ZFIRE: using Hα equivalent widths to investigate the in situ initial mass function at z ~ 2

We use the ZFIRE (http://zfire.swinburne.edu.au) survey to investigate the high-mass slope of the initial mass function (IMF) for a mass-complete (log(10)(M-*/M-circle dot) similar to 9.3) sample of 102 star-forming galaxies at z similar to 2 using their H alpha equivalent widths (H alpha EWs) and rest-frame optical colours. We compare dust-corrected H alpha EW distributions with predictions of star formation histories (SFHs) from PEGASE. 2 and STARBURST99 synthetic stellar population models. We find an excess of high H alpha EWgalaxies that are up to 0.3-0.5 dex above the model-predicted Salpeter IMF locus and the H alpha EW distribution is much broader (10-500 angstrom) than can easily be explained by a simple monotonic SFH with a standard Salpeter-slope IMF. Though this discrepancy is somewhat alleviated when it is assumed that there is no relative attenuation difference between stars and nebular lines, the result is robust against observational biases, and no single IMF (i.e. non-Salpeter slope) can reproduce the data. We show using both spectral stacking and Monte Carlo simulations that starbursts cannot explain the EW distribution. We investigate other physical mechanisms including models with variations in stellar rotation, binary star evolution, metallicity and the IMF upper-mass cut-off. IMF variations and/or highly rotating extreme metal-poor stars (Z similar to 0.1 Z(circle dot)) with binary interactions are the most plausible explanations for our data. If the IMF varies, then the highest H alpha EWs would require very shallow slopes (Gamma > -1.0) with no one slope able to reproduce the data. Thus, the IMF would have to vary stochastically. We conclude that the stellar populations at z greater than or similar to 2 show distinct differences from local populations and there is no simple physical model to explain the large variation in H alpha EWs at z similar to 2.