%0 Generic %1 elbadry2017statistical %A El-Badry, Kareem %A Weisz, Daniel R. %A Quataert, Eliot %D 2017 %K IMF JWST variation %T The statistical challenge of constraining the low-mass IMF in Local Group dwarf galaxies %U http://arxiv.org/abs/1701.02347 %X 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.

@misc{elbadry2017statistical, 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 $\lesssim 20\%$ requires that observations be complete to $\lesssim 0.2 M_{\odot}$, if the IMF is similar to the MW IMF. A similar statistical precision can be obtained if observations are only complete down to $0.4M_{\odot}$, but this requires measurement of nearly 100$\times$ more stars, and thus, a significantly more massive satellite ($M_{V} \sim -12$). 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 $\sim 4$ for typical observations). If the IMFs of nearby dwarf galaxies are lognormal and \textit{do} vary, observations must reach down to $\sim m_c$ 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.}, added-at = {2017-01-11T10:11:09.000+0100}, author = {El-Badry, Kareem and Weisz, Daniel R. and Quataert, Eliot}, biburl = {https://www.bibsonomy.org/bibtex/2d611d2a3985858e283fafaca9b9c7868/miki}, description = {[1701.02347] The statistical challenge of constraining the low-mass IMF in Local Group dwarf galaxies}, interhash = {f03dedc1c8d5a1041de1887833273152}, intrahash = {d611d2a3985858e283fafaca9b9c7868}, keywords = {IMF JWST variation}, note = {cite arxiv:1701.02347Comment: Submitted to MNRAS. 12 pages, 9 figures, plus appendix}, timestamp = {2017-01-11T10:11:09.000+0100}, title = {The statistical challenge of constraining the low-mass IMF in Local Group dwarf galaxies}, url = {http://arxiv.org/abs/1701.02347}, year = 2017 }