2. ICRS and ICRF, Hipparcos, FK5, Equator and Equinox
By Reference System it is meant the set of prescriptions and conventions together with the modelling required to define, at any time, a triad of axes.
By Reference Frame it is meant a practical realization with given fiducial directions agreeing with the concepts introduced in the corresponding Reference System.
2.1. ICRS: The International Celestial Reference System
The ICRS (Arias et al. 1995) complies with the conditions specified by the 1991 IAU Recommendations. The origin of the ICRS axes is located at the barycentre of the solar system and the directions of its axes are fixed relative to distant extragalactic sources. For the sake of continuity with the FK5 pole, the ICRS pole is in the J2000.0 direction defined by the conventional IAU models for precession (Lieske et al. 1977) and nutation (Seidelmann 1982). The origin of right ascensions is also defined consistently with that of the FK5 by fixing the right ascension of 3C 273B to the Hazard et al. (1971) FK4 value transformed to the J2000(FK5) System (Kaplan et al. 1982).
The Hipparcos star positions and proper motions (ESA 1997) and the JPL solar system ephemerides (starting with DE403, see Standish 1997) are already expressed in the ICRS and several new catalogues (Urban et al. 1997a,b) in the visible have been aligned with the Hipparcos system, the latter being used as a secondary realization of the ICRS. The International Terrestrial Reference System (ITRS), also maintained and made available by the IERS as the International Terrestrial Reference Frame (ITRF), is connected to the ICRS at any time by the IERS Earth Orientation Parameters (EOP) with an accuracy equivalent to 1 cm at the surface of the Earth.
2.2. ICRF: The International Celestial Reference Frame
The choice of extragalactic objects to realize the fiducial directions was made possible by the availability of a mature and highly precise observing technique, Very Long Baseline radio Interferometry (VLBI). A detailed description of astrometric and geodetic VLBI analysis is given by Sovers and Jacobs (1996). The major sets of software in use for this modelling have been intensively tested and compared to each other. They are considered to be implemented consistently within one picosecond for the delay and one femtosecond/second for the delay rate, one order of magnitude better than the observations (Jacobs et al. 1997).
The ICRF consists of a catalogue of equatorial coordinates of 608 extragalactic radio sources derived from about 1.6 million observations accumulated by a worldwide network over 1979-1995. It was derived by a sub-group of the WGRF that agreed on an optimal data analysis strategy (Ma et al. 1998). It includes three lists of objects, with
The accuracy of the ICRF realization of the ICRS axes is estimated to be 0.02 mas.
Extensive information on the ICRF is available in (Ma & Feissel 1997) and electronically (anonymous ftp and WWW site: hpiers.obspm.fr).
2.3. The Hipparcos Catalogue and the ICRF
The direct result of the data processing of the Hipparcos observations was a catalogue of astrometric positions for about stars of exceptionally good precision and free of regional error at the level of 0.1 mas. The intermediate frame in which these positions and proper motions were given was still arbitrary. A connection between the intermediate Hipparcos frame and the ICRS was carried out by using various data and methods (Lindegren & Kovalevsky 1975; Kovalevsky et al. 1997). The resulting alignment of the published Hipparcos Catalogue with the ICRS was eventually realized with standard errors for each axis of 0.6 mas for the orientation at J1991.25 and 0.25 mas/a for the spin. Consequently the Hipparcos Catalogue provides the master realization of the ICRS in the optical domain with the above uncertainties.
2.4. The FK5 and the ICRS
As the complete FK5 catalogue was observed by Hipparcos, the directions of the pole and origin of right ascensions of the FK5 relative to Hipparcos were determined, with an accuracy of 2.3 mas at the mean epoch J1991.25. The relative spin between the FK5 and Hipparcos frames was also assessed from the systematic deviations between the proper motions, with an accuracy of 0.1 mas/a. Eventually the directions of the FK5 axes in the ICRS were estimated (Table 1), taking into account the propagation of the uncertainty of the Hipparcos tie to the ICRS. The modelling of the FK5 non global deformations affect marginally the estimation of the orientation and spin.
Table 1. Global orientation and spin between the FK5 and the ICRS at J2000.0. The Hipparcos Catalogue has been used as intermediate frame and the uncertainties propagated accordingly (Mignard & Froeschlé 1997).
The infinitesimal angles , , are defined as direct rotations around the ICRS axes pointing in the directions = 0 h, = 6 h, = respectively; , , are defined as their corresponding time derivatives.
2.5. The mean pole and equinox at J2000.0 in the ICRS
According to their authors, the realizations of the mean pole and equinox at J2000.0 by means of the FK5 (Fricke et al. 1988) have respective uncertainties of 50 mas and 80 mas. VLBI and Lunar Laser Ranging (LLR) allow more accurate determination of these physical directions in the ICRS.
Using a state of the art precession-nutation model (McCarthy 1996), the analysis of long VLBI series of the observed motion of the celestial pole in the ICRS allows us to derive the coordinates of the mean pole at J2000.0 in the ICRS (IERS 1997). Combining VLBI and LLR Earth orientation and terrestrial reference frames and using the JPL planetary ephemeris DE200, Folkner et al. (1994) derived the offset of the mean equinox at J2000.0 relative to the ICRS origin of right ascensions. Resulting values are summarized in Table 2.
Table 2. ICRS coordinates of the mean celestial pole (, ) and of the equinox (), see Fig. 1.
The infinitesimal rotations of Tables 1 and 2 can be transformed into the coordinates of the poles on a plane tangent to the ICRS pole, as shown in Fig. 1. The position of the origins of right ascensions are also depicted along the equator.
© European Southern Observatory (ESO) 1998
Online publication: March 3, 1998