The Hubble Ultracool Multiplicity (HUM) Survey. I. Characterizing Sensitivity to Companions at Sub-Diffraction Limit Separations with HST WFC3/IR

We characterize the sensitivity of a double point-spread function (PSF) fitting algorithm -- employing empirical, position-dependent PSF models -- for detecting companions using the infrared channel of the Wide Field Camera 3 (WFC3/IR) on the Hubble Space Telescope (HST). The observed separation distribution of known brown dwarf (BD) binaries is potentially biased towards separations larger than the angular resolution limits of current techniques. Previous imaging analyses suffer from incompleteness at separations $<2\lambda/D$; our aim is to probe within this limit to identify previously missed companions. We evaluate the performance of our technique on artificial data across 8 WFC3/IR filters and a broad range of signal-to-noise ratios (S/N), determining our ability to accurately recover injected companions and identifying the region of parameter space where false positive fits are likely. Here, we demonstrate the capability of this technique to recover companions at sub-pixel separations on the WFC3/IR detector -- below the diffraction limit in multiple filters. For F160W at a typical S/N of 75, we resolve companions separated by 0.8 pixels (104 mas, $0.759\lambda/D$) at 1.5 magnitudes contrast with $>90\%$ confidence. We achieve the closest angular resolution for any detection method with WFC3/IR imaging to date. Compared to previous BD multiplicity surveys with WFC3/IR, we achieve a 2.5$\times$ improvement in separation sensitivity at contrasts of 0-3 magnitudes in F127M. We have demonstrated that applying our improved technique to archival HST images of field BDs will thus probe down to separations of 1 au, in one of the largest high angular resolution surveys of such objects to date.