THE INTERNATIONAL CELESTIAL REFERENCE FRAME REALIZED BY VLBI Extracted from IERS Technical Note 23, Part II, (Ma et al., 1997) Introduction There exists a large resource of high accuracy, dual frequency VLBI data which were acquired from various networks for geodetic and astrometric purposes over a span of more than fifteen years and from which various radio source catalogues have been constructed. The goal of the work described below was to create the definitive catalogue for the ICRF (International Celestial Reference Frame) using the best data and methods available at the time the work was done. This work is the joint cooperative effort of a subgroup of the IAU Working Group on Reference Frames (WGRF) formed expressly for this purpose. The subgroup has taken an empirical approach in the selection of data, analysis, estimation of errors, and categorization of the final results. The characterization of a radio source, i.e., its position, how it was treated in the analysis, and whether it is suitable for use as a defining object, is derived entirely from the VLBI data and analysis and not from any other information. This approach leads to a rigorous selection of defining objects and a reliable realization of the ICRF as a set of relative positions oriented to the axes of the International Celestial Reference System, ICRS (Arias et al., 1995). This realization of the ICRF was considered only one of many, both actual and potential, better than preceding ones but by no means attaining perfection. The geodetic/astrometric VLBI data set has a rich variety of stations and networks. The entire data set was used (except for sessions entirely between antennas at a single observatory), pooled cooperatively from all the various observing programs. Besides providing the potential for extracting the maximum information, the use of the entire data set includes the widest variation that the network geometry and station size can impose upon the realized ICRF. The ICRF positions and stated uncertainties should then represent realistically how confidently the positions can be used in the future with arbitrary VLBI measurements. The VLBI data for this work were edited following the usual procedures of each contributing group. It was considered essential that the realization of the ICRF be derived from a single analysis, even if imperfect, rather than from a combination catalogue made of several VLBI solutions. While the various recent catalogues are not inconsistent, except for a few discrepant sources, a combination loses certain information. The operational realization of the ICRF is a set of right ascensions and declinations, but the actual information is the much larger set of relative positions, whose quality is contained in the full covariance matrix. ICRF analysis The underlying conceptual basis of this type of realization of the celestial reference frame is that radio source positions are invariant with time. A series of solutions was made to ensure that this condition was not significantly violated. The solution for the ICRF was made at Goddard Space Flight Center (GSFC). The configuration of the ICRF analysis was developed as a balance between competing goals: the most data and the least systematic error, the best models and available options, the largest number of useful estimated parameters and computer speed, and the like. As improvements occur in the future, the balance will shift and the results will be better still. The most important choices are related to data and modeling/estimation. To extract the most information from the data set both delay and delay rates were used, and only observations below 6 degrees were excluded. The troposphere was modeled using the MTT mapping function (Herring, 1992) and estimates of the zenith troposphere effects in the form of 1-hr piecewise linear, continuous functions with constraints on the size of variations. Time-variable troposphere gradients were estimated. Because it was not available in the Goddard analysis system, no atmosphere structure information was used. The primary geodetic parameters, the station positions, were estimated separately for each session. Station motions within a day from solid Earth tides and ocean loading were derived from unadjusted a priori models (McCarthy, 1992). The weighting of the data followed the usual Goddard practice. For each session a pair of added noise values was computed for delays and delay rates which caused the reduced chi-2 to be close to unity when added to the variance of the observations derived from the correlation and fringe-finding process as well as the calibration of the ionosphere. Other modifications of the observation errors such as elevation-dependent and source-dependent noise were not used. The unadjusted a priori models for geophysical effects and precession/nutation generally followed the IERS Standards (1992) (McCarthy, 1992). The VLBI theoretical model was the so-called consensus model given in the IERS Conventions (1996) (McCarthy, 1996). The parameters were estimated using arc-parameter elimination (Ma et al., 1990). In the ICRF analysis several classes of parameters were adjusted. For each observing session, the adjusted arc parameters included: 1) positions of "arc" sources with identified excessive apparent motion or random variation, 2) two celestial pole offsets to account for errors in the standard precession/nutation models, 3) positions of the stations, 4) the rate of UT1 relative to a good a priori time series, 5) 1-hour troposphere parameters described above, 6) troposphere gradients in the E-W and N-S directions, linear in time, 7) quadratic clock polynomials for the gross clock behavior, 8) 1-hour clock parameters similar to the 1-hr troposphere parameters, and 9) necessary nuisance parameters such as clock jumps and baseline clock offsets. Certain parameters were adjusted as invariant quantities from the entire data set. These global parameters included: 1) invariant source positions, 2) geometric axis offsets for all fixed antennas, and 3) 252 parameters for Earth rotation variations in the diurnal and semidiurnal bands caused by ocean tides. The axis offset and ocean tide Earth rotation adjustments were all small but the estimates were included to eliminate any influence on the source positions. After a series of test solutions to refine various aspects of the analysis, a final solution was run which included 1.6 million pairs of delays and rates from August 1979 through July 1995. The postfit weighted root-mean- square residuals were 32.6 ps for delay and 104.2 fs/s for rates with chi-2 per degree of freedom of 1.08. There were 1305 global parameters, 650 000 arc parameters, and over 2.5 million degrees of freedom. Determination of Realistic Error Given the very large number of observations for some sources, the error contribution from their observation noise is very small and not a meaningful measure of uncertainty. It is necessary to consider several other effects to assign realistic errors. One is the statistical validity of the formal errors. Another is the cumulative influence of all modeling errors and editing decisions. Yet another is the magnitude of specific, identifiable systematic errors that could have distorted the results. From the consideration of error sources the subgroup concluded that a realistic error estimate for the invariant source positions could be made by inflating the formal errors by a factor of 1.5 followed by a root-sum-square increase of 0.25 mas. For the most frequently observed sources the 0.25 mas is the dominant error. The errors of the arc sources were also increased by 0.25 mas. The method adopted at the IERS until 1995 for the realization of the extragalactic reference frame consisted of combining individual VLBI frames by applying an algorithm based on catalogue comparison. The position uncertainties derived from the combination reflected the disagreement between individual analyses. To address the question of whether adopting a unique "error calibration law" for all sources eliminated or at least minimized systematic effects, a combined frame was made by adopting a 6-parameter comparison model (three angles, drifts in right ascension and declination as functions of declination, and a bias in declination). Individual VLBI frames submitted by GSFC, JPL, NOAA and USNO to the IERS in 1995 (Charlot, 1995) were then included in this combination. The comparison of the "inflated" uncertainties with those obtained from catalogue combination showed that there were still a non-negligible number of sources whose inflated uncertainties were smaller than those resulting from the comparison of parallel analyses with a deformation correction model. For these sources the uncertainty for each coordinate was set to be the larger of the inflated or the comparison value. Astrophysical Causes for Source Position Variations Many extragalactic sources display structure on milliarcsecond scales for the strong radio emission associated with their compact cores. Temporal variations of the intrinsic structure of these objects may result in apparent motion when observations are made at several epochs. Until recently, the intrinsic structure of the majority of the sources has been mostly unknown. The surveys of Fey, Clegg, and Fomalont (1996) and Fey and Charlot (1997) show that most sources, when examined in detail, exhibit spatial structure on milliarcsecond scales. Their results show that the variation of intrinsic structure from source to source can be quite extreme, ranging from relatively compact naked-core objects, to compact double sources, to complex core-jet objects. The situation is exacerbated by the fact that compact extragalactic radio sources are known to have variable intensity and to have frequency and time-dependent intrinsic structure. Consequently, unknown and/or unmodeled source structure effects may be introduced into the astrometric solution. Charlot (1990) has modeled the effects of radio source structure on measured VLBI group delays and delay rates. Results of this modeling suggest that these effects can be significant for extended sources (typically at a level of 100 picoseconds [ 3 cm at the surface of the Earth or 1 mas] in the group delay). Fey and Charlot (1997) calculated structure corrections based on the Charlot analysis using source models derived from Very Long Baseline Array (VLBA) observations of 169 extragalactic sources. Results of these calculations show that intrinsic structure contributions to the measured bandwidth synthesis delay are significant, ranging from maximum corrections of only a few picoseconds for the most compact sources to maximum corrections of several nanoseconds for the most extended sources. Fey and Charlot found a correlation between the compactness of the sources and their position uncertainties indicating that the more extended sources have larger position formal errors. They also define a source "structure index" based on the median of the calculated structure corrections. They suggest that this index can be used as an estimate of the astrometric quality of the sources as follows. Sources with an X band structure index of 1 may be considered very good astrometric sources. Sources with an X band index of 2 may be considered good sources while sources with an X band index of 3 should be considered marginal (and should only be used with caution). Finally, sources with an X band index of 4 should not be used at all for astrometric work. Additionally, sources should have an S band structure index of either 1 or 2, with a preferred value of 1, regardless of the value of their X band structure index. Since even apparently stable sources can suddenly begin exhibiting rapid structure variations, the entire ICRF catalogue must be reobserved over time to ensure its continued precision on the submilliarcsecond level. Structure observations of the entire set of ICRF sources are either planned or in progress. This is being accomplished in the Northern Hemisphere with the VLBA. It will be more difficult to ascertain the structure of sources in the Southern Hemisphere due to the lack of observing facilities capable of adequate spatial imaging on the required scales. Almost all of the ICRF sources whose detailed structure is known are in the Northern Hemisphere. In addition, the ICRF can be improved in the future by enhancing the accuracy of the observations and the number of sources defining the frame can be expanded. New sources will continually be evaluated for addition to the ICRF catalogue and the radio positions of sources already in the catalogue will be revised through improved observational techniques. New data will be added to the existing database and reanalyzed, producing from first principles an improved and updated version of the catalogue whenever necessary. Categorization of sources To be most useful in defining the ICRF a source should ideally show no variation in position in the data set, have sufficient data to support the absence of variation, and not have shown unexplained differences in position between realizations of equivalent validity. Several quality levels can be established for each of the 608 sources in the WGRF catalogue. These are based on one of three sets of criteria: 1) quality of data and observation history 2) consistency of coordinates derived from subsets of data 3) repercussions of source structure To qualify for the list of sources that was used to orient the WGRF catalogue with respect to the IERS celestial reference system, a source must pass muster in all three categories. We summarize hereafter the somewhat arbitrary criteria used to reject sources based on their data, behavior, and structure: ------------------------------------------------------------------ Sources fail to be defining sources for any of the following: * Arclength formal error >1 mas * <20 observations * <2-year span of data * 3 sigma or >0.5 mas discrepancy between catalogues * Excessive structure * Large, significant apparent motions * Arc source, i.e., position adjusted for each session ------------------------------------------------------------------ The sources then fall into three categories: 212 defining sources that fail none of the criteria, 294 candidate sources that fail some or all of the criteria, and 102 sources with identified excessive position variation, either linear or random. Some candidate sources have insufficient observations or duration for reliable designation as defining sources while others with many observations may have larger than expected differences in position between catalogues. Candidate sources potentially could be designated defining sources in future realizations of the ICRF as more data become available or analysis improves. The third category of other sources does include sources that may be useful for purposes such as radio-optical frame ties. While only the defining sources have a formal role in the ICRF, the positions of all sources are consistent with the ICRF. Orientation of the ICRF The VLBI analysis for the WGRF catalogue described above provided accurate relative positions and an overall orientation very near to the ICRS (Arias et al., 1995). However, the solution was not designed to obtain results directly on the ICRS. The final stage in the ICRF realization was the rigid rotation of the relative positions to the ICRS maintained by the IERS. The extragalactic radio source catalogue obtained in the WGRF solution was aligned to the ICRS by rotating it onto the last realization of the IERS celestial reference frame, RSC(IERS) 95 C 02 (IERS, 1996). In the procedure applied to rotate the WGRF solution to IERS frame, care was taken not to transfer to the former the deformations of the latter. The algorithm used to put the WGRF coordinates in ICRS was based on catalogue comparison on the basis of common sources (Arias et al., 1988). The extragalactic frame RSC(WGRF) 95 R 01 was obtained by putting the radio source coordinates from the WGRF solution in ICRS via comparison to RSC(IERS) 95 C 02. Both frames are aligned to better than 0.010 mas. The deformation of RSC(IERS) 95 C 02 relative to RSC(WGRF) 95 R 01 is represented mainly by a bias of the principal plane. To test the stability of the axes of the system, we estimated the relative orientation between RSC(WGRF) 95 R 01 and RSC(IERS) 95 C 02 on the basis of different subsets of sources. The scattering of the rotation parameters obtained in the different comparisons indicate that the axes are stable within 0.020 mas. Evolution of the ICRF The current realization condenses the information from a particular VLBI data set spanning a defined interval and reflects a certain state of VLBI analysis. As time progresses we expect the realization of the ICRF to evolve although changes in the ICRF catalogue will be infrequent compared to past practice in VLBI astrometry. There are several features that distinguish this type of realization from the conventional stellar catalogues that formerly defined the celestial reference frame. First, while we know the positional history of the sources, we cannot predict with absolute certainty what future observations will reveal. The current positions and velocities are a snapshot (or a movie), and continued observations are essential to maintain the viability and integrity of the ICRF. New sources must be observed to replenish and expand the list of candidates, and their positions in the ICRF must be determined. Current sources need to be observed periodically to track their behavior. Second, as observations accumulate, it should be possible to move candidate sources up or down the scale of usefulness. However, it is conceivable, perhaps even probable, that an identical categorization of sources from an analysis using twice as long an interval would show sources changing categories in unpredictable ways. For example, there is no physical reason to expect that linear position changes can continue indefinitely. Such motion would call into question the fundamental basis of the extragalactic frame, the great distances of the objects. Directed position changes should cease at some time. Conversely, a source now stationary could start apparent motion. Only the data analysis will show. The problem of position variation may be solved in the future if the application of source structure information permits the identification and use of truly kinematically stable points in the sky. This remains to be demonstrated. Unlike stellar catalogues, however, the original VLBI observations should always be accessible for improved analysis de novo. Despite the burden of maintenance, the ICRF realized by VLBI astrometry is a great step forward. Compared to stellar realizations it is intrinsically simpler, much more accurate, more stable, and less susceptible to systematic deformations. It will serve the purposes of astronomy well. References ARIAS, E.F., FEISSEL, M., LESTRADE, J.-F., 1988: Comparison of VLBI celestial reference frames, Astron. Astrophys., 199, p. 357-363. (1988A&A...199..357A) ARIAS, E.F., CHARLOT, P., FEISSEL, M., LESTRADE, J.-F., 1995: The Extragalactic Reference System of the International Earth Rotation Service, ICRS, Astron. Astrophys., 303, p. 604-608. (1995A&A...303..604A) CHARLOT, P., 1990: Radio-source structure in astrometric and geodetic very long baseline interferometry, Astron. J., 99, p. 1309-1326. (1990AJ.....99.1309C) CHARLOT, P., 1995: IERS Technical Note 19, Observatoire de Paris. FEY, A.L., CLEGG, A.W., FOMALONT, E.B., 1996: VLBA Observations of radio reference frame sources. I., Astrophys. J. Suppl., 105, p. 299-330. (1996ApJS..105..299F) FEY, A.L., CHARLOT, P., 1997: VLBA Observations of radio reference frame sources. II. Astrometric suitability based on observed structure, Astrophys. J. Suppl., 111, in press. (1998ApJS..119...75K) HERRING, T.A., 1992: Modeling atmospheric delays in the analysis of space geodetic data, Symposium on Refraction of Transatmospheric Signals in Geodesy, J. C. De Munk and T. A. 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