Contributing to TAI with a Secondary Representation of the SI Second

We report the first contribution to the international atomic time (TAI) based on a secondary representation of the SI second. This work is done with the LNE-SYRTE FO2-Rb fountain frequency standard using the $^{87}$Rb ground state hyperfine transition. We describe FO2-Rb and how it is connected to local and international time scales. We report on local measurements of this frequency standard in the SI system, i.e. against primary frequency standards, down to a fractional uncertainty of $4.4\times 10^{-16}$, and on the establishment of the recommended value for the $^{87}$Rb hyperfine transition by the CIPM. We also report on the process that led to the participation of the FO2-Rb frequency standard to $Circular~T$ and to the elaboration of TAI. This participation enables us to demonstrate absolute frequency measurement directly in terms of the SI second realized by the TAI ensemble with a statistical uncertainty of $1.1\times 10^{-16}$, therefore at the limit allowed by the accuracy of primary frequency standards. This work constitutes a demonstration of how other secondary representations, based on optical transitions, could also be used for TAI, and an investigation of a number of issues relevant to a future redefinition of the SI second.