10.8.4 Processing steps
The processing flow consists of the search of the period (Section 10.8.4), the computation of a model fit to the light curve (Section 10.8.4), and the Crich/Orich classification (Section 10.8.4).
Period search
The frequency is determined from the $G$band time series cleaned from outliers (Section 10.2.3). It uses a Least Squares method on a frequency range from 0.007 d${}^{1}$ to 0.1 d${}^{1}$ with a frequency step of ${\mathrm{3.3\hspace{0.17em}10}}^{5}$ d${}^{1}$. In order for the frequency to be published in Gaia DR3, the following conditions must be met:

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the period (1/frequency) must be greater than 35 d, in particular to avoid aliasing effects that lead to spurious periods below this limit;

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the period must be smaller than the duration of the time series;

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no strong correlation must exist between the Image Parameters Determination (IPD) Goodness of Fit (GoF) time series and the $G$ time series, which would indicate a potential spurious variability in the $G$band; quantitatively, the Spearman correlation between these two time series must be lower than 0.75;

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the signaltonoise ratio in the $G$band must be greater than 15.
Model fit
Model amplitudes are computed by fitting a single Fourier series model to the light curves with the period published in the catalogue and up to three harmonics. The published amplitude corresponds to the amplitude of the fundamental harmonic of the Fourier series (amplitude of the sine function, i.e., half peaktopeak).
Carbon star classification
The two main peaks in each RP spectrum $i$ of a given LPV candidate are identified and the pseudowavelength separation $\mathrm{\Delta}{\lambda}_{\mathrm{RP},i}^{\ast}$ between them is computed. The median value $\mathrm{\Delta}{\lambda}_{\mathrm{RP}}^{\ast}$ of these $\mathrm{\Delta}{\lambda}_{\mathrm{RP},i}^{\ast}$ time series is then used to determine the Orich or Crich nature of the star. It is published in the attribute median_delta_wl_rp of the Gaia DR3 catalogue of LPV candidates.
From the analysis of the distribution of $\mathrm{\Delta}{\lambda}_{\mathrm{RP}}^{\ast}$ and inspection of RP spectra, the transition between O and Crich stars is identified at $\mathrm{\Delta}{\lambda}_{\mathrm{RP}}^{\ast}=7$. Sources with $\mathrm{\Delta}{\lambda}_{\mathrm{RP}}^{\ast}>7$ are classified as Crich and their Crich flag is_cstar is set to TRUE in the catalogue.
It must be noted that the simple criterion adopted above to distinguish between Crich and Orich red giants leads to a small percentage of misclassifications, specifically when $\mathrm{\Delta}{\lambda}_{\mathrm{RP}}^{\ast}$ is very large. A procedure to identify these cases and improve the classification is provided in the paper describing the catalogue (Lebzelter et al. 2023).