Infrared helium–hydrogen line ratios as a measure of stellar effective temperature

We have observed a large sample of compact planetary nebulae in the near-infrared to determine how the 2¹P–2¹S He  i line at 2.058 μm varies as a function of stellar effective temperature, T _eff. The ratio of this line with H  i Br γ at 2.166 μm has often been used as a measure of the highest T _eff present in a stellar cluster, and hence of whether there is a cut-off in the stellar initial mass function at high masses. However, recent photoionization modelling has revealed that the behaviour of this line is more complex than previously anticipated. Our work shows that in most aspects the photoionization models are correct. In particular, we confirm the weakening of the 2¹P–2¹S line as T _eff increases beyond 40 000 K. However, in many cases the model underpredicts the observed ratio when we consider the detailed physical conditions in the individual planetary nebulae. Furthermore, there is evidence that there is still significant 2¹P–2¹S He  i line emission even in the planetary nebulae with very hot     central stars. It is clear from our work that this ratio cannot be considered as a reliable measure of effective temperature on its own.