somewhat (for example because the attitude is less accurately determined), but we have verified that TGAS works with as few as one million [*Tycho*]{} stars. The bright-star performance is a more serious issue for the HTPM solution, as more than half of the [Hipparcos]{} stars are brighter than 8.84 mag.

Systematics in the [*Tycho-2*]{} data
-------------------------------------

The present TGAS experiments assume that the [*Tycho*]{} positions give the barycentric directions to the stars at the standard [Hipparcos]{} epoch J1991.25. In reality the [*Tycho-2*]{} positions refer to slightly different epochs, which could even be different in $\alpha$ and $\delta$. The actual TGAS solution should use the mean effective epoch $(t_\alpha+t_\delta)/2$ of each star rather than J1991.25.

A potentially more serious complication is that the [*Tycho*]{} positions do not strictly represent the barycentric directions at the given epochs of observation. The positions were derived from the stacked star mapper photon count records accumulated over the whole [Hipparcos]{} mission . Parallaxes were typically not taken into account in this process, and the resulting positions are therefore offset by a fraction of the parallax. Both the fraction and direction of the offset depend in a complex way on the distribution, geometry, and weights of the 