Numerical Biases on Initial Mass Function Determinations Created by Binning

We detect and quantify significant numerical biases in the determination ofthe slope of power laws with Salpeter (or similar) indices fromuniformly-binned data using chi-square minimization. The biases are caused bythe correlation between the number of stars per bin and the assigned weightsand are especially important when the number of stars per bin is small. Thisresult implies the existence of systematic errors in the values of IMFscalculated in this way. We propose as an alternative using variable-size binsand dividing the stars evenly among them. Such variable-size bins yield verysmall biases that are only weakly dependent on the number of stars per bin.Furthermore, we show that they allow for the calculation of reliable IMFs withonly a small total number of stars. Therefore, they are a preferred alternativeto the standard uniform-size binning.Comment: 21 pages, 6 figures, to appear in the 20 August 2005 issue of the Ap