Non-variation of the solar diameter with the cycle: the end of a possible link between activity and diameter

We have reanalyzed the 7 years of filtregrams data (150 000 photograms and magnetograms) of the SOHO/MDI experiment. We used the maximum possible sampling compatible with full frame recording, carefully avoiding any suspicious filtregram. Going further than the previous analysis of 2 years of data by Emilio et al. (Ap. J. 543,1007, 2000), we better corrected for changes in optical aberrations and, along Turmon et al. (Ap. J., 568, 396, 2002), we reduced radius measurement errors by identifying active regions and avoiding radius measurements herein. We found that, within the limit of our noise level uncertainties (2 mas), the solar diameter could be constant over the half cycle investigated. Our results confirm the recent reanalysis of the 7 years of MDI data made by Antia (Ap. J. 590, 567, 2003), with a completely different method since using the ultra-precise frequency variation of the f-modes (fundamental modes linked to the diameter). He found (carefully removing the yearly Earth induced variations and avoiding the SOHO data gap of 1999) that the diameter is constant over the half solar cycle (radius variation are less than 0.6 km, 0.8 mas - nothing over noise level). Along Antia, we can conclude that: "If a careful analysis is performed, then it turns out that there is no evidence for any variation in the solar radius." There were no theoretical reasons for large solar radius variations and there is no observational evidence for them with consistent space observations.