The impact of improved estimates of radio star astrometric models on the alignment of the Gaia bright reference frame to ICRF3

Aims. We investigated the residual orientation offset and spin between the bright (G <= 13 mag) frame of the Gaia Early Data Release 3 (Gaia EDR3) and the third realization of the International Celestial Reference Frame (ICRF3). For this purpose, six rotation parameters (orientation offset and its time derivative, the spin), as well as corrections to the Gaia astrometric model for each star involved, are fitted to the differences in the astrometric models derived from very long baseline interferometry (VLBI) and Gaia. This study aims to find reliable estimates for the rotation parameters between the two frames. Methods. We reprocessed our previous analyses while taking into account the effect of Galactocentric acceleration on the VLBI observations. Furthermore, we replaced VLBI data for 12 stars by improved estimates of models of stellar motion from combining historical data with the new positions, rather than including the new observations directly as single-epoch positions in the analysis of the rotation parameters. Additionally, we replaced the model positions by positions obtained without correcting the calibrator data for source structure whenever possible to better reference the star position to ICRF3. In the same fashion, the VLBI proper motion and parallax were included for two of the stars for the first time, and data for five new stars were added. Results. The iterative solutions for the spin parameters show less scatter in the X component when the new models of stellar motion from VLBI are applied. The mean formal errors of the spin parameters decrease by about 15%, whereas those of the orientation offsets increase by about 15%. Small additional improvements in the mean formal error were achieved by including new VLBI data and by excluding stars that produce offsets in the iterative rotation parameter estimates from the beginning. The orientation offset [epsilon(X)(T), epsilon(Y)(T), epsilon(Z)(T)] and the spin [omega(X), omega(Y), omega(Z)] of the final baseline solution of this work were found to be (+0.322, +0.228, +0.163)+/-(0.203, 0.251, 0.155) mas and (+0.034, +0.072, -0.026)+/-(0.023, 0.025, 0.023) mas yr(-1). As a consequence, no significant orientation offset of Gaia EDR3 toward ICRF3 is detected; however, the spin omega(Y) is statistically significant at the 3 sigma level. The rotation parameters between the Gaia and VLBI frames in the Y direction remain the least well determined in terms of formal errors. The impact of Galactocentric acceleration on the rotation parameter analysis was found to be negligible with the currently available VLBI data. As a result, it was found that the uncorrected bright Gaia frame exhibits a closer alignment with ICRF3 compared to the corrected frame.