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gaia data release 3 documentation

10.6 Compact companions

10.6.3 Processing steps

A three-harmonic model is fitted to each light curve in the G band:

G=A0+i=13ai,ccos[2πiP(t-T0)]+ai,ssin[2πiP(t-T0)], (10.2)

with seven free parameters, A0,ai,c,ai,s, and T0 derived from the condition a2,s=0. A0 reflects the mean magnitude of the model and is named model_mean_g. Three-harmonic models are derived also for time series in the GBP and GRP bands with at least 25 measurements (for fewer measurements, the model-related parameters are set to null or to an array of NaN). The semi-amplitude of each harmonic is defined as

Ai=ai,c2+ai,s2for i=1,2,3, (10.3)

and additional selection cuts based on semi-amplitudes in the G band are performed on each system:

  1. 1.


  2. 2.


  3. 3.

    A1/A1,err>3 or A3/A3,err>3,

  4. 4.

    A1/A2<1 and A3/A2<0.3.

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 A2 as a function of the fill-out factor f, the inclination i, and the mass ratio q:

A21L¯/L0α2f3E3(q)qsin2iC(q,f), (10.4)

where L¯ is the average luminosity of the star, L0 being the stellar brightness with no secondary at all, and E(q) is the Eggleton (1983) approximation for the volume-averaged Roche-lobe radius in binary semi-major axis units. The ellipsoidal coefficient α2 depends on the linear limb- and gravity-darkening coefficients of the primary and is expected to be in the 12 range. The correction coefficient C(q,f) starts at 1 for f=0 (no correction), as expected, and rises monotonically as f1, obtaining a value of 1.5 at f0.9 (Gomel, Faigler, and Mazeh 2021b).

Assuming a fill-out factor f=0.95, inclination of 90 and a typical α2 of 1.3 for the G-band (Claret 2019), the modified minimum mass ratio, mod_min_mass_ratio q^min (Gomel, Faigler, and Mazeh 2021a) is solved for each ellipsoidal, within 10-9<q^min<100, based on the observed second harmonic amplitude, A2, in the G band. The uncertainty of q^min is inherently large because of the uncertainty of α2, which somewhat arbitrarily is adopted to be 0.1. Because the resulting distribution of q^min is highly asymmetric, the following quantity is computed:

mod_min_mass_ratio_one_sigmaq^min-σ-(q^min), (10.5)

to represent the 15.9th percentile of its distribution, where σ-(q^min) is the negative-side 1σ uncertainty of q^min. In the same manner,

mod_min_mass_ratio_three_sigmaq^min-3σ-(q^min) (10.6)

represents the 0.135th percentile of the q^min distribution.

If no solution is found for Equation 10.4, then the minimum value of α2 for a solution of q^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. 1.


  2. 2.

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

  3. 3.

    P<2.5 day,

  4. 4.