Determination of a magnetization parameter of the parsec-scale AGN jets

arXiv:1107.0565v2 [astro-ph.HE] 5 Jul 2011 Determination of a magnetization parameter of the parsec-scale AGN jets V. S. Beskin1, Y. Y. Kovalev1 and E. E. Nokhrina2 1P.N.Lebedev Physical Institute, Leninsky prosp., 53, Moscow, 119991, Russia 2Moscow Institute of Physics and Technology, Dolgoprudny, 141700, Russia Abstract The observed shift of the core of the relativistic AGN jets as a function of frequency allows us to evaluate the number density of outflowing plasma and, hence, the multiplicity parameter λ = n/nGJ. The value λ ∼1013 obtained from the analysis of more than 20 sources shows that for most of jets the magnetization parameter σ ∼10–100. Since the magnetization parameter is the maximum possible value of the Lorentz factor of the relativistic bulk flow, this estimate is consistent with the observed superluminal motion. 1 Introduction One of the most important parameters in magneto-hydrodynamic (MHD) models of relativistic jets is the dimensionless multiplicity parameter λ = n/nGJ, which is defined as the ratio of the number density n to the so-called Goldrech-Julian (GJ) number density nGJ = ΩB/2πce (i.e., the minimum concentration required for the screening of the longitudinal electric field in the magnetosphere). It is important that the multiplicity parameter associates with the magnetization parameter σ, which determines the maximum possible bulk Lorentz-factor of the flow, which can be achieved (Beskin, 2010) σ ≈1 λ Wtot WA 1/2 . (1) Here WA = m2 ec5/e2 ≈1017 erg/s, and Wtot is the total energy losses of the compact object. If the inner parts of the accretion disc are hot enough, these electron-positron pairs can be produced by two-photon collisions, the photons with sufficient energy delivering from the inner parts of the accretion disk (Blandford & Znajek, 1977). In this case λ ∼1010–1013, and the magnetization parameter σ ∼102–103. The second model takes into account the appearance of the region where the GJ plasma density is equal to zero due to the GR effects that corresponds to the outer gap in the pulsar magnetosphere (Beskin et al, 1992, Hirotani & Okamoto, 1998). This model gives λ ∼102–103, and σ ∼1010–1012. 2 The method To determine the multiplicity parameter λ and the magnetization parameter σ one can use the dependence on the visible position of the core of the jet from the observation frequency (Gould, 1979, Howatta et al, 1979, Marscher, 1983, Lobanov, 1998, Hirotani, 2005, Gabuzda et al, 2008). This effect is associated with the absorption of the synchrotron photon gas 1 by relativistic electrons in a jet. The apparent position of the nucleus is determined by the distance at which for a given frequency the optical depth reaches unity. Such measurements were performed by Sokolovsky et al, (2011) for 20 objects. Observations at nine frequencies allowed to approximate the apparent position of the nucleus as a function of frequency r0 −r = ξ −η  ν GHz −1 , (2) where r0 is the position of the bright area of the emission, r is the apparent position of the nucleus in mas, and ν is the frequency. Here, the quantities ξ (in mas) and η (in mas · GHz) are the measured parameters of this approximation. Knowing this dependence and assuming the equipartition of energy between the particles and the magnetic field, one can write down λ = 2.6 × 1012  η mas GHz 3/2 Wtot 1047erg/s !−1/2  DL 1 GPc 3/2 s K γ2 in 1 √χ sin ϕ δ (1 + z)2. (3) Here DL (Gpc) is the object distance, χ (rad) is the opening angle of ejection, ϕ (rad) is the angle of view, δ is the Doppler factor, z is the red-shift, and K is the dimensionless function of the minimum and maximum Lorentz-factor of electrons in their power-law distribution in energy (Marscher, 1983). Thus, for the 20 objects for which parameter η was measured, we can estimate the magnetization parameter σ. In Table 1 we present the obtained results. Here η are taken from observations of 20 objects Sokolovdsky et al, (2011), the red-shifts z are taken from Kovalev et al, (2008), and the distance to the object was determined from the redshift. For the five objects for which the red-shift is unknown, we took z = 1. As the half-opening angle, the angle between the jets and the line of sight (viewing angle) and Doppler factors were taken typical values: δ = 6◦, χ = 9◦, ϕ = 2◦, except for objects 1803+784 and 2201+315. Doppler factor and the angle of view for the source 1803+784 was taken from Homatta et al, (2008), and the half opening angle of jet of this object was taken from Jorstad et al, (2005). Doppler factor and viewing angle for 2201+315 is taken from Jorstad et al, (2005). In addition, we have put for the full power losses Wtot = 1047 erg/s, which corresponds to the Eddington luminosity for the central object mass 109 M⊙. 3 Conclusion The obtained values of the multiplicity parameter λ of the order 1013–1014 are consistent with the Blandford-Znajek model. At the same time, this value corresponds to the concentration of particles which were found by Lob

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