Distribution of period ratio PA/PB for binaries in quadruple systems (the limiting maximum value of 4 was chosen because information beyond this threshold is very sparse and certainly heavily biased). Top panel: all quadruples in the 2+2 architecture. Blue histograms for previously known doubly eclipsing systems, orange histograms for our new discoveries (see Table 2). The data include the cases where the relative motion of the binaries A and B was proven, and those where we lack this information. Green histograms are other quadruple systems in the 2+2 architecture from the MSC catalogue (Tokovinin 2018a). Bottom panel: same as above, but only for the doubly eclipsing systems (sum of blue and orange above). Declining curves at the bottom panel are predictions in a simple model where periods PA and PB are entirely independent variables and have identical probability density distribution: uniform (black) or linearly increasing towards longer orbital periods (red; see discussion in Sect. 7). Both are able to explain the preferential PA ≃ PB configuration. While still noisy, there are two major deviations from their prediction: (i) dearth of systems with period ratio between ≃1.2 and ≃1.5, and (ii) excess of systems with PA/PB ≃ 3/2. On the contrary, the dip at PA/PB ≃ 2 may still reflect data fluctuations.
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