Evidence for Dynamical Filtering: High Binary Fraction, Hard-binary Excess, and Unresolved Triples in the Surviving Core of NGC 6791

Abstract: We present a deep photometric analysis of the main-sequence (MS) population in the old, metal-rich open cluster (OC) NGC 6791 using Gaia Data Release 3 data. After correcting for differential reddening, we use the Bayesian model comparison to test whether stellar rotation can account for the observed MS broadening and find that a rotation-dominated interpretation is strongly disfavored. We therefore infer that unresolved multiplicity is the primary contributor to the photometric offsets. We derive a high-q companion fraction of $54.3\% \pm 2.8\%$ for systems with $q \gtrsim 0.5$, significantly higher than typical values reported for most OCs and the field. The inferred offset distribution is not consistent with a flat mass-ratio distribution but instead shows an excess toward high mass ratios ($q \sim 0.8$--$1.0$), suggestive of preferential survival of hard binaries in a dynamically evolved environment. We also identify a population of stars lying above the equal-mass binary limit ($ΔG > 0.75$ mag), which is difficult to explain with ordinary MS binaries alone and is plausibly interpreted as candidate unresolved triple or higher-order multiple systems. A Kolmogorov--Smirnov test, together with Monte Carlo label-shuffling experiments, shows no statistically significant difference between the projected radial distributions of the single-star and binary/multiple populations within the observed field. Taken together, these results are consistent with the picture that NGC 6791 is the dynamically processed inner remnant of a once more massive cluster.