Author: L. Petrov
Memo:   Proposed update of the geodetic source list 
Date:   2007.03.02

Introduction

The list of geodetic sources currently has 114 objects. It is known that the list contains the objects which are a) very weak at long baselines; b) have complex and variable structure. At the time when the list was generated, in 1980s, information about sources structure was scarce. To date, owing to enormous efforts of Dr. Kovalev, Dr. Pushkraev, Dr. Fey, Dr. Corey, Dr. Ojha, S/X images for 3300 objects, i.e. 97% sources with declination > -40° ever detected in geodetic/astrometric mode, are available. Circulation of this information and anticipation that in Q1 2007 analysis software will be in a position to compute static component of contributions of the source structure to group delays and apply them to routine analysis, prompts us to reconsider the list of the best sources for geodetic applications.

Data transformation

First, the original files with source maps and visibilities were collected and scrutinized. By 2007.02.28, we have 211671 files related to source images. The files were analyzed, the sources were identified. 39082 files with visibility and image data were found. They were renamed and copied in destination directory. Then for each pair visibility data + image data, two output files were created: a file withj contour source map and the plot of dependence of the calibrated visibility (i.e. correlated flux density) versus the length of the baseline projection to the plane normal to the source direction.

The contour maps were drawn using the pixel array stored in the image file. These images are result of convolution of the set of δ-functions that represent an image with the synthesized response of the network to the point-like source, the so-called "clean beam", with residual noised added.

The default image box is [-50, +50] mas for an S band image and [-15, +15] mas for an X band image. However, if the image has details with correlated flux density greater than 3 times the rms of the image noise, the image box is extended to show this detail. The first contour level is set to 5 times the rms of the image noise. The contour levels forms the geometric progression with the base 2. The following algorithm was used for computing the rms of the image noise. The rms of the flux density in four corners, each of 1/4 size of the original image, i.e. 1/16 of the image area, is computed independently. The maximal over 4 estimates of the rms noise is discarded, and the remaining three estimates are averaged. At the second iteration the rms in three remaining corners is computed the second times using the iterative procedure. The points which exceed the 4 times the rms estimated at the first iteration are discarded. The ``clean beam'' is shown in the bottom left corner. The clean beam is modeled by a two-dimensional Gaussian function. The area at 1/2 of the peak value of the response is shown by gray color.

The plots of dependence of the correlated flux density on the length of the baseline projection to the image plane at S band and X-bands were generated. Each point at the plot represents the amplitude of the complex visibility averaged over frequency of the band and over time within a scan. Observations with time tags greater than 300 seconds are considered to belong to different scans. The rms of the averaged visibility for each point was computed on the basis of their scatter with respect to the mean value. The vertical error bar at the plot corresponds to the 1-σ error. The points with errors greater than {\tt f * Amp}, where {\tt Amp} is the averaged visibility and f is a certain factor, are not shown. The factor f was selected depending on experiment in the range of [0.25, 0.50].

Tables with correlated and integrated flux density, the flux density at short and long baselines for both S band and X bands were generated. The integrated flux density in the first column of the table is defined as the sum of flux densities over all δ-function components of the image. The correlated flux density at short baselines in the second column is defined as the median value of the correlated flux density averaged over intermediate frequencies of the band and over time within a scan at baselines with projections to the source plane shorter than 900 km. The correlated flux density at long baselines in the third column is defined as the median value of the correlated flux density averaged over intermediate frequencies of the band and over time within a scan at baselines with projections to the source plane longer than 5000 km.

First selection

The sources with declination in range [+10°, +40°] with the median correlated flux density greater than 200 mJy at both X and S bands at baselines longer than 5000 km were included. The sources with declination in ranges [-40°, +10°), (+40°, +90°] with the median correlated flux density greater than 300 mJy at both X and S bands at baselines longer than 5000 km were also included. In total, 567 objects were included in the first selection.

Procedure for making the second selection

The Web-oriented software program for selecting representative images was developed. If images of the same source for more than one epoch were available, than image for one of the epoch is considered as "representative". By default, the last epoch is considered as representative. If the circumstances of observations were not favorable, and the uv-coverage was poor, another epoch with an image of better quality was selected. Subjective criteria were used. Finally, representative images for all sources were found.

Then each representative image and the plot of calibrated visibilities versus the length of the baseline projected to the plane normal to the source direction was scrutinized using another web-oriented computer program. A class in range 1-4 was assigned to each object. That class characterizes the suitability of designating this object as a geodetic source.

  1. Suitability class 1 ("perfect") means that the source has the compactness index greater than 0.8, and it has a very small spread at plots of calibrated visibilities versus the length of the baseline projected to the plane normal to the source direction, because it does not have image asymmetries . The compactness indes is defined as the ratio of the median correlated flux density at baselines longer 5000 km to the median correlated flux density at baselines shorter than 900 km,

  2. Suitability class 2 means that the source has the compactness index in the range of 0.4--0.8, does not have a significant spread at plots of calibrated visibilities versus the length of the projected baseline, the image does not show significant extended details, and the source core does not have significant deviations from the circular structure.

  3. Suitability class 3 means that the source is still detected even at long baselines, but either has the compactness index less than 0.4 or has significant image asymmetries that causes a large spread at plots of calibrated visibilities versus the length of the baseline projected to the plane normal to the source direction.
  4. Suitability class 4 means that the source is too weak and not compact enough to be even detected at baselines longer than 5000 km ( correlated flux density at long baselines less than 100mJy).

The sources of class 1 and 2 are considered as candidates to geodetic sources. The sources of class 3 and 4 are excluded from the pool of candidates.

Rationals for the criteria for source selection

Obviously, the sources which are too weak at long baselines are not interesting objects. A 300 mJy source can be detected with the required SNR for several minutes at 1000 Jy SEFD class antennas. Weaker sources can be detected for several minutes only at 200--400 Jy SEFD antennas.

The ideal source has a) the flat dependence of visibility versus the length of the projected baseline (compactness); b) a very small spread of visibilities with respect to a smooth curve (lack of image asymmetries).

Non-compactness at scales of image resolution tends to evolve at time scales of years. These source are better to be avoided.

The asymmetry, or core ellipticity, also tends to evolve at time scales of years. The asymmetry contributes to phase and group delay casued by source structure. These source are better to be avoided.

The method of source selection is rather subjective. Another person would select a list which would be 5-20% different. I do not think it is worth to spend significant resources for developing fully automatic methods. Source variability makes any method of source selection uncertain to some extent.

List of recommended geodetic sources

The list of recommended geodetic sources has 234 objects. Among them, 45 objects are of class 1 and 180 objects are of class 2. In total, 40% of the sources from the first selection are recommended to be considered as geodetic. The representative images and visibilities of recommended sources are available. The representative images and visibilities of sources which are not recommended are also shown.

Statistics

The old pre-2007 geodetic source list contains 114 objects, 12 of them with declination below -40°. Among 114 objects, 9 turned out too weak to follow the first selection criteria.

Among old 114 geodetic sources, 46 objects are in the proposed list of recommended sources, 68 sources are suggested to be excluded. Thus, the new list contains 46 old sources and 188 new sources.

On average, the new geodetic source list contains weaker objects than the old one.

All recommended sources have inflated position errors better than 0.7 mas. The majority of them were observed in RDV experiments.

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