10.6.3 Processing steps
A threeharmonic model is fitted to each light curve in the $G$ band:
$$G={A}_{0}+\sum _{i=1}^{3}{a}_{i,\mathrm{c}}\mathrm{cos}\left[\frac{2\pi i}{P}(t{T}_{0})\right]+{a}_{i,\mathrm{s}}\mathrm{sin}\left[\frac{2\pi i}{P}(t{T}_{0})\right],$$  (10.2) 
with seven free parameters, ${A}_{0},{a}_{i,\mathrm{c}},{a}_{i,\mathrm{s}}$, and ${T}_{0}$ derived from the condition ${a}_{2,\mathrm{s}}=0$. ${A}_{0}$ reflects the mean magnitude of the model and is named model_mean_g. Threeharmonic models are derived also for time series in the ${G}_{\mathrm{BP}}$ and ${G}_{\mathrm{RP}}$ bands with at least 25 measurements (for fewer measurements, the modelrelated parameters are set to null or to an array of NaN). The semiamplitude of each harmonic is defined as
$${A}_{i}=\sqrt{{a}_{i,\mathrm{c}}^{2}+{a}_{i,\mathrm{s}}^{2}}\text{for}i=1,2,3,$$  (10.3) 
and additional selection cuts based on semiamplitudes in the $G$ band are performed on each system:

1.
$$,

2.
${A}_{2}/{A}_{2,\mathrm{err}}>7$,

3.
${A}_{1}/{A}_{1,\mathrm{err}}>3$ or ${A}_{3}/{A}_{3,\mathrm{err}}>3$,

4.
$$ and $$.
The final stage is to identify ellipsoidal candidates that might have compact companions. This is done by using equation 1 of Gomel, Faigler, and Mazeh (2021a), which estimates the ellipsoidal leading amplitude ${A}_{2}$ as a function of the fillout factor $f$, the inclination $i$, and the mass ratio $q$:
$${A}_{2}\approx \frac{1}{\overline{L}/{L}_{{}_{0}}}{\alpha}_{2}{f}^{3}{E}^{3}(q)q{\mathrm{sin}}^{2}iC(q,f),$$  (10.4) 
where $\overline{L}$ is the average luminosity of the star, ${L}_{{}_{0}}$ being the stellar brightness with no secondary at all, and $E(q)$ is the Eggleton (1983) approximation for the volumeaveraged Rochelobe radius in binary semimajor axis units. The ellipsoidal coefficient ${\alpha}_{2}$ depends on the linear limb and gravitydarkening coefficients of the primary and is expected to be in the $1$–$2$ range. The correction coefficient $C(q,f)$ starts at $1$ for $f=0$ (no correction), as expected, and rises monotonically as $f\to 1$, obtaining a value of $\sim $$1.5$ at $f\gtrsim 0.9$ (Gomel, Faigler, and Mazeh 2021b).
Assuming a fillout factor $f=0.95$, inclination of ${90}^{\circ}$ and a typical ${\alpha}_{2}$ of 1.3 for the $G$band (Claret 2019), the modified minimum mass ratio, mod_min_mass_ratio ${\widehat{q}}_{\mathrm{min}}$ (Gomel, Faigler, and Mazeh 2021a) is solved for each ellipsoidal, within $$, based on the observed second harmonic amplitude, ${A}_{2}$, in the $G$ band. The uncertainty of ${\widehat{q}}_{\mathrm{min}}$ is inherently large because of the uncertainty of ${\alpha}_{2}$, which somewhat arbitrarily is adopted to be $0.1$. Because the resulting distribution of ${\widehat{q}}_{\mathrm{min}}$ is highly asymmetric, the following quantity is computed:
$$\mathtt{\text{mod\_min\_mass\_ratio\_one\_sigma}}\equiv {\widehat{q}}_{\mathrm{min}}{\sigma}^{}({\widehat{q}}_{\mathrm{min}}),$$  (10.5) 
to represent the $15.9$th percentile of its distribution, where ${\sigma}^{}({\widehat{q}}_{\mathrm{min}})$ is the negativeside $1\sigma $ uncertainty of ${\widehat{q}}_{\mathrm{min}}$. In the same manner,
$$\mathtt{\text{mod\_min\_mass\_ratio\_three\_sigma}}\equiv {\widehat{q}}_{\mathrm{min}}3{\sigma}^{}({\widehat{q}}_{\mathrm{min}})$$  (10.6) 
represents the $0.135$th percentile of the ${\widehat{q}}_{\mathrm{min}}$ distribution.
If no solution is found for Equation 10.4, then the minimum value of ${\alpha}_{2}$ for a solution of ${\widehat{q}}_{\mathrm{min}}=100$ is calculated.
The final list of 6336 candidates is obtained by applying additional cuts to the results of the Compact Companion work package:

1.
${A}_{2}/{A}_{2,\mathrm{err}}>10$,

2.
frequencygram peak $>12$ (in units of standard deviation of the frequencygram),

3.
$$ day,

4.
${\widehat{q}}_{\mathrm{min}}>0.5$.