# 7.4.5 Quality assessment and verification: verification

The resulting data coming out of the pipeline were systematically inspected in order to verify the conformity to the expectation and to the expected statistical behaviour of the fitted parameters. Basically the SB1 class was treated excluding the SB1 solutions that were later combined with the solutions from other channels (Section 7.7.1). The dataset contains 181 327 objects. As a first test, the histogram of the argument of periastron distribution is created (see Figure 7.23). The distribution is rather homogeneous with a very slight tendency to have more objects at 90${}^{\circ}$ and at 270${}^{\circ}$. This results from a very small bias because saw-tooth RV curves are easier to detect than square-tooth RV curves, particularly at high eccentricity. The effect is practically negligible.

Another interesting plot is the distribution of ${T}_{0}$ versus the period. It is given in Figure 7.24. It is clear that the graph is essentially as expected with a rather homogeneous density of data points slowly decreasing towards the largest periods. Above 800-day periods, there is a tendency to have a larger density near the values ${T}_{0}\sim \pm P/2$. This effect is explained by the increased uncertainty on the parameters when the number of observed cycles decreases when the period is approaching the span of time of the analysed data set (34 months). In the next figure, Figure 7.25, we plotted the histogram of the distribution of the RVs of the centres of mass $\gamma $. This histogram is very similar to the one built for the constant stars (see figure 4, Seabroke et al. 2021) which is a strong indication of the quality of these centres of mass RVs.

The observed distribution of the goodness of fit $F2$ deduced from the chi-square is given for the filtered dataset of solutions (see Figure 7.26). The recommended and applied cut-off at $F2=3$ is clearly visible. Along with the observed distribution, a Gaussian around the mean zero and with a $\sigma =1$ dispersion (in magenta) and another one with a $\sigma =1.2$ (in blue) are plotted. This suggests a most probable slight underestimate of the uncertainties associated with the radial velocities. Figure 7.27 presents the distribution of the uncertainties on the semi-amplitude $K$ as a function of the uncertainties on the RV of the centre of mass $\gamma $. The ratio of the two is expected to be square root of 2 which is what is observed despite a rather large dispersion. No particular anomaly is present on the errors of the considered parameters.

The critical point when fitting the orbital SB1 models is the determination of the period (see above). Figure 7.28 displays the histogram of the period (in $\mathrm{log}$). Several features are visible. The log-distribution is rather flat with a marked excess at very large periods. This excess can be due to the fact (see above) that the periods of the same order of magnitude than the span of time of the mission are rather indicative and certainly not a perfect estimator of the true period. This uncertainty implies the concentration of several solutions near these long-periods. This excess is very sensitive to the threshold separating SB1 solutions from the TrendSB1. On the other hand, the deficit of solutions around the period of 182.6 days is due to the yearly Earth orbit that Gaia accompanies that produces regular gaps with a scale of half a year. These gaps presented by the sampling are associated with large gaps in phase that have been eliminated because they correspond to badly determined periods and orbits. The decrease of density of solutions for lower periods is an artefact of the application of an ad hoc selection criterion that prevents the proliferation of the small periodicities. This correction is described in detail in Gosset et al. (2022). This effect should be further investigated for the next Data Releases. Figure 7.29 represents the plot of the derived SB1 mass function as a function of the adopted period. One clearly sees that the majority of the data points are between 0.001 and 0.5 (the yellow borders). Objects outside this range are very few, in particular on the side of the high mass function. From the statistical point of view, the diagram is rather close to the expected one. Data points at an unexpected location could be due to problems in the derivation of the period or of the eccentricity. In particular, one should be very careful while searching for abnormal mass function values or massive black hole. In addition, the overdensities tracing vertical lines at $P=63.7$days and at one year (much broader) are due to objects with a varying apparent position inducing systematic effects on the RVs associated with the variation of the scan-angle. These are objects presenting small amplitudes at these particular periodicities (bad astrometry inducing bad wavelength calibration). These objects could easily be filtered out but they were not before the application of the combiner with the astrometric channel in order not to miss interesting objects. The effect of scan-angle dependent signals and spurious periods is described in Holl et al. (2023a).