Intrinsic Physical Conditions and Structure of Relativistic Jets in Active Galactic Nuclei
aa r X i v : . [ a s t r o - ph . H E ] D ec Mon. Not. R. Astron. Soc. , 1–11 (2014) Printed 23 July 2018 (MN L A TEX style file v2.2)
Intrinsic Physical Conditions and Structure of RelativisticJets in Active Galactic Nuclei
E. E. Nokhrina ⋆ , V. S. Beskin , , Y. Y. Kovalev , and A. A. Zheltoukhov , Moscow Institute of Physics and Technology, Institutsky per. 9, Dolgoprudny 141700, Russia Lebedev Physical Institute, Russian Academy of Sciences, Leninsky prospekt 53, Moscow 119991, Russia Max Planck Institute for Radio Astronomy, Auf dem H¨ugel 69, D-53121 Bonn, Germany
Accepted 4 December 2014; Received 24 November 2014; in original form 22 September 2014
ABSTRACT
The analysis of the frequency dependence of the observed shift of the cores of rela-tivistic jets in active galactic nuclei (AGN) allows us to evaluate the number densityof the outflowing plasma n e and, hence, the multiplicity parameter λ = n e /n GJ ,where n GJ is the Goldreich-Julian number density. We have obtained the medianvalue for λ med = 3 · and the median value for the Michel magnetization parame-ter σ M , med = 8 from an analysis of 97 sources. Since the magnetization parameter canbe interpreted as the maximum possible Lorentz factor Γ of the bulk motion whichcan be obtained for relativistic magnetohydrodynamic (MHD) flow, this estimate isin agreement with the observed superluminal motion of bright features in AGN jets.Moreover, knowing these key parameters, one can determine the transverse structureof the flow. We show that the poloidal magnetic field and particle number density aremuch larger in the center of the jet than near the jet boundary. The MHD model canalso explain the typical observed level of jet acceleration. Finally, casual connectivityof strongly collimated jets is discussed. Key words: galaxies: active — galaxies: jets — quasars: general — radio continuum:galaxies — radiation mechanisms: non-thermal
Strongly collimated jets represent one of the most visiblesigns of the activity of compact astrophysical sources. Theyare observed both in relativistic objects such as active galac-tic nuclei (AGNs) and microquasars, and in young starswhere the motion of matter is definitely nonrelativistic. Thisimplies that we are dealing with some universal and ex-tremely efficient mechanism of energy release.At present the magnetohydrodynamic (MHD) model ofactivity of compact objects is accepted by most astrophysi-cists (Mestel 1999; Krolik 1999). At the heart of the MHDapproach lies the model of the unipolar inductor, i.e., a ro-tating source of direct current. It is believed that the electro-magnetic energy flux — the Poynting flux — plays the mainrole in the energy transfer from the ‘central engine’ to activeregions. The conditions for the existence of such a ‘centralengine’ are satisfied in all the compact sources mentionedabove. Indeed, all compact sources are assumed to harbor arapidly spinning central body (black hole, neutron star, oryoung star) and some regular magnetic field, which leads tothe emergence of strong induction electric fields. The electric ⋆ E-mail: [email protected] (EEN) fields, in turn, lead to the appearance of longitudinal elec-tric currents resulting in effective energy losses and particleacceleration.The first studies of the electromagnetic model of com-pact sources (namely, radio pulsars) were carried out as earlyas the end of the 1960s (Goldreich & Julian 1969; Michel1969). It was evidenced that there are objects in the Uni-verse in which electrodynamical processes can play the de-cisive role in the energy release. Then, Blandford (1976)and Lovelace (1976) independently suggested that the samemechanism can also operate in active galactic nuclei, and fornearly 40 years this model has remained the leading one.Remember that within the MHD approach the totalenergy losses P jet can be easily evaluated as P jet ∼ IU ,where I is the total electric current flowing along the jet,and U ∼ ER is the electro-motive force exerted on theblack hole on the scale R . If the central engine (blackhole for AGNs) rotates withthe angular velocity Ω in theexternal magnetic field B , one can evaluate the electricfield as E ∼ (Ω R /c ) B . On the other hand, assuming thatfor AGNs the current density j is fully determined by therelativistic outflow of the Goldreich-Julian charge density ρ GJ = Ω B / (2 πc ) (i.e., the minimum charge density re- c (cid:13) E. E. Nokhrina, V. S. Beskin, Y. Y. Kovalev, and A. A. Zheltoukhov quired for the screening of the longitudinal electric field inthe magnetosphere), one can write down j ≈ cρ GJ . It gives I ∼ Ω B R . (1)As for AGNs, one can set R ≈ r g = 2 GM/c to obtain thewell-known evaluation (Blandford & Znajek 1977) P jet ∼ (cid:18) Ω r g c (cid:19) B r c. (2)In particular, comparing expressions (1) and (2), one canstraightforwardly obtain I ≈ c / P / . (3)For AGNs it corresponds to 10 –10 A. Certainly, thequestion as to whether it is possible to consider a black holeimmersed in an external magnetic field as a unipolar induc-tor turned out to be also rather nontrivial (Punsly 2001;Okamoto 2009; Beskin 2009).As a result, the MHD model was successfullyused to describe a lot of processes in active nuclei in-cluding the problem of the stability of jets (Benford1981; Hardee & Norman 1988; Appl & Camenzind 1992;Istomin & Pariev 1994; Bisnovatyi-Kogan 2007; Lyubarsky2009) and their synchrotron radiation (Blandford & K¨onigl1977; Pariev, Istomin & Beresnyak 2003;Lyutikov, Pariev & Gabuzda 2005). In particular,it was shown both analytically (Bogovalov 1995;Heyvaerts & Norman 2003; Beskin & Nokhrina 2009) andnumerically (Komissarov et al. 2006; Tchekhovskoy et al.2009; Porth et al. 2011; McKinney et al. 2012) that forsufficiently small ambient pressure the dense core canbe formed. This is related both to advances in the the-ory which have at last formulated sufficiently simpleanalytical relations (Blandford & Znajek 1977; Beskin2010), and to the breakthrough in numerical simula-tions (Komissarov et al. 2006; Tchekhovskoy et al. 2009;Porth et al. 2011; McKinney et al. 2012) which confirmedtheoretical predictions.Moreover, recently Kronberg et al. (2011) demon-strated that in QSO 3C303 the jet does possess large enoughtoroidal magnetic field, the apropriate longitudinal electriccurrent along the jet I ≈ . × A being as large as theelectric current I GJ (Eq. 1) which is necessary to support thePoynting energy flux. Besides, the lack of γ -ray radiation asprobed by the Fermi
Observatory for AGN jets observedat small enough viewing angles ϑ < ◦ (Savolainen et al.2010) can be easily explained as well. Indeed, as was found(see, e.g., Beskin 2010), within well-collimated magneticallydominated MHD jets the Lorentz factors of the particle bulkmotion can be evaluated asΓ ≈ r ⊥ /R L , (4)where r ⊥ is the distance from the jet axis, and R L = c/ Ω isthe light cylinder radius. Thus, the energy of particles radi-ating in small enough angles ϑ with respect to the jet axisis to be much smaller than that corresponding to peripheralparts of a jet.The most important MHD parameters describing rela-tivistic flows (which was originally introduced for radio pul-sars) are the Michel magnetization parameter σ M and themultiplicity parameter λ . The first one determines the max-imum possible bulk Lorentz factor Γ of the flow when all the energy transported by the Poynting flux is transmittedto particles. The second one is the dimensionless multiplic-ity parameter λ = n e /n GJ , which is defined as the ratio ofthe number density n e to the Goldrech-Julian (GJ) numberdensity n GJ = Ω B/ πce . It is important that these two pa-rameters are connected by the simple relation (Beskin 2010) σ M ≈ λ (cid:18) P jet P A (cid:19) / . (5)Here P A = m c /e ≈ erg/s is the minimum energylosses of the central engine which can accelerate particles torelativistic energies, and P jet is the total energy losses of thecompact object.Unfortunately, up to now neither the magnetization northe multiplicity parameters were actually known as the ob-servations could not give us the direct information aboutthe number density and bulk energy of particles. The coreshift method has been applied to obtain the concentration n e , magnetic field B (Lobanov 1998; O’Sullivan & Gabuzda2009; Pushkarev et al. 2012; Zdziarski et al. 2014), and thejet composition (Hirotani 2005) in AGN jets. However,evaluation of multiplicity and Michel magnetization pa-rameters, which needs to estimate the total jet power,has not been done. From a theoretical point of view ifthe inner parts of the accretiondisc are hot enough, thenelectron-positron pairs can be produced by two-photon col-lisions,where photons with sufficient energy originate fromthe inner parts of the accretion disk (Blandford & Znajek1977; Moscibrodzka et al. 2011). In this case λ ∼ –10 ,and Michel magnetization parameter σ M ∼ . The sec-ond model takes into account the appearance of the regionwhere the GJ plasma density is equal to zero due to gen-eral relativity effects that corresponds to the outer gap inthe pulsar magnetosphere (Beskin, Istomin & Pariev 1992;Hirotani & Okamoto 1998). This model gives λ ∼ –10 ,and σ M ∼ –10 .This large difference in the estimates for the magneti-zation parameter σ M leads to two completely different pic-tures of the flow structure in jets. In particular, it determineswhether the flow is magnetically or particle dominated. Thepoint is that for ordinary jets r ⊥ /R L ∼ –10 . As a result,using the universal asymptotic solution Γ ≈ r ⊥ /R L (4), onecan obtain that the values σ M ∼ correspond to thesaturation regime when almost all the Poynting flux W em is transmitted to the particle kinetic energy flux W part . Onthe other hand, for σ M ∼ the jet remains magneti-cally dominated ( W part ≪ W em ). Thus, the determinationof Michel magnetization parameter σ M is the key point inthe analysis of the internal structure of relativistic jets.The paper is organized as follows. In section 2 itis shown that VLBI observations of synchrotron self-absorbtion in AGN jets allow us to evaluate the numberdensity of the outflowing plasma n e and, hence, the mul-tiplicity parameter λ . We discuss the source sample andpresent the result for multiplicity and Michel magnetizationmparameters in section 3. The values λ ∼ obtainedfrom the analysis of 97 sources shows that for most jets themagnetization parameter σ M .
30. Since the magnetizationparameter is the maximum possible value of the Lorentz fac-tor of the relativistic bulk flow, this estimate is consistentwith observed superluminal motion.In section 4 it is shownthat for physical parameters determined above, the poloidal c (cid:13) , 1–11 ntrinsic conditions and structure of AGN jets magnetic field and particle number density are much largerin the center of the jet than near its boundary. Finally, insection 5 the casual connectivity of strongly collimated su-personic jets is discussed. Throughout the paper, we use theΛCDM cosmological model with H = 71 km s − Mpc − ,Ω m = 0 .
27, and Ω Λ = 0 .
73 (Komatsu et al. 2009).
To determine the multiplicity parameter λ and Michel mag-netization parameter σ M one can use the dependence onthe visible position of the core of the jet from the obser-vation frequency (Gould 1979; Blandford & K¨onigl 1977;Marscher 1983; Lobanov 1998; Hirotani 2005; Kovalev et al.2008; O’Sullivan & Gabuzda 2009; Sokolovsky et al. 2011;Pushkarev et al. 2012). This effect is associated with the ab-sorption of the synchrotron photon gas by relativistic elec-trons (positrons) in a jet.Typically, the parsec-scale radio morphology of a brightAGN manifests a one-sided jet structure due to Dopplerboosting that enhances the emission of the approaching jet.The apparent base of the jet is commonly called the “core”,and it is often the brightest and most compact feature inVLBI images of AGN. The VLBI core is thought to repre-sent the jet region where the optical depth is equal to unity.We will employ the following model to connect the phys-ical parameters at the jet launching region with the observ-able core-shift. There is a magnetohydrodynamic relativisticoutflow of non-emitting plasma moving with bulk Lorentzfactor Γ and concentration n e in the observer rest frame. Onthe latter we superimpose the flow of emitting particles withdistribution d n syn ∗ = k e ∗ γ − α ∗ d γ ∗ , γ ∗ ∈ [ γ min ∗ ; γ max ∗ ].Here n syn ∗ is concentration of emitting plasma, k e ∗ is con-centration aplitude, and γ ∗ is the emitting particles’ Lorentzfactor. All the parameters with subscript ‘*’ are taken in thenon-emitting plasma rest frame, i.e., in the frame which lo-cally moves with the bulk Lorentz factor Γ.We suppose that the emitting particles radiate syn-chrotron photons in the jet’s magnetic field, and these pho-tons scatter off the same electrons, which lead to the pho-ton absorption (Gould 1979; Lobanov 1998; Hirotani 2005).The corresponding turn-over frequency ν m ∗ , the frequencyat which the flux density S ν has a maximum, can be evalu-ated using expressions from Gould (1979) as ν (5 − α )m ∗ = c α (1 − α )5(5 − α ) e m c (cid:16) e πmc (cid:17) − α R ∗ B − α ∗ k ∗ . (6)The function c α ( · ) is a composition of gamma-functions de-fined by Gould (1979), and for α = − / c α (2) =1 . e , m , and c are the electron charge, electronmass, and the speed of light correspondingly. Finally, B ∗ isthe magnitude of disordered magnetic field in an emittingregion with a characteristic size R ∗ along the line of sight.Although we assume that the toroidal magnetic fielddominates in the jet, an assumption of disordered magneticfield in our opinion can be retained, because, for an opticallythin jet, the photon meets both directions of field. Thus, themean magnetic field along the photon path is almost zero,which mimics the behaviour of a disordered field. As a result, the parameters in the observer rest frame and plasma restframe are connected by the following equations: ν m ∗ ν m = 1 + zδ , (7) R ∗ = 2 r ∗ χ ∗ sin ϕ ∗ = 2 rχδ sin ϕ , (8) B ∗ = p B − E ≈ B ϕ Γ ≈ B Γ , (9) k e ∗ = k e Γ , (10)where z is the red-shift, δ = 1Γ (1 − β cos ϕ ) (11)is the Doppler factor, χ is the jet half-opening angle, and ϕ is a viewing angle.Further, the number density of emitting electrons n syn is connected with the amplitude k e as k e = n syn αγ α max − γ α min , (12)where γ = γ ∗ Γ. For α = − / k e ≈ n syn γ min . (13)We also put n syn = ξn e . Here ξ is a ratio of the number den-sity of emitting particles to the MHD flow number density.The portion of particles effectively accelerated by the inter-nal shocks was found by Sironi, Spitkovsky & Arons (2013)to be about 1%, so we take ξ ≈ . B ( r ) = B (cid:18) rr (cid:19) − , (14) n e ( r ) = n (cid:18) rr (cid:19) − , (15)where B is the magnetic field and n is the number den-sity at r = 1 pc respectively. For these scalings of particledensity and magnetic field with the distance the turn-overfrequency ν m as a function of r does not depend on α andcan be written as ν m ∝ r − . (16)This scaling has been confirmed by Sokolovsky et al. (2011)in measurements of core-shifts for 20 AGNs made for 9 fre-quencies each. Using these dependencies of magnetic fieldand particle number density of distance r , we obtain in theobserver rest frame (cid:18) ν m zδ rr (cid:19) − α = C (cid:18) e mc (cid:19) (cid:16) e πmc (cid:17) − α ×× (cid:18) r χδ sin ϕ ξγ min (cid:19) Γ − α B − α n , (17)where C = c α (1 − α ) / − α ).On the other hand, the values B and n can be relatedthrough introducing the flow magnetization parameter σ —the ratio of Poynting vector to particle kinetic energy fluxat a given distance along the flow (see Appendix A). Let usdefine the magnetization σ ξ as a ratio of Poynting vector to c (cid:13) , 1–11 E. E. Nokhrina, V. S. Beskin, Y. Y. Kovalev, and A. A. Zheltoukhov the total kinetic energy flux of emitting and non-emittingparticles: σ ξ = (cid:12)(cid:12)(cid:12) ~S (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) ~K + ~K syn (cid:12)(cid:12)(cid:12) . (18)Here the kinetic energy flux of emitting electrons is (cid:12)(cid:12)(cid:12) ~K syn (cid:12)(cid:12)(cid:12) = Z γ max γ min ( γmc )( | ~v p | )d n syn = k e mc F ( γ min , γ max ) , (19)and function F ( · ) for α = − / F ( γ min , γ max ) = (cid:0) ch − γ max − ch − γ min (cid:1) −− p γ − γ max − p γ − γ min ! ≈ ln (2 γ max ) − . (20)Estimating now the Poynting vector as (cid:12)(cid:12)(cid:12) ~S (cid:12)(cid:12)(cid:12) ≈ cB ϕ π , (21)and particle kinetic energy fluxes as (cid:12)(cid:12)(cid:12) ~K + ~K syn (cid:12)(cid:12)(cid:12) ≈ mc n e (Γ + ξF γ min ) , (22)we obtain the following relationship between magnetic fieldand particle number density: B = σ ξ πmc n e Γ . (23)In what follows, we neglect the term ξF γ min in comparisonwith Γ. Further on we omit the index ξ . Using (23), we get (cid:18) ν m zδ rr (cid:19) − α = C (cid:18) e mc (cid:19) (cid:16) e πmc (cid:17) − α ×× (cid:0) πmc (cid:1) . − α (cid:18) r χδ sin ϕ ξγ min (cid:19) Γ − α ×× ( σ Γ ) . − α n . − α . (24)As to the number density n , it can be defined throughthe multiplicity parameter λ and total jet energy losses P jet as (see Appendix B for more detail) n = λ π ( r χ ) mc e r P jet P A . (25) To determine the intrinsic parameters of relativistic jets, letus consider two cases for the different magnetization at 1 pc.In what follows we assume that the flow at its base is highly,or at least mildly, magnetized, i.e. σ M ≫ r = 1 pc theplasma has been effectivily accelerated so that the Poyntingflux is smaller in comparison with the particle kinetic energyflux, i.e., σ .
1. In other words, the acceleration reachedthe saturation regime (Beskin 2010). Combining now (4)and (A8), it is easy to obtain that this case corresponds to σ M < . Accordingly, the bulk Lorentz factor at r = 1 pccan be evaluated asΓ ≈ σ M . (26) In this case Eqn. (24) can be rewritten as (cid:18) ν m zδ rχc (cid:19) − α = C (cid:18) − . α π − α (cid:19) (cid:18) ξγ min δ sin ϕ (cid:19) λ − α . (27)Using now the relationship between the angular distance θ d and the distance from the jet base rr sin ϕ = θ d D L (1 + z ) , (28)where D L is the luminosity distance, we obtain (cid:18) θ d mas (cid:19) = 3 . · − (cid:18) D L Gpc (cid:19) − (cid:16) ν m GHz (cid:17) − δ (1 + z ) ×× sin ϕχ (cid:18) ξγ min δ sin ϕ (cid:19) / (5 − α ) λ (7 − α ) / (5 − α ) . (29)This expression can be rewritten as a following relationshipbetween the core position and the observation frequency: (cid:18) θ d mas (cid:19) = (cid:16) η mas · GHz (cid:17) (cid:16) ν m GHz (cid:17) − . (30)Having the measured core-shift ∆ r mas in milliarcseconds fortwo frequencies ν m , and ν m , , we obtain for α = − / λ = 7 . · (cid:16) η mas · GHz (cid:17) / (cid:18) D L Gpc (cid:19) / ×× (cid:18) χ z (cid:19) / δ sin ϕ ) / ξγ min ) / == 2 . · (cid:18) η pc · GHz (cid:19) / (cid:18) D L Gpc (cid:19) / ×× (cid:18) χ z (cid:19) / δ sin ϕ ) / ξγ min ) / . (31)Accordingly, using (5), we obtain σ M = 1 . · (cid:20)(cid:16) η mas · GHz (cid:17) (cid:18) D L Gpc (cid:19) χ z (cid:21) − / ×× p δ sin ϕ ( ξγ min ) / r P jet erg · s − == 0 . · (cid:20)(cid:18) η pc · GHz (cid:19) (cid:18) D L Gpc (cid:19) χ z (cid:21) − / ×× p δ sin ϕ ( ξγ min ) / r P jet erg · s − . (32)As we see, this value is in agreement with our assumption σ M < . Let us now assume that the flow is still highly magnetizedat a distance of the observale core. This implies that theMichel magnetization parameter σ M > . Using now rela-tion (A8), one can obtain σ Γ ≈ σ M . (33)On the other hand, Eqn. (24) can be rewritten as c (cid:13) , 1–11 ntrinsic conditions and structure of AGN jets λ = 2 . · (cid:20)(cid:16) η mas · GHz (cid:17) (cid:18) D L Gpc (cid:19) (cid:18) χ z (cid:19)(cid:21) ×× Γ / δ sin ϕ ) ξγ min (cid:18) P jet erg · s − (cid:19) − / . (34)This gives the following expression for the Michel magneti-zation parameter σ M = 4 · (cid:20)(cid:16) η mas · GHz (cid:17) (cid:18) D L Gpc (cid:19) (cid:18) χ z (cid:19)(cid:21) − ×× Γ − / ( δ sin ϕ ) ξγ min (cid:18) P jet erg · s − (cid:19) . (35)As we see, these values are in contradiction with our as-sumption σ M > . Thus, one can conclude that it is thesaturation limit that corresponds to parsec-scale relativisticjets under consideration. Several methods can be applied to measure the apparentshift of the core position as discussed by Kovalev et al.(2008). As a result, a magnitude of the shift, designated by η , can be measured and presented in units [mas · GHz] or[pc · GHz]. Knowing this quantity, one can use the expres-sions (31)–(35) to estimate the multiplicity and magneteza-tion parameters.
In our analysis we use the results of two surveys of theapparent core shift in AGN jets: Sokolovsky et al. (2011)show results for 20 objects obtained from nine frequenciesbetween 1.4 and 15.3 GHz (S-sample) and Pushkarev et al.(2012) have results for 163 AGN from four frequencies cov-ering 8.1-15.3 GHz (P-sample). Of these we use only thosesources for which the apparent opening angle is known fromPushkarev et al. (2009). As a result, 97 sources are left fromthe P-sample and 5 from the S-sample. Although all of S-sample sources are in P-sample, we have included them asan independent measurment of core shift. Moreover, for theobjects 0215+015 and 1219+285 the two measurements ofcore-shift has been made for two different epochs, and weincluded them too. This leaves us with 97 sources and 104measurements of core shift.The distance to the objects is determined from the red-shift and accepted cosmology model. For a Doppler factorwe use the estimate δ ≈ β app , where measured apparentvelocity β app is a ratio of apparent speed of a bright fea-ture in a jet to the speed of light. We believe this to bea good estimate because Cohen et al. (2007) have showedusing Monte-Carlo simulations that the probability density p ( δ | β app ) to observe a Doppler factor for a given appar-ent velocity is peaked around unity. This is done under anassumption that the measured β app does represent the un-derlying jet flow. The redshifts z and the apparent velocities β app are taken from Lister et al. (2013).The value of observation angle ϕ we obtain from the setof equations for Doppler factor δ and apparent velocity β app = β sin ϕ − β cos ϕ . (36)Taking δ = β app , we obtain from (11) and (36) for the ob-servation angle the relation ϕ = atan (cid:18) β app β − (cid:19) . (37)The half-opening angle related to the observed opening angle χ app as χ = χ app sin ϕ/ . (38)We use the values for χ app derived by Pushkarev et al.(2009) with typical errors of 1 . ◦
5. We also have chosen pa-rameter γ min = 1.We evaluate the total jet power P jet through the rela-tionship (Cavagnolo et al. 2010) between the luminosities ofjets in radio band and mechanical jet power, needed to formthe cavities in surrounding gas. The power law, found byCavagnolo et al. (2010) for a range of frequencies 200 – 400MHz is (cid:18) P jet erg · s − (cid:19) = 3 . (cid:18) P − erg · s − (cid:19) . . (39)In order to find flux density measurements at the92 cm band for each source we use the CATS database(Verkhodanov et al. 1997) which accumulates measurementsat different epoches and from the different catalogues.The data which we use in this paper were originally re-ported by De Breuck et al. (2002); Douglas et al. (1996);Ghosh, Gopal-Krishna & Rao (1994); K¨uhr et al. (1979,1981); Gregory & Condon (1991); Mitchell et al. (1994);Rengelink et al. (1997) with a typical flux density accuracyof about 10%.The typical error for core shift measurements inPushkarev et al. (2012) and Sokolovsky et al. (2011) is0 .
05 mas. There are 23 objects in our sample that have thecore shift values less than 0 .
05 mas. For them we have re-placed the core shift values by 0 .
05 mas for our calculationsfor convenience of the λ and σ M analysis. Using the formula (31), we obtain the following result forthe equipartition regime. The obtained values for the mul-tiplication parameter λ and magnetization parameter σ M are presented in Table 1. Their distributions are shown inFig. 1 and Fig. 2, respectively. In cases when more than oneestimate is determined per source (e.g., for 0215+015), anaverage value is used in the histograms. The resultant me-dian value for the multiplicity parameter λ med = 3 · ,and median value for magnetization parameter σ M , med = 8.The multiplicity parameter for our sample lies in the inter-val (3 · ; 4 · ), and Michel magnetization parameter σ M lies correspondingly in the (0 .
4; 61) interval.The Doppler factor of a flow can be also obtainedthrough the variability method by measuring the amplitudeand duration of a flare (Hovatta et al. 2009). Making an as-sumption that the latter corresponds to the time neededfor light to cross the emitting region, and assuming the in-trinsic brightness temperature is known (from the equipar-tition argument), one can derive the beaming Doppler fac-tor. We have used the variability Doppler factors obtained c (cid:13) , 1–11 E. E. Nokhrina, V. S. Beskin, Y. Y. Kovalev, and A. A. Zheltoukhov l
20 5 15 20 N Figure 1.
Distributions of the multiplicity parameter λ for thesample of 97 sources. Two objects with λ = 2 . · and 3 . · lie out of the shown range of values. N M Michel magnetization parameter s Figure 2.
Distributions of the Michel magnetization parameter σ M for the sample of 97 sources. by Hovatta et al. (2009) for 50 objects with measured coreshifts (Pushkarev et al. 2012) instead of our original assump-tion for Doppler factor δ = β app and have found that ourestimates for λ and σ M stay the same within a factor of 2.We estimate the total typical accuracy of λ and σ M values in Table 1 to be of a factor of a few. It is mostly due tothe assumptions and simplifications introduced and, to a lessof an extent, due to accuracy of observational parameters ofthe jets. We note that while an estimate for every source isnot highly accurate, the distributions in Figs. 1, 2 shouldrepresent the sample properties well.There are 3 objects in our sample that have Michel mag-netization parameter σ M <
1, which means that the flow isnot magnetically dominated at its base. And we have overall9 sources with σ M <
2, which is in contradiction with our as-sumption of at least a mildly magnetized flow. This a smallfraction (9%) of all 97 sources, so we feel that for the major-ity sources there is no contradiction of our assumptions andthe resultant value for Michel magnetization parameter.For the highly magnetized regime we come to a con-tradiction. Indeed, taking, for example, a source 0215+015,which has Michel magnetization parameter σ = σ M , med , we obtain from (35) for a highly magnetized regimethe following value: σ M , mag = 3 . · Γ / . (40)In highly magnetized regime the scaling (4) holds, and forΓ = r ⊥ /R L ≈ − we come to σ M , mag ≈ − ÷ -3 -1-2-41.02345716 (a) log(r ) pc] [ l og ( G ) l og ( n )[ c m ] - Figure 3.
Transversal profile of the number density n e (a) andLorentz factor Γ (b) in logarithmical scale for λ = 10 , jet radius R jet = 1 pc and three different values of σ : 5 (solid line), 15(dashed line), and 30 (dotted line). − . This is in contradiction with our assumption for amagnetized regime with initial magnetization σ M > .We see that the magnetization parameter λ obtainedfrom the observed core-shift has the order of magnitude10 ÷ which agrees with the two-photon conver-sion model of plasma production in a black hole mag-netosphere (Blandford & Znajek 1977; Moscibrodzka et al.2011). Thus, we obtain the key physical parameters of thejets being σ M ∼
10 and λ ∼ . As a result, knowing theseparameters and using rather simple one-dimensional MHDaproach, we can determine the internal structure of jets. As was shown by Beskin & Malyshkin (2000);Beskin & Nokhrina (2009); Lyubarsky (2009), for well-collimated jets the one-dimensional cylindrical MHDapproximation (when the problem is reduced to the systemof two ordinary differential equations, see above mentionedpapers for more detail) allows us to reproduce mainresults obtained later by two-dimensional numerical simu-lation (Komissarov et al. 2006; Tchekhovskoy et al. 2009;Porth et al. 2011; McKinney et al. 2012). In particular,both analytical and numerical consideration predict theexistence of a dense core in the centre of a jet for low enough c (cid:13) , 1–11 ntrinsic conditions and structure of AGN jets -3 -1-2-4-1.0-4-3-2-11-50 (a) log(r ) pc] [ f l og ( B )[ G s ] -1.5-0.5 p l og ( B )[ G s ] Figure 4.
Transversal profile of poloidal (a) and toroidal (b)components of magnetic field in logarithmical scale for the sameparameters and line types as in Fig. 3. ambient pressure P ext . Thus, knowing main parametersobtained above we can determine the transverse structureof jets using rather simple 1D analytical approximation.The only parameters we need are the Michel magnetization σ M and the transverse dimension of a jet R jet (or, theambient pressure P ext ). In particular, transversal profilesof the Lorentz factor Γ, number density n e , and magneticfield B can be well reproduced. In this section we apply thisapproach to clarify the real structure of relativistic jets.In Fig. 3 we present logarithmic plots of Lorentz factorand number density across the jet for λ = 10 , jet radius R jet = 1 pc and σ = 5, 15, and 30. Fig. 4 shows logarithmicplots of poloidal and toroidal components of magnetic fieldacross the jet with the same parameters as in Fig. 3. As wesee, these results point to the existence of more dense centralcore in the centre of a jet. Indeed, for our parameters thenumber density in the center of a jet is greater by a factorof a thousand than at the edge. However the Lorentz factorin the central core is small (see Fig. 3b). Thus, these resultsare in qualitative agreement with previous studies.Knowing how the Lorentz factor on the edge of jet de-pends on its radius and making a simple assumption aboutthe form of the jet, we can calculate the dependence of theLorentz factor on the coordinate along the jet. The resultis presented in Fig. 5 for the cases of parabolic ζ ∝ r ⊥ and ζ ∝ r ⊥ form of the jet. Here ζ is the distance along the axis. -3 1-1-41.21.221.241.261.28 log( ) pc] z [ l og ( G ) -2 01.30 2 Figure 5.
Dependence of Lorentz factor on coordinate along thejet in assumption of parabolic ζ ∝ r ⊥ (solid line) and ζ ∝ r ⊥ (dashed line) form of the jet. We also assume that the jet has a radius of about 10 pc atthe distance 100 pc in both cases, which corresponds to ahalf-opening angle of the jet θ jet ≈ .
1. According to Fig. 5,particle acceleration in the frame of the AGN host galaxy onthe scales 60–100 pc has values about ˙Γ / Γ = 10 − per yearwith very little dependence of this value on the particularform of a jet boundary. This agrees nicely with results ofthe VLBI acceleration study in AGN jets by Homan et al.(2009, 2015). The calculated multiplication parameter λ with Michel mag-netization σ M as well as the observed half-opening angleof a jet χ allow us to test causal connectivity across a jetfor the cylindrical model. Every spacial point of a super-magnetosonic outflow has its own “Mach cone” of causalinfluence. In case of a uniform flow the cone originating atthe given point with its surface formed by the characteris-tics of a flow is a domain, where any signal from the pointis known. For a non-uniform flow the cone becomes somevortex-like shape, depending on the flow property, but sus-taining the property of a causal domain for a given point.In a jet, if the characteristic inlet from any point of aset of boundary points reaches the jet axis, we say that theaxis is causally connected with the boundary. On the con-trary, if there is a characteristic that does not reach the axis,we have a causally disconnected flow. In the latter case, aquestion arises about the self-consistency of an MHD solu-tion of the flow, since the inner parts of such a flow do nothave any information about the properties of the confiningmedium. The examples of importance of causal connectivityin a flow and its connection with the effective plasma ac- c (cid:13) , 1–11 E. E. Nokhrina, V. S. Beskin, Y. Y. Kovalev, and A. A. Zheltoukhov -1 10 2-2 log(r ) [pc]02468101214 l og f z r µ z r µ z r µ Figure 6.
The causality function f for different magnetic surfaceshapes for Γ > Γ max /
2, i.e. further the equipartition. Solid linesare shown for σ M = 100 while dotted — for σ M = 10. The uppercurves correspond to ζ ∝ r ⊥ , the curves in the middle — to ζ ∝ r ⊥ , and the lower curves — to ζ ∝ r / ⊥ . celeration has been pointed out by Komissarov et al. (2009)and Tchekhovskoy et al. (2009).In the case of the cylindrical jet model the question ofcasuality is even more severe. For a cylindrical model we takeinto account the force balance across a jet only, so the trans-field equation governing the flow becomes one-dimensional.For every initial condition at the axis its solution gives theflow profile and the position of a boundary, defined so as tocontain the whole magnetic flux. Any physical value at theboundary such as, for example, the pressure, may be calcu-lated from this solution. Or, we in fact reverse the problem,and for a given outer pressure at the boundary we find theinitial conditions at the jet axis. Thus, we use the depen-dence of the jet properties at the axis from the conditions atthe boundary. In this case, the boundary and the axis mustbe causally connected. In other words, for a strictly cylin-drical flow the conditions at the boundary at the distance ζ from the jet origin must be “known” to the point at theaxis at the same ζ .In the cylindrical model the dynamics of a flow along thejet is achieved by “piling up” the described above cross cutsso as to either make the needed boundary form, or to modelthe variable outer pressure. In this case the jet boundariesshould be constrained by the “Mach cone” following causalconnection for the model to be self-consistent.Thus, we cometo the following criteria: we may assert that we can neglectthe jet-long derivatives in a trans-field equation if any char-acteristic, outlet from a boundary at ζ , not only reachesthe axis, but does it at ζ : | ζ − ζ | ≪ ζ .For an axisymmetric flow the condition of a causal connectivity across the flow may be writ-ten (Tchekhovskoy et al. 2009) in the simplest case as θ F > θ j , (41)where θ F is a half-opening angle of a fast Mach cone atthe boundary. This condition means that the characteristicfrom the jet boundary, locally having its half-opening angle θ F with regard to the local poloidal flow velocity, reachesthe axis. For an ultra-relativistic flow, θ F may be defined as(Tchekhovskoy et al. 2009)sin θ F = 1 M = Γ max − ΓΓ . (42)In the cylindrical approach, we can check the causalconnection across the jet both by applying condition (41),and by tracking the net of characteristics, outlet from theboundary. This can be done for a different jet boundaryshapes. Let us introduce the causality function f = Γ max − ΓΓ · θ j . (43)It follows from (41) and (42) that for f > f < ζ = ζ ( r ⊥ ), where r ⊥ is an axialradius, the half-opening jet angle is defined bysin θ j = ∂r ⊥ ∂ζ " (cid:18) ∂r ⊥ ∂ζ (cid:19) − / . (44)Fig. 6 shows the causality function for a paraboloidal flow(see Beskin & Nokhrina 2009) ζ ∝ r ⊥ , for a jet with aboundary shaped as ζ ∝ r ⊥ , and ζ ∝ r / ⊥ . For the latter flowshape f < ζ -component, we may introduce the r ⊥ -component by taking into account the given form of eachmagnetic surface. The latter is defined by the function X = q r ⊥ + ζ − ζ = const , (45)and for inner parts of a flow Ψ = Ψ X . Thus, we definethe angle θ ℓ of a field-line tangent to a vertical directionas tg θ ℓ = | B r ⊥ | / | B ζ | = ∂r ⊥ /∂ζ , and at the given point ofa flow we outlet the fast characteristic with regard to thusdefined flow direction. We present in Fig. 7 (center panel)the net of characteristics for a paraboloidal flow depicted asdescribed above. The characteristics are calculated startingfrom the jet boundary towards the axis. They are param-eterized by the square of fast magnetosonic Mach number M at the axis at the same ζ , where the characteristic starts.This is done uniformly regarding the Mach number, thus thecharacteristics are plotted at different distances from eachother. It can be seen that all the characteristics for parabolicjet boundary reach the axis at ζ not much greater than ζ . c (cid:13) , 1–11 ntrinsic conditions and structure of AGN jets z [ p c ] r pc] [10 -3 Figure 7.
The net of inbound characteristics for a parabolic form of a jet boundary ζ ∝ r ⊥ (left panel), ζ ∝ r ⊥ (center panel), ζ ∝ r / ⊥ (right panel). The same result holds for a flow ζ ∝ r ⊥ either (see Fig. 7,left panel). On the contrary, each characteristic, depicted inFig. 7 (right panel) for a flow ζ ∝ r / ⊥ , reaches the axis ata distance along a flow much greater than the ζ -coordinateof its origin. This suggests that the cylindrical approach isdefinitely not valid in this case. We show that the multiplicity parameter λ , which is the ra-tio of number density n e of outflowing plasma to Goldreich-Julian number density n GJ , can be obtained from the directobservations of core shift, apparent opening angle and radiopower of a jet. The formula (31) uses the following assump-tions, taken from the theoretical model: (i) the accelerationprocess of plasma effectivily stops (saturates) when thereis an equipartion regime, i.e. the Poynting flux is equal tothe plasma kinetic energy flux; (ii) we assume the certainpower-law scalings for magnetic field B ( r ) and number den-sity n e ( r ) as a functions of distance r (Lobanov 1998). Thesescalings are confirmed by Sokolovsky et al. (2011). We alsosee that these power-laws are a good approximation frommodelling the internal jet structure in section 4.In contrast with Lobanov (1998) and Hirotani (2005) wedo not assume the equipartition regime of radiating particleswith magnetic field, but the relation between the particles(radiating and non-radiating) kinetic energy and Poyntingflux. We assume that only the small fraction of particles ∼
1% radiates (Sironi, Spitkovsky & Arons 2013) and in-troduce the correlation between particle number density andmagnetic field through the flow magnetization σ . Althoughfor σ ∼ σ ≫ σ ∼ σ ≫ σ M , one can easily explain the observationally derived values2Γ χ ≈ . χ is a jet half-openong angle. Indeed, as was found byTchekhovskoy et al. (2008); Beskin (2010), 2Γ χ ≈ ≪ σ , independent of the collima-tion geometry. This implies that 2Γ χ ≈ R jet /R L = σ M . At larger distances Γ remains practicallyconstant, but for a parabolic geometry the opening angledecreases with the distance ζ as ζ − / ≈ r − / . As a result,one can write down2Γ χ ∼ s σ M R L R jet ∼ . . (46)This result is in agreement with the criteria of casual connec-tivity across a jet. Indeed, for an outflow with an equiparti-tion between the Poynting and particle energy flux, we canwrite down2Γ χ = 1 √ f < > Γ max / The analysis of the frequency dependence of the observedshift of the core of relativistic AGN jets allows us to de- c (cid:13)000
1% radiates (Sironi, Spitkovsky & Arons 2013) and in-troduce the correlation between particle number density andmagnetic field through the flow magnetization σ . Althoughfor σ ∼ σ ≫ σ ∼ σ ≫ σ M , one can easily explain the observationally derived values2Γ χ ≈ . χ is a jet half-openong angle. Indeed, as was found byTchekhovskoy et al. (2008); Beskin (2010), 2Γ χ ≈ ≪ σ , independent of the collima-tion geometry. This implies that 2Γ χ ≈ R jet /R L = σ M . At larger distances Γ remains practicallyconstant, but for a parabolic geometry the opening angledecreases with the distance ζ as ζ − / ≈ r − / . As a result,one can write down2Γ χ ∼ s σ M R L R jet ∼ . . (46)This result is in agreement with the criteria of casual connec-tivity across a jet. Indeed, for an outflow with an equiparti-tion between the Poynting and particle energy flux, we canwrite down2Γ χ = 1 √ f < > Γ max / The analysis of the frequency dependence of the observedshift of the core of relativistic AGN jets allows us to de- c (cid:13)000 , 1–11 E. E. Nokhrina, V. S. Beskin, Y. Y. Kovalev, and A. A. Zheltoukhov termine physical parameters of the jets such as the plasmanumber density and the magnetic field inside the flow. Wehave estimated the multiplicity parameter λ to be of theorder 10 –10 . It is consistent with the Blandford-Znajekmodel (Blandford & Znajek 1977) of the electron-positrongeneration in the magnetosphere of the black hole (seeMoscibrodzka et al. 2011, as well). These values are in agree-ment with the particle number density n e which was foundindependently by Lobanov (1998).As the transverse jet structure depends strongly on theflow regime, whether it is in equipartition or magneticallydominated, it is imporatant to know the relation between theobserved and maximum Lorentz factor. The Michel magne-tization parameter σ M is equal to the maximum Lorentz fac-tor of plasma bulk motion. Typical derived values of σ M .
30, in agreement with the Lorentz factor estimated fromVLBI jet kinematics (e.g., Cohen et al. 2007; Lister et al.2009a, 2013) and radio variability (Jorstad et al. 2005;Hovatta et al. 2009; Savolainen et al. 2010). This impliesthat a flow is in the saturation regime. Since for strongly col-limated flow the condition of causial connection is fullfilled(see, e.g., Komissarov et al. (2009); Tchekhovskoy et al.(2009)), the internal structure of an outflow can be mod-elled within the cylindrical approach (Beskin & Malyshkin2000; Beskin & Nokhrina 2009). It has been shown that theresults of the modelling, such as Lorentz factor dependenceon the jet distance, are in a good agreement with the obser-vations. In particular, the relative growth of Lorentz factor˙Γ / Γ with the distance along the axis is slow for the jets insaturation regime, having the magnitude ∼ − per year.This result may account for the recent masurements of ac-celeration in AGN jets (Homan et al. 2015).We plan to address the following points in a separatepaper: (i) the role of the inhomogeneity of the magneticfield and particle number density in a core, (ii) the actionof the radiation drag force (Li, Begelman & Chiueh 1992;Beskin, Zakamska, & Sol 2004; Russo & Thompson 2013),(iii) the possible influence of mass loading (Komissarov 1994;Stern & Poutanen 2006; Derishev et al. 2003) on the jetmagnetization and dynamics. ACKNOWLEDGMENTS
We would like to acknowledge E. Clausen-Brown,D. Gabuzda, M. Sikora, A. Lobanov, T. Savolainen,M. Barkov, and the anonymous referee for useful com-ments. We thank the anonymous referee for suggestionswhich helped to imporve the paper. This work was sup-ported in part by the Russian Foundation for Basic Re-search grant 13-02-12103. Y.Y.K. was also supported in partby the Dynasty Foundation. This research has made use ofdata from the MOJAVE database that is maintained by theMOJAVE team (Lister et al. 2009b), and data accumulatedby the CATS database (Verkhodanov et al. 1997). This re-search has made use of NASA’s Astrophysics Data System.
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APPENDIX A: MAGNETIZATIONPARAMETER
The standart Grad-Shafranov approach for MHD flows usesthe following energy integral E , conserved at the magneticflux surface Ψ: E (Ψ) = c Ω F (Ψ) I π + mη (Ψ) c Γ . (A1)Here magnetic field in spherical coordinates { r ; θ ; ϕ } is de-fined by ~B = ~ ∇ Ψ × ~e ϕ πr sin θ − Icr sin θ ~e ϕ , (A2)electric field ~E = − Ω F πc ~ ∇ Ψ , (A3)Ω F is a rotational velocity and a function of magnetic fluxΨ, I is a current, and η (Ψ) = n e , ∗ | ~u p || ~B p | = n e | ~v p || ~B p | . (A4)Here we assume the flow to be cold, so the particle enthalpyis simply its rest mass. The Poynting vector ~S = c π ~E × ~B = c π Ω F I ~B p . (A5)The particle kinetic energy flux ~K = (cid:0) Γ mc (cid:1) ( n e ~v p ) = Γ mc η (Ψ) ~B p . (A6)Thus, we can introduce the magnetization parameter, vari-able along the flow, as σ = | ~S || ~K | = 1Γ 12 πc Ω F Imη . (A7)On the other hand, there is Michel’s magnetization param-eter σ M , which has a meaning of magnetization at the baseof an outflow, is constant, and is defined by σ M = Emc η = c Ω F I πmηc + Γ = Γ ( σ + 1) . (A8) APPENDIX B: MULTIPLICITY PARAMETER
The continuity of relativistic plasma number density fluxthrough two cuts, perpendicular to bulk flow, can be writtenas λn GJ R c = n ( r χ ) c. (B1)Here we assume the flow velocity equal to c . Using the ex-pression for the Goldreich-Julian concetration n GJ = Ω B πce (B2)and expression for the full losses due to currents flowing ina magnetosphere P jet = (Ω B ) R c , (B3)we get n = λ π ( r χ ) mc e r P jet P A . (B4) c (cid:13) , 1–11 E. E. Nokhrina, V. S. Beskin, Y. Y. Kovalev, and A. A. Zheltoukhov
Table 1.
Jet parameters and derived multiplication and magnetization parameters.Source z β app χ app S . P jet Reference ∆ r core Epoch λ σ ( c ) ( ◦ ) (Jy) (10 erg/s) for S . (mas) for ∆ r core (10 )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)0003 −
066 0.347 8.40 16.3 2.17 1.07 2 0.035 2006-07-07 1.21 9.690106+013 2.099 24.37 23.6 2.85 10.50 6 0.005 2006-07-07 2.02 23.670119+115 0.570 18.57 15.6 2.24 1.86 6 0.347 2006-06-15 3.84 4.270133+476 0.859 15.36 21.7 1.63 2.54 8 0.131 2006-08-09 3.52 5.800202+149 0.405 15.89 16.4 6.25 2.39 3 0.122 2006-09-06 1.63 10.900202+319 1.466 10.15 13.4 0.76 2.99 8 0.013 2006-08-09 2.17 11.130212+735 2.367 6.55 16.4 1.54 5.17 8 0.149 2006-07-07 9.82 4.410215+015 1.715 25.06 36.7 0.88 3.90 5 0.088 2006-04-28 3.75 7.540.241 2006-12-01 7.97 3.540234+285 1.206 21.99 19.8 1.45 3.52 5 0.275 2006-09-06 5.29 4.790333+321 1.259 13.07 8.0 3.68 6.72 7 0.279 2006-07-07 4.10 8.620336 −
019 0.852 24.45 26.8 2.49 3.26 6 0.117 2006-08-09 2.66 8.680403 −
132 0.571 20.80 16.4 7.62 4.45 2 0.346 2006-05-24 3.66 6.950420 −
014 0.916 5.74 22.7 0.87 1.84 3 0.267 2006-10-06 13.49 1.300458 −
020 2.286 13.57 23.1 3.54 11.20 3 0.006 2006-11-10 3.20 17.260528+134 2.070 17.34 16.1 1.02 5.85 2 0.167 2006-10-06 4.81 7.400529+075 1.254 18.03 56.4 1.75 4.54 2 0.110 2006-08-09 3.83 7.580605 −
085 0.870 19.19 14.0 1.43 2.39 3 0.096 2006-11-10 1.66 11.950607 −
157 0.323 1.918 35.1 2.31 0.96 3 0.240 2006-09-06 28.46 0.380642+449 3.396 8.53 23.4 0.70 7.68 8 0.110 2006-10-06 5.27 8.290730+504 0.720 14.07 14.8 0.71 1.20 8 0.262 2006-05-24 4.27 3.210735+178 0.450 5.04 21.0 1.81 1.23 8 0.039 2006-04-28 2.56 5.070736+017 0.189 13.79 17.9 1.79 0.42 3 0.079 2006-06-15 0.82 8.380738+313 0.631 10.72 10.5 1.26 1.48 3 0.183 2006-09-06 2.85 5.230748+126 0.889 14.58 16.2 1.45 2.65 2 0.098 2006-08-09 2.41 8.690754+100 0.266 14.40 13.7 0.74 0.39 2 0.266 2006-04-28 2.06 3.320804+499 1.436 1.15 35.3 0.60 2.49 8 0.094 2006-10-06 35.88 0.610805 −
077 1.837 41.76 18.8 2.60 9.26 2 0.207 2006-05-24 3.12 14.090823+033 0.505 12.88 13.4 0.63 0.71 5 0.141 2006-06-15 2.12 4.710827+243 0.942 19.81 14.6 0.71 1.80 2 0.150 2006-05-24 2.52 6.920829+046 0.174 10.13 18.7 0.67 0.21 2 0.109 2006-07-07 1.28 3.820836+710 2.218 21.08 12.4 5.06 17.75 2 0.186 2006-09-06 3.81 16.430851+202 0.306 15.14 28.5 1.11 0.56 3 0.028 2006-04-28 1.08 7.690906+015 1.026 22.08 17.5 1.54 3.05 3 0.168 2006-10-06 3.04 7.560917+624 1.453 12.07 15.9 1.27 4.07 8 0.112 2006-08-09 3.95 7.140923+392 0.695 2.76 10.8 3.28 3.03 5 0.042 2006-07-07 3.23 6.690945+408 1.249 20.20 14.0 2.94 6.30 2 0.083 2006-06-15 1.80 18.921036+054 0.473 5.72 6.5 0.75 0.80 2 0.195 2006-05-24 2.77 3.801038+064 1.265 10.69 6.7 1.59 4.32 2 0.106 2006-10-06 2.02 14.011045 −
188 0.595 10.51 8.0 2.79 2.46 2 0.156 2006-09-06 2.01 9.451127 −
145 1.184 14.89 16.1 5.63 8.94 6 0.096 2006-08-09 2.73 14.771150+812 1.250 10.11 15.0 1.39 3.81 8 0.087 2006-06-15 3.31 8.031156+295 0.725 24.59 16.7 4.33 3.89 8 0.162 2006-09-06 2.15 11.401219+044 0.966 0.82 13.0 1.14 2.52 4 0.133 2006-05-24 22.11 0.941219+285 0.103 9.12 13.9 1.77 0.19 3 0.182 2006-02-12 1.11 4.040.142 2007-04-30 0.93 4.870.199 2006-11-10 1.19 3.781222+216 0.434 26.60 10.8 3.98 1.90 5 0.180 2006-04-28 1.14 14.131226+023 0.158 14.86 10 63.72 3.25 3 0.020 2006-03-09 0.31 60.771253 −
055 0.536 20.58 14.4 16.56 6.31 3 0.048 2006-04-05 0.75 39.841308+326 0.997 27.48 18.5 1.42 2.79 8 0.143 2006-07-07 2.35 9.331334 −
127 0.539 16.33 12.6 1.91 1.71 2 0.237 2006-10-06 2.61 5.981413+135 0.247 1.78 8.8 2.74 0.81 2 0.230 2006-08-09 6.02 1.641458+718 0.904 6.61 4.5 19.64 13.30 8 0.081 2006-09-06 1.46 32.220.136 2007-03-01 2.16 21.841502+106 1.839 17.53 37.9 1.08 4.92 3 0.052 2006-07-07 3.59 8.921504 −
166 0.876 3.94 18.4 1.80 2.79 3 0.148 2006-12-01 9.56 2.051510 −
089 0.360 28.00 15.2 2.75 1.22 3 0.122 2006-04-28 0.93 13.471514 −
241 0.049 6.39 7.8 2.06 0.08 3 0.188 2006-04-28 0.56 5.15c (cid:13) , 1–11 ntrinsic conditions and structure of AGN jets Table 1 – continued Source z β app χ app S . P jet Reference ∆ r core Epoch λ σ ( c ) ( ◦ ) (Jy) (10 erg/s) for S . (mas) for ∆ r core (10 )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)1538+149 0.606 8.74 16.1 2.82 2.36 3 0.032 2006-06-15 1.68 11.091546+027 0.414 12.08 12.9 0.70 0.61 3 0.010 2006-08-09 0.87 10.321606+106 1.232 19.09 24.0 2.67 5.30 7 0.057 2006-07-07 2.11 14.841611+343 1.400 29.15 26.9 4.20 8.44 3 0.057 2006-06-15 1.79 22.541633+382 1.813 29.22 22.6 2.51 8.28 8 0.119 2006-09-06 3.07 13.501637+574 0.751 13.59 10.7 1.32 1.88 8 0.117 2006-05-24 1.92 8.941638+398 1.666 15.85 53.8 0.64 3.11 8 0.007 2006-08-09 4.68 5.361641+399 0.593 19.27 12.9 9.93 5.13 8 0.211 2006-06-15 2.29 11.991655+077 0.621 14.77 5.5 2.36 2.33 6 0.080 2006-11-10 0.73 25.390.086 2007-06-01 0.77 24.051726+455 0.717 2.30 16.5 0.49 0.95 8 0.009 2006-09-06 5.18 2.341730 −
130 0.902 27.35 10.4 6.46 6.54 3 0.174 2006-07-07 1.67 19.721749+096 0.322 7.90 16.8 1.20 0.61 6 0.061 2006-06-15 1.43 6.151751+288 1.118 3.87 12.1 0.40 1.55 2 0.007 2006-10-06 3.60 4.621758+388 2.092 2.21 17.9 0.18 1.82 8 0.079 2006-11-10 13.98 1.421803+784 0.680 10.79 18.4 1.92 2.23 8 0.029 2006-09-06 1.71 10.800.061 2007-05-03 1.98 9.311823+568 0.664 26.17 6.8 2.63 2.52 8 0.052 2006-07-07 0.42 46.211828+487 0.692 13.07 7.1 47.78 15.60 3 0.117 2006-08-09 1.39 35.351849+670 0.657 23.08 16.6 0.86 1.22 8 0.024 2006-05-24 0.88 15.501908 −
201 1.119 4.39 23.9 2.70 5.21 2 0.246 2006-03-09 18.03 1.691928+738 0.302 8.17 9.8 4.81 1.40 8 0.147 2006-04-28 1.72 7.661936 −
155 1.657 5.34 35.2 0.67 3.45 2 0.215 2006-07-07 22.92 1.152008 −
159 1.180 4.85 9.7 0.73 2.41 2 0.008 2006-11-10 2.65 7.892022 −
077 1.388 23.23 19.6 2.63 6.67 2 0.006 2006-04-05 1.51 23.672121+053 1.941 11.66 34.0 0.63 3.99 2 0.152 2006-06-15 10.29 2.832128 −
123 0.501 5.99 5.0 1.47 1.23 3 0.223 2006-10-06 2.52 5.202131 −
021 1.284 19.96 18.4 2.66 6.11 6 0.089 2006-08-09 2.39 14.142134+004 1.932 5.04 15.2 0.99 4.85 6 0.188 2006-07-07 12.35 2.602136+141 2.427 4.15 32.5 0.94 6.16 6 0.008 2006-09-06 10.28 3.642145+067 0.999 2.83 23.2 3.76 5.18 3 0.008 2006-10-06 6.97 4.312155 −
152 0.672 18.12 17.6 2.41 2.43 3 0.405 2006-12-01 5.34 3.602200+420 0.069 9.95 26.2 1.82 0.12 8 0.032 2006-04-05 0.47 7.302201+171 1.076 17.66 13.6 1.00 2.63 2 0.380 2006-05-24 5.64 3.822201+315 0.295 8.27 12.8 1.82 0.88 3 0.347 2006-10-06 3.90 2.670.192 2007-04-30 2.50 3.802209+236 1.125 2.29 14.2 0.39 1.51 2 0.038 2006-12-01 6.03 2.732216 −
038 0.901 6.73 15.6 2.25 3.57 6 0.011 2006-08-09 2.55 9.572223 −
052 1.404 20.34 11.7 13.59 18.00 3 0.199 2006-10-06 3.21 18.332227 −
088 1.560 2.00 15.8 1.41 5.14 2 0.186 2006-07-07 22.85 1.402230+114 1.037 8.62 13.3 8.51 9.25 3 0.278 2006-02-12 7.36 5.452243 −
123 0.632 5.24 14.8 1.45 1.71 1 0.161 2006-09-06 5.73 2.792251+158 0.859 13.77 40.9 12.47 9.39 3 0.124 2006-06-15 8.31 4.722345 −
167 0.576 11.47 15.8 2.81 2.21 3 0.167 2006-11-10 3.24 5.542351+456 1.986 21.56 20.1 2.23 8.54 8 0.196 2006-05-24 5.35 7.99
Notes.
Columns are as follows: (1) source name (B1950); (2) redshift z as collected by (Lister et al. 2013); (3)apparent velocity measured by (Lister et al. 2013); (4) apparent opening angle measured by (Pushkarev et al. 2009);(5) flux density at the 92 cm band; (6) derived total jet power; (7) 92 cm flux density reference: 1 — De Breuck et al.(2002), 2 — Douglas et al. (1996), 3 — Ghosh, Gopal-Krishna & Rao (1994), 4 — Gregory & Condon (1991), 5 —K¨uhr et al. (1979), 6 — K¨uhr et al. (1981), 7 — Mitchell et al. (1994), 8 — Rengelink et al. (1997); (8) core shiftfor frequencies 8 . − . (cid:13)000