Active Galactic Nuclei are active in the radio wave portion of the electromagnetic spectrum. They are observed on a milliarcsecond resolution. In order to achieve a resolution this high, radio astronomers use the Very Long Baseline Array (VLBA). The VLBA is an interferometer that correlates data received from telescopes stationed across North America to create radio images on a milliarcsecond scale. These images are turned into contour maps showing areas of brightest intensity.

Images of Active Galactic Nuclei often reveal jets composed of hot plasma radiating outward from their core. Many of these jets demonstrate a Kelvin-Helmholtz instability. This is an effect occurring when two fluids with different velocities move against each other, causing the fluids to deviate from a linear path. As a result of the Kelvin-Helmholtz instability, the jets emanating from Active Galactic Nuclei are often observed to take a helical structure, where the jets fit a continually expanding sinusoidal pattern. Radio astronomers still know relatively little about the kinematics of these helical jets and are endeavoring to find a model that fits the observed astronomical data. One such model has already been proposed (Hardee, 78). Observations over time have revealed shocks moving along the jets of certain Active Galactic Nuclei. It is the movement of these shocks that has been the focus of this summer research project.

Observations
We have generated contour maps of the Active Galactic Nuclei of interest using data received from the VLBA. The maps we were able to generate are as follows (Table 1):

Table 1: Observations Data
The contour maps produced from the VLBA data appear as follows
(Figures 1-13):

Figure 1: 1749 +096, August 2001, 22.4 MHz	Figure 2: 1749 +096, January 2002, 22.4 MHz
Figure 3: 1823 +568, January 2002, 15.4 MHz	Figure 4: 1823 +568, January 2002, 22.4 MHz
Figure 5: 1823 +568, January 2002, 43 MHz	Figure 6: BL Lac, August 2001, 15.4 MHz
Figure 7: BL Lac, August 2001, 22.4 MHz	Figure 8: BL Lac, January 2002, 15.4 MHz
Figure 9: BL Lac, January 2002, 22.4 MHz	Figure 10: BL Lac, January 2002, 43 MHz
Figure 11: 2134 +004, January 2002, 15.4 MHz	Figure 12: 2134 +004, January 2002, 22.4 MHz
Figure 13: 2134 +004, January 2002, 43 MHz

Analysis
The goal of this research was to create a helical model for the motion of shocks along the jets of the four Active Galactic Nuclei 1749 +096, 1823 +568, BL Lac, and 2134 +004. A helix is characterized by a set of helical parameters. We varied six of these parameters in an attempt to find the best possible match. The parameters are as follows: ro represents the opening radius of the helix, lo represents the initial wavelength of the helix, y represents the opening angle of the helix, x represents the angle that the helix forms with the sky coordinate North, f represents the starting point of the helix, and q represents the angle between the axis of the helix and the line of sight. Each parameter was tested within a specific range; we tested ro from .05 to .20, lo from 0.1 to 10.0, y from 1.0 to 4.0, x from 175.0 to 183.0 for the object BL Lac and from 265.0 to 273.0 for source 2134 +004, f from 0.0 to 360.0, and q from 4.0 to 10.0. We performed a reduced chi-squared test on each combination of parameters to determine the fitness of the overall helix. Our desired value for reduced chi-squared was one.

The contour maps revealed the BL Lac object 1749 +096 to be a point source (Figures 1 - 2). No jets appeared emanating from the core of this active galaxy, and thus there were no data to model. We did no further analysis on this object.

The BL Lac object 1823 +568 also had insufficient data to analyze (Figures 3-5). The contour map of this object produced in January 2002 at 15.4 MHz (Figure 3) suggests the beginning of a jet. However, this jet does not appear in the other maps of 1823 +568 (Figures 4-5). More data needs to be collected on this object before it is apparent whether or not a jet exists. We performed no further analysis on this object.

The BL Lac object BL Lac (Figures 6-10) shows evidence of a helical jet emanating from the core. As we have observed this object over time, we have seen a series of shocks move along this jet. These shocks appear on the contour maps as areas of brighter intensity. The shock that appears in the BL Lac contour maps from August 2001 and January 2002 is called S11. We have combined the data from these two maps with previously generated data to fit a helical model to shock S11 on the object BL Lac. When only considering the data available through August 2001, we were able to find a suitable helical model (Figure 14).

Figure 14: A proposed helical model for shock S11 using data through August 2001.

This helix has the following helical parameters: ro =.05, lo =1.9, y =3.2, x =183.0,
f =240.0, and q = 9.0. The reduced chi-squared value for this helix is .05. This is less than the value of 1 that we set as our limit for reduced chi-squared, which indicates this helix is a good model of the data. However, when we added in data from January 2002, it became apparent that this helix did not sufficiently describe the observed data. We attempted to find a helical model that would account for the observations taken in January 2002 (Figure 15).


Figure 15: A proposed helical model for shock S11 using data through January 2002.

This model has the following helical parameters: ro =.11, lo =5.3, y =2.3, x =180.2, f =208.0, and q = 6.6. When we performed the reduced chi-squared test on this helix, we arrived at a value of 4.304 for reduced chi-squared. This value did not meet our qualification of being close to one, and thus we concluded that this helical model did not accurately fit our data. We have been unable to find a better helical model for shock S11 of the object BL Lac.

Quasar 2134 +004 did not show evidence of a jet emanating from the core (Figures 11-13). However, we noticed that the contour maps revealed an overall helical shape to the quasar. We endeavored to model the shape of 2134 +004 (Figure 16).

Figure 16: A helical model of quasar 2134 +004

This model has the following helical parameters: ro =.10, lo =3.7, y =3.8, x =280.0, f =130.0, and q = 8.5. The reduced chi-squared value for this helix is 1.06, which is significantly close to our desired value of 1.0. Thus, we concluded that this model fit the data well and accurately describes the shape of quasar 2134 +004.

Conclusion
Through analyzing contour maps created using the VLBA, we were able to propose new models to describe the motion of active galactic nuclei. We were unable to analyze two sources we observed, 1749 +096 and 1823 +568. We analyzed the source BL Lac, but were not able to find an accurate model. Our greatest success was with the source 2134 +004, for which we were able to propose a helical model that accurately describes the observed data.

For future research, we hope to find a helical model that more accurately describes shock S11 for the object BL Lac. We will also continue observing source 1823 +568 in hopes of finding a jet emanating from its core, at which time we will attempt to fit a helical model to this jet.

Works Cited

Hardee, P.E., (1987), "Spatial Stability of Relativistic Jets - Application to 3C345" Astrophysical Journal, 318, 78.

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This page updated February 27, 2004