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

TL;DR

This study constrains the low-mass stellar initial mass function of the Boötes I ultrafaint dwarf galaxy using deep Hubble data, Bayesian member identification, and proper motion analysis, finding results consistent with the Milky Way's IMF.

Contribution

It provides the first detailed IMF constraints for Boötes I using advanced Bayesian and proper motion techniques, comparing its IMF to that of the Milky Way.

Findings

Best-fit single power-law slope: α = -1.95

Broken power-law slopes: α₁ = -1.67, α₂ = -2.57

Lognormal parameters: M_c = 0.17 M_⊙, σ = 0.49

Abstract

This paper presents improved constraints on the low-mass stellar initial mass function (IMF) of the Bo\"otes 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 $\rm{M}_{\rm{c}} = 0.17_{-0.11}^{+0.05} \cal M_\odot$ 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{\"o}tes I and the Milky Way are populated by the same stellar IMF.