MOJAVE: Monitoring of Jets in Active Galactic Nuclei with VLBA Experiments. IX. Nuclear opacity

MOJAVE: Monitoring of Jets in Active Galactic Nuclei with VLBA Experiments. IX. Nuclear opacity

Key Words.:
galaxies: active – galaxies: jets – quasars: general – radio continuum: galaxies

Abstract

Context:

Aims:We have investigated a frequency-dependent shift in the absolute position of the optically thick apparent origin of parsec-scale jets (“core shift” effect) to probe physical conditions in ultra-compact relativistic outflows in active galactic nuclei.

Methods:We used multi-frequency Very Long Baseline Array (VLBA) observations of 191 sources carried out in 12 epochs in 2006 within the Monitoring Of Jets in Active galactic nuclei with VLBA Experiments (MOJAVE) program. The observations were performed at 8.1, 8.4, 12.1, and 15.4 GHz. We implemented a method of determining the core shift vector based on (i) image registration by two-dimensional normalized cross-correlation and (ii) model-fitting the source brightness distribution to take into account a non-zero core component offset from the phase center.

Results:The 15.4-8.1, 15.4-8.4, and 15.4-12.1 GHz core shift vectors are derived for 163 sources, and have median values of 128, 125, and 88 as, respectively, compared to the typical measured errors of 50, 51, 35 as. The effect occurs predominantly along the jet direction, with departures smaller than from the median jet position angle in over 80% of the cases. Despite the moderate ratio of the observed frequencies (2), core shifts significantly different from zero () are detected for about 55% of the sources. These shifts are even better aligned with the jet direction, deviating from the latter by less than in over 90% of the cases. There is an indication that the core shift decreases with increasing redshift. Magnetic fields in the jet at a distance of 1 parsec from the central black hole, calculated from the obtained core shifts, are found to be systematically stronger in quasars (median  G) than those in BL Lacs (median  G). We also constrained the absolute distance of the core from the apex of the jet at 15 GHz as well as the magnetic field strength in the 15 GHz core region.

Conclusions:

1 Introduction

Bipolar relativistic outflows (jets) in active galactic nuclei (AGN) are formed in the immediate vicinity of the supermassive central black hole and become detectable at distances of gravitational radii () at millimeter wavelengths (Junor et al., 1999; Lobanov & Zensus, 2007; Hada et al., 2011). The jets take away a substantial fraction of the energy and angular momentum stored in the accretion flow (Hujeirat et al., 2003) and spinning central black hole (Koide et al., 2002; Komissarov, 2005). As discussed by Vlahakis & Königl (2004), a poloidal-dominated magnetic field embedded in the accretion disk or in the black hole ergosphere is wound-up into toroidal loops that may provide effective jet collimation via hoop stress and accelerate the flow by magnetic pressure gradient up to a distance of  .

Very Long Baseline Interferometry (VLBI) observations provide us with the perfect zoom-in tool to explore AGN jets with a milliarcsecond angular resolution corresponding to parsec-scale linear resolution. Typically, the parsec-scale radio morphology of a bright AGN manifests a one-sided jet structure due to Doppler boosting (e.g., Blandford & Königl, 1979; Kellermann et al., 2007; Lister et al., 2009) 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 in VLBI images of AGN. The VLBI core is thought to represent the jet region, located at the distance to the central engine, at which its optical depth reaches at a given frequency. At short mm-wavelengths the core may also be the first recollimation shock downstream of the surface instead of the surface itself. This does not affect our analysis, which uses longer wavelengths. Thus, the absolute position of the radio core is frequency-dependent and varies as (Blandford & Königl, 1979; Königl, 1981), i.e., it shifts upstream at higher frequencies and downstream at lower frequencies (the so-called “core shift” effect). The first core shift measurement from VLBI observations was performed by Marcaide & Shapiro (1984). Recent multi-frequency studies of the core shift effect (O’Sullivan & Gabuzda, 2009; Fromm et al., 2010; Sokolovsky et al., 2011; Hada et al., 2011) showed that in most sources and epochs. This is consistent with the Blandford & Königl (1979) model of a synchrotron self-absorbed conical jet in equipartition between energy densities of the magnetic field and the radiating particle population. Nonetheless, departures in from unity are also possible and can be caused by pressure and density gradients in the jet or by external absorption from the surrounding medium (Lobanov, 1998; Kadler et al., 2004).

The frequency-dependent offsets of the core positions can be used for astrophysical studies of ultra-compact AGN jets to calculate the magnetic fields, synchrotron luminosities, total (kinetic and magnetic field) power, maximum brightness temperature and geometrical properties of the jet (Lobanov, 1998). The core shift effect also has immediate astrometric applications. A typical shift between the radio (4 cm) and optical (6000 Å) domains for distant quasars is estimated to be at the level of 0.1 mas (Kovalev et al., 2008), which is comparable with the expected positional accuracy of the GAIA astrometric mission (Lindegren & Perryman, 1996). Thus, the core shifts are likely to influence not only the positional accuracy of the radio reference frame but also an alignment of optical and radio astrometry catalogs. Moreover, it is natural to expect that opacity properties are variable on a time scale from months to years due to the continuous emergence of new jet components, and especially during strong nuclear flares. Therefore, as discussed by Kovalev et al. (2008), a special coordinated program is required to perform multi-frequency and multi-epoch VLBI observation of a pre-selected source sample to investigate the problem of core shift variability.

A major difficulty in measuring the core shift is the accurate registration of the VLBI images taken at different frequencies. The problem stems from the loss of absolute position information in the standard VLBI data reduction path, which involves self-calibration of the station phases. Several approaches have been presented to overcome this difficulty and measure core shifts. One of them is based on relative VLBI astrometry, i.e., phase-referencing to a calibrator source (e.g. Marcaide & Shapiro, 1984; Lara et al., 1994; Guirado et al., 1995; Ros & Lobanov, 2001; Bietenholz et al., 2004; Hada et al., 2011). This particular technique is resource-consuming and has been used for a limited number of sources only. Another approach is the self-referencing method (Lobanov, 1998; Kovalev et al., 2008; Sokolovsky et al., 2011), in which the core shift is derived by referencing the core position to bright optically thin jet features whose positions are expected to be achromatic. Although this method has provided the majority of known core shift measurements, it has a certain limitation. It cannot be applied for faint or smooth jets that lack compact bright feature(s) well separated from the core at different frequencies. A proper alignment of the optically thin parts of the jet can also be accomplished by two-dimensional cross-correlation of the images, initially suggested and performed by Walker et al. (2000) for multi-frequency VLBA observations of 3C 84. The algorithm was also discussed by Croke & Gabuzda (2008) and Fromm et al. (in prep.), and applied by O’Sullivan & Gabuzda (2009) to obtain core shifts in four BL Lac objects. This approach, in conjunction with source model fitting, presents a more widely applicable method for deriving core shifts (see Sect. 3 for detailed discussion), which we use in this paper. Another alternative indirect method recently proposed by Kudryavtseva et al. (2011) is based on an analysis of time lags of flares monitored with single-dish observations. Although it has obvious limitations on the epoch at which the core shift can be measured, the method is promising for highly compact sources, which pose problems for other opacity study methods due to the lack of optically thin jet structure. It is noteworthy that all of the aforementioned techniques provide a comparable accuracy level. To date, only two core shift studies (Kovalev et al., 2008; Sokolovsky et al., 2011) have been carried out on large samples. They have shown that the effect is significant for many sources.

In this paper, we measure frequency-dependent shifts in the absolute core positions and study the statistical properties of the detected core shift vectors by using a large sample of sources from the MOJAVE (Monitoring Of Jets in Active galactic nuclei with VLBA Experiments) program (Lister et al., 2009). We also analyze systematics and discuss the uncertainties of the two-dimensional cross-correlation technique, investigating its properties for different jet morphologies. We constrain the basic physical properties of the jets, such as the magnetic field strength in the core region and at the true base of the flow, the distance from the jet apex to the radio core, as well as the estimate of the central black hole mass from the derived core shifts.

Throughout the paper, we assume the power index , i.e., (see model assumptions for this case above). We use the CDM cosmological model with  km s Mpc, , and (Komatsu et al., 2009). All position angles are given in degrees from north through east.

2 Observations and data processing

The MOJAVE project (Lister et al., 2009) is a long-term VLBA program aimed at investigating the structure and evolution of extragalactic relativistic radio jets in the northern sky. The full monitoring list currently consists of about 300 sources, and includes a statistically complete, flux-density limited sample of 135 AGN, referred to as MOJAVE-1. In addition to the program’s usual single-frequency setup at 15.4 GHz, 12 monthly separated epochs of observations during 2006 were carried out simultaneously also at 12.1, 8.4, and 8.1 GHz. The observations were made in dual circular polarization mode, with a bandwidth of 16 MHz at two lower bands and 32 MHz at two upper bands, and recorded with a bit rate of 128 Mbit s. In total, 191 sources were observed.

The initial calibration was performed with the NRAO Astronomical Image Processing System (AIPS) (Greisen, 2003) following the standard techniques. All frequency bands were processed separately throughout the data reduction. CLEANing (Högbom, 1974), phase and amplitude self-calibration (Jennison, 1958; Twiss et al., 1960), were performed in the Caltech Difmap (Shepherd, 1997) package. In all cases a point-source model was used as an initial model for the iterative procedure. Final maps were produced by applying natural weighting of the visibility function. For a more detailed discussion of the data reduction and imaging process schemes, see Lister et al. (2009); Hovatta et al. (2012).

The structure of each source at each frequency band was model-fitted in the visibility () plane in Difmap using circular and elliptical Gaussian components. To achieve matched resolution in all bands in the image plane, we appropriately cut the long baselines from the 15.4 and 12.1 GHz interferometric visibility data sets and short baselines from 8.1 and 8.4 GHz data sets. For each source, all maps were restored with the same beam size taken from lowest frequency (8.1 GHz) data using a pixel size of 0.03 mas, and these images were cross-correlated to register them as explained in Sect. 3.

This set of observations was also used to investigate the jet Faraday rotation measures (Hovatta et al., 2012) and spectral index distributions (Hovatta et al., in prep.).

3 Method for measuring the core shift

Registration of two VLBI images taken at different frequencies provides a shift between the image phase centers, such that they are co-aligned to the same position on the sky. This image shift is not equal to the core shift we want to measure. In general, the presence of the jet structure we detect results in a non-zero offset of the core from the phase center. As the core components significantly dominate in total flux, the magnitude of the offsets is typically small, but at the same time not negligible. When a distant jet component is brighter than the core, the offset can be large, as in the case of the quasar 0923+392, where the offset is about 2.6 mas. Extreme cases are discussed in Petrov et al. (2011). Moreover, these offsets are different at different frequencies for a given source, and become statistically larger at lower frequencies due to spectral properties of the jets. Figure 1 shows the core offsets at 15.4 and 8.1 GHz, with the median values being 36 and 81 as, respectively.

The core position departures from the phase center thus have to be taken into account to derive the core shifts. Because the image shift is independent of the core component position, it measures the vector sum of the absolute core shift () and the difference in the coordinates (offset shift relative to the map center) :

(1)

from which the magnitude and direction of the core shift vector can be readily calculated.

We used the fast normalized cross-correlation (NCC) algorithm by Lewis (1995) to register the images across the frequencies. The algorithm allows one to apply frequency domain methods to calculate the unnormalized cross correlation and then efficiently normalizes it by using precomputed integrals of the images over the search area. Thus, spatial domain computation of the cross correlation function is not needed and for large images the decrease in computing time is significant. The features that were matched between the images were selected from the optically thin part of the jet and assumed to have constant spectral index across them. The effect of possible spectral index gradients across the features is discussed in Sect. 5. In all cases, the image shifts , obtained with NCC, were verified by visually inspecting the corresponding spectral index images before and after the alignment, because the latter are extremely sensitive to the (in)accurate image alignment, as was shown by Kovalev et al. (2008). The spectral index images are presented and discussed by Hovatta et al. (in prep.). The image shifts between 15.4 GHz and other bands are found to be within a range of 0 and 1.11 mas, with a median value of 0.13 mas. The extreme value of 1.11 mas was detected in 3C 273 between 15.4 and 8.4 GHz, where the peak of brightness at those two frequencies corresponds to different features in the source structure. In some rare cases (e.g., 1928+738 at epoch 2006 Apr 28 of and 2128123 at epoch of 2006 Oct 6), when an optically thin, bright, compact jet component dominates in flux density, the image shift was measured to be zero, as expected for achromatic jet components. The accuracy of the two-dimensional cross-correlation technique is discussed in Sect. 5.

The magnitude of the core offset difference vector between 15.4 GHz and other bands ranged between 0 and 1.09 mas, with a median value of 0.05 mas. The maximum value of 1.09 mas holds also for quasar 3C 273 due to the same reason.

Figure 1: Phase center offsets of the core components at 8.1 GHz versus that at 15.4 GHz taken from model fits.
Source Epoch Median 15.4-8.1 GHz core shift 15.4-8.4 GHz core shift 15.4-12.1 GHz core shift
jet PA PA total proj PA total proj PA total proj
(deg) (deg) (mas) (mas) (deg) (mas) (mas) (deg) (mas) (mas)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)
0003066 2006-07-07 82.1 60.3 0.035 0.033 25.8 0.019 0.011 62.5 0.015 0.014
0003380 2006-03-09 117.0 77.2 0.134 0.103 79.6 0.139 0.110 77.2 0.124 0.095
0003380 2006-12-01 116.2 115.5 0.063 0.063 121.7 0.106 0.106 103.0 0.046 0.044
0007106 2006-06-15 67.6 88.5 0.008 0.007 20.1 0.011 0.007 146.2 0.008 0.007
0010405 2006-04-05 31.8 38.3 0.013 0.013 64.7 0.008 0.001
0010405 2006-12-01 32.6 0.3 0.005 0.004 39.1 0.005 0.001 89.9 0.010 0.006
0055300 2006-02-12 50.1 45.2 0.179 0.179 10.2 0.083 0.064 61.5 0.053 0.052
0106013 2006-07-07 125.2 113.7 0.005 0.005 139.2 0.005 0.005 20.2 0.002 0.001
1
Table 1: Derived core shift vectors.
Figure 2: Polar plots of the 15.4-8.1 (top), 15.4-8.4 (middle), and 15.4-12.1 GHz (bottom) core shift vectors. The polar axis is pointing to the right and co-aligns with the median jet direction of a source. Radial distance is given in mas. Dotted lines are drawn at intervals of .

4 Core shift measurement results

Substituting the results of model fitting and two-dimentional cross correlation into Eq. (1), we calculated the magnitude and direction of the 15.4-8.1, 15.4-8.4, and 15.4-12.1 GHz core shift vectors for 160, 158, and 147 sources (Table 5), respectively. For the other 31, 33, and 44 sources we could not measure the respective 15.4-8.1, 15.4-8.4, and 15.4-12.1 core shifts, mostly due to the weakness of their jet emission (especially at 15.4 GHz). This made the cross-correlation technique inapplicable, since there was no sufficiently large optically thin emission structure for feature matching. We also excluded those sources, mostly nearby galaxies listed in Table 2, whose core region was complex (e.g., 3C 84, M 87; the core shift in M 87 was studied by Hada et al. 2011 using phase-referencing VLBA observations) or for which the identification of the core component was unclear (e.g., 0108+388, 1509+054). The maximum and median magnitude of the derived 15.4-8.1, 15.4-8.4, and 15.4-12.1 GHz core shift vectors in angular and linear scale are summarized in Table 3. As seen from Table 3, the median values of the 15.4-8.1 and 15.4-8.4 GHz core shifts are comparable, while the 15.4-12.1 GHz ones are statistically smaller, as expected. In angular scale, these values are of about 8% of the corresponding FWHM beam size at 8.1 GHz.

In Fig. 2, we present plots of the derived core shifts in polar coordinates, where the head of each core shift vector represents the core position at lower frequency, while all core positions at higher frequency are placed at the origin. The polar axis corresponds to the median jet direction calculated from position angles of the jet components with respect to the core component, using a corresponding model fit at 15.4 GHz. Thus the polar coordinates of the head of each vector represent the magnitude of the core shift vector, , and the angular deviation from the jet direction, . The shift effect occurs predominantly along the jet direction. In more than 80% of cases, the core shift vectors deviate less than from the median jet position angle. Statistically, the larger core shifts have better alignment with the jet direction because (i) they are less influenced by random errors and (ii) the core shift takes place along the jet in most cases. The weighted average of is close to zero. Significant angular deviations of the core shift vectors from the median jet direction may take place in sources with substantial jet bending, either within an unresolved region near the VLBI core, or in the outer jet, thus affecting the median jet position angle. We have also analyzed distributions of the angular deviation between the core shift vectors and (i) inner jet direction determined as a position angle of the innermost jet component at 15.4 GHz and (ii) flux density-weighted average of the position angles of all Gaussian jet components at 15.4 GHz. In both these cases the scatter was larger, indicating that the median jet position angle is a better estimate for the direction of the outflow for the majority of sources.

Source Alias Opt. class    
0108388 G 0.668
0238084 NGC 1052 G 0.005037
0316413 3C 84 G 0.0176
0429415 3C 119 Q 1.022
0710439 G 0.518
1228126 M 87 G 0.00436
1404286 OQ 208 G 0.077
1509054 G 0.084
1607268 CTD 93 G 0.473
1957405 Cygnus A G 0.0561
2021614 OW 637 G 0.227
2
Table 2: Sources excluded from the analysis due to unclear core position.
Core shift angular linear
N max med N max med
(as) (as) (pc) (pc)
15.4-8.1 GHz 160 525 128 154 3.108 0.658
15.4-8.4 GHz 158 449 125 152 2.927 0.643
15.4-12.1 GHz 147 286 188 142 2.012 0.429
Table 3: Core shift statistics.

Our median 15.4-8.1 GHz core shift of 0.128 mas exceeds that of 0.080 mas reported by Sokolovsky et al. (2011), which was based on a smaller sample of 20 sources, for which the core shifts were derived using the self-referencing method. But if the 15.4-8.1 GHz core shifts for the 20-source sample are calculated from the fitted hyperbolas (Sokolovsky et al., 2011), which provide more accurate core shift values, the corresponding median yields 0.127 mas, which agrees well with the median of our sample.

The sources with the largest angular shifts are all at , as shown in Fig. 3 (top), where we plot the 15.4-8.1 GHz core shift against redshift values. All measurements are confined under the aspect line corresponding to 3.1 pc, the maximum linear 15.4-8.1 GHz shift (see Table 3). In contrast, in linear projected scale (Fig. 3, bottom), low-redshift sources are characterized by small shifts due to quick falling of the scale factor, while more distant sources have larger shifts. We have found evidence that the angular core shift decreases with increasing redshift by binning the data into nine equally populated bins, though we cannot claim the dependence to be highly significant due to the large scatter in measured core shifts, which stems from different physical conditions and viewing angles in different sources at the same redshift. The plots for 15.4-8.4 and 15.4-12.1 GHz core shifts are qualitatively similar to Fig. 3.

Additionally, we tested whether the core shift measurements are affected by limited angular resolution blending following the approach used by Kovalev et al. (2008). If present, this effect would preferentially increase the magnitude of the core shift vectors when they are better aligned with the major axis of the interferometric restoring beam resulting in a U-shape dependence between and , where is the position angle of the major axis of the beam, and . We found no such trend in the 15.4-8.1 GHz measurements, confirming that the registered core shifts are not dominated by blending.

Figure 3: Top: 15.4-8.1 GHz core shift in angular scale versus redshift. The dashed lines correspond to a fixed projected linear scale of 0.1, 1, and 3.1 pc. The latter curve envelopes all the measurements. Bottom: 15.4-8.1 GHz core shifts in projected linear scale versus redshift. Typical error values are discussed in Sect. 5.

5 Accuracy of the method

5.1 Random errors

As seen from Eq. (1), the uncertainty of the core shift is determined by errors of the core positions and image registration. However, individual a posteriori estimates of the image registration accuracy are problematic, since (1) in our case the values of the applied similarity criterion (NCC) are not normally distributed, making an estimation of random errors difficult, and since (2) systematic errors can only be addressed by simulations. Therefore, we used a statistical approach to assess the typical random core shift error in our sample. If we assume that (i) the core shift occurs along the jet and (ii) the errors are random in direction and comparable to each other, then the standard deviation of the transverse projections of the core shift vectors onto the jet direction yields the typical error. In Fig. 4, we plot the corresponding 15.4-8.1, 15.4-8.4, and 15.4-12.1 GHz distributions, from which we find  as,  as, and  as. From these values, we determine that in 57%, 59%, and 58% of cases the respective core shifts are significantly () different from zero, more than 90% of which in turn deviate less than from the median jet direction. The derived error estimates are conservative, since in some cases the angular deviations of the core shift vector from the median jet direction can be real, for instance, in curved jets.

Figure 4: Distributions of transverse projections of the 15.4-8.1, 15.4-8.4, and 15.4-12.1 GHz core shift vectors onto the jet direction.

An alternative way to estimate a typical random error in core shift is based on the fact that 8.1 and 8.4 GHz bands are closely separated, but were processed independently. Therefore, the 15.4-8.1 and 15.4-8.4 GHz core shifts are expected to be virtually the same and the non-zero difference between them is due purely to errors. This approach was also used in Sokolovsky et al. (2011). Constructing a distribution of these differences and calculating its standard deviation, we found  as, which is consistent with the error estimates obtained using the first method.

Since there is some freedom in selecting the jet feature to be matched in NCC, there is a possibility that user decisions affect the image registration results. We tested the robustness of the registration algorithm to “user bias” by having two different people separately perform the image alignment for one of the observing epochs. They both had similar instructions regarding the selection of the matched feature, i.e., (1) it should be optically thin, (2) and it should have as much structural variation as possible. The distribution of the differences in had a standard deviation of  as for pairs of images. This also closely matches the typical random error estimated above.

Figure 5: Naturally weighted total intensity CLEAN image of 0716+714 at 15.4 GHz (top). The alignment error (in beam widths) along the jet as a function of frequency ratio (middle). The alignment error (in beam widths) perpendicular to the jet (bottom). The error is defined as where is the position in the low-frequency image and is the corresponding position in the high-frequency image. The different spectral index gradients are shown in different colors: 0.1 mas (black squares), 0.2 mas (blue crosses), and 0.3 mas (red circles).
Figure 6: Naturally weighted total intensity CLEAN image of 3C273 at 15.4 GHz (top). The alignment error (in beam widths) along the jet as a function of frequency ratio (middle). The alignment error (in beam widths) perpendicular to the jet (bottom). The error is defined as where is the position in the low-frequency image and is the corresponding position in the high-frequency image. The different spectral index gradients are shown in different colors: 0.1 mas (black squares), 0.2 mas (blue crosses), and 0.3 mas (red circles).

5.2 Systematic errors

So far we have discussed random errors, but the image registration method is also prone to systematic errors that may bias our core shift measurements. Namely, the assumption of a constant spectral index across the matched features does not necessarily hold in real jets. Indeed, it is known that spectral index gradients occur along the jet. The spectral index images between 8.1 and 15.4 GHz typically show gradients in the optically thin part of the jet from  mas to  mas with an average of  mas (Hovatta et al., in prep.).

We tested the systematic effect that such gradients may have on image registration results by performing simulations. For the simulations we selected five sources with different jet morphologies: NGC 315 (straight, long and very smooth jet), 0716+714 (straight, short and smooth jet; Fig. 5, top), 3C 273 (long, wiggling jet with prominent knots; Fig. 6, top), BL Lac (wide, curved jet having one prominent knot downstream of the core), and 3C 454.3 (complex, curved jet with knots). For each source we created three sets of simulated images at six different frequencies exhibiting three different spectral index gradients along the jet: , , and  mas. The simulated images were based on a real 15.4 GHz image of a given source, to which a constant spectral index gradient along the jet was applied and new images at frequencies of 1.25, 1.50, 1.75, 2.00, 2.25, and 2.50 times the original frequency were calculated. Finally, random noise at the same level as in the original image was added to simulated images to ensure that background noise patterns between the images do not correlate. The original image and the simulated one were then registered using NCC. Note that this simulation setup provides a worst-case scenario in the sense that the gradient is assumed to be constant for the whole jet length, whereas in the real jets this is typically not the case.

The simulation results show that spectral index gradients along the jet can indeed affect the registration results and that the systematic error introduced this way depends on the jet morphology, the magnitude of the gradient, and the frequency ratio of the registered pair of images. In 3C 273 and BL Lac, which have significant structural detail in the optically thin part of the jet, the errors in the registered shift along the jet are less than 5% and less than 3% of the beam size, respectively, for all values of the gradient and for frequency ratios lower than 2. For 3C 273, a gradient of  mas results in an error that is less than 1% of the beam size (Fig. 6, middle). The jet in 3C 454.3 also has significant structural detail, and the systematic errors for a gradient of  mas stay below 4% of the beam size. However, for steeper gradients, the errors increase significantly, being less than 10% of the beam size for frequency ratios below 2. The featureless jets of NGC 315 and 0716+714 are the most prone to systematic errors caused by spectral index gradients along the jet: even the flattest gradient results in errors in the range of 10–18% of the beam size. In 0716+714 the gradients of and  mas result in errors of 24% and 27% of the beam size, respectively, at a frequency ratio of 2 (Fig. 5, middle). In NGC 315 the steeper gradients cause a significant jump in the image shift that exceeds the beam size.

The above simulation demonstrates that the level of detail in the optically thin part of the jet is crucial for the reliability of the cross-correlation based image registration. If the jet has knots or bends, cross-correlation is rather robust against possible spectral index gradients. On the other hand, the method clearly does not work with smooth, straight jets that exhibit spectral index gradients. Also, the direction of the erroneous image shift due to spectral index gradient along these smooth, straight jets is such that it can mimic a true core shift. Therefore, we have repeated the core shift analysis in a “clean sample” from which such jets are removed. Statistics on the clean sample that comprises 94 sources, however, did not show lower median values for 15.4-8.1, 15.4-8.4, and 15.4-12,1 GHz core shift distributions. This indicates that the effect of a possible overestimation of image shifts (and consequently core shifts) owing to a spectral index gradient along the jet is weak.

We also estimated positional errors (from the image plane) of the core components using the relation suggested by Fomalont (1999): , where and are the convolved size and peak intensity of the component, is the post-fit r.m.s. error associated with the pixels in a nine-beam area region under the component in the residual image. Because the cores are bright and compact, their signal-to-noise ratio values are high, with a median value of a few hundred, making the corresponding positional errors small, with a median value of about  as. This implies that the core shift error is typically dominated by the uncertainty of the image alignment for a sample of core-dominated AGN jets.

The typical accuracy level of about 50 as achieved in our core shift measurements is comparable to that from the self-referencing approach (Sokolovsky et al., 2011), where the errors are dominated by position uncertainties of a referencing jet component, which is usually larger in size and weaker in flux density with respect to the core. Phase-referencing observations may provide slightly better accuracy, down to 30 as, for the 15.4-8.4 GHz core shift, as reported by Hada et al. (2011), but cannot be used for a large number of sources as discussed in Sect. 1. Another complication of the phase-referencing method comes from the fact that the calibrator has its own core shift.

5.3 Stationary jet feature problem

Jets can exhibit standing features, like re-collimation shocks, in or close to their core region and these features could in principle introduce a level of artificial core shift owing to the degradation of the angular resolution with wavelength. To study how strong an effect these standing features could have, we used the AIPS task UVMOD to create simulated VLBA data sets at 8.1, 8.4, 15.3, 23.8, and 43.2 GHz. We used a real multi-wavelength VLBA observation to provide the plane sampling and noise properties at every frequency, and as an input model for UVMOD we used three Gaussian components representing the core, a standing feature, and a jet feature. A set of simulated data was generated with different flux ratios between the core and the standing feature (ranging from 10% to 50%) and with different distances between the two (0.15 mas and 0.3 mas). As a result, we had a simulated multi-wavelength VLBA data set in which all wavelengths had exactly the same sky brightness distribution, but different sampling and noise. Any apparent core-shift in this data set would be purely caused by the coverage differences at different frequencies. Analyzing the simulated data sets, we found that a close (within 0.3 mas from the 43 GHz core) standing jet feature can contribute to the expected core shift effect between 43 GHz and 8 GHz owing to frequency-dependent blending on the level of 10% of the expected core shift if the flux density ratio of the stationary feature and the core %, and reaching up to 30% of the expected core shift if %. Between the frequencies used in this study, i.e., 15 and 8 GHz, the core shift is affected by the frequency-dependent blending by  as, which is less than the estimated accuracy of our measurements. We note that these simulations describe a very simple situation and a more detailed study of the effect of stationary features to the measured core shift using real data is warranted. However, this is beyond the scope of the current work.

6 Jet physics with core shifts

To increase the robustness of our subsequent calculations, from now on we use a vector average for each pair of the 15.4-8.1 and 15.4-8.4 GHz core shifts. Moreover, if the core shift magnitude is smaller than 1 sigma level, we set  as to be used as the upper limit, since eliminating the small core shifts would introduce a bias. We excluded only the core shift vectors with , which are likely to be dominated by errors. In total, we have core shifts between 15 and 8 GHz for 136 sources, 108 of which have both redshift (Fig. 7, left) and apparent jet speed measurements. If a source had a second epoch, we selected the one at which the dynamic range of the 15 GHz image was higher.

Figure 7: Distribution of redshift (left) and core shift measure (right) for 136 sources with the core shift derived between 15 and 8 GHz. Gray filled bins represent 98 quasars (top), dashed bins represent 28 BL Lacs (middle), and cross-hatched bins represent 10 galaxies (bottom). Empty bins show upper limits.

As shown by Lobanov (1998), core shift measurements can be used for deriving a variety of physical conditions in the compact jets. In particular, assuming equipartition between the particle and magnetic field energy density () and a jet spectral index (), the magnetic field in Gauss at 1 pc of actual distance from the jet vertex can be calculated through the following proportionality (Hirotani, 2005; O’Sullivan & Gabuzda, 2009)

(2)

where is the half jet opening angle, is the viewing angle, is the Doppler factor, and is the core shift measure defined in Lobanov (1998) as

(3)

where is the core shift in milliarcseconds, and is the luminosity distance in parsecs. The calculated values of in pcGHz form a distribution ranging from 0.8 to 54.1 and peaking near the median of 13.6 (Fig. 7, right). The distributions of for quasars and BL Lacs are significantly different () as indicated by Gehan’s generalized Wilcoxon test from the ASURV survival analysis package (Lavalley et al., 1992), with medians of 18.6 and 7.1 pcGHz, respectively.

Figure 8: Distribution of magnetic field at a distance of 1 pc from the black hole for 84 quasars (top), 18 BL Lacs (bottom). Empty bins represent upper limits.

The combination of , , and in Eq. (2) is typically known for only a small fraction of sources, limiting the applicability of the formula. Therefore, the number of sources in our subsample with known apparent jet speed (Lister et al., 2009) is larger by a factor of 2 than the number of sources with known variability Doppler factor (Hovatta et al., 2009), intrinsic opening angle and viewing angle (e.g. Pushkarev et al., 2009; Savolainen et al., 2010). The denominator in (2) can be expressed through only by substituting and , and also taking into account that (Pushkarev et al., 2009) and . With these substitutions we are assuming the the jet is viewed at the critical angle that maximizes . We therefore obtain

(4)

where for we use the fastest non-accelerating, radial apparent speed measured in the source (Lister et al., 2009).

First, we tested the consistency of values calculated from Eqs. (2) and (4) for sources with previously measured and values. For 40 sources out of 43 in common, comprising 35 quasars and 8 BL Lacs, the results agree within the errors, with a median value of their ratio of 0.99. For three sources (0420014, 0804+499, and 1413+135), Eq. (2) gives several times higher values, most probably due to underestimated apparent speeds, to which (2) is more sensitive than (4), because the viewing angle and the opening angle . Indeed, these sources have low apparent speeds but high Doppler factors, leading to low viewing angle estimates of , , (Savolainen et al., 2010), respectively, and in turn to overestimated magnetic field strengths. The uncertainties in from Eq. 4 were calculated taking into account the errors in the core shifts, apparent speeds, and also from the assumption , which is known to introduce an additional source of errors, as discussed by Lister (1999). Since the aforementioned assumption is less correct for sources with low Lorentz factors, we excluded galaxies from the subsequent analysis.

Source Epoch Opt. class
(mas) (pc GHz) (G) (G) (pc)
0003066 2006-07-07 B 0.347 2.89 0.051 4.55 0.20 0.22 0.91
0106013 2006-07-07 Q 2.099 26.50 0.051 7.86 0.79 0.06 13.56
0119115 2006-06-15 Q 0.570 17.10 0.324 37.75 1.63 0.04 42.07
0133476 2006-08-09 Q 0.859 12.98 0.099 13.69 0.77 0.07 11.60
0149218 2006-02-12 Q 1.320 18.55 0.196 29.64 1.69 0.05 35.83
0202149 2006-09-06 Q 0.405 6.41 0.113 10.87 0.48 0.10 4.59
0212735 2006-07-07 Q 2.367 7.64 0.143 21.24 1.27 0.12 10.65
0215015 2006-04-28 Q 1.715 34.16 0.111 17.08 1.41 0.04 37.98
0224671 2006-10-06 Q 0.523 11.63 0.139 15.47 0.75 0.06 11.75
0234285 2006-09-06 Q 1.207 12.26 0.239 35.82 1.71 0.06 28.67
3
Table 4: Jet parameters derived for the sources with significant core shifts between 8 and 15 GHz.

The distributions of values derived from Eq. (4) for 84 quasars and 18 BL Lacs shown in Fig. 8 have medians of and  G, respectively, where the errors derived from a bootstrapping method indicate 95% confidence intervals. Gehan’s generalized Wilcoxon test from the ASURV survival analysis package indicates that the distributions of for quasars and BL Lacs are different at 99.6% confidence level. The difference is driven mainly by statistically higher redshifts for the quasars, and, though to a lesser degree, also by higher (Fig. 9). The values would be comparable for these classes of objects, if the ratio of the median core shifts for BL Lacs to that of quasars was about 2.7, but that is not the case. Systematically stronger magnetic fields in quasars can be a result of more massive black holes hosted by them and/or higher accretion rate in these objects, bacause larger black holes can accrete more matter, effectively powering the jets and accelerating particles to higher speeds. This scenario is also supported by an indication for quasars to have on average narrower intrinsic opening angles than those of BL Lacs, as reported by Pushkarev et al. (2009). At the same time, Woo & Urry (2002) argued that BL Lacs host black holes of comparable mass to quasars, though the estimates of black hole masses for quasars and BL Lacertae objects have been generated by different methods, and this may introduce a bias while comparing the mass assessments.

Figure 9: Magnetic field at a distance of 1 pc from the central black hole versus fastest non-accelerating, radial apparent speed. The measurements are enveloped under the dashed aspect line. The middle dotted line shows the dependence based on the medians for redshift and core shift measure .

The absolute distance in parsecs of the apparent VLBI core measured from the jet vertex is given by (Lobanov, 1998)

(5)

where is the observed frequency in GHz. Then the corresponding magnetic field strength is . In Fig. 10, we plot the derived and for the 15 GHz cores. Note that the core magnetic fields show a reverse tendency compared to the values, with a median of 0.10 G for BL Lacs and 0.07 G for quasars, because their apparent cores are at different separations from the true jet base, with medians of 4.0, and 13.2 pc, respectively.

On the projected plane (i.e., a VLBI map), the median separation of the 15 GHz core from the central black hole is about 1 pc, corresponding to about 0.14 mas for a source at . We summarize the derived physical quantities, such as , , , and in Table 6.

Figure 10: Magnetic field in the 15 GHz core versus its deprojected separation from the true jet base. The dashed line is the linear least-squares fit for quasar measurements.

The mass of a central black hole can be related to , such that (Lobanov, 1998). Its typical value is for quasars and BL Lacs. can also be used to estimate the magnetic field near the central black hole, assuming a dependence, where is the half-width of the jet. Thus, we have , where and are the the half-widths of the jet at 1 pc from the jet vertex and near the black hole, respectively. To derive , we assume that the jet is conical at distances larger than 1 pc. Then, we have , where is the half-width of the 15 GHz core, is the 15 GHz core separation from the jet vertex (both measured in pc), and is the intrinsic half jet opening angle. Because the black hole masses for BL Lacs are poorly known due to their weak emission lines, we restrict our analysis to quasars only. We derived the following median values: (Pushkarev et al., 2009),  pc,  pc. Then  pc and  G, assuming the jet width near the black hole to be on the order of its gravitational radius. The derived assessment of the magnetic field near the black hole is consistent with the theoretical value calculated from a model of a thin, magnetically driven accretion disk (Field & Rogers, 1993).

7 Summary

We have implemented a method for measuring the frequency-dependent shift in absolute position of the parsec-scale core and applied it to multi-frequency (8.1, 8.4, 12.1, and 15.4 GHz) VLBA observations of 191 sources performed during 2006 within the MOJAVE program. The method is based on results from (i) image registration achieved by a two-dimensional cross-correlation technique and (ii) structure model fitting. It has proved to be very effective and provided the core shifts in 163 sources (85%), with a median of 128 as between 15 and 8 GHz, and 88 as between 15 and 12 GHz. Despite the moderate separation of the observing frequencies, the derived core shifts are significant () in about 55% of cases, given an estimated typical uncertainty of 50 as between 15 and 8 GHz, and 35 as between 15 and 12 GHz. The errors are dominated by uncertainties from the two-dimentional cross-correlation procedure, because the relative positional uncertainties of the compact bright cores are at a level of a few microarcseconds. The significant core shift vectors are found to be preferentially aligned with the median jet direction, departing from it by less than in more than 90% of cases.

We used the measured core shifts for constraining magnetic field strengths and core sizes for 89 sources. The magnetic field at a distance of 1 pc from the jet injection point is found to be 0.9 G for quasars and 0.4 G for BL Lacs. Extrapolating all the way back by assuming a dependence, the magnetic field in the close vicinity of the black hole is about  G. The core sizes, i.e., the distances from the true jet base to its apparent origin at 15.4 GHz are statistically larger in quasars than in BL Lacs, with a median of 13.2 and 4.0 pc, respectively. At these distances, the magnetic field has a median of 0.07 G for quasars and 0.1 G for BL Lacertae objects.

Future multi-epoch and multi-frequency VLBI observations (including phase-referencing) of a pre-selected sample of sources with prominent core shifts are needed to address the question of the core shift variability, which can be used not only for astrophysical studies but also for astrometric applications. Ideally, these observations should be performed during and after strong nuclear flares that can be detected in advance in higher energy domains, e.g., optical or gamma-ray, and cover a wide range of observing frequencies, extending down to 5 or 2 GHz, where synchrotron self-absorption is essential.

Acknowledgements.
We would like to thank K. I. Kellermann, E. Ros, D. C. Homan and the rest of the MOJAVE team for the productive discussions. We thank the anonymous referee for useful comments, which helped to improve the manuscript. This research has made use of data from the MOJAVE database that is maintained by the MOJAVE team (Lister et al., 2009). The MOJAVE project is supported under National Science Foundation grant AST-0807860 and NASA Fermi grant NNX08AV67G. T.H. was supported in part by the Jenny and Antti Wihuri foundation. YYK is partly supported by the Russian Foundation for Basic Research (project 11-02-00368), Dynasty Foundation, and the basic research program “Active processes in galactic and extragalactic objects” of the Physical Sciences Division of the Russian Academy of Sciences. Part of this work was supported by the COST Action MP0905 “Black Holes in a Violent Universe”. The VLBA is a facility of the National Science Foundation operated by the National Radio Astronomy Observatory under cooperative agreement with Associated Universities, Inc.
\onllongtab

1

Source Epoch median 15.4–8.1 GHz core shift 15.4–8.4 GHz core shift 15.4–12.1 GHz core shift
jet PA PA total proj PA total proj PA total proj
(deg) (deg) (mas) (mas) (deg) (mas) (mas) (deg) (mas) (mas)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)
0003066 2006-07-07 82.1 60.3 0.035 0.033 25.8 0.019 0.011 62.5 0.015 0.014
0003380 2006-03-09 117.0 77.2 0.134 0.103 79.6 0.139 0.110 77.2 0.124 0.095
0003380 2006-12-01 116.2 115.5 0.063 0.063 121.7 0.106 0.106 103.0 0.046 0.044
0007106 2006-06-15 67.6 88.5 0.008 0.007 20.1 0.011 0.007 146.2 0.008 0.007
0010405 2006-04-05 31.8 38.3 0.013 0.013 64.7 0.008 0.001
0010405 2006-12-01 32.6 0.3 0.005 0.004 39.1 0.005 0.001 89.9 0.010 0.006
0055300 2006-02-12 50.1 45.2 0.179 0.179 10.2 0.083 0.064 61.5 0.053 0.052
0106013 2006-07-07 125.2 113.7 0.005 0.005 139.2 0.005 0.005 20.2 0.002 0.001
0109224 2006-05-24 85.1 65.3 0.147 0.138 91.6 0.073 0.072 75.8 0.120 0.118
0111021 2006-03-09 129.8 114.4 0.137 0.132 158.1 0.174 0.154 140.4 0.087 0.086
0119115 2006-06-15 3.7 1.0 0.347 0.346 0.7 0.300 0.299 17.0 0.221 0.207
0133476 2006-08-09 34.7 22.4 0.131 0.128 22.1 0.068 0.066 93.4 0.025 0.013
0149218 2006-02-12 13.9 7.3 0.168 0.167 5.4 0.223 0.221 23.3 0.107 0.106
0202149 2006-09-06 41.5 3.0 0.122 0.087 24.4 0.110 0.105 20.2 0.164 0.153
0202319 2006-08-09 7.9 158.2 0.013 0.012 96.9 0.003 0.001
0212735 2006-07-07 114.8 108.0 0.149 0.148 112.9 0.138 0.137 79.2 0.054 0.044
0215015 2006-04-28 105.7 89.3 0.088 0.084 127.0 0.147 0.137 143.6 0.003 0.001
0215015 2006-12-01 114.5 76.6 0.241 0.190 106.4 0.167 0.165 95.2 0.059 0.056
0219428 2006-04-05 173.2 170.7 0.080 0.080 159.0 0.076 0.073 154.0 0.031 0.029
0219428 2006-11-10 172.9 179.5 0.173 0.171 175.4 0.128 0.125 179.1 0.179 0.177
0224671 2006-10-06 8.2 20.9 0.134 0.131 19.9 0.143 0.140 0.9 0.125 0.124
0234285 2006-09-06 10.1 1.7 0.275 0.269 29.6 0.218 0.168 1.4 0.171 0.167
0235164 2006-06-15 15.2 18.7 0.004 0.003 0.8 0.007 0.006
0241622 2006-04-05 125.3 123.6 0.525 0.524 136.9 0.449 0.440
0300470 2006-11-10 142.7 147.9 0.298 0.297 147.4 0.312 0.311 161.7 0.094 0.089
0305039 2006-02-12 54.8 53.2 0.303 0.303 55.3 0.271 0.271 60.6 0.127 0.127
0309411 2006-04-28 56.8 36.6 0.005 0.000 97.0 0.005 0.004 118.5 0.007 0.007
0333321 2006-07-07 125.5 142.9 0.279 0.266 143.4 0.273 0.259 139.1 0.087 0.084
0336019 2006-08-09 57.3 97.4 0.117 0.089 117.2 0.096 0.048 83.8 0.131 0.117
0403132 2006-05-24 173.3 179.6 0.346 0.343 179.6 0.224 0.222
0415379 2006-05-24 65.2 75.8 0.315 0.310 79.2 0.191 0.185 90.3 0.122 0.111
0420014 2006-10-06 167.3 171.3 0.267 0.248 168.6 0.244 0.223 175.5 0.099 0.094
0430052 2006-05-24 116.3 163.6 0.075 0.051 171.5 0.071 0.041 144.2 0.118 0.104
0430289 2006-04-28 47.0 70.4 0.053 0.048 75.5 0.047 0.041 68.8 0.055 0.051
0440003 2006-07-07 134.7 81.2 0.008 0.006 115.6 0.008 0.003 15.8 0.007 0.004
0446112 2006-09-06 113.2 158.8 0.001 0.001 73.6 0.010 0.010
0454844 2006-03-09 164.8 163.3 0.344 0.292 147.5 0.266 0.179 132.9 0.127 0.059
0458020 2006-11-10 50.7 169.1 0.006 0.005 171.6 0.004 0.002 61.1 0.000 0.000
0528134 2006-10-06 49.5 39.0 0.167 0.164 44.5 0.134 0.133 55.5 0.095 0.095
0529075 2006-08-09 23.6 158.1 0.011 0.008 142.5 0.001 0.001 172.1 0.003 0.003
0552398 2006-07-07 74.1 84.5 0.007 0.007 90.4 0.008 0.007
0605085 2006-11-10 123.7 133.1 0.092 0.091 156.5 0.103 0.086 150.7 0.105 0.093
0607157 2006-09-06 57.3 95.5 0.240 0.188 95.2 0.268 0.212 94.6 0.065 0.052
0642449 2006-10-06 96.1 161.4 0.011 0.002 63.7 0.002 0.001 133.2 0.006 0.004
0648165 2006-12-01 69.5 106.7 0.225 0.179 107.4 0.206 0.163 85.5 0.062 0.060
0707476 2006-04-05 1.9 17.7 0.153 0.147 25.4 0.200 0.183 52.2 0.073 0.046
0716714 2006-05-24 22.9 16.8 0.127 0.097 33.8 0.150 0.148 15.7 0.198 0.196
0723008 2006-07-07 44.9 17.6 0.001 0.001 58.9 0.009 0.009 127.9 0.002 0.002
0727115 2006-10-06 63.9 63.7 0.240 0.240 63.2 0.246 0.246 42.0 0.198 0.183
0730504 2006-05-24 146.9 145.7 0.262 0.262 152.2 0.249 0.248 131.3 0.051 0.049
0735178 2006-04-28 61.8 79.7 0.039 0.037 80.0 0.158 0.150 74.8 0.157 0.153
0736017 2006-06-15 73.6 91.7 0.079 0.075 98.4 0.006 0.006 162.8 0.002 0.000
0738313 2006-09-06 170.8 168.2 0.183 0.183 179.0 0.093 0.092 174.2 0.100 0.099
0748126 2006-08-09 101.1 89.6 0.098 0.096 91.0 0.095 0.094 91.2 0.041 0.041
0754100 2006-04-28 19.2 12.7 0.266 0.264 12.7 0.294 0.293 19.6 0.073 0.073
0804499 2006-10-06 106.1 169.0 0.094 0.043 165.1 0.052 0.027 148.6 0.032 0.024
0805077 2006-05-24 29.4 14.8 0.207 0.201 41.2 0.260 0.255 10.1 0.162 0.153
0808019 2006-08-09 168.7 101.7 0.010 0.004
0814425 2006-11-10 99.2 89.1 0.145 0.143 110.9 0.124 0.122 91.4 0.090 0.089
0823033 2006-06-15 30.2 9.5 0.141 0.132 9.2 0.143 0.133 16.3 0.083 0.080
0827243 2006-05-24 116.6 126.4 0.150 0.148 129.2 0.127 0.124 114.0 0.155 0.155
0829046 2006-07-07 66.0 78.4 0.109 0.106 75.1 0.153 0.151 7.6 0.025 0.007
0834201 2006-03-09 115.9 76.3 0.147 0.113 50.3 0.123 0.051 58.4 0.064 0.034
0836710 2006-09-06 144.7 148.5 0.186 0.185 135.8 0.159 0.157 120.7 0.163 0.149
0847120 2006-12-01 64.0 64.4 0.007 0.007 170.1 0.003 0.001 158.0 0.005 0.000
0851202 2006-04-28 121.2 121.9 0.028 0.028 123.5 0.021 0.021 125.3 0.018 0.018
0859140 2006-02-12 157.3 164.5 0.266 0.209 155.6 0.167 0.167 171.4 0.147 0.142
0906015 2006-10-06 43.4 34.4 0.168 0.166 26.6 0.239 0.229 43.2 0.201 0.201
0917624 2006-08-09 26.2 8.4 0.112 0.107 6.6 0.111 0.104 23.2 0.089 0.058
0923392 2006-07-07 98.9 141.9 0.042 0.031 147.7 0.032 0.021 88.3 0.168 0.165
0945408 2006-06-15 114.2 125.9 0.083 0.081 113.0 0.145 0.145 75.9 0.027 0.021
0953254 2006-03-09 120.3 166.5 0.019 0.006 140.8 0.023 0.022 71.5 0.074 0.049
0954658 2006-04-05 41.8 16.1 0.005 0.003 97.7 0.004 0.003 65.1 0.012 0.011
0955476 2006-11-10 20.9 86.9 0.040 0.016
1015359 2006-03-09 175.7 156.6 0.151 0.143 129.8 0.061 0.042 176.2 0.061 0.061
1036054 2006-05-24 9.2 10.1 0.195 0.195 5.0 0.170 0.169 3.3 0.043 0.043
1038064 2006-10-06 155.2 167.2 0.106 0.084 177.3 0.188 0.174 171.0 0.074 0.072
1045188 2006-09-06 151.5 157.8 0.156 0.155 158.9 0.179 0.177 159.0 0.218 0.217
1055018 2006-11-10 56.3 97.0 0.074 0.056
1101384 2006-04-05 24.7 0.1 0.230 0.209 3.4 0.280 0.260 1.5 0.147 0.132
1127145 2006-08-09 82.3 141.7 0.096 0.049 130.6 0.082 0.055 91.5 0.052 0.051
1128047 2006-02-12 161.4 168.1 0.131 0.130 173.8 0.307 0.300 178.0 0.209 0.200
1128047 2006-12-01 155.2 161.0 0.250 0.181 167.4 0.251 0.200
1148001 2006-07-07 121.9 155.8 0.128 0.106 121.8 0.100 0.100 104.5 0.117 0.112
1150812 2006-06-15 128.7 132.8 0.087 0.087 134.5 0.077 0.076 138.0 0.141 0.139
1156295 2006-09-06 4.6 0.0 0.162 0.162 4.1 0.147 0.145 12.7 0.088 0.084
1213172 2006-10-06 117.2 111.0 0.056 0.056 110.4 0.132 0.131 156.0 0.174 0.136
1219044 2006-05-24 172.1 179.4 0.133 0.131 179.7 0.206 0.204 173.1 0.054 0.054
1219285 2006-02-12 109.3 95.5 0.182 0.177 63.4 0.068 0.047 114.9 0.078 0.078
1219285 2006-11-10 110.2 101.5 0.199 0.196 98.7 0.230 0.226 118.5 0.062 0.061
1222216 2006-04-28 0.6 9.3 0.180 0.178 11.0 0.159 0.156 3.1 0.074 0.073
1226023 2006-03-09 137.3 48.0 0.020 0.020 97.8 0.022 0.017 149.5 0.118 0.115
1243072 2006-04-05 91.6 167.3 0.012 0.003 119.9 0.018 0.016 105.3 0.015 0.014
1253055 2006-04-05 130.2 107.4 0.048 0.045 124.8 0.076 0.076 94.9 0.098 0.080
1253055 2006-09-06 126.7 132.6 0.026 0.026 85.5 0.059 0.044 87.1 0.118 0.091
1302102 2006-03-09 30.5 47.1 0.220 0.211 46.8 0.321 0.308 64.8 0.064 0.053
1308326 2006-07-07 44.0 53.2 0.143 0.142 5.8 0.059 0.047 3.5 0.034 0.026
1324224 2006-12-01 36.4 23.6 0.001 0.000 167.2 0.006 0.004 104.7 0.007 0.003
1331170 2006-04-05 18.8 18.0 0.145 0.145 14.2 0.153 0.152 15.8 0.114 0.114
1334127 2006-10-06 149.6 174.8 0.237 0.193 177.3 0.311 0.260 175.3 0.167 0.137
1345125 2006-11-10 164.7 155.1 0.126 0.124 161.5 0.117 0.097 174.0 0.166 0.155
1406076 2006-04-05 96.3 131.6 0.092 0.075 36.7 0.120 0.061 124.9 0.101 0.089
1413135 2006-08-09 113.5 112.3 0.230 0.230 112.3 0.226 0.225 111.2 0.238 0.238
1418546 2006-02-12 131.3 122.2 0.067 0.066 121.3 0.103 0.101 130.5 0.142 0.142
1418546 2006-11-10 133.7 135.3 0.076 0.076 135.2 0.085 0.085 131.8 0.047 0.047
1458718 2006-09-06 164.1 173.1 0.081 0.075 170.4 0.054 0.049 118.9 0.031 0.022
1502106 2006-07-07 122.6 164.6 0.052 0.039 159.1 0.059 0.048 140.8 0.126 0.120
1504166 2006-12-01 163.7 174.7 0.148 0.138 174.2 0.081 0.075 79.0 0.019 0.009
1508055 2006-03-09 81.5 97.3 0.210 0.202 99.8 0.149 0.141 70.4 0.007 0.007
1510089 2006-04-28 33.2 4.2 0.122 0.097 16.2 0.184 0.176 65.2 0.047 0.040
1514004 2006-04-05 28.1 36.5 0.139 0.138 8.6 0.178 0.168 20.7 0.190 0.188
1514241 2006-04-28 171.7 179.0 0.188 0.187 174.9 0.217 0.217 177.3 0.135 0.134
1532016 2006-03-09 139.8 126.6 0.144 0.140 123.7 0.103 0.099 147.2 0.178 0.177
1538149 2006-06-15 36.5 81.7 0.032 0.022 47.2 0.127 0.125 47.7 0.116 0.114
1546027 2006-08-09 172.3 87.2 0.010 0.001 131.9 0.000 0.000 79.1 0.006 0.002
1606106 2006-07-07 44.3 23.3 0.057 0.053 0.1 0.092 0.066 55.0 0.032 0.032
1611343 2006-06-15 157.7 161.0 0.057 0.043 173.6 0.063 0.055 177.9 0.094 0.088
1633382 2006-09-06 72.8 66.6 0.119 0.119 68.3 0.158 0.157 66.9 0.157 0.156
1637574 2006-05-24 156.4 167.3 0.117 0.115 162.2 0.089 0.088 135.0 0.013 0.005
1637826 2006-03-09 61.5 54.0 0.210 0.208 63.6 0.148 0.148 55.7 0.155 0.154
1638398 2006-08-09 89.8 39.4 0.007 0.005 103.7 0.011 0.011
1641399 2006-06-15 90.5 90.8 0.211 0.211 91.5 0.190 0.190 89.0 0.121 0.121
1642690 2006-03-09 165.6 165.2 0.056 0.055 165.6 0.048 0.048
1652398 2006-02-12 147.9 171.5 0.289 0.265 171.5 0.269 0.246 160.4 0.200 0.196
1655077 2006-11-10 41.4 82.8 0.080 0.060 84.3 0.042 0.031 45.3 0.046 0.046
1725044 2006-03-09 120.5 135.3 0.100 0.097 139.7 0.057 0.054 125.4 0.062 0.062
1726455 2006-09-06 113.2 87.8 0.009 0.008 116.1 0.011 0.007
1730130 2006-07-07 8.3 20.9 0.174 0.170 21.9 0.216 0.210 20.8 0.112 0.109
1741038 2006-12-01 130.0 74.7 0.001 0.000 52.6 0.014 0.014 63.3 0.002 0.001
1749096 2006-06-15 25.4 26.9 0.061 0.061 11.9 0.106 0.103 16.3 0.123 0.121
1749701 2006-04-05 59.4 34.9 0.196 0.179 64.0 0.224 0.223 37.5 0.184 0.170
1751288 2006-10-06 2.2 87.6 0.007 0.000 105.1 0.010 0.003
1758388 2006-11-10 92.4 31.5 0.079 0.038 44.9 0.079 0.053
1803784 2006-09-06 86.0 112.7 0.029 0.026 70.5 0.067 0.064 91.4 0.076 0.076
1807698 2006-02-12 101.3 104.9 0.249 0.248 92.8 0.186 0.184 73.3 0.019 0.019
1823568 2006-07-07 160.8 177.1 0.052 0.048 156.6 0.140 0.140 101.1 0.013 0.002
1828487 2006-08-09 40.5 53.7 0.117 0.114 59.1 0.075 0.071 60.7 0.060 0.056
1845797 2006-02-12 37.3 17.8 0.084 0.079 62.7 0.111 0.100 34.1 0.140 0.139
1849670 2006-05-24 41.0 29.7 0.024 0.024 19.4 0.010 0.010 24.6 0.014 0.013
1901319 2006-02-12 119.6 107.2 0.283 0.277 148.6 0.222 0.194 52.2 0.022 0.008
1908201 2006-03-09 6.4 4.5 0.246 0.246 1.9 0.219 0.219 7.6 0.189 0.183
1928738 2006-04-28 160.7 163.1 0.147 0.147 162.9 0.163 0.162 160.3 0.012 0.009
1936155 2006-07-07 122.1 139.0 0.215 0.206 143.4 0.258 0.240 153.6 0.138 0.118
1958179 2006-10-06 122.9 2.5 0.003 0.002
2005403 2006-09-06 107.0 94.9 0.280 0.274 89.2 0.336 0.320 111.9 0.122 0.121
2008159 2006-11-10 21.8 51.9 0.008 0.007 152.6 0.013 0.013
2021317 2006-08-09 156.5 173.5 0.384 0.367 157.9 0.218 0.218 166.3 0.120 0.118
2022077 2006-04-05 4.8 111.4 0.006 0.003 78.5 0.007 0.001 7.4 0.008 0.008
2037511 2006-05-24 142.1 122.5 0.024 0.002 136.7 0.051 0.051 119.5 0.052 0.048
2113293 2006-02-12 170.8 165.4 0.268 0.267 164.0 0.225 0.224 169.3 0.114 0.114
2121053 2006-06-15 95.4 127.5 0.152 0.129 107.1 0.149 0.146 83.0 0.102 0.100
2128123 2006-10-06 149.0 142.5 0.223 0.221 143.7 0.261 0.260 125.8 0.055 0.050
2131021 2006-08-09 93.0 83.7 0.089 0.088 88.6 0.109 0.109 126.4 0.063 0.053
2134004 2006-07-07 76.7 83.6 0.188 0.186 94.7 0.158 0.150
2136141 2006-09-06 98.3 88.7 0.008 0.008 126.5 0.011 0.009
2145067 2006-10-06 129.1 152.0 0.008 0.007 12.6 0.007 0.003
2155152 2006-12-01 139.0 126.6 0.405 0.395 149.6 0.296 0.291 143.2 0.286 0.286
2200420 2006-04-05 175.4 142.0 0.032 0.023 166.0 0.074 0.070 177.6 0.160 0.160
2200420 2006-11-10 167.4 173.6 0.031 0.031 178.7 0.135 0.131 171.4 0.124 0.124
2201171 2006-05-24 48.6 34.2 0.380 0.368 33.8 0.358 0.346 20.7 0.136 0.121
2201315 2006-10-06 140.4 137.7 0.347 0.346 137.7 0.343 0.343 147.5 0.110 0.109
2209236 2006-12-01 36.6 71.0 0.038 0.012 101.8 0.085 0.036
2216038 2006-08-09 165.8 68.0 0.011 0.006 47.1 0.005 0.002 18.0 0.010 0.008
2223052 2006-10-06 96.3 97.1 0.199 0.199 89.1 0.125 0.124 153.0 0.098 0.054
2227088 2006-07-07 18.4 1.4 0.186 0.175 2.6 0.200 0.187 0.8 0.209 0.199
2230114 2006-02-12 150.0 166.5 0.278 0.266 175.1 0.363 0.329 147.2 0.111 0.111
2243123 2006-09-06 13.2 6.9 0.161 0.160 1.6 0.167 0.163 7.2 0.140 0.139
2251158 2006-03-09 83.5 104.6 0.124 0.116 111.6 0.115 0.101 99.9 0.053 0.050
2251158 2006-06-15 83.9 85.0 0.177 0.177 110.7 0.150 0.134 96.2 0.114 0.112
2320035 2006-04-05 23.7 53.5 0.009 0.008 36.9 0.040 0.038 35.8 0.044 0.043
2345167 2006-11-10 120.8 132.9 0.167 0.163 125.2 0.148 0.148 135.6 0.166 0.160
2351456 2006-05-24 79.2 113.1 0.196 0.163 119.7 0.146 0.111 112.6 0.061 0.051
2356196 2006-04-05 149.0 156.4 0.203 0.201 154.9 0.185 0.184 174.6 0.166 0.150
2356196 2006-10-06 147.3 178.2 0.163 0.140 117.1 0.118 0.102 176.7 0.135 0.109
Table 5: Continued.

Columns are as follows: (1) IAU name (B1950.0); (2) epoch of observations; (3) 15.4 GHz median jet position angle; (4) position angle of the 15.4–8.1 GHz core shift vector; (5) magnitude of the 15.4–8.1 GHz core shift vector; (6) 15.4–8.1 GHz core shift vector in projection on the median position angle; (7), (8), (9), and (10), (11), (12) the same as (4), (5), (6) but for 15.4–8.1 GHz and 15.4–12.1 GHz core shifts, respectively.

\onllongtab

4

Source Epoch Opt. 4
cl.
(mas) (pc GHz) (G) (G) (pc)
0003066 2006-07-07 B 0.347 2.89 0.051 4.55 0.20 0.22 0.91
0106013 2006-07-07 Q 2.099 26.50 0.051 7.86 0.79 0.06 13.56
0119115 2006-06-15 Q 0.570 17.10 0.324 37.75 1.63 0.04 42.07
0133476 2006-08-09 Q 0.859 12.98 0.099 13.69 0.77 0.07 11.60
0149218 2006-02-12 Q 1.320 18.55 0.196 29.64 1.69 0.05 35.83
0202149 2006-09-06 Q 0.405 6.41 0.113 10.87 0.48 0.10 4.59
0212735 2006-07-07 Q 2.367 7.64 0.143 21.24 1.27 0.12 10.65
0215015 2006-04-28 Q 1.715 34.16 0.111 17.08 1.41 0.04 37.98
0224671 2006-10-06 Q 0.523 11.63 0.139 15.47 0.75 0.06 11.75
0234285 2006-09-06 Q 1.207 12.26 0.239 35.82 1.71 0.06 28.67
0333321 2006-07-07 Q 1.259 12.76 0.276 41.51 1.95 0.06 34.57
0336019 2006-08-09 Q 0.852 22.36 0.105 14.41 0.92 0.04 20.99
0403132 2006-05-24 Q 0.571 19.69 0.285 33.30 1.54 0.04 42.72
0420014 2006-10-06 Q 0.914 7.36 0.256 35.94 1.41 0.08 17.37
0454844 2006-03-09 B 0.112 0.14 0.302 10.91 0.27 0.37 0.72
0528134 2006-10-06 Q 2.070 19.20 0.150 22.71 1.60 0.06 28.41
0552398 2006-07-07 Q 2.363 0.36 0.051 7.72 0.36 0.68 0.53
0605085 2006-11-10 Q 0.872 19.79 0.096 13.24 0.84 0.05 17.07
0607157 2006-09-06 Q 0.324 3.93 0.254 21.22 0.68 0.12 5.60
0716714 2006-05-24 B 0.310 10.06 0.125 10.16 0.49 0.07 6.68
0730504 2006-05-24 Q 0.720 14.06 0.255 33.04 1.47 0.05 30.30
0736017 2006-06-15 Q 0.191 14.32 0.051 2.94 0.20 0.07 2.75
0738313 2006-09-06 Q 0.631 10.76 0.138 16.85 0.81 0.07 11.85
0748126 2006-08-09 Q 0.889 18.37 0.097 13.49 0.84 0.05 16.15
0754100 2006-04-28 B 0.266 14.40 0.280 20.38 0.88 0.05 19.14
0804499 2006-10-06 Q 1.436 1.83 0.073 11.15 0.48 0.32 1.51
0805077 2006-05-24 Q 1.837 50.60 0.228 34.84 2.71 0.02 114.73
0823033 2006-06-15 B 0.506 17.80 0.142 15.57 0.83 0.05 18.06
0827243 2006-05-24 Q 0.940 22.01 0.139 19.64 1.18 0.04 28.16
0829046 2006-07-07 B 0.174 10.09 0.131 6.85 0.34 0.08 4.52
0836710 2006-09-06 Q 2.218 25.38 0.172 25.72 1.93 0.05 42.51
0851202 2006-04-28 B 0.306 15.17 0.051 4.18 0.28 0.07 4.13
0859140 2006-02-12 Q 1.339 16.47 0.204 30.96 1.70 0.05 33.24
0906015 2006-10-06 Q 1.024 20.68 0.203 29.45 1.61 0.04 39.67
0917624 2006-08-09 Q 1.446 15.57 0.111 16.99 1.09 0.06 17.25
0923392 2006-07-07 Q 0.695 4.29 0.051 6.64 0.33 0.17 1.90
0945408 2006-06-15 Q 1.249 18.60 0.113 17.02 1.10 0.05 20.63
0953254 2006-03-09 Q 0.712 11.52 0.051 6.71 0.42 0.08 5.05
1015359 2006-03-09 Q 1.226 12.46 0.104 15.55 0.92 0.07 12.65
1036054 2006-05-24 Q 0.473 6.15 0.182 19.26 0.74 0.09 7.81
1038064 2006-10-06 Q 1.265 11.87 0.146 21.97 1.19 0.07 17.03
1045188 2006-09-06 Q 0.595 8.57 0.167 19.94 0.86 0.08 11.19
1101384 2006-04-05 B 0.031 0.82 0.254 2.81 0.10 0.42 0.24
1127145 2006-08-09 Q 1.184 14.18 0.089 13.24 0.84 0.07 12.25
1150812 2006-06-15 Q 1.250 7.09 0.082 12.34 0.68 0.12 5.75
1156295 2006-09-06 Q 0.729 24.73 0.154 20.11 1.17 0.04 32.39
1219044 2006-05-24 Q 0.965 2.35 0.169 24.16 0.81 0.20 4.01
1222216 2006-04-28 Q 0.432 21.10 0.170 17.03 0.90 0.04 23.41
1253055 2006-09-06 Q 0.536 20.57 0.051 5.88 0.42 0.05 7.88
1302102 2006-03-09 Q 0.278 5.41 0.271 20.34 0.70 0.10 7.28
1308326 2006-07-07 Q 0.997 27.17 0.095 13.61 0.96 0.04 24.08
1334127 2006-10-06 Q 0.539 10.26 0.274 31.08 1.23 0.06 20.85
1413135 2006-08-09 B 0.247 1.80 0.228 15.70 0.44 0.21 2.10
1458718 2006-09-06 Q 0.904 7.04 0.068 9.46 0.51 0.12 4.38
1502106 2006-07-07 Q 1.839 14.77 0.056 8.50 0.69 0.08 8.19
1504166 2006-12-01 Q 0.876 4.31 0.115 15.90 0.66 0.15 4.58
1508055 2006-03-09 Q 1.191 18.64 0.179 26.81 1.52 0.05 32.56
1510089 2006-04-28 Q 0.360 20.14 0.151 13.50 0.73 0.04 17.71
1532016 2006-03-09 Q 1.420 14.11 0.123 18.81 1.14 0.07 17.31
1538149 2006-06-15 B 0.605 8.73 0.077 9.25 0.49 0.09 5.29
1546027 2006-08-09 Q 0.414 12.08 0.051 5.09 0.32 0.08 4.01
1606106 2006-07-07 Q 1.226 18.91 0.073 10.97 0.79 0.06 13.52
1611343 2006-06-15 Q 1.397 14.11 0.059 9.07 0.66 0.08 8.35
1633382 2006-09-06 Q 1.814 29.45 0.139 21.21 1.62 0.04 40.67
1637574 2006-05-24 Q 0.751 10.61 0.103 13.51 0.71 0.08 9.37
1641399 2006-06-15 Q 0.593 19.27 0.201 23.85 1.20 0.04 29.94
1642690 2006-03-09 Q 0.751 16.65 0.051 6.85 0.48 0.06 7.43
1652398 2006-02-12 B 0.033 0.21 0.279 3.25 0.10 0.48 0.22
1655077 2006-11-10 Q 0.621 14.45 0.061 7.45 0.47 0.07 7.02
1726455 2006-09-06 Q 0.717 1.82 0.051 6.73 0.28 0.30 0.91
1730130 2006-07-07 Q 0.902 35.69 0.195 27.31 1.69 0.03 63.44
1749096 2006-06-15 B 0.322 6.84 0.083 6.92 0.33 0.11 3.11
1749701 2006-04-05 B 0.770 6.03 0.203 27.03 1.04 0.10 10.75
1803784 2006-09-06 B 0.680 8.97 0.051 6.58 0.39 0.10 3.86
1807698 2006-02-12 B 0.051 0.10 0.216 3.81 0.12 0.47 0.25
1823568 2006-07-07 B 0.664 20.85 0.094 11.79 0.74 0.05 16.01
1828487 2006-08-09 Q 0.692 13.65 0.096 12.24 0.69 0.06 10.90
1849670 2006-05-24 Q 0.657 30.63 0.051 6.48 0.52 0.04 12.92
1901319 2006-02-12 Q 0.635 2.67 0.236 29.03 0.87 0.16 5.39
1928738 2006-04-28 Q 0.302 8.43 0.155 12.31 0.54 0.08 6.80
1936155 2006-07-07 Q 1.657 2.60 0.236 36.23 1.31 0.20 6.57
2005403 2006-09-06 Q 1.736 12.21 0.308 47.18 2.34 0.06 37.61
2037511 2006-05-24 Q 1.686 3.30 0.051 7.98 0.45 0.25 1.79
2113293 2006-02-12 Q 1.514 1.40 0.247 37.78 1.16 0.27 4.23
2121053 2006-06-15 Q 1.941 13.29 0.148 22.61 1.43 0.07 19.61
2128123 2006-10-06 Q 0.501 6.94 0.242 26.41 0.98 0.08 12.05
2131021 2006-08-09 B 1.285 20.02 0.099 14.94 1.02 0.05 19.49
2134004 2006-07-07 Q 1.932 5.94 0.172 26.23 1.31 0.13 10.28
2136141 2006-09-06 Q 2.427 5.43 0.051 7.68 0.55 0.20 2.76
2145067 2006-10-06 Q 0.990 2.52 0.051 7.48 0.34 0.26 1.32
2155152 2006-12-01 Q 0.672 18.11 0.343 43.23 1.89 0.04 51.02
2200420 2006-04-05 B 0.069 10.57 0.052 1.21 0.09 0.11 0.84
2201171 2006-05-24 Q 1.076 2.55 0.369 54.08 1.55 0.16 9.64
2201315 2006-10-06 Q 0.295 7.87 0.345 27.04 0.95 0.07 13.96
2209236 2006-12-01 Q 1.125 3.43 0.051 7.69 0.39 0.22 1.79
2223052 2006-10-06 Q 1.404 17.34 0.162 24.63 1.47 0.05 27.83
2227088 2006-07-07 Q 1.560 8.14 0.193 29.60 1.44 0.09 15.80
2230114 2006-02-12 Q 1.037 15.41 0.320 46.48 2.12 0.05 46.70
2243123 2006-09-06 Q 0.632 5.49 0.164 20.10 0.78 0.11 7.30
2251158 2006-06-15 Q 0.859 14.19 0.159 22.00 1.13 0.06 20.36
2345167 2006-11-10 Q 0.576 13.45 0.157 18.44 0.90 0.06 16.18
2351456 2006-05-24 Q 1.986 18.01 0.171 25.97 1.72 0.06 30.48
Table 6: Continued.

Footnotes

  1. (1) IAU name (B1950.0); (2) epoch of observations; (3) 15.4 GHz median jet position angle; (4) position angle of the 15.4-8.1 GHz core shift vector; (5) magnitude of the 15.4-8.1 GHz core shift vector; (6) 15.4-8.1 GHz core shift vector in projection on the median position angle; (7), (8), (9), and (10), (11), (12) the same as (4), (5), (6) but for 15.4-8.4 GHz and 15.4-12.1 GHz core shifts, respectively. Table 5 is published in its entirety in the electronic version of Astronomy & Astrophysics. A portion is shown here for guidance regarding its form and content.
  2. As compiled by Lister et al. (2009)
  3. Apparent speed values are taken from Lister et al. (2009). Table 6 is published in its entirety in the electronic version of Astronomy & Astrophysics. A portion is shown here for guidance regarding its form and content.
  4. From Lister et al. (2009)

References

  1. Bietenholz, M. F., Bartel, N., & Rupen, M. P. 2004, ApJ, 615, 173
  2. Blandford, R. D. & Königl, A. 1979, ApJ, 232, 34
  3. Croke, S. M. & Gabuzda, D. C. 2008, MNRAS, 386, 619
  4. Field, G. B. & Rogers, R. D. 1993, ApJ, 403, 94
  5. Fomalont, E. B. 1999, in Astronomical Society of the Pacific Conference Series, Vol. 180, Synthesis Imaging in Radio Astronomy II, ed. G. B. Taylor, C. L. Carilli, & R. A. Perley, 301–320
  6. Fromm, C. M., Ros, E., Savolainen, T., et al. 2010, arXiv:1011.4825
  7. Greisen, E. W. 2003, in Astrophysics and Space Science Library 285, Information Handling in Astronomy – Historical Vistas, ed. A. Heck (Dordrecht: Kluwer), 109
  8. Guirado, J. C., Marcaide, J. M., Alberdi, A., et al. 1995, AJ, 110, 2586
  9. Hada, K., Doi, A., Kino, M., et al. 2011, Nature, 477, 185
  10. Hirotani, K. 2005, ApJ, 619, 73
  11. Högbom, J. A. 1974, A&AS, 15, 417
  12. Hovatta, T., Lister, M. L., Aller, M. F., et al. 2012, AJ, submitted
  13. Hovatta, T., Valtaoja, E., Tornikoski, M., & Lähteenmäki, A. 2009, A&A, 498, 723
  14. Hujeirat, A., Livio, M., Camenzind, M., & Burkert, A. 2003, A&A, 408, 415
  15. Jennison, R. C. 1958, MNRAS, 118, 276
  16. Junor, W., Biretta, J. A., & Livio, M. 1999, Nature, 401, 891
  17. Kadler, M., Ros, E., Lobanov, A. P., Falcke, H., & Zensus, J. A. 2004, A&A, 426, 481
  18. Kellermann, K. I., Kovalev, Y. Y., Lister, M. L., et al. 2007, Ap&SS, 311, 231
  19. Koide, S., Shibata, K., Kudoh, T., & Meier, D. L. 2002, Science, 295, 1688
  20. Komatsu, E., Dunkley, J., Nolta, M. R., et al. 2009, ApJS, 180, 330
  21. Komissarov, S. S. 2005, MNRAS, 359, 801
  22. Königl, A. 1981, ApJ, 243, 700
  23. Kovalev, Y. Y., Lobanov, A. P., Pushkarev, A. B., & Zensus, J. A. 2008, A&A, 483, 759
  24. Kudryavtseva, N. A., Gabuzda, D. C., Aller, M. F., & Aller, H. D. 2011, MNRAS, 415, 1631
  25. Lara, L., Alberdi, A., Marcaide, J. M., & Muxlow, T. W. B. 1994, A&A, 285, 393
  26. Lavalley, M., Isobe, T., & Feigelson, E. 1992, in Astronomical Society of the Pacific Conference Series, Vol. 25, Astronomical Data Analysis Software and Systems I, ed. D. M. Worrall, C. Biemesderfer, & J. Barnes, 245–247
  27. Lewis, J. P. 1995, Vision Interface, 120
  28. Lindegren, L. & Perryman, M. A. C. 1996, A&AS, 116, 579
  29. Lister, M. L. 1999, PhD thesis, Boston University
  30. Lister, M. L., Aller, H. D., Aller, M. F., et al. 2009, AJ, 137, 3718
  31. Lobanov, A. P. 1998, A&A, 330, 79
  32. Lobanov, A. P. & Zensus, J. A. 2007, Exploring the Cosmic Frontier, ed. Lobanov, A. P., Zensus, J. A., Cesarsky, C., & Diamond, P. J. (Springer-Verlag), 147–162
  33. Marcaide, J. M. & Shapiro, I. I. 1984, ApJ, 276, 56
  34. O’Sullivan, S. P. & Gabuzda, D. C. 2009, MNRAS, 400, 26
  35. Petrov, L., Kovalev, Y. Y., Fomalont, E. B., & Gordon, D. 2011, AJ, 142, 35
  36. Pushkarev, A. B., Kovalev, Y. Y., Lister, M. L., & Savolainen, T. 2009, A&A, 507, L33
  37. Ros, E. & Lobanov, A. P. 2001, in 15th Workshop Meeting on European VLBI for Geodesy and Astrometry, ed. D. Behrend & A. Rius, 208
  38. Savolainen, T., Homan, D. C., Hovatta, T., et al. 2010, A&A, 512, A24
  39. Shepherd, M. C. 1997, in Astronomical Society of the Pacific Conference Series, Vol. 125, Astronomical Data Analysis Software and Systems VI, ed. G. Hunt & H. E. Payne (San Francisco: ASP), 77
  40. Sokolovsky, K. V., Kovalev, Y. Y., Pushkarev, A. B., & Lobanov, A. P. 2011, A&A, 532, A38
  41. Twiss, R. Q., Carter, A. W. L., & Little, A. G. 1960, The Observatory, 80, 153
  42. Vlahakis, N. & Königl, A. 2004, ApJ, 605, 656
  43. Walker, R. C., Dhawan, V., Romney, J. D., Kellermann, K. I., & Vermeulen, R. C. 2000, ApJ, 530, 233
  44. Woo, J.-H. & Urry, C. M. 2002, ApJ, 579, 530
Comments 0
Request Comment
You are adding the first comment!
How to quickly get a good reply:
  • Give credit where it’s due by listing out the positive aspects of a paper before getting into which changes should be made.
  • Be specific in your critique, and provide supporting evidence with appropriate references to substantiate general statements.
  • Your comment should inspire ideas to flow and help the author improves the paper.

The better we are at sharing our knowledge with each other, the faster we move forward.
""
The feedback must be of minimum 40 characters and the title a minimum of 5 characters
   
Add comment
Cancel
Loading ...
220541
This is a comment super asjknd jkasnjk adsnkj
Upvote
Downvote
""
The feedback must be of minumum 40 characters
The feedback must be of minumum 40 characters
Submit
Cancel

You are asking your first question!
How to quickly get a good answer:
  • Keep your question short and to the point
  • Check for grammar or spelling errors.
  • Phrase it like a question
Test
Test description