Do We Have Sufficient Knowledge of the Galactic Foreground Emission in Cosmic Microwave Background Science?

Galactic foreground emission plays a key role in cosmic microwave background (CMB) science, particularly for detecting primordial gravitational waves. A well-known lesson is the ``dust wave'' identified by BICEP2 in 2014, which was ruled out through a more careful analysis of foreground emission. To date, most estimates of Galactic foreground emission have relied on the assumption that for each line of sight, only one component is considered per emission mechanism. However, the results in this work suggest that more complex modeling -- particularly involving multiple components arising from either line-of-sight complexity or pixel mixing -- may be necessary to fully account for Galactic foregrounds, including dust and other components. More interestingly, the only available two-component dust estimate also fails due to oversimplified emission parameters, although it is conceptually superior to single-component alternatives. These results yield three key conclusions: (1) Due to the intrinsic three-dimensional complexity of the Galactic environment, where physical conditions vary with both distance and direction, the actual radiation from Galactic foreground components cannot be accurately characterized by single-component models. (2) Consequently, CMB experiments require more frequency bands to resolve these components. (3) Spatial variations of foreground emission parameters should not be simplified, because in this work, all such simplifications are found to degrade the estimates significantly.