Abstract
We use Monte Carlo simulations to explore the statistical challenges of
constraining the characteristic mass ($m_c$) and width ($\sigma$) 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 $\sigma$ to a precision of $20\%$
requires that observations be complete to $0.2 M_ødot$, if the IMF
is similar to the MW IMF. A similar statistical precision can be obtained if
observations are only complete down to $0.4M_ødot$, but this requires
measurement of nearly 100$\times$ 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 $\sigma$ fixed. We show that the former approximation leads to
best-fit 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
$\sigma$ 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 JWST and WFIRST 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.
Description
[1701.02347] The statistical challenge of constraining the low-mass IMF in Local Group dwarf galaxies
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