Willman 1 Revisited: The Kinematics, Chemistry, and Orbital Properties of a Potentially-Disrupting Dwarf Galaxy

The ultra-faint Milky Way satellite Willman 1 (W1; $M_V = -2.6$; $r_{\rm half} \sim27$ pc) was the first stellar over-density found via resolved stars in the Sloan Digital Sky Survey, yet its classification as either a dwarf galaxy or star cluster remains ambiguous. Using new Keck/DEIMOS spectroscopy, HST/ACS photometry, and orbital modeling, we re-examine the nature of W1. From our updated sample of 56 member stars, we find that past analyses included four binaries and seven nonmembers, identified here using Gaia proper motions and updated velocities. We continue to find a velocity dispersion consistent with previous analyses, measuring $σ_v = 4.7^{+1.5}_{-1.3}$ km s$^{-1}$ from 49 stars out to $3~r_{\rm half}$. If W1 is in equilibrium, this suggests a dynamical mass of $5.9^{+3.7}_{-3.4} \times 10^5~M_{\odot}$ and a mass-to-light ratio of $(M/L)_V = 660 \pm 590$. Based on Ca II triplet measurements, we estimate an iron abundance of [Fe/H] $= -2.45^{+0.12}_{-0.13}$ and a metallicity dispersion of $σ_{\rm [Fe/H]} = 0.30^{+0.15}_{-0.11}$ dex. We confirm that W1 does not exhibit mass segregation inside $\sim1~r_{\rm half}$. Our best-fit orbital model predicts that W1 is at apocenter, implying that W1 has been closer to the Milky Way in the recent past, reaching a pericentric distance $\lesssim 25$ kpc from the Galactic center $\sim0.3$ Gyr ago. Given its internal kinematics, metallicity spread, and lack of mass segregation, we conclude that W1 is a galaxy. However, given its orbit and structural properties, which suggest that W1 might be tidally disrupted, and the difficulty of identifying a pure member sample, we caution that the measured internal velocity dispersion may not accurately reflect the dynamical mass of this system.