Binarity Enhances the Occurrence Rate of Radiation Belt Emissions in Ultracool Dwarfs

Despite a burgeoning set of ultracool dwarf ($\leq$M7) radio detections, their radio emissions remain enigmatic. Open questions include the plasma source and acceleration mechanisms for the non-auroral "quiescent" component of these objects' radio emissions, which can trace Jovian synchrotron radiation belt analogs. Ultracool dwarf binary systems can provide test beds for examining the underlying physics for these plasma processes. We extend a recently developed occurrence rate calculation framework to compare the quiescent radio occurrence rate of binary systems to single objects. This generalized and semi-analytical framework can be applied to any set of astrophysical objects conceptualized as unresolved binary systems with approximately steady-state emission or absorption. We combine data available in the literature to create samples of 179 single ultracool dwarfs (82 M dwarfs, 74 L dwarfs, and 23 T/Y dwarfs) and 27 binary ultracool dwarf systems. Using these samples, we show that quiescent radio emissions occur in $54^{+11}_{-11}$ - $65^{+11}_{-12}$ per cent of binaries where both components are ultracool dwarfs, depending on priors. We also show that binarity enhances the ultracool dwarf quiescent radio occurrence rate relative to their single counterparts. Finally, we discuss potential implications for the underlying drivers of ultracool dwarf quiescent radio emissions, including possible plasma sources.