From observing strategies to velocity dispersion bias: forward modeling unresolved binaries in ultra-faint dwarf galaxies
Ultra-faint dwarf galaxies (UFDs) in the Milky Way are ideal probes of low-mass galaxy formation and dark matter because they are highly dark-matter dominated. In the lowest-mass systems, however, unresolved binary orbital motion complicates dynamical mass estimates by inflating measured velocity dispersions and biasing the interpretation of the inferred masses. We develop a flexible forward-modeling pipeline, the Binary Observation Simulator, to generate mock multi-epoch radial-velocity observations of binary populations in dwarf galaxies and to quantify how binary-induced biases depend on both galaxy properties and observing strategy. We generate mock samples spanning true velocity dispersion of $σ_{\rm true}\sim0.75$-$3.5$ km/sec, binary fractions of $0.1$-$0.9$, and multi-epoch baselines of up to $10$ yr. We find that, while multi-epoch monitoring reduces the binary-induced bias, residual contamination remains significant for low-mass halos: even a $10$-yr baseline can leave $\sim10$-$120\%$ relative bias for systems with $σ_{\rm true}\lesssim1$ km/sec. We also note that small sample sizes ($\lesssim20$) introduce substantial stochastic scatter in the recovered dispersions, sometimes masking the expected improvement from longer observational baselines. Applying the framework to the real $\sim17$-yr Bootes I observing record reproduces the literature velocity dispersions, yields an empirical correction conditioned on that cadence, and shows that redistributing the same observations onto half the number of stars would have removed roughly half of the residual binary bias. These results emphasize that robust dispersion estimates for the faintest dwarfs require forward modeling of both binary populations and survey cadence.