A determination of the mass function ( MF ) of stellar clusters can be quite dependent on the range of measured masses , the fitting technique , and the analytic function that is being fit to the data .
Here , we use Hubble Space Telescope/WFPC2 data of NGC 1711 , a stellar cluster in the Large Magellanic Cloud , as a test case to explore a range of possible determinations of the MF from a single dataset .
We employ the analytic modified lognormal power-law ( MLP ) distribution , a hybrid function that has a peaked lognormal-like body and a power-law tail at intermediate and high masses .
A fit with the MLP has the advantage that the resulting best-fit function can be either a hybrid function , a pure lognormal , or a pure power law , in different limits of the function .
The completeness limit for the observations means that the data contains masses above \sim 0.90 M _ { \odot } .
In this case , the MLP fits yield essentially a pure power-law MF .
We demonstrate that the nonlinear regression/least-squares approach is not justified since the underlying assumptions are not satisfied .
By using maximum-likelihood estimation , which is independent of binning , we find a best-fit functional form dN / d \ln m \propto m ^ { - \alpha } , where \alpha = 1.72 \pm 0.05 or 1.75 \pm 0.05 for two different theoretical isochrone models , respectively .
Furthermore , we explore the possibility of systematic errors in the determination of the power-law index due to the depth of the observations .
When we combine the observational data with artificially generated data from the lognormal Chabrier initial MF for masses below 0.90 M _ { \odot } , the best-fit MLP is a hybrid function but with a steeper asymptotic slope i.e. , \alpha = 2.04 \pm 0.07 .
This illustrates the systematic uncertainties in commonly used MF parameters that can depend on the range of data that is fitted .