Faint Stars in a Faint Galaxy: II. The Low Mass Stellar Initial Mass Function of the Boötes I Ultrafaint Dwarf Spheroidal Galaxy

Abstract

This paper presents improved constraints on the low-mass stellar initial mass function (IMF) of the Boötes I (Boo~I) ultrafaint dwarf galaxy, based on our analysis of recent deep imaging from the Hubble Space Telescope. The identification of candidate stellar members of Boo~I in the photometric catalog produced from these data was achieved using a Bayesian approach, informed by complementary archival imaging data for the Hubble Ultra Deep Field. Additionally, the existence of earlier-epoch data for the fields in Boo~I allowed us to derive proper motions for a subset of the sources and thus identify and remove likely Milky Way stars. We were also able to determine the absolute proper motion of Boo~I, and our result is in agreement with, but completely independent of, the measurement(s) by \textit{Gaia}. The best-fitting parameter values of three different forms of the low-mass IMF were then obtained through forward modeling of the color-magnitude data for likely Boo~I member stars within an approximate Bayesian computation Markov chain Monte Carlo algorithm. The best-fitting single power-law IMF slope is $\alpha =-1.95_{-0.28}^{+0.32}$, while the best-fitting broken power-law slopes are ${\alpha }_1=-1.67_{-0.57}^{+0.48}$ and ${\alpha }_2=-2.57_{-1.04}^{+0.93}$. The best-fitting lognormal characteristic mass and width parameters are ${\mathrm{M}}_{\mathrm{c}}=0.17_{-0.11}^{+0.05}{\mathcal{M}}_{\odot }$ and $\sigma =0.49_{-0.20}^{+0.13}$. These broken power-law and lognormal IMF parameters for Boo~I are consistent with published results for the stars within the Milky Way and thus it is plausible that Bo{ö}tes I and the Milky Way are populated by the same stellar IMF.

27 pages, 14 figures, 4 tables, 3 appendices. Accepted for publication in ApJ

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