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 (MV = -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 (MV ∼ -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 mc 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 ∼mc 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.
- Publication:
-
Monthly Notices of the Royal Astronomical Society
- Pub Date:
- June 2017
- DOI:
- 10.1093/mnras/stx436
- arXiv:
- arXiv:1701.02347
- Bibcode:
- 2017MNRAS.468..319E
- Keywords:
-
- methods: statistical;
- stars: low-mass;
- stars: luminosity function;
- mass function;
- Astrophysics - Astrophysics of Galaxies
- E-Print:
- Accepted to MNRAS with minor revisions since v1. 12 pages, 9 figures, plus appendices