Context. Comparisons of optical positions derived from the Gaia mission and radio positions measured by very long baseline interferometry (VLBI) probe the structure of active galactic nuclei (AGN) on the milliarcsecond scale. So far, these comparisons have focused on using the S∕X-band (2/8 GHz) radio positions, but did not take advantage of the VLBI positions that exist at higher radio frequencies, namely at K-band (24 GHz) and X∕Ka-band (8/32 GHz). Aims. We extend previous works by considering two additional radio frequencies (K-band and X∕Ka-band) with the aim to study the frequency dependence of the source positions and its potential connection with the physical properties of the underlying AGN. Methods. We compared the absolute source positions measured at four different wavelengths, that is, the optical position from the Gaia Early Data Release 3 (EDR3) and the radio positions at the S∕X-, K-, and X∕Ka-band, as available from the third realization of the International Celestial Reference Frame (ICRF3), for 512 common sources. We first aligned the three ICRF3 individual catalogs to the Gaia EDR3 frame and compared the optical-to-radio offsets before and after the alignment. Then we studied the correlation of optical-to-radio offsets with the observing (radio) frequency, source morphology, magnitude, redshift, and source type. Results. The deviation among optical-to-radio offsets determined in the different radio bands is less than 0.5 mas, but there is statistical evidence that the optical-to-radio offset is smaller at K-band compared to S∕X-band for sources showing extended structures. The optical-to-radio offset was found to statistically correlate with the structure index. Large optical-to-radio offsets appear to favor faint sources, but are well explained by positional uncertainty, which is also larger for these sources. We did not detect any statistically significant correlation between the optical-to-radio offset and the redshift. Conclusions. The radio source structure appears to be a major cause for the radio-to-optical offset. For the alignment of the Gaia celestial reference frame, the S∕X-band frame remains the preferred choice at present.

Aims. The first Gaia data release (Gaia DR1) provides 2 191 ICRF2 sources with their positions in the auxiliary quasar solution and five astrometric parameters -positions, parallaxes, and proper motions -for stars in common between the Tycho-2 catalogue and Gaia in the joint Tycho-Gaia astrometric solution (TGAS). We aim to analyze the overall properties of Gaia DR1 reference frame. Methods. We compare quasar positions of the auxiliary quasar solution with ICRF2 sources using different samples and evaluate the influence on the Gaia DR1 reference frame owing to the Galactic aberration effect over the J2000.0-J20015.0 period. Then we estimate the global rotation between TGAS with Tycho-2 proper motion systems to investigate the property of the Gaia DR1 reference frame. Finally, the Galactic kinematics analysis using the K-M giant proper motions is performed to understand the property of Gaia DR1 reference frame.Results. The positional comparison between the auxiliary quasar solution and ICRF2 shows negligible orientation and validates the declination bias of ∼−0.1 mas in Gaia quasar positions with respect to ICRF2. Galactic aberration effect is thought to cause an offset ∼0.01 mas of the Z axis direction of Gaia DR1 reference frame. The global rotation between TGAS and Tycho-2 proper motion systems, obtained by different samples, shows a much smaller value than the claimed value 0.24 mas yr −1 . For the Galactic kinematics analysis of the TGAS K-M giants, we find possible non-zero Galactic rotation components beyond the classical Oort constants: the rigid part ω Y G = −0.38±0.15 mas yr −1 and the differential part ω ′ Y G = −0.29±0.19 mas yr −1 around the Y G axis of Galactic coordinates, which indicates possible residual rotation in Gaia DR1 reference frame or problems in the current Galactic kinematical model. Conclusions. The Gaia DR1 reference frame is well aligned to ICRF2, and the possible influence of the Galactic aberration effect should be taken into consideration for the future Gaia-ICRF link. The cause of the rather small global rotation between TGAS and Tycho-2 proper motion systems is unclear and needs further investigation. The possible residual rotation in Gaia DR1 reference frame inferred from the Galactic kinematic analysis should be noted to and examined in future data release.

Aims. In order to investigate the systematic errors in the very long baseline interferometry (VLBI) positions of extragalactic sources (quasars) and the global differences between Gaia and VLBI catalogs, we use the first data release of Gaia (Gaia DR1) quasar positions as the reference and study the positional offsets of the second realization of the International Celestial Reference Frame (ICRF2) and the Goddard VLBI solution 2016a (gsf2016a) catalogs. Methods. We select a sample of 1032 common sources among three catalogs and adopt two methods to represent the systematics: considering the differential orientation (offset) and declination bias; analyzing with the vector spherical harmonics (VSH) functions. Results. Between two VLBI catalogs and Gaia DR1, we find that: i) the estimated orientation is consistent with the alignment accuracy of Gaia DR1 to ICRF, of ~0.1 mas, but the southern and northern hemispheres show opposite orientations; ii) the declination bias in the southern hemisphere between Gaia DR1 and ICRF2 is estimated to be +152 μas, much larger than that between Gaia DR1 and gsf2016a which is +34 μas. Between two VLBI catalogs, we find that: i) the rotation component shows that ICRF2 and gsf2016a are generally consistent within 30 μas; ii) the glide component and quadrupole component report two declination-dependent offsets: dipolar deformation of ~+50 μas along the Z-axis, and quadrupolar deformation of ~−50 μas that would induce a pattern of sin2δ. Conclusions. The significant declination bias between Gaia DR1 and ICRF2 catalogs reported in previous studies is possibly attributed to the systematic errors of ICRF2 in the southern hemisphere. The global differences between ICRF2 and gsf2016a catalogs imply that possible, mainly declination-dependent systematics exit in the VLBI positions and need further investigations in the future Gaia data release and the next generation of ICRF.

Aims. We propose to estimate the accuracy of current very long baseline interferometry (VLBI) catalogs. Methods. The difference of source position estimated from two decimation solutions was analyzed to estimate the scale factor and noise floor for the formal error of radio source positions by two different methods. In one method, we investigated the weighted root-square-mean (wrms) scatter of source positional differences versus the number of observed sessions; for the other one, we compared the wrms difference versus the formal error. Based on the estimated noise floor and scale factor, we determined the realistic error of radio source positions in the standard solution and compared it with that of Gaia DR2 and ICRF2 catalogs. Results. The estimated scale factors from two methods are rather consistent, which is of ∼1.3 in both coordinates. As for the noise floor, it is estimated to be 20–25 μas for sources observed in at least ten sessions, and it could reduce down to ∼10 μas for sources which have been observed more than 1000 times. The inflated median formal error of our solution is of the same order as the Gaia DR2 catalog in declination and the direction of major axis of the error ellipse, but smaller by a factor of two in right ascension. With respect to the ICRF2 catalog, our solution yields an improved accuracy by a factor of about three. Conclusions. Currently, the VLBI radio source catalog still provides source positions with the best accuracy which is about 20–25 μas. Moreover, the noise floor of VLBI catalogs could potentially reach 10 μas with more observations in the future.

The link between the International Celestial Reference Frame at radio wavelength and the forthcoming Gaia optical reference frame is a mandatory task after the completion of the Gaia mission. Starting from the provisional reference frame in which Gaia astrometric solutions were obtained, we discuss the ways to correct the residual rotation and acceleration effects and investigate three potential options for linking the two frames realized by extragalactic sources. We have estimated the accuracy for the frame alignment assuming different astrometric models of quasar proper motions observed by very long baseline interferometry (VLBI). Using about 500,000 high-precision proper motions of extragalactic sources, the residual rotation of the Gaia reference frame is evaluated under 1 μas yr−1. In view of its favorable properties, Gaia should be given priority to be considered as the future fundamental reference frame that is consistent with the principle of the International Celestial Reference System. The VLBI reference frame can be linked to Gaia based on thousands of common quasars with an accuracy of 10 μas for each axis.