Mass functions for massive stars in Cyg OB2 derived using the rotating stellar models of Ekström et al. (2012). Left: histograms showing the distribution of derived masses for all 167 stars in our sample (black histogram, with 1σ error bars determined from MC simulations) and for an age-unbiased sample of 82 stars aged <3.5 Myr (red histogram, with 1σ error bars). Both histograms have been fitted using an ordinary least-squares regression of Y on X (OLS (Y|X), Isobe et al. 1990) for the mass bins >20 M_⊙, giving slopes of Γ = 2.06 ± 0.06 and 1.39 ± 0.19 for the complete and age-unbiased samples, respectively (note that these uncertainties do not take into account random sampling of the IMF). Right: a cumulative mass function showing N (M_⋆ < M) as a function of M for all 98 stars in our sample more massive than 10 M_⊙ (black line) with the 1σ uncertainty (calculated from MC simulations) shown in grey. Also shown are the results of simulated IMFs for Γ = 1.3 (red line, with 1σ random sampling uncertainty shown in pink) and Γ = 2.2 (green line) calculated using the equations of Maschberger (2013, see full explanation in the text). The blue line shows a simulated and evolved IMF for Γ = 1.3 for stars aged 3–7 Myr (i.e. a constant star formation rate from 3 to 7 Myr ago, and no star formation since then). The uncertainties for three simulated IMFs are similar and so only one is shown for clarity.