The statistical challenge of constraining the low-mass IMF in Local Group dwarf galaxies

Abstract

We use Monte Carlo simulations to explore the statistical challenges of constraining the characteristic mass (mc) 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 mc 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 100× 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꜀ 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 mc (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꜀ 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.

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