| Summary: | Star formation theories have struggled to reproduce binary brown dwarf population demographics (e.g., frequency, separation, and mass ratio). Kernel-phase interferometry is sensitive to companions at separations inaccessible to classical imaging, enabling tests of these theories at new physical scales below the hydrogen burning limit. We analyze the detections and sensitivity limits from our previous kernel-phase analysis of archival HST/NICMOS surveys of field brown dwarfs. After estimating physical properties of the 105 late-M to T dwarfs using Gaia distances and evolutionary models, we use a Bayesian framework to compare these results to a model companion population defined by log-normal separation and power-law mass-ratio distributions. When correcting for Malmquist bias, we find a companion fraction of $F={0.11}_{-0.03}^{+0.04}$ and a separation distribution centered at $\rho ={2.2}_{-1.0}^{+1.2}$ au, smaller and tighter than seen in previous studies. We also find a mass-ratio power-law index that strongly favors equal-mass systems: $\gamma ={4.0}_{-1.5}^{+1.7}-{11}_{-3}^{+4}$ depending on the assumed age of the field population (0.9–3.1 Gyr). We attribute the change in values to our use of kernel-phase interferometry, which enables us to resolve the peak of the semimajor axis distribution with significant sensitivity to low-mass companions. We confirm the previously seen trends of decreasing binary fraction with decreasing mass and a strong preference for tight and equal-mass systems in the field-age substellar regime; only ${0.9}_{-0.6}^{+1.1}$ % of systems are wider than 20 au and $\lt {1.0}_{-0.6}^{+1.4}$ % of systems have a mass ratio q < 0.6. We attribute this to turbulent fragmentation setting the initial conditions followed by a brief period of dynamical evolution, removing the widest and lowest-mass companions, before the birth cluster dissolves.
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