1. VLBA Observations of Blazars
S. Jorstad / Boston U., USA
/St. Petersburg State U., Russia

2. Spectral Energy Distribution of Blazars
Marscher 2008, in press

3. Very Long Baseline Array (VLBA), National Radio Astronomy Observatory, USA
Compact Jets
3pc

4. Instruments and Wavelengths
The Sample
Quasars BL Lac Objects Radio galaxies
PKS C 66A C 111
PKS OJ C 120 3C 3C
PKS BL Lac
3C 345
CTA 102
3C 454.3
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

5. Collaborations 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. R. Foster / U. of California, Berkeley, USA
I. Robson / Royal Observatory, UK

6. Motion in Compact Jets

7. OUTLINE
Study of apparent speed distributions in individual sources and
in different group of AGNs.
Determination of jet parameters: Doppler and Lorentz factors,
viewing and opening angles.
Analysis of polarization properties at different wavelengths
Direction of the magnetic field with respect to the jet direction
5. Where does emission at different wavelengths originate in
compact jet?

8. 2cm
Apparent Speed
7mm
n=57
n=22
n=23
Quasars: app 7mm =(12.75.3 )c
Quasars: app 2cm =( 7.3±0.8 )c
Kellermann et al. 2004
Quasars: app 6cm =( 2.90.9 )c
(186 components) Britzen et al. 2008

9. Traditional Estimate of Lorentz factor & Viewing Angle of Jet
app =  sino (1- coso)-1
 ≈ appmax ; o ≈ 1/appmax ;  = (1 - 2)-1/2
= -1(1- coso)-1;  ≈ appmax

10. Derivation of Lorentz & Doppler factors & Viewing Angle of Jet
Method of Jorstad et al. (2005, AJ, 130, 1418))
Variability Doppler Factor
var ≈ aD/[c tvar (1+z)]
tvar = dt/ln(Smax/Smin)
a: angular diameter of component
- method requires that light-travel effects determine time scale (works at 43 GHz)
= -1(1- coso)-1
app =  sino (1- coso)-1
= (1 - 2)-1/2

11. Jet Parameters for a Source
Although there is a scatter of Lorentz factors and viewing angles derived for a given source from  and app of different superluminal components, the values for
a given source are closely grouped

12. 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.

13. Opening Angles of Jets Projected Opening Angle, p p = tan -1 
< strans = slong   + so>
slong = R
strans = R sin (|jet- |)+a/2
slong
strans
Intrinsic Opening Angle, 
 1/
(Blandford & Königl 1979,
ApJ, 232, 34)
 = 2p sin < o>
 = / (rad), where  = 0.6 ± 0.1

14. Dependence of Jet Parameters on Source Type
Radio galaxies
=4.81.5, o=19o 4o
= 6.4o 1o , =2.80.9
Quasars
=19.28.6, o=2.6o 1.9o
= 1.0o 0.6o , =2311
BL Lac objects
=12.85.3, o=4.4o 3.0o
= 1.2o 0.8o , =13.56.7

15. High Variability of Polarization Parameters in the VLBI core
Epoch
min = 12 days

16. Intermediate Variability of Polarization Parameters in the VLBI core
Epoch
min = 56 days

17. Low Variability of Polarization Parameters in the VLBI core

18. Polarization Variability Indices in the VLBI Core
Va7mm
(mmax -max)-(mmin +min )
Vp=____________________________
(mmax -max)+(mmin +min )
mmax  max - maximum observed
percentage of
polarization
mmin  min - minimum observed
OJ287
CTA102
3C454.3
3C66A
3C279
3C345
BLLac
- (12 +22 )1/2
Va=___________________ 90
- observed range of EVPAs
1,2 - the uncertainties in the
values of EVPAs that
define the range.
3C273
3C111
3C120

19. Dependence of degree of polarization on wavelengths
For a given variability group,
the peak of the distribution
shifts to higher degree of
polarization at shorter mm-.
This suggests that the emission
region is larger at longer
wavelengths.
The peak of the distribution
has the highest degree of
polarization in the IVP group
and the lowest degree of
polarization in the LVP group,
independent of .
This suggests that either
the emission regions of the
LVP and HVP sources are
larger than those in the IVP
sources or magnetic field in the
LVP and HVP sources has finer
structure than in the IVP
sources.

20. Correlation of degree of polarization at different wavelengths
Lister & Smith 2000
There is a strong correlation between the
polarization in the radio core at 7 mm
and overall optical polarization in radio-loud
AGN.

21. Faraday rotation in the VLBI core in the HVP and IVP groups
EVPA (deg.)
2 (cm2)
EVPA (deg.)
2 (cm2)
 = 1mm + RM 2
IVP
HVP

22. Faraday Rotation in the LVP group
7mm
3mm
3C273
Polarization, %
Epoch
Polarization, %
Epoch
Polarization, %
Epoch
RM=2.1104 rad m-2
Attridge et al. 2005
RM>5105 rad m-2

23. Dependence of Faraday Rotation on group
LVP
IVP
RMo> 5  105 rad m-2
RMo= (1.10.3)  104 rad m-2
HVP
RMo= (8.56.5)  104 rad m-2

24. Comparison of EVPAs at different wavelengths
The distributions of offsets between
polarization position angles at
different wavelengths show
1) excellent agreement between
polarization position angles in the
IVP sources;
2) for the HVP sources the result is
qualitatively different, however the
best agreement is observed between
EVPAs at optical wavelengths and
in the 7mm core (64% out of 22
measurements are located within
20 degrees.

25. Position angle of polarization relative to the Jet Axis
The properties of polarization
position angle with respect to the jet
direction are distinct for each group,
independent of wavelength.
1. Intrinsic difference in the
structure of the magnetic field
- large scale in the IVP
- fine structure in the HVP
- the finest structure in the LVP
2. Difference in the amount of
hot gas in the core region
3. Difference in morphology of the
inner jet:
- straight symmetric jets in the IVP
- curved asymmetric jets in the HVP
- wide, with a velocity gradient
across the jet, jets in the LVP
4. Difference in shock strengths
(Lister & Smith 2000)

26. Connection between Lorentz factor and Polarization Variability
1mm
7mm
In the shock-in-jet model (e.g.
Marscher & Gear 1985) polarized
regions at different wavelengths are
partially co-spacial and have
essentially the same Lorentz factor.
In this model a correlation between
bulk Lorentz factor and polarization
variability index is expected if the
minimum degree of polarization is
corresponding to unshocked plasma
and the maximum - to faster,
shocked plasma.

27. Where does polarized emission at different wavelengths originate?
Correlation Optic.  1mm 7mm
m7mm wrt m
opt - <20o % %
Vp wrt 
The findings suggest:
1. Another emission component in
addition to shocks is prominent at 1 mm.
A primary candidate is the “true” core -
bright narrow end of the jet observed at
a wavelength where the emission is
completely optically thin.
2. The true core does not possess
relativistic electrons energetic enough to
produce the optical synchrotron
emission.
3. The nonthermal optical emission arises
in shocks close to the 7mm VLBI core.