S. Jorstad / Boston U., USA /St. Petersburg State U., Russia A.Marscher / Boston U., USA M. Lister / Purdue U., USA A. Stirling / U. of Manchester, Jodrell Bank Obs., UK T. Cawthorne / Central Lancashire U., UK W. Gear / Cardiff U., UK J.L. Gómez / IAA, Granada, Spain J. Stevens / Royal Observatory, UK P. Smith / Steward Observatory, USA J. Foster / U. of California, Berkeley, USA I. Robson / Royal Observatory, UK Apparent Speed as a Probe of Parsec-Scale Jet in AGN

The Sample Quasars BL Lac Objects Radio galaxies PKS C 66A 3C 111 PKS OJ 287 3C 120 3C C PKS BL Lac 3C 345 CTA 102 3C Instruments and Wavelengths VLBA (7 mm ) March April epochs BIMA (3 mm) April April epochs JCMT (0.85/1.3 mm) March April epochs 1.5m Steward Obs. (~6500 Å) Feb April epochs

OUTLINE 1.Study of apparent speed distributions in individual sources and in different group of AGNs. 2.Determination of jet parameters: Doppler and Lorentz factors, viewing and opening angles. 3.Searching for acceleration/deceleration in the jets 4.Analysis of the brightness temperature on parsec scales.

Imaging

Modeling Parameters of Component S (mJy) - flux density S p (mJy) - polarized flux density R (mas) - distance from the core  (deg) - PA relative to the core EVPA(deg) - electric vector PA a (mas) - size

Classification of Component’s Motion We determine the apparent speeds,  app, for 109 knots. Superluminal apparent speeds occur in 82% of the knots. Statistically significant deviation from ballistic motion is observed in 22% of superluminal knots.

Acceleration of the Jet Flow The majority of non-ballistic components undergo an increase of apparent speed with distance from the core. This could be the result of physical accelerations (Vlahakis & Königl 2004, ApJ, 605, 656) or from selection of sources whose angles to the line of sight < sin -1 (1/  ) near the core and closer to this value farther out.

Light Curves of Jet Components Time Scale of Variability Burbidge, Jones, & O’Dell 1974, ApJ, 193, 43  t var = dt/ln(S max /S min ) Variability Doppler Factor  var = aD/[c  t var (1+z)] D - luminosity distance a - VLBI size of component c - speed of light z - redshift S max S min dt

Flux Variability Time Scale vs. Size Variability Time Scale The straight line indicates The expected relation between  t var and  t a for adiabatic losses for optically thin shock with  =0.7, S  -  (Marscher & Gear 1985, ApJ, 298, 114)

Apparent Speed - Doppler Factor Relation 2-cm survey (Kellermann et al. 2004)

Lorentz Factor and Viewing Angle of Jet Components The Lorentz factors of the jet flows in the quasars and BL Lac objects range from  ~ 5 to  >30; the radio galaxies have lower Lorentz factors and wider viewing angles than the blazars.

Intrinsic Brightness Temperature of Jet Components T b,obs = 7.5  10 8 S max /a 2 K T b.int = T b,obs (1+z) 1.7 /  1.7 K  =0.7 S  -  Quasars: =3.5  10 9 K BL Lacs: =5.5  10 7 K RG: =1.4  10 9 K Comparison of these values with the equipartion brightness temperature of the optically thick part of the jets, T b.int >=2-5  K, implies a faster decrease of T b with distance down the jet, which suggests a stronger magnetic field in the BL Lac objects (Readhead 1994, ApJ, 426, 51).

Projected Half Opening Angles of Jets Projected Opening Angle,  p  p = tan -1  s trans = R s long = R sin (|  jet -  |)+a/2

Intrinsic Half Opening Angles of Jets  1/  (Blandford & Königl 1979, ApJ, 232, 34) Intrinsic Half Opening Angle,   =  p sin  =  /  (rad), where  = 0.2 ± 0.1  = √(P ext / P o ) (Daly & Marscher 1988, ApJ, 334, 539)  =0.5  P ext / P o = 1/4

Conclusions 1. We have measured the apparent speed of 106 features in the inner jets of 15 AGNs. Superluminal apparent speeds occur in 80% of the knots, 26% of which show statistically significant deviations from ballistic motion. The majority of non-ballistic components undergo an increase of apparent speed with distance from the core. 2. We suggest a new method to define Doppler factor, based on the assumption that the decay in flux of the superluminal components is caused by radiative losses rather than by cooling from expansion, and is subject to light-travel delays. 3. The derived parameters of the jets indicate that in our sample the quasars have the highest Doppler factors and smallest viewing and opening angles, while the two radio galaxies possess significantly lower Doppler factors, larger viewing angles, and wider opening angles despite their `blazar-like'' radio properties. 4. We have estimated the intrinsic brightness temperatures of jet components in the quasars, BL Lacs, and radio galaxies on parsec scales. Comparison of these values with the equipartition brightness temperature of the optically thick part of the jets suggests a stronger magnetic field in the BL Lac objects.