The SVDSolarLikeSOSRotationalModulation pipeline was able to detect 723 315
solarlike 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 solarlike 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:

$R\ge 1.4$ 

(7.6) 

$R\le 0.5$ 

(7.7) 
where the values 0.5 and 1.4 correspond the 5th and 95th percentile of the
$R$ distribution. The second filter is based on the PhaseCoverage (PC) and the
MaximumPhaseGap (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 periodsearch 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 phasecoverage
histogram contains at least one observation, the phase coverage will be 1,
indicating that for the given model, the data are quasiuniformly 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

$$MPG=\mathrm{max}(\mathrm{\Delta}{\varphi}_{i,j})$$ 

(7.8) 
where

$$\mathrm{\Delta}{\varphi}_{i,j}={\varphi}_{i}{\varphi}_{j}$$ 

(7.9) 
where ${\varphi}_{i}$ and ${\varphi}_{j}$ are the phases of the ith and jth observations when
folded according to the detected period.
We applied a filter that flags a candidate as valid only if the requirements:

$PC\ge 0.4$ 

(7.10) 

$$ 

(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 solarlike
stars but Cepheids. This can happen if the star has an overestimated parallax
and, consequently, un underestimated luminosity. In such a case the location of
the star in the magnitudecolour 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 CU7Classification package. By applying
all these filters, the final number of solarlike candidates reported in Gaia DR2 is
147 535.