2017MNRAS.468..319E

We use Monte Carlo simulations to explore the statistical challenges of constraining the characteristic mass (m_c) and width (σ) of a lognormal sub-solar initial mass function (IMF) in Local Group dwarf galaxies using direct star counts. For a typical Milky Way (MW) satellite (M_V = -8), jointly constraining m_c and σ to a precision of <= 20 per cent requires that observations be complete to <= 0.2 M_☉, if the IMF is similar to the MW IMF. A similar statistical precision can be obtained if observations are only complete down to 0.4 M_☉, but this requires measurement of nearly 100x more stars, and thus, a significantly more massive satellite (M_V ∼ -12). In the absence of sufficiently deep data to constrain the low-mass turnover, it is common practice to fit a single-sloped power law to the low-mass IMF, or to fit m_c for a lognormal while holding σ fixed. We show that the former approximation leads to best-fitting power-law slopes that vary with the mass range observed and can largely explain existing claims of low-mass IMF variations in MW satellites, even if satellite galaxies have the same IMF as the MW. In addition, fixing σ during fitting leads to substantially underestimated uncertainties in the recovered value of m_c (by a factor of ∼4 for typical observations). If the IMFs of nearby dwarf galaxies are lognormal and do vary, observations must reach down to ∼m_c in order to robustly detect these variations. The high-sensitivity, near-infrared capabilities of the James Webb Space Telescope and Wide-Field Infrared Survey Telescope have the potential to dramatically improve constraints on the low-mass IMF. We present an efficient observational strategy for using these facilities to measure the IMFs of Local Group dwarf galaxies.