Both the emission properties and evolution of Active Galactic Nuclei (AGN) radio jets are dependent on the magnetic fields that thread them. A better understanding of these magnetic fields is therefore important in helping our understanding of jets in AGN. Several observations of jets have suggested that, on parsec scales, the jet magnetic field may have a significant helical component. Using a model first proposed by Laing and developed by Papageorgiou and Cawthorne, all of the above observations can be reproduced by varying only the helical pitch angle of the magnetic field and the line of sight angle. In order to reduce the total polarization to agree with observed values, a tangled magnetic field component is also introduced to the model, via another parameter, the degree of entanglement. We are in the process of comparing data from observations of several AGN with this model, making it possible to derive estimates of the helical pitch angle, the

viewing angle and the degree of entanglement for these jets in the framework of this model. The observed profiles are compared with a set of theoretical profiles. This proves to be an objective approach to profile fitting that should enable analysis of a large number of AGN jets, making it

possible to look for trends. Results for Mrk501 are presented

Cawthorne, Timothy Vernon

Gabuzda, Denise

Murphy, Eoin

English

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PoS(10th EVN Symposium)041.Gleaning Secrets from the Transverse Profiles ofAGN jetsEoin Murphy∗University College Cork, IrelandE-mail: eoin.g.murphy@gmail.comDenise GabuzdaUniversity College Cork, IrelandE-mail: d.gabuzda@ucc.ieTim CawthorneUniversity of Central Lancashire, EnglandE-mail: tvcawthorne@uclan.ac.ukBoth the emission properties and evolution of Active Galactic Nuclei (AGN) radio jets are depen-dent on the magnetic fields that thread them. A better understanding of these magnetic fields istherefore important in helping our understanding of jets in AGN. Several observations of jets havesuggested that, on parsec scales, the jet magnetic field may have a significant helical component.Using a model first proposed by Laing and developed by Papageorgiou and Cawthorne, all ofthe above observations can be reproduced by varying only the helical pitch angle of the magneticfield and the line of sight angle. In order to reduce the total polarization to agree with observedvalues, a tangled magnetic field component is also introduced to the model, via another param-eter, the degree of entanglement. We are in the process of comparing data from observations ofseveral AGN with this model, making it possible to derive estimates of the helical pitch angle, theviewing angle and the degree of entanglement for these jets in the framework of this model. Theobserved profiles are compared with a set of theoretical profiles. This proves to be an objectiveapproach to profile fitting that should enable analysis of a large number of AGN jets, making itpossible to look for trends. Results for Mrk501 are presented10th European VLBI Network Symposium and EVN Users Meeting: VLBI and the new generation of radioarraysSeptember 20-24, 2010Manchester, UK∗Speaker.© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/PoS(10th EVN Symposium)041Gleaning Secrets from the Transverse Profiles of AGN jets Eoin Murphy1. IntroductionAt radio wavelengths the jets of active galaxies emit synchrotron radiation, which occurs whencharged particles move relativistically through magnetic fields. This is characterised by appre-ciable linear polarization with the plane of the polarization perpendicular to the plane of the jetmagnetic field in the optically thin region. The polarization structure of the jets provides informa-tion about the structure of the magnetic fields threading these jets. In order to understand both theevolution and emission properties of AGN an understanding of the magnetic fields that thread themis important. Yet despite much observational effort the nature of the magnetic field structures ofAGN are not well understood. Several observational results for jets have suggested that the mag-netic field threading the jet may have a significant helical component on parsec scales.[3, 4, 5]There are primarily 3 different types of observational results that support the theory that the jetsof AGN are threading by helical magnetic fields, all of which have been observed in the jets of anumber of AGN.• Asymmetric profiles of total intensity and polarization across jets.• Magnetic field orientation changing from longitudinal to transverse within a given jet profile.• Systematic Faraday Rotation Measure gradients across jets.These properties can also be attributed to physical asymmetries, such as differing pressures andsurrounding jet environments on either side of the jet [1]. Examples include edge brightening dueto compression on one side of the jet and a change of the magnetic field orientation from transverseto longitudinal due to sheering between the jet and external medium. However, a helical magneticfield threading the jet of an AGN can elegantly describe all these observations while requiring nofurther phenomena to be occurring in the jet environment.2. Helical Magnetic Field ModelThe model we have used consists of a helical magnetic field of constant pitch angle and uniformflux density threading a cylindrical jet. This model geometry was first proposed by Laing [2] andfurther investigated by Papageorgiou [3]. It makes predictions of both the total intensity and polar-ized intensity distributions across a jet using only 2 parameters, the helical pitch angle γ and theviewing angle δ .This model produces 4 different magnetic field configurations, as is shown in Figure 1 (from top tobottom).1. Longitudinal all across the jet2. Longitudinal on one side and transverse on the other3. Longitudinal at the edges and transverse at the centre4. Transverse all across2PoS(10th EVN Symposium)041Gleaning Secrets from the Transverse Profiles of AGN jets Eoin MurphyFigure 1: Theoretical pro-files for every magnetic fielddistribution. Solid line cor-responds to total intensity,purple region to expectedtransverse polarization andgreen region to expectedlongitudinal polarization.Configuration 2 only occurs when γ = δ and configuration4 only occurs when γ = δ = 90 degrees. These specialcases would not be expected to be observed often in na-ture. However, these theoretical profiles assume infinite reso-lution. Mimicing the effects of finite resolution by convolvingthe profiles with a Gaussian beam of a suitable full width athalf maximum (FWHM) increases the range of parameter val-ues for which the different polarization configurations are ob-served.Observations analysed by Papageorgiou [3] showed that this modelproduced polarized intensity distributions which were much greaterthan observed. The model was accordingly modified by introducinga disordered, tangled magnetic field component. As result the mag-netic field geometry is described as the sum of two components; onecorresponding to a helical field, as described by Laing [2], and a sec-ond, corresponding to a field that is tangled on angular scales muchsmaller than the width of the jet. Introducing this tangled magneticfield introduces a third parameter to the model, the degree of disor-der, f. This parameter is defined as the fraction of the magnetic fieldenergy density in tangled form.〈B2T 〉〈B2H〉=f1− f (2.1)where 〈B2T 〉 and 〈B2H〉 are the magnetic field energy densities of thetangled field and the helical field respectively. Increasing the degreeof disorder, f, decreases asymmetries in the total intensity profilesgenerated by the model in addition to decreasing the degree of po-larization.3. Method of ComparisonFor comparison with the observed profiles a database of theoretical profiles was generated. Thedatabase profiles were convolved with a Gaussian of FWHM equal to that of the beam used in theobservations. The best fit profile is determined via a χ2 minimisation. The database profiles arescaled so that the maximum total intensity of the theoretical profile is equal to the maximum totalintensity of the observed profile. As the range of parameters that can reproduce a total polarizationdistribution is much smaller than the range of values that can reproduce a total intensity distributionthe total polarization profile were given more weight than the total intensity profile in the compar-ison algorithm. Errors are calculated by changing one of the parameters in steps from it’s best fitvalue and allowing the other 2 parameters to vary, until the χ2 value increases by unity comparedto the best fit χ2 . This is continued until such a fit cannot be found. Repeating this procedure gives1 σ errors for all 3 parameters.3PoS(10th EVN Symposium)041Gleaning Secrets from the Transverse Profiles of AGN jets Eoin MurphyThe total time taken for this method to find the best fit values of γ , δ and f and their correspond-ing errors is approximately 20 minutes per profile (for a 3GHz Dual Core processor and 3.2 GBof RAM) . The time required for the algorithm is due to the fact that it carries out an exhaustivesearch for the χ2 minimum. However, it’s advantages are that it provides an objective way to fitmultiple profiles for a single source or profiles for multiple sources, and also provides informationabout secondary local minima.4. Markarian 501VLBI images of Markarian 501 (also known as DA426 or 1652+398) often show excellent ex-amples of sudden magnetic field orientation changes across the jet [4]. Figure 2 shows the 6 cmpolarization map of this source for the data of [4]. Three slices were taken across this map usingthe SLICE task in the NRAO AIPS package. Both Slice 1 (Orange) and Slice 3 (Green) were takenin regions of the jet without any unusual polarization structure. Slice 2 (Yellow) was taken in theregion of sudden magnetic field orientation changes. These slices were compared to a database oftheoretical slices and the values of γ , δ and f which resulted in the best fit (minimum χ2) werefound, presented in Table 1. The observed profile and the model’s best fit profile for Slice 2 canbe seen in Figure 3. The overall consistency of the fitted γ , δ and f for the three slices is strik-Figure 2: 6cm Polarization Map of Mrk501 [4]. Magnetic field orientation is perpendicular to polarizationlines. The 3 lines across the jet show the 3 transverse slices that were analysed.4PoS(10th EVN Symposium)041Gleaning Secrets from the Transverse Profiles of AGN jets Eoin MurphyTable 1: Best fit Parameters for 6cm Mrk501 Slices.Slice γ δ fSlice 1 49+11−4 Degrees 78+2−1 Degrees 0.40+0.10−0.13Slice 2 53+7−3 Degrees 80+1−4 Degrees 0.40+0.31−0.09Slice 3 58+11−5 Degrees 78+3−1 Degrees 0.80+0.12−0.33ing. These results show tentative evidence that the pitch angle of the helical field threading this jetincreases with distance from the core, consistent with the expectation that the toroidal field com-ponent should become more dominant with distance.Table 2 shows our best fit parameters for slices taken at four different wavelengths: the 4cm and6cm maps of Pushkarev et al [4] for February 2007, and the 13cm and 18cm maps of Croke at al[5] for May 1998. These 4 slices were all taken in the same region of the jet, specifically the regionof Slice 2 in Figure 2 The derived parameters are consistent for the slices in the same region of thejet observed at 4cm, 6cm, 13cm and 18 cm (at two different epochs).It is important to note that the viewing angle of the jet determined by this method is the viewingangle in the rest frame of the jet. The viewing angle that we observe δ ′ is given by:δ ′ =δΓ(1−β cosδ ) (4.1)where Γ is the Lorentz factor of the jet and β = vc . For δ close to 90 degrees this simplifies toδ ′ ≈ δΓ .5. ConclusionUsing a relatively simple model for a helical magnetic field threading an AGN jet it is possible toderive estimates of the helical pitch angle, the viewing angle and the degree of entanglement forthese jets (in the framework of this model). Preliminary results for Mrk501 demonstrate a consis-tency in these estimates for both slices across different regions at one frequency and slices acrossthe same region at different frequencies. These results suggest that this jet carries a helical B fieldwith pitch angle γ ' 55 degrees viewed at an angle of δ ' 85 in the jet rest frame, and providetentative evidence that the pitch angle of the helical field threading this jet increases with distanceTable 2: Best fit Parameters for Mrk501 Slices at 4 different frequencies.Slice γ δ f Epoch4 cm 53+1−1 Degrees 83+1−3 Degrees 0.40+0.05−0.04 February 19976 cm 53+7−3 Degrees 80+1−4 Degrees 0.40+0.31−0.09 February 199713 cm 54+1−2 Degrees 85+1−5 Degrees 0.45+0.02−0.05 May 199818 cm 53+2−1 Degrees 86+2−4 Degrees 0.45+0.02−0.26 May 19885PoS(10th EVN Symposium)041Gleaning Secrets from the Transverse Profiles of AGN jets Eoin MurphyFigure 3: Plot of model fit for Slice 2 of 6 cm MK501 map for γ = 53 degrees, δ = 80 degrees and f =0.4. Solid line corresponds to observed profile while dashed line corresponds to model profile. Blue linescorrespond to longitudinal magnetic field orientation while red lines correspond to transverse magnetic fieldorientation. The polarization has been scaled by a factor of 3.from the core.Future work involves applying this method to different sources and devising a way to ensure theobserved profiles are taken perpendicular to the jet direction. We also hope to compare observedFaraday rotation measure gradients to gradients generated by this model.6. AcknowledgementsFunding for this research was provided by the Irish Research Council for Science Engineering andTechnology (IRCSET).References[1] Attridge J. M., Roberts D. H., Wardle J. F. C., 1999, ApJ, 518, 87[2] Laing R. A., 1981, ApJ, 248, 87[3] Papageorgiou A, 2005, PhD. Thesis[4] Pushkarev A. B., Gabuzda D. C., Vetukhnovskaya Yu. N.,Yakimov V. E. 2005, MNRAS, 356, 859[5] Croke S.M., O’Sullivan S.P., Gabuzda D.C., 2010, MNRAS, 402,2596

Gleaning Secrets from the Transverse Profiles of AGN jets

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