A new concept of the International Celestial Reference Frame: the epoch ICRF

Abstract

1 INTRODUCTION

At the 23th International Astronomical Union (IAU) General Assembly in 1997, the International Celestial Reference Frame (ICRF: Ma et al. 1998) was officially adopted to replace its predecessor, the FK5 Frame, as the realization of the International Celestial Reference System (ICRS: Arias et al. 1995). The ICRF consists of 608 extragalactic radio sources, including 212 well-observed sources defining the orientations of the ICRS axes, 294 candidate sources that improve ability to access the ICRF more effectively and 102 ‘other’ unstable sources. The stability of the frame axes is at the level of approximately 20 μas.

Although definitions of the ICRF are no longer related to the equinox or equator, for the sake of continuity the IAU recommended that the new reference frame should be consistent with the FK5 system, the principal plane should be close to the mean equator at J2000.0 and the origin of right ascension should be close to the dynamical equinox at J2000.0. Feissel & Mignard (1998) concluded that the final orientations of the ICRF axes were coincident with those of the FK5 J2000.0 system within the uncertainties of the latter. The connection between the ICRF and the Hipparcos frame (Perryman et al. 1997), which was also adopted as a realization of the ICRS in optical wavelengths, showed that this optical reference frame orientation was secured with respect to the ICRF, with standard errors of 0.25 milliarcsecond (mas) per year in rotation and 0.6 mas in origin position at epoch J1991.25 (Kovalevsky et al. 1997).

The ICRF was intrinsically simpler, much more accurate and stable, well-tied with the optical frame and met all the resolutions of the IAU for a celestial reference frame. However, there were two reasons why the ICRF required continuous maintenance as time elapsed. First, the ICRF needed to be more densely defined because it comprised only 608 sources and had a largely non-uniform distribution over the sky. Secondly, the defining sources have to be monitored to verify whether they are still proper and stable for realization of the ICRS. This is because the underlying physics of extragalactic radio sources is not as well understood as that of stars (Ma et al. 1998) and their positions cannot be expected to be steady over a long time-scale. In 1999, the first extension of ICRF (ICRF-Ext1: Gambis 1999) was released with 59 new sources as candidate sources, whereas the positions and errors of the ICRF defining sources remained unchanged.

In the second extension of the ICRF (ICRF-Ext2: Fey et al. 2004b), the positions of 50 new sources were added and the positions of ICRF candidate and ‘other’ sources were revised. The orientations of the ICRF-Ext2 axes and their uncertainties, however, still remained at the same level as for the original ICRF. Almost simultaneously, additional accurate positions of 22 Southern Hemisphere radio sources were reported by Fey at al. (2004a).

The second realization of the ICRF (ICRF2; Fey, Gordon & Jacobs 2009), which is the first revision of its categorization, is a great step forward. The axis stability of the ICRF2 is estimated at approximately 10 μas, which is nearly twice as stable as the original ICRF. There are at least two advantages of the ICRF2 with respect to its predecessors. The sky distribution of radio sources is largely improved by 1383 sources in the Southern Hemisphere, with 133 defining sources and 417 sources located at a declination of lower than −30°. Secondly, the source categorization is subject to a more rigorous criterion. Only 97 defining sources of the ICRF remain as ICRF2 defining sources and 39 unstable sources, some of which were ICRF defining sources, are identified as requiring special handling, with their positions treated as arc parameters in very long baseline interferometry (VLBI) data analysis. Statistical information on the evolution of the realization of the ICRS is given in Table 1.

Great improvements have been achieved in axis stability and number of fiducial points from ICRF to ICRF2, but their definitions have not been changed. The reference frame defined by the positions of extragalactic radio sources is a quasi-inertial frame with little or no time dependence (see e.g. Ma et al. 1998; Johnston & de Vegt 1999). However, because the Solar system rotates around the Galactic Centre within the Galactic plane (Perryman 2009) and oscillates perpendicular to the latter (Gould & Vandervoort 1972; Binney & Tremaine 2008), acceleration of these movements causes systematic apparent proper motions of the observing sources with a predicted magnitude of 5–6 μas yr^{− 1} at the great circle of the celestial sphere normal to the acceleration vector, which is referred to as secular aberration drift. Theoretical discussions on this issue have been reported in a series of papers (see, e.g. Eubanks et al. 1995; Sovers, Fanselow & Jacobs 1998; Perryman et al. 2001; Kovalevsky 2003; Kopeikin & Makarov 2006; Titov 2010). Thus, the radio source positions in the ICRF2 catalogue measured by a fictitious observer located at the origin of the ICRS, the Solar system barycentre, vary with time. It is therefore technically incorrect to state that the ICRF has no dependence on time.

This paper is an extension of previous work by Titov, Lambert & Gontier (2011) and Xu, Wang & Zhao (2012a,b), who have determined the solar acceleration from VLBI observations. We propose the concept of the ‘epoch ICRF’ based on consideration of the effects of secular aberration drift and describe how to construct this epoch ICRF. In principle, the apparent proper motion field should present a dipole structure and cause distortion of the ICRF2 axes. However, the non-uniform mean observational epochs of the 295 defining sources can lead to a constant shift and the non-uniform distribution of these defining sources over the sky can lead to spurious global rotation in the ICRF2. These issues are fully investigated here in this context. In Section 2, we present our model of secular aberration drift and outline the acceleration vector used. The results are reported in Section 3. Section 4 contains a discussion and conclusions.

2 MODEL

From equation (1) it is obvious that the acceleration vector is a basic parameter in the model of secular aberration drift. On the basis of the analysis of VLBI observations, Titov et al. (2011) and Xu et al. (2012a,b) obtained results for solar acceleration, which are listed in Table 2. These results show that the first two components coincide with each other within their uncertainties, while there is an obvious discrepancy for the Galactic pole component due to the significant vertical component in the second result. This significant vertical component can be explained by three potential physical phenomena or may even be caused by the systematic effect of intrinsic proper motions of the ICRF2 radio sources. Details are given in Xu et al. (2012b). Since this effect is systematic, it should be accounted for, as well as the other two components for the model. Moreover, because the second result has greater accuracy, it is adopted to construct a model of secular aberration drift.

Because of the apparent proper motion, the ICRF catalogue should also specify an epoch in addition to positions, like the optical catalogue. For continuity, we use J2000.0 as the common reference epoch. In fact, the positions of radio sources in the ICRF2 catalogue are essential relative to their mean observational epochs, although it is stated that the ICRF2 is epoch-independent. Fortunately, the ICRF2 catalogue provides the mean observational epochs for 3414 sources. Fig. 1 shows the distribution of the mean observing epochs of 3414 ICRF2 radio sources. The source positions in the ICRF2 catalogue then need a small modification to transfer the reference time from the mean observing epochs to J2000.0.

Figure 1.

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The distribution of mean observing epochs of 3414 ICRF2 radio sources.

3 RESULTS

Using equation (1) as a model of secular aberration drift and the acceleration vector (7.47 ± 0.46, 0.17 ± 0.57, 3.95 ± 0.47) mm s⁻¹ yr⁻¹ in the Galactic coordinate system (Blaauw et al. 1960; Murray 1989), we constructed the epoch ICRF with positions at J2000.0 and apparent proper motions. Fig. 2 shows the apparent proper motion field for 295 ICRF2 defining sources due to the effect of secular aberration drift. This dipole structure towards the acceleration vector leads to time-dependent warping with a magnitude of 5.8 μas yr^{− 1}. The dipole direction, almost along the equator, points to a right ascension of approximately 242|${^{\circ}_{.}}$|4. The ICRF2 will distort with time if this effect is not modelled. The positions in the ICRF2 catalogue are with respect to the mean observing epochs; in light of secular aberration drift, these should be transformed to the J2000.0 epoch.

Figure 2.

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Apparent proper motion field for 295 ICRF2 defining sources based on a model of secular aberration drift. Figs 2, 3, and 5 are plotted in right ascension and declination coordinates.

The position corrections from mean observing epochs to J2000.0 for 295 defining sources are shown in Fig. 3. The maximum adjustment of the right ascension coordinate exceeds 100 μas for some sources, such as 2229+695 and 0016+731, and that of the declination coordinate exceeds 30 μas for some other sources, such as 1725−795, 1823+689 and 0524−485. These are of the same magnitude as the uncertainties for the ICRF2 defining sources. Moreover, slight rotation is found in these coordinate corrections. The magnitude of this rotation is approximately 2.2 μas and the direction of the rotating axis is towards α = 331°, δ = 2|${^{\circ}_{.}}$|2, which is almost along the equator and normal to the acceleration vector. This shift occurs because the mean observing times for Northern Hemisphere sources basically occur before those for Southern Hemisphere sources. Fig. 4 shows the distribution of mean observing epochs of the 295 defining sources with respect to declination. Fortunately, this shift is a constant.

Figure 3.

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Position corrections for the transformation of the reference time from mean observing times to J2000.0.

Figure 4.

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The distribution of mean observing epochs with respect to declination for 295 ICRF2 defining sources.

Thus, rotation |$\boldsymbol {\omega }$| is calculated as (0.05, −0.08, 0.25) μas yr^{− 1}. This means that the direction of origin of right ascension is moving on the equator with a magnitude of 25 μas per century. When ‘no net rotation’ constraints are imposed on 295 ICRF2 defining sources in the VLBI data analysis, this movement will directly affect the determination of precession parameters and its magnitude is largely beyond the accuracy requirement of precession theory at the level of 1 μas per century (Capitaine, Wallace & Chapront 2003). We calculated the global solution twice to obtain the radio source positions with and without modelling the effect of secular aberration drift. Details of the parametrization and estimation configuration are given in Xu et al. (2012b). The differences between these two solutions for 295 defining sources are shown in Fig. 5.

Figure 5.

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Two global solutions with and without modelling the effect of secular aberration drift were calculated, to obtain radio source positions. The position differences between these two solutions are shown here for 295 defining sources.

4 DISCUSSION AND CONCLUSION

Secular aberration drift changes the apparent positions of radio sources over time by approximately 5.8 μas yr^{− 1}, which breaks the rules of establishment of the current ICRF. If this effect is not taken into account, the position discrepancy for 295 defining sources will exceed 100 μas for the approximately 30-year history of VLBI observations. Furthermore, global rotation caused by solar acceleration and a non-uniform distribution for 295 defining sources is identified to exist in the ICRF2. The main term is movement of the x-axis with a magnitude of 25 μas per century, which cannot be negligible.

We proposed the concept of the epoch ICRF, consisting of source positions at J2000.0 and apparent proper motions, which are available from the Appendix for 295 ICRF2 defining sources. In this case, the procedure for establishing this new ICRF in VLBI data analysis should be redefined according to the following steps:

1. transformation of the ICRF2 source positions from mean observing epochs to the J2000.0 epoch;

2. imposition of ‘no net rotation’ constraints on 295 defining sources with respect to their positions at J2000.0;

3. correction of the effect of secular aberration drift based on equation (1) for all observing sources.

In addition, the acceleration vector (7.47 ± 0.46, 0.17 ± 0.57, 3.95 ± 0.47) mm s⁻¹ yr⁻¹ in the Galactic coordinate system, is adopted in the model of apparent proper motion. The concept and establishment of the epoch ICRF would have benefits for the overall quality, utility and longevity of the ICRF2.

This research was supported by the National Science Foundation of China (Grant No. 10793032) and also by Shanghai Municipal Key Laboratory (Grant No. DZ22101).

REFERENCES

APPENDIX A Catalogue of the Epoch ICRF

Table A1 lists the coordinates at J2000.0 and apparent proper motions for a sample of ICRF2 defining sources. The complete table is available as Supporting Information in the online version of this article.

SUPPORTING INFORMATION

Additional Supporting Information may be found in the online version of this article:

Table S1. Coordinates at J2000.0 and apparent proper motions for 295 ICRF2 defining sources. (http://mnras.oxfordjournals.org/lookup/suppl/doi:10.1093/mnras/stt044/-/DC1).

Please note: Oxford University Press are not responsible for the content or functionality of any supporting materials supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the article.