Identifying frequency de-correlated dust residuals in B-mode maps by exploiting the spectral capability of bolometric interferometry

Context. Astrophysical polarized foregrounds represent the most critical challenge in cosmic microwave background (CMB) B-mode experiments, requiring multifrequency observations to constrain astrophysical foregrounds and isolate the CMB signal. However, recent observations indicate that foreground emission may be more complex than anticipated. Not properly accounting for these complexities during component separation can lead to a bias in the recovered tensor-to-scalar ratio. Aims. In this paper we investigate how the increased spectral resolution provided by band-splitting in bolometric interferometry (BI) through a technique called spectral imaging can help control the foreground contamination in the case of an unaccounted-for Galactic dust frequency de-correlation along the line of sight (LOS). Methods. We focused on the next-generation ground-based CMB experiment CMB-S4 and compared its anticipated sensitivity, frequency, and sky coverage with a hypothetical version of the same experiment based on BI (CMB-S4/BI). We performed a Monte Carlo analysis based on parametric component separation methods (FGBuster and Commander) and computed the likelihood of the recovered tensor-to-scalar ratio, r. Results. The main result is that spectral imaging allows us to detect systematic uncertainties on r from frequency de-correlation when this effect is not accounted for in the component separation. Conversely, an imager such as CMB-S4 would detect a biased value of r and would be unable to spot the presence of a systematic effect. We find a similar result in the reconstruction of the dust spectral index, and we show that with BI we can more precisely measure the dust spectral index when frequency de-correlation is present and not accounted for in the component separation. Conclusions. The in-band frequency resolution provided by BI allows us to identify dust LOS frequency de-correlation residuals where an imager with a similar level of performance would fail. This creates the possibility of exploiting this potential in the context of future CMB polarization experiments that will be challenged by complex foregrounds in their quest for B-mode detection.