Distribution of primary mass in the sample of Brown et al. (2013). The sample contains many objects with primary mass equal to 0.17  M_⊙.

Maximum deviation between the observed sample with N = 54 and a synthetic sample containing N′ = 10 000 objects, with the companion mass being distributed as a Gaussian with a mean mass as given by the abscissa. The blue dotted line is drawn at D^∗ = 0.2628: all simulations with a higher value of the estimator can be rejected at the 99.9% level as being drawn from the same population as the observed distribution. The magenta dashed line is drawn at D^∗ = 0.1274 and provide a 1σ estimate of the allowed parameter range, while the red solid line is drawn at D^∗ = 0.0506.

Top: maximum deviation as a function of the highest mass of the companion if the latter is uniformly distributed between a lowest and highest mass. Bottom: the same, but as a function of the lowest mass. The lines are drawn at the same value of D^∗ as in Fig. A.2.

Reduced χ² map in the mean companion mass vs. standard deviation for an assumed Gaussian functional form of the companion mass distribution – contours are shown at levels of 1, 1.5, 2, and 2.5. The red dot shows the position of the best fit of Andrews et al. (2014). The χ² map confirms the result that was obtained with the K-S statistics.

Comparison between the two best functional forms that lead to the lowest values of D^∗: a Gaussian distribution with μ = 0.76 M_⊙ and σ = 0.27 M_⊙ (solid black line) and a uniform distribution with M_2,l = 0.25 M_⊙ and M_2,u = 1.28 M_⊙ (dotted red line).

Distribution of the mass ratios as determined by the Richardson-Lucy algorithm (solid black line) for all systems with a primary mass below 0.2  M_⊙, and as obtained for the best fits with a Gaussian (red dotted line) and a uniform (blue dashed line) distribution of companions.