attitude and calibration noise, but still provides improvements in all respects: the positions are at least a factor two better and the proper motions improved by about 16%. More importantly, the resulting parallax errors are 26% smaller and centred on zero (median error $-0.03$ $\mu$as), while HTPM-B gave systematically underestimated parallaxes for the [Hipparcos]{} stars (median error $-591~\mu$as). This clearly demonstrates that the additional prior provided by the [*Tycho*]{} positions also benefits the [Hipparcos]{} subset.

### Spatial characteristics of the solution

![image](actualerror_varpiMEDIAN){width="\columnwidth"} ![image](actualerror_varpiRSE){width="\columnwidth"} ![image](formalerror_varpiMEDIAN){width="\columnwidth"} ![image](normalizederror_varpiRSE){width="\columnwidth"}

The quality of the TGAS results for a particular star depends on the number and temporal distribution of its [*Gaia*]{} observations, which in turn depends on the position in the sky. Figure \[fig:maps-simulations\] (right) shows the number of field-of-view transits per star as set by the scanning law, yielding relatively few transits in areas within 45$^\circ$ of the ecliptic. Figure \[fig:maps-results\] shows the error characteristics for the [*Tycho*]{}-only subset. Panel **(a)** displays the median of the actual parallax errors (TGAS solution minus the simulated true values). In the well observed areas these are centred on zero, showing that the parallaxes are unbiased. The statistical scatter is larger in areas with few observations and unfavourable temporal 