The foreground transfer function for H I intensity mapping signal reconstruction: MeerKLASS and precision cosmology applications

Blind cleaning methods are currently the preferred strategy for handling foreground contamination in single-dish H I intensity mapping surveys. Despite the increasing sophistication of blind techniques, some signal loss will be inevitable across all scales. Constructing a corrective transfer function using mock signal injection into the contaminated data has been a practice relied on for H I intensity mapping experiments. However, assessing whether this approach is viable for future intensity mapping surveys, where precision cosmology is the aim, remains unexplored. In this work, using simulations, we validate for the first time the use of a foreground transfer function to reconstruct power spectra of foreground-cleaned low-redshift intensity maps and look to expose any limitations. We reveal that even when aggressive foreground cleaning is required, which causes ${\gt }\, 50~{{\ \rm per\ cent}}$ negative bias on the largest scales, the power spectrum can be reconstructed using a transfer function to within sub-per cent accuracy. We specifically outline the recipe for constructing an unbiased transfer function, highlighting the pitfalls if one deviates from this recipe, and also correctly identify how a transfer function should be applied in an autocorrelation power spectrum. We validate a method that utilizes the transfer function variance for error estimation in foreground-cleaned power spectra. Finally, we demonstrate how incorrect fiducial parameter assumptions (up to ${\pm }100~{{\ \rm per\ cent}}$ bias) in the generation of mocks, used in the construction of the transfer function, do not significantly bias signal reconstruction or parameter inference (inducing ${\lt }\, 5~{{\ \rm per\ cent}}$ bias in recovered values).