We used the database of eclipsing binaries detected by the OGLE microlensing project in the pencil-beam search volume toward Baade's Window to define a sample of 74 detached, equal-mass, main-sequence binary stars with short orbital periods in the range 0.19 < P < 8 days. The logarithmic slope of the period distribution log N ∝ (-0.8 ± 0.2) was used to infer the angular-momentum–loss (AML) efficiency for the late, rapidly rotating members of close binaries. It is very likely that the main cause of the negative slope is a discovery selection bias that progressively increases with the orbital period length. Assuming a power-law dependence for the correction for the bias ∝ -C log P (with C ≥ 0) the AML braking-efficiency exponent α in dH/dt = P-α can take any value α = -1.1 (±0.2) + C. Very simple considerations of discovery biases suggest C 4/3, which would give an AML braking law very close to the "saturated" one, with no dependence on the period. However, except for plausibility arguments, we have no firm data to support this estimate of C, so that α remains poorly constrained. The results signal the utmost importance of the detection bias evaluation for variable star databases used in analyses similar to the one presented in this study.
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