21cm foregrounds and polarization leakage: a user's guide on cleaning and mitigation strategies

The success of HI intensity mapping is largely dependent on how well 21cm foreground contamination can be controlled. In order to progress our understanding further, we present a range of simulated foreground data from four different $\sim3000$\,deg$^2$ sky regions, with and without effects from polarization leakage. Combining these with underlying cosmological HI simulations creates a range of single-dish intensity mapping test cases that require different foreground treatments. This allows us to conduct the most generalized study to date into 21cm foregrounds and their cleaning techniques for the post-reionization era. We first provide a pedagogical review of the most commonly used blind foreground removal techniques (PCA/SVD, FASTICA, GMCA). We also trial a non-blind parametric fitting technique and discuss potential hybridization of methods. We highlight the similarities and differences in these techniques finding that the blind methods produce near equivalent results, and we explain the fundamental reasons for this. The simulations allow an exact decomposition of the resulting cleaned data and we analyse the contribution from foreground residuals. Our results demonstrate that polarized foreground residuals should be generally subdominant to HI on small scales ($k\gtrsim0.1\,h\,\text{Mpc}^{-1}$). However, on larger scales, results are more region dependent. In some cases, aggressive cleans severely damp HI power but still leave dominant foreground residuals. We also demonstrate the gain from cross-correlations with optical galaxy surveys, where extreme levels of residual foregrounds can be circumvented. However, these residuals still contribute to errors and we discuss the optimal balance between over- and under-cleaning.