Orateur
Description
The B-mode polarization of the cosmic microwave background (CMB) is a sensitive probe of primordial gravitational waves. A precise measurement of the tensor-to-scalar ratio $r$ enables stringent tests of inflation, yet the B-mode signal is hidden beneath Galactic foregrounds. Delta-map approximates the line-of-sight dependence of the foreground spectral energy distribution to first order, capturing spatial variation in frequency scaling. We present Hybrid Delta-map, which retains Delta-map’s first-order line-of-sight expansion of the foreground SED while modeling the foregrounds in a spherical-harmonic basis restricted to the multipoles actually retained in the analysis ($\ell \le \ell_{\max}$), and then projects back to real space to build the likelihood. This preserves the advantages of real-space analysis (e.g., flexible masking), enforces strict control of $\ell_{\max}$, and removes the mismatch that arises when fully pixel-space fits at high resolution carry more free parameters than a band-limited data set ($\ell \le \ell_{\max}$) can support—an imbalance that can bias $r$. In realistic multi-frequency simulations including beams, sky masking, and instrument noise, Hybrid Delta-map shows no statistically significant bias in estimates of $r$ at the reionization bump (within our simulation precision) and reduces computational cost.
