The Tycho-Gaia Astrometric Solution (TGAS) is specific to Gaia DR1 and
will not be used in future releases. It was implemented in AGIS as a way to
obtain an internally consistent five-parameter astrometric solution early
in the mission. The problem with any early solution is that a limited time
coverage (e.g. one year) is not sufficient to reliably disentangle the five
astrometric parameters of a given source. In particular, strong correlations between
the parallax and proper motion components very much weaken the solution.
One way to avoid this partial degeneracy is to solve only some of the astrometric
parameters, for example only the two position parameters $\alpha $ and $\delta $.
But this will not produce a solution that is internally consistent at sub-mas level,
because the proper motion and parallax effects over a year are larger than a mas
for most stars.

Conceptually, TGAS developed as a logical extension of the Hundred Thousand
Proper Motion (HTPM) project originally proposed by F. Mignard (2009, unpublished
technical note) and further developed and studied by Michalik et al. (2014).
The basic principle of TGAS (and HTPM) is very simple: include the positions
of stars around the epoch 1991.25, as given in the Hipparcos and Tycho catalogues,
as additional ‘observations’ in an astrometric solution of the Gaia data for these
stars. The $\sim $25 year time difference between the earlier catalogues and Gaia ensures that the proper motions can be determined with reasonable precision,
which greatly facilitates the disentangling of the other parameters and in particular
the determination of parallax from the Gaia data. Because the full five-parameter
model can be used, the solution should ideally be internally consistent with small
residuals. TGAS therefore gave the opportunity to investigate the behaviour of
Gaia in a much more stringent manner than would otherwise be possible with such
a limited stretch of data. Since TGAS was also found to deliver astrophysically
very interesting data it was decide to incorporate TGAS results in Gaia DR1.

The principle of TGAS is described in Michalik et al. (2015), which also
provides a practical recipe for its implementation in AGIS and the results of
simulated solutions. In Michalik and Lindegren (2016) it was shown how quasars
can also be incorporated in TGAS, using the circumstance that their proper
motions can be assumed to be negligible. Both TGAS and the auxiliary quasar
solution were used in the production of Gaia DR1 as described elsewhere in
this document and in Lindegren et al. (2016).