Theoretical predictions for IMF diagnostics in UV spectroscopy of star clusters

We explore the possibility of using UV spectroscopy in combination with broad-band photometry as diagnostic tools for understanding the shape of the initial mass function (IMF) in unresolved stellar populations. Building on our previous work, we extend the Stochastically Lighting Up Galaxies (SLUG) code to include a high-resolution UV spectral synthesizer and equivalent width calculation capabilities. We first gain a qualitative understanding of how UV spectral features behave as the parameters that define a star cluster in SLUG (mass, age, extinction, and IMF slope α3) are changed. We then exploit Bayesian inference techniques to recover the α3 values for clusters simulated with SLUG, using mock observations of these clusters comprised of broad-band photometry and equivalent width measurements of a selection of UV spectral features. We find some improvement when compared to attempts using broad-band photometry alone (with the interquartile range of the α3 posterior PDF shrinking by ≃ 32%), although we still do not yet fully break the known degeneracy between the cluster mass and α3. Finally, we make predictions about how effective real observations will be by quantifying our ability to constrain α3 as a function of limiting equivalent width. We find that observations sensitive to a modest equivalent width of ≃ 9 Å are sufficient to improve the recovery of the IMF slope parameter by ≃ 32% (interquartile range of posterior PDF median residuals), moving to ≃ 39% when we include all the significant spectral features in the wavelength range 900 - 3000 Å.