# 4.1 Introduction

Author(s): David Hobbs

This chapter is unique with respect to the other chapters, in that, it supplements the previous astrometry Chapter 3 and will only appear in Gaia DR1. In this chapter we document only those extra steps needed to implement the TGAS solution as opposed to a Gaia only solution which will form the basis of all later data releases. All the astrometric models and processing steps are the same as outlined in Chapter 3. An evaluation of the TGAS data are also to be found in Section 3.5 which represents a basic quality assessment and validation of the scientific results which will also be published in detail in Lindegren et al. (2016). A more independent catalogue consolidation and validation of the science results for Gaia DR1 was also performed and are documented in Chapter 7 and will be published in Arenou et al. (2017).

## 4.1.1 Overview

Author(s): Lennart Lindgren

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as a logical extension of the Hundred Thousand Proper Motion (HTPM) project originally proposed by F. Mignard (2009, unpublished technical note) and further developed and studied by Michalik et al.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).