The He I 2.06 microns/Br-gamma ratio in starburst galaxies - An objective constraint on the upper mass limit to the initial mass function

The use of the He I 2.06 microns/Br-gamma ratio as a constraint on the massive stellar population in star-forming galaxies is developed. A theoretical relationship between the He I 2.06 microns/Br-gamma ratio and the effective temperature of the exciting star in H II regions is derived. The effects of collisional excitation and dust within the nebula on the ratio are also considered. It is shown that the He I 2.06 microns/Br-gamma ratio is a steep function of the effective temperature, a property which can be used to determine the upper mass limit of the initial mass function (IMF) in galaxies. This technique is reliable for upper mass limits less than about 40 solar masses. New near-infrared spectra of starburst galaxies are presented. The He I 2.06 microns/Br-gamma ratios observed imply a range of upper mass limits from 27 to over 40 solar masses. There is also evidence that the upper mass limit is spatially dependent within a given galaxy. These results suggest that the upper mass limit is not a uniquely defined parameter of the IMF and probably varies with local physical conditions.