# 7.5.4 Quality assessment and validation

Quality assessment and validation of the results were performed by means of three different methods:

• Cross-match between Gaia DR2 results and solar-like variables with a known rotation period;

• statistical analysis of the stellar parameters inferred by the pipeline;

• visual inspection of folded light-curves of a few hundred selected examples.

## Verification

The optimal method to verify the SVD-Solar-Like-SOS-Rotational modulation pipeline should be the comparison of Gaia DR2 results with surveys dedicated to solar-like variables like Kepler of Corot. Unfortunately the number of observations and the Gaia sampling in the sky fields covered by Kepler Corot do not allow the selection of input sources in those sky areas. A comparison between Gaia results and these surveys will be possible only for the DR3 release. In spite of everything, there are several studies on rotational modulation in open-clusters stars that can be used to verify Gaia DR2 data. The Pleiades field, for instance, has been well studied and the rotation period has been estimated for a few hundred of stars belonging to this field (see e.g. Hartman et al. 2010). See Lanzafame et al. (2018) for details on the comparison between Gaia DR2 results and those of Hartman et al. (2010).

## Validation

The SVD-Solar-Like-SOS-Rotational-Modulation pipeline was able to detect 723 315 solar-like candidates. The statistical analysis of the parameters inferred by the pipeline and the visual inspection of hundreds of folded light curves showed that a certain fraction of the selected candidates was doubtful. In many stars there was a strong discrepancy between the parameters AI and $A_{fit}$ (defined in Equation 7.4). In certain segments, where a significant period was detected, the visual inspection of the folded light curve revealed that the phase coverage of the data is really poor making the detected period doubtful. The folded light curves of some stars have the typical shape of other variable objects like Cepheids stars or Eclipsing Binaries. In order to deal with these issues, we applied four different filters to the sample of solar-like candidates. The first filter takes into account the ratio $R$ between AI and $A_{fit}$. We rejected all the stars satisfying one of the conditions:

 $\displaystyle R\geq 1.4$ (7.6) $\displaystyle R\leq 0.5$ (7.7)

where the values 0.5 and 1.4 correspond the 5-th and 95-th percentile of the $R$ distribution. The second filter is based on the Phase-Coverage (PC) and the Maximum-Phase-Gap (MPG) parameters. The PC parameter measures how uniformly the observations are distributed over phase when the data are folded with the period detected by the period-search module. The observations collected in a given segment are folded according the period detected in that segment and their phases are binned in 10 equally spaced intervals in the range [0,1]. The number of bins that contains at least one observation is divided by the total number of bins, to obtain a phase coverage number in [0,1]. If every bin in the phase-coverage histogram contains at least one observation, the phase coverage will be 1, indicating that for the given model, the data are quasi-uniformly distributed in phase. At the other extreme, if all the observations fall into the same bin, a value tending to 0 will be obtained. The MPG parameter is defined as the maximum gap in phase between the data i.e. as

 $MPG=\max(\Delta\phi_{i,j})$ (7.8)

where

 $\Delta\phi_{i,j}=\phi_{i}-\phi_{j}$ (7.9)

where $\phi_{i}$ and $\phi_{j}$ are the phases of the i-th and j-th observations when folded according to the detected period.

We applied a filter that flags a candidate as valid only if the requirements:

 $\displaystyle PC>=0.4$ (7.10) $\displaystyle MPG<=0.3$ (7.11)

are satisfied in one segment at least. Finally, visual inspection of the folded light curves revealed that some of the detected variables were not solar-like stars but Cepheids. This can happen if the star has an over-estimated parallax and, consequently, un under-estimated luminosity. In such a case the location of the star in the magnitude-colour diagram can fall in the region used for the selection of the input sources. In order to avoid these problems, we rejected all the stars classified as Cepheids from the CU7-Classification package. By applying all these filters, the final number of solar-like candidates reported in Gaia DR2 is 147 535.