  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.
