# 7.2.2 Preprocessing: rejection of outliers and correction of perspective acceleration

Before trying the different models of astrometric binaries, the stars selected in Section 7.1.2 go through the preprocessing, which is a shaping common to all astrometric processes in Gaia DR3. This step begins with a first rejection of outlier CCD transits (a second rejection takes place in the calculation of linear solutions, Section 7.2.3) and continues with a modification of the measurements of some stars, in order to take into account the perspective acceleration.

Each transit of a star in the Gaia field results in two-dimensional coordinates with respect to a fixed reference position, close to that of the star: an abscissa along the satellite’s scanning direction, and an ordinate measured on the axis perpendicular to it. Since the along-scan abscissa is much more precise than the ordinate, the latter is not taken into account. However, they must first be purged of aberrant transits.

Each field-of-view transit is composed of up to 9 CCD transits, each of which is supposed to give, roughly, the same along-scan abscissa. Outliers are detected by comparing the abscissae of the CCD transits to the median abscissa. CCD transits for which the deviation exceeds 5 times the abscissa uncertainty are rejected. After this cleaning operation, the transits can be corrected for perspective acceleration.

The perspective acceleration is the only perspective effect that should be taken into account, since the effects due to the change of orbit orientation are negligible for Gaia (Halbwachs 2009). The perspective acceleration depends on the trigonometric parallax, the proper motion and the radial velocity (Dravins et al. 1999; Lindegren and Dravins 2003). The latter has been measured by the RVS spectroscopic processing pipeline (see Chapter 6), and the astrometric parameters are known with sufficient accuracy from the Gaia DR3 solution.

The radial velocity, $\mathrm{RV}$, and the parallax, $\varpi $, of the star are used to derive the radial proper motion, ${\mu}_{r}$, through the following equation:

$${\mu}_{r}=\mathrm{RV}\varpi \times \frac{24\pi \times {\mathrm{year}}_{\mathrm{days}}}{180\times {\mathrm{au}}_{\mathrm{m}}}$$ | (7.1) |

where $\mathrm{RV}$ is in $\mathrm{km}{\mathrm{s}}^{-1}$, $\varpi $ is in mas, ${\mathrm{year}}_{\mathrm{days}}$ is the duration of the year in days, and ${\mathrm{au}}_{\mathrm{m}}$ is the length of the astronomical unit in meters.

The quantity that must be added to the along-scan abscissa of a star $w$ to free it from perspective acceleration is then:

$$\mathrm{\Delta}w={\mu}_{r}t\times ({f}_{\varpi}\varpi +{f}_{{\mu}_{\alpha *}}{\mu}_{\alpha *}+{f}_{{\mu}_{\delta}}{\mu}_{\delta})$$ | (7.2) |

where $t$ is the epoch in year, measured from the reference epoch 2016.0, which is approximately the middle of the Gaia DR3 mission; ${f}_{\varpi}$, ${f}_{{\mu}_{\alpha *}}$ and ${f}_{{\mu}_{\delta}}$ are the partial derivatives of $w$ with respect to the parallax and to the proper motion coordinates. This correction has been made for all stars with $\varpi >5$ mas, since the effects of perspective acceleration are negligible beyond 200 pc.

After this correction, the transits are ready for the calculation of the solutions. This will only be done when the number of visibility periods (VP) is higher than the number of model parameters. Therefore, the number of CCD transits is always very high, since each VP can have several Field-of-View (FoV) transits, and each FoV transits has up to 9 CCD transits.

The single-star solution was derived again from the corrected $w$. Among the 4 115 743 stars entering the calculation process, 28 obtained a 5-parameter solution with a goodness_of_fit $$. As mentioned above, a few solutions with a negative goodness-of-fit despite a large Gaia DR3 ruwe were not unexpected given the different astrometric solution approach adopted. It was not considered useful to search for an astrometric binary solution for these stars.