the parsec-scale jets of an increasing numberof AGNs have been reported in the literature over the past sev-eral years (Gabuzda et al. 2014, 2015b, 2017), and have been in-terpreted as reflecting the systematic change in the line-of-sightcomponent of a toroidal or helical jet B field across the jets (a he-lical B field includes both toroidal and poloidal components; it isthe toroidal component that gives rise to the transverse RM gra-dient). Basic physics leads to the conclusion that these jets carrycurrents, whose direction can be inferred from the direction ofthe toroidal B field component giving rise to the transverse RMgradients.Because the relativistic jets of AGNs are typically very nar-row structures, it is important to verify that RM structures acrossjets that are not well resolved in the transverse direction are re-liable. As has been discussed earlier by Gabuzda et al. (2015b),the Monte Carlo simulations of Hovatta et al. (2012), Mahmud etal. (2013) and Murphy and Gabuzda (2013) have demonstratedthat, for RM maps made at wavelengths in the range 2–6 cm, theprobability that an individual RM gradient with a significance ofabout 3 σ or more is spurious is less than 1%, even when the ob-served width of the RM distribution across the jet is comparableto the resolution (beam size). These simulations also showed thatRM gradients with significances of 2 − σ can also be consid-ered trustworthy if they span at least two beam widths, or if theyare observed at two or more epochs. In addition, simulated RMgradients remained visible even when the intrinsic jet width wasmuch less than the beam width (Mahmud et al. 2013; Murphyand Gabuzda 2013).These results led to a series of analyses (Mahmud et al. 2013;Gabuzda et al. 2014, 2015b, 2017) focusing on (i) monotonicityof the RM gradients, (ii) the range of values encompassed by thegradients relative to the uncertainties in the RM measurementsand (iii) steadiness of the change in the RM values across thejet (ensuring an apparent “gradient” is not due only to values ina few edge pixels). These were taken to be the key factors indetermining the trustworthiness of an RM gradient, that is, theprobability that it is not spurious. These were all based on dataobtained with the Very Long Baseline Array (VLBA) at varioussets of frequencies between 4.6 GHz and 15.3 GHz, and include both reanalyses of data for previously published RM maps andthe publication of new RM maps. One key motivation for thesestudies was the need for a meaningful statistical analysis of thedirections of the detected transverse RM gradients, that is, thedirections of the toroidal B -field components, and thus of thedirections of the currents carried by AGN jets. Table 1: Integrated RM valuesSource Taylor et al. (2009) Hovatta et al. (2012)Int. RM (rad / m ) Int. RM (rad / m )0059 + − . ± . − . + − . ± . − . + + . ± . + . − + . ± . + . + + . ± . + . +
398 1 . ± . − . − − . ± . + −
140 17 . ± . + . +
476 22 . ± . + . − − . ± . − . +
812 80 . ± . − . − − . ± . − . +
343 14 . ± . + . +
399 18 . ± . + . − − . ± . − . + − . ± . − . −
038 * + . + − . ± . − .
5* No entry is given for this RM by Taylor et al. (2009;the value given by Simard–Normandin et al. (1981) is − ± / m , consistent with the value ofHovatta et al. (2012). Section 2 describes the observations and data reduction proce-dures used, in particular how these are the same as and di ff erfrom those applied by Hovatta et al. (2012). The results are pre-sented in Section 3, and discussed in Section 4. Our conclusionsare summarized in Section 5.
2. Observations and data reduction
We carried out new analyses of the data used to produce theFaraday RM maps previously published by Hovatta et al. (2012).These observations were obtained at 8.1, 8.4, 12.1 and 15.3 GHzin 2006 on the NRAO Very Long Baseline Array (VLBA).The self-calibrated visibility data were downloaded from theMOJAVE project website ; information about all steps of thecalibration and initial imaging can be found in Hovatta et al.(2012).We carried out the following aspects of our analysis in thesame way as Hovatta et al. (2012): Image alignment.
We aligned the polarization-angle imagesat the di ff erent frequencies by determining the shifts between thecorresponding intensity images required to align their optically http: // / MOJAVE / / beam) contour (%) (mas) (mas) (deg)0059 +
581 2.89 0125 1.40 1.20 49.80059 +
581 2.88 0125 1.30 1.30 00133 +
476 0.951 0.250 1.39 1.17 − +
476 0.954 0.250 1.28 1.28 00212 +
735 3.01 0.250 1.28 1.22 43.80212 +
735 3.01 0.250 1.25 1.25 00403 −
132 1.38 0.250 2.49 1.03 0.50403 −
132 1.37 0.250 1.60 1.60 00446 +
112 1.61 0.250 2.15 1.03 − +
112 1.66 0.250 1.49 1.49 00552 +
398 3.36 0.125 1.56 1.13 − +
398 3.45 0.125 1.33 1.33 00834 −
201 2.78 0.250 2.79 0.87 − −
201 2.98 0.250 1.56 1.56 00859 −
140 0.627 1.00 2.91 1.01 − −
140 0.601 1.00 1.71 1.71 00955 +
476 1.43 0.250 1.48 1.21 1.70955 +
476 1.44 0.250 1.34 1.34 01124 −
186 1.26 0.250 2.90 0.94 − −
186 1.26 0.250 1.65 1.65 01150 +
812 1.36 0.250 1.22 1.16 3.11150 +
812 1.36 0.250 1.19 1.19 01504 −
166 0.981 0.250 2.79 0.86 − −
166 0.868 0.500 1.55 1.55 01611 +
343 3.58 0.500 1.64 1.14 1.51611 +
343 3.54 0.500 1.37 1.37 01641 +
399 1.99 0.500 1.59 1.15 4.71641 +
399 2.06 0.500 1.35 1.35 01908 −
201 2.80 0.250 2.68 0.93 1.41908 −
201 2.82 0.250 1.58 1.58 02005 +
403 0.843 0.500 1.78 1.26 21.42005 +
403 0.863 0.500 1.50 1.50 02216 −
038 1.852 0.250 2.42 0.98 − −
038 1.854 0.250 1.54 1.54 02351 +
456 0.978 0.500 1.60 1.12 18.52351 +
456 1.005 0.500 1.34 1.34 0 thin regions, in our case using a cross-correlation method (Croke& Gabuzda 2010).
Treatment of polarization-angle calibration errors.
Wedid not include the systematic errors due to the absolutepolarization-angle calibration when searching for significantRM gradients, since these cannot give rise to spurious RM gra-dients (Mahmud et al. 2009, Hovatta et al. 2012).
Error estimation.
We applied the improved error estimationformula of Hovatta et al. (2012) to determine the uncertainties inthe polarization angles in individual pixels.
Treatment of Galactic Faraday Rotation.
We took intoaccount the estimated Faraday rotation occurring in our ownGalaxy in the direction toward a source when significant, in or-der to better estimate the RM distribution in the immediate vic-nity of the source.Our imaging and RM analysis di ff ers from that of Hovatta etal. (2012) in the following ways: Technique used to match resolution.
Hovatta et al. (2012)edited out the shortest baselines at the higher frequencies and thelongest baselines at the two lower frequencies and used only therange of baselines common to all four datasets. In contrast, be-cause the range of frequencies analyzed is not large, we used allavailable baselines, but ensured that the images at the di ff erentfrequencies were compared using a common beam (correspond-ing to the lowest frequency). Widths spanned by RM gradients.
Hovatta et al. (2012)only searched for transverse RM gradients in RM distributionsspanning more than about 1.5 beamwidths across the VLBI jet.Guided by the Monte Carlo simulation results described above(Hovatta et al 2012, Mahmud et al. 2013, Murphy & Gabuzda2013), we placed no formal limit on the width spanned by anRM gradient (although in practice only 4 of the 18 significantRM gradients we have detected are less than 1 beam width, andall are greater than 0.75 beam widths).
Treatment of core-region RM gradients.
Hovatta et al.(2012) did not consider potential transverse RM gradients inthe vicinity of the VLBI core, on the grounds that this regionwas at least partially optically thick, increasing the possibilityof spurious gradients. This issue has been discussed in a num-ber of recent studies (Motter & Gabuzda 2017, Gabuzda et al.2017, Wardle 2018). Because the expected 90 ◦ “flip” in the po-larization angle in the transition from the optically thin to theoptically thick regime does not occur until an optical depth of τ ≃
6, which is far upstream of the observed VLBI core region,there is no reason to expect severe departures from a linear λ law for the Faraday rotation in the vast majority of cases, andwe, like a number of earlier studies (Gabuzda et al. 2014, 2015b,2017; Motter & Gabuzda 2017), therefore analyzed core-regionRM gradients in the same way as those located in the jet, havingverified an absence of appreciable deviations from a λ law. Estimation of significance.
Hovatta et al. (2012) took thesignificance of an RM gradient to be the absolute value of thedi ff erence in RM values at the two ends of the gradient dividedby the largest RM error at the edge of the jet (without includ-ing the systematic error due to the absolute polarization-anglecalibration, which cannot give rise to spurious RM gradients, aswas noted above (Mahmud et al. 2009, Hovatta et al. 2012)). Weused a somewhat more conservative approach to calculating thesignificance of gradients, by comparing the absolute value of theRM di ff erence across a gradient with the square root of the sumof the errors on the two RM values added in quadrature: σ = | RM − RM | q σ + σ . (2)Roughly speaking, our significances will usually be lowerthan those of Hovatta et al. (2012), by up to about a factor of √
2. We note that in both of these approaches, the RM valuesconsidered will be near the edges of the RM maps, where theuncertainties are highest, so that both approaches are inherentlyconservative.
Supplementary analysis using circular beams.
We consid-ered versions of all the RM maps convolved using circular beamswith areas equal to those of the natural-weighted elliptical beams(i.e., the radius of the circular beam was R = √ ( BMAJ )( BMIN ),where
BMAJ and
BMIN are the major and minor axes of theelliptical beam), as has been discussed in some earlier studies(Gabuzda et al. 2017, Motter & Gabuzda 2017). This helped testthe robustness of gradients present in the RM maps made usingthe elliptical beams, and in some cases helped clarify the direc-tion of a gradient relative to the local jet direction.The observed Faraday rotation occurs predominantly in twolocations: in the immediate vicinity of the AGN and in our ownGalaxy. The latter “Galactic” RM must be estimated and re-moved if we wish to identify Faraday rotation occurring in thevicinity of the AGN itself. Low-resolution, low-frequency inte-grated RM measurements will generally be dominated by this
Galactic RM component, which is uniform across the sourceon milliarcsecond scales, and it is usually supposed that suchlow-frequency, low-resolution (compared to the VLBI images)integrated RM measurements provide a good estimate of theGalactic RM, although they will formally include some contribu-tion from plasma in the vicinity of the source as well. Consistentwith the approach adopted in the previous studies consideredhere (Gabuzda et al. 2014, 2015b, 2017), we used the inte-grated RM measurements of Taylor et al. (2009) at the posi-tions of the sources considered directly; these values, given inTable 1, are based on the VLA Sky Survey (NVSS) observa-tions at two bands near 1.4 GHz. The integrated RMs for mostof these AGNs are low, less than about 30 rad / m in absolutevalue; this is smaller than the typical uncertainties in the RMvalues measured in our maps, and we did not remove the ef-fect of these small integrated RM values. Six of the objects havehigher integrated RMs, ranging in absolute value from 80 rad / m to 175 rad / m , and we removed these integrated RMs from allvalues in the RM maps for these two sources. We note that thisprocedure is slightly di ff erent to the approach of Hovatta et al.(2012), who removed the average RM from the vicinity of thesource on the sky based on the overall RM image of Taylor et al.(2009), rather than the value at the position of the source itself.This leads to small di ff erences in the ranges of our RM mapsfor these six sources compared to the previously published RMmaps (Hovatta et al. 2012), although the maps are very simi-lar overall. The Galactic RM values estimated by Hovatta et al.(2012) and subtracted from their own initial RM maps are alsogiven in Table 1.We tested the derived shifts between images at the di ff er-ent frequencies by making spectral-index maps after applyingthese shifts in order to verify that they did not show any spuri-ous features that could be due to residual misalignment. We alsochecked for broad consistency with the shifts derived earlier forthese same data (Pushkarev et al. 2012). Hovatta et al. (2012)also noted that their analyses confirmed that the appearance ofthe spectral-index maps provides a good test of the correctnessof the relative alignment of the images at the various frequencies.Hovatta et al. (2012) made RM maps for a sample of 191extragalactic radio sources, but due to the limits they imposedon their analysis of possible transverse RM gradients, they onlywere able to identify transverse RM gradients that satisfied theircriteria in four sources. We visually inspected each of their 191maps and identified for analysis 38 sources that showed possibletransverse RM gradients by eye. For each of these, we recon-structed the RM maps using the methods described above andtook RM slices in any region potentially displaying transverseRM gradients, applying the new error estimation approach ofHovatta et al. (2012) to estimate the RM uncertainties in indi-vidual pixels as input to our estimate of the significances of anyRM gradients analyzed.We detected statistically significant, monotonic transverseRM gradients across the jets of 18 of the 38 sources investigated,which are considered further below. The main factors contribut-ing to the larger number of such transverse RM gradients wewere able to detect, compared to the much smaller number re-ported by Hovatta et al. (2012), was the exclusion by Hovattaet al. (2012) of transverse RM gradients arising within one beamwidth of the core, and spanning less than 1.5 beam widths acrossthe jet.
3. Results
This paper represents the culmination of a series of studies car-ried out by Gabuzda et al. (2014, 2015a, 2017). Here, we presentthe results of a reanalysis of data used to produce the RM imagespreviously published by Hovatta et al. (2012), based on VLBAdata at 8.1, 8.4, 12.1 and 15.3 GHz, together with an overall sta-tistical analysis for the collected results for transverse RM gra-dients across parsec-scale RM jets.Our analysis of the 38 candidate AGNs with transverse RMgradients from among the overall sample of 191 sources fromthe study of Hovatta et al. (2012) indicated that 18 of theseAGNs have firm, monotonic transverse RM gradients (signifi-cances of 2 . σ or greater, corresponding to a probability of oc-curring by chance of no more than 0.5%). Figure 1 presents 8.1-GHz intensity maps made with the nominal, naturally weightedelliptical beams with the corresponding RM distributions super-posed (left), the corresponding intensity and RM maps made us-ing equal-area circular beams (middle), and slices taken alongthe lines drawn across the RM distributions in the middle pan-els (right). These maps are all based on the 8.1–15.2 GHz dataof Hovatta et al. (2012); information about the map peaks andbottom contours and the beam sizes is given in Table 2.All 18 of these AGNs display statistically significant trans-verse RM gradients across their jets, consistent with these jet B fields having significant toroidal components, possibly asso-ciated with helical jet B fields. Transverse RM gradients are de-tected in 13 of these AGNs for the first time, while the remaining5 cases correspond to AGNs in which transverse RM gradientshave been observed previously.We note that, in large source samples, a small number ofspurious 3 σ gradients can appear purely by chance. In a sampleof 191 sources, with the probability that a 3 σ gradient is spuriousbeing no larger than about 1%, we would expect no more thanone or two such cases. Thus, it is possible that one or two of the18 transverse RM gradients we have identified are spurious; thus,the vast majority of the statistically significant transverse RMgradients we have detected in these data represent real physicalgradients, and the number of possible spurious gradients is toosmall to a ff ect our overall results.
4. Discussion
A list of our 13 new and 5 confirmed transverse RM gradientstogether with all other known statistically significant transverseRM gradients on parsec scales from the literature (based on 5–15 GHz and 8–15 GHz RM maps) is given in Table 3. We notethat the other AGNs analyzed to obtain these collected results arecontained in subsamples of the 191 AGNs considered by Hovattaet al. (2012), each containing no more than 40 AGNs, making itunlikely that a significant number of the gradients detected inthose samples are spurious. Thus, we expect overall that at mosttwo of the transverse RM gradients listed in Table 1 are spurious.The key importance of these new results is that they appre-ciably increase the total number of AGNs in which firm trans-verse RM gradients have been found, raising this number to 52,enabling for the first time a reliable statistical analysis of the di-rections of these transverse RM gradients on the sky; that is, thedirections of the jet currents implied by the toroidal B field com-ponents giving rise to the RM gradients. Five of these 52 sourcesshow time variability in the directions of their transverse FaradayRM gradients, and so cannot be used straightforwardly in such † CommentsFirm, ≥ . σ or confirmed0059 +
581 * Out Reversal0133 +
476 * Out0212 +
735 G17,* In Reversal0256 +
075 G15b In0300 +
470 G17 In0305 +
039 G17 In0333 +
321 G14 In0355 +
508 G15b Out0403 −
132 * In Possible reversal0415 +
379 G17 In0430 +
052 Go11 In0446 +
112 * Out0552 +
398 * In0716 +
714 M13 In Reversal0735 +
178 G15b In0738 +
313 G14 Out0745 +
241 G15b In0748 +
126 G15b In0820 +
225 G15b In0823 +
033 G15b Out0834-201 * Out0859-140 * In Reversal0923 +
392 G14 In Reversal0945 +
408 G17 In0955 +
476 * In1124-186 * In1156 +
295 G15b In1218 +
285 G15b In1226 +
023 H12 Out1334 −
127 G15b Out1502 +
106 G17 Out1504-166 * In1611 +
343 G17,* Out1633 +
382 G14 In1641 +
399 *,MG17 In1652 +
398 G15b Out1749 +
096 G15b In1749 +
701 M13 In Reversal1807 +
698 G15b In1908-201 * In2007 +
777 G15b Out2037 +
511 G14 In Reversal2155 −
152 G15b In2216-038 * In2230 +
114 H12 In2345 −
167 G14 Out2351 +
456 * InSignificant RM Gradients Showing Time Variability0836 +
710 G14,MG171150 +
812 G14,* Possible reversal1803 +
784 M092005 +
403 G17,*2200 +
420 G17,MG17G14 = Gabuzda et al. 2014; G15b = Gabuzda et al. 2015b; G17 = Gabuzda et al. 2017; Go11 = G´omez et al. 2011; H12 = Hovattaet al. 2012; M09 = Mahmud et al. 2009; M13 = Mahmud et al.2013; MG17 = Motter & Gabuzda 2017; * = this paper; † Current corresponding to direction of innermostgradient is given for sources displaying reversals. an analysis (we will discuss a possible origin for this variabilitybelow).Among the 47 sources for which the available data show noevidence of time variability, the transverse RM gradients in 33imply inward jet currents and those in the remaining 14 outward jet currents. The probability of this asymmetry coming about bychance can be estimated using a simple analysis based on a bi-nomial probability distribution: the probability of obtaining N in inward currents and N out outward currents in a total of N in + N out jets by chance, if the probabilities of each of these jets havinginward or outward current are both equal to 0.5, is P chance = ( N in + N out ) ( N in + N out )! N in ! N out ! . (3)With N in =
33 and N out =
14, this yields a probability of0 . . ff ect.This asymmetry was in fact noted earlier by Contopoulos etal. (2009), but their analysis was marred by a lack of estimates ofthe significances for the 29 transverse RM gradients considered,which were found from a purely visual inspection of RM mapsin the literature. This cast substantial doubt over those results.This has been remedied by the analysis of the collected resultspresented here: in the course of the analyses leading to the re-sults listed in Table 3, the significances of all 29 potential RMgradients identified earlier by Contopoulos et al. (2009) by eyewere checked: of these 29 RM gradients, 22 proved to be statis-tically significant, 5 to be not statistically significant, and 2 to bestatistically significant but time variable. The fact that 24 of the29 proved to be statistically significant simply reflects the factthat the human eye is a reasonably good 3 σ gradient detector. Inaddition to clarifying which of the gradients considered earlierby Contopoulos et al. (2009) are robust, the results in Table 3,including those presented in this paper, have added another 28cases, more than doubling the available statistics.We note that the absolute values of the observed RMs willbe a ff ected by the local Doppler factor, however, it is physicallyimplausible for this to give rise to systematic gradients in the ob-served RM across the jet. The Doppler factor depends on the in-trinsic flow speed and the viewing angle, neither of which is ex-pected to change systematically across the jet. An RM gradientcould in principle be associated with a gradient in the electrondensity; however, electron-density gradients cannot give rise tothe changes in the sign of the RM across the jets observed for asubstantial number of the AGNs displaying transverse RM gra-dients. In addition, there is certainly no physically plausible pic-ture in which electron-density gradients could have a preferreddirection across the jet, whereas this comes about naturally ifthere is a preferred direction for the jet current (i.e, for the jettoroidal B -field component).Thus, it is now possible to assert with confidence that theorientations of the toroidal B field components of AGN jets onthe sky are not random, and that inward currents are consider-ably more common in AGN jets on parsec scales than outwardcurrents.This result would be extremely interesting even on its own;however, it becomes truly intriguing when combined with theresults of Christodoulou et al. (2016) and Knuettel et al. (2018),which indicate a strong, highly significantly significant predom-inance of outward currents implied by transverse RM gradientson decaparsec-to-kiloparsec scales: 11 of 11 such gradients withsignificances ≥ σ correspond to outward currents. The proba-bility of this coming about by chance is only ≃ . jet currents on parsec scales, but outward jet currents on largerscales. However, here we must recall that these currents can bedistributed across the cross section of the jet and surroundingspace, and the e ff ect that we are using to trace these currents isthe observed transverse RM gradients.In fact, as was proposed earlier (Contopoulos et al. 2009,Mahmud et al. 2013) these collected results are consistent witha B -field configuration forming a nested helical-field structure,with one region of helical field inside the other and with the twohaving oppositely directed toroidal components. The orientationof the inner toroidal component corresponds to inward currentsalong the jet, and that of the outer toroidal component to out-ward currents along the jet direction, as shown schematicallyin Fig. 2. This forms a system of currents and fields similarto that of a co-axial cable, with inward current along the cen-ter of the cable and outward current in a more extended sheath.Both of the regions of helical field contribute to the overall ob-served Faraday rotation; the inner region of helical field makesthe dominant contribution on parsec scales, while the outer re-gion of helical field makes the dominant contribution beyond afew tens of parsec from the jet base. Changes in the conditionsin di ff erent regions along and across the jet with time could alsoexplain the changes in the direction of the significant transverseRM gradients observed in some sources as being due to changesin whether the inner or outer region of helical B field dominatesthe overall Faraday-rotation integral at that location.The inner and outer regions of helical field correspond tothe inner and outer sections of B field loops that have both been“wound up” by the di ff erential rotation of the central black holeand its accretion disk. The distance at which each region domi-nates the observed transverse Faraday rotation gradients can berelated to the scale on which the inner and outer (relative tothe jet axis) sections of the initial loops of field are e ff ectively“wound up” by the rotation (Christodoulou et al. 2016). The cur-rent flows inward along the jet axis and outward in a more ex-tended region surrounding the jet, closing in the kiloparsec-scalelobes and in the accretion disk.The physical origin of this system of fields and currents iskey to understanding the launching and propagation of astro-physical jets. It is also important to note that the detection of sta-tistically significant transverse Faraday rotation gradients evenout to kiloparsec scales (Gabuzda et al. 2015a, Christodoulou etal. 2016, Knuettel at al. 2018) demonstrates that an ordered he-lical or toroidal field component at least partially survives alongthe entire length of the jet, though it may be masked by turbu-lence in some regions.It has already been pointed out (Contopoulos et al. 2009,Christodoulou et al. 2016) that the configuration described aboveis in fact predicted by a “cosmic battery” model, in which cur-rents are generated in the accretion disk by the action of thePoynting–Robertson e ff ect, giving rise to a correlation betweenthe direction of the poloidal B field that is “wound up” and the di-rection of rotation of the accretion disk. This correlation leads toa preferred orientation for the resulting toroidal B field compo-nent, which corresponds to an inward current along the jet axis.This mechanism produces loops of magnetic field whose innerand outer parts relative to the jet axis have opposite poloidal fielddirections, giving rise to opposite toroidal field directions whenthey are wound up — a nested helical-field configuration such ashas been proposed as a way of explaining the opposite preferreddirections for the observed transverse RM gradients (toroidal B -field components) on parsec and decaparsec-kiloparsec scales.
5. Conclusions
We identify 13 new cases and confirm another 5 previously iden-tified cases of statistically significant transverse RM gradientsacross the parsec-scale jets of AGNs in the sample initially ana-lyzed by Hovatta et al. (2012). According to the Monte Carlosimulations of Hovatta et al. (2012) and Murphy & Gabuzda(2013), the probability of a ≃ σ RM gradient arising by chancein RM maps based on VLBA snapshot data at the frequenciesconsidered here is no more than about 1%; we accordingly ex-pect no more than ≃ ≃ . B -field components); one possibility is the mechanismdescribed by Contopoulos et al. (2009) and Christodoulou et al.(2016).A very interesting question that remains to be addressed iswhy a sizeable minority of the 47 AGNs listed in Table 2 havetransverse RM gradients on parsec scales whose directions im-ply outward rather than inward currents. One possibility is thatthe transition from dominance of the inner to dominance of theouter region of helical B field expected in the cosmic-batterymodel occurs on smaller angular scales than those probed by theavailable observations in these sources. It is also possible thatthe physical conditions in the accretion disks of some AGNs areless conducive to e ffi cient operation of the battery mechanism;in this case, some fraction of the observed RM gradients wouldin fact have random directions, with an excess corresponding toinward current arising due to the operation of some mechanismthat facilitates the development of inward jet currents. It mayalso be that the direction of the jet current is also a ff ected byother factors, such as Hall currents, as was suggested by K¨onigl(2010). Finally, the numerical computations of Koutsantoniouand Contopoulos (2014) suggest that the cosmic battery de-scribed above may operate in reverse when the central blackhole rotates at more than about 70% of its maximal rotation; insuch a case, the inner edge of the accretion disk would be closeenough to the black hole horizon for the e ff ect of the rotationof space–time to dominate over the e ff ect of the disk’s rotation,leading to a reversal in the direction of the radiation force on theelectrons in the accretion disk in the toroidal direction. Futurestudies aimed at characterizing the properties of the minority ofAGNs whose transverse RM gradients imply outward currentson parsec scales and possible di ff erences from the properties ofthe majority of AGNs whose jets are observed to have inwardcurrents are certainly of interest.Whether or not the particular “cosmic battery” model de-scribed above is indeed operating in the jet–accretion disk sys- tems of AGNs has not been settled. However, our results havenow yielded firm evidence that many — possibly all — AGN jetshave inward currents along their axes and outward currents in amore extended region surrounding the jets. This provides funda-mental information about the conditions leading to the formationand launching of the jets, as well as key input to theoretical sim-ulations of astrophysical jets. It also indicates that astrophysicaljets are fundamentally electromagnetic structures, which mustbe borne in mind when interpreting observed features in the dis-tributions of both their intensity and linear polarization. Acknowledgements.
We thank the referee for his / her clear and pertinent com-ments, which have helped improve the overall clarity of this paper. References
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Polarised Emission from Astrophysical Jets , Galaxies ,in press 794, 27 !! Fig. 1. +
581 (top), 0133 +
476 (middle) and 0212 +
735 (bottom).
Fig. 1.
Continued. Results for 0403 − + +
398 and 0834 −
201 (from top to bottom).
Fig. 1.
Continued. Results for 0859 − + −
186 and 1150 +
812 (from top to bottom).
Fig. 1.
Continued. Results for 1504 − + +
399 and 1908 −
201 (from top to bottom).
Fig. 1.
Continued. Results for 2005 +
403 (top), 2216 −
038 (middle)) and 2351 +
456 (bottom).
Fig. 2.
Schematics of the system of B fields and currents sug-gested by the collected data on transverse Faraday rotation gra-dients, as viewed from above (i.e., looking down the jet) (upper)and from the side (lower). The region of inner helical field isshown in brown, the region of outer helical field in blue, and thecurrents in black. The partially transparent gray arrows in thelower panel represent the jet outflow. A circled dot representscurrent or field oriented out of the page and a circled X currentor field oriented into the page.fields and currents sug-gested by the collected data on transverse Faraday rotation gra-dients, as viewed from above (i.e., looking down the jet) (upper)and from the side (lower). The region of inner helical field isshown in brown, the region of outer helical field in blue, and thecurrents in black. The partially transparent gray arrows in thelower panel represent the jet outflow. A circled dot representscurrent or field oriented out of the page and a circled X currentor field oriented into the page.