Using Two-Frequency Dust Spectral Matching to Separate Galactic Synchrotron and Free-Free Temperature Foregrounds from the CMB

We introduce a method for removing CMB and anomalous microwave emission (AME, or spinning dust) intensity signals at high to intermediate Galactic latitudes in temperature sky maps at frequencies roughly between 5 and 40 GHz. The method relies on the assumption of a spatially uniform combined dust (AME and thermal) rms spectral energy distribution for these regions, but is otherwise model independent. A difference map is produced from input maps at two different frequencies in thermodynamic temperature: the two frequencies are chosen such that the rms AME signal in the lower frequency ( 5 - 40 GHz) map is equivalent to the thermal dust emission rms in the higher frequency ( 95 - 230 GHz) map. Given the high spatial correlation between AME and thermal dust, the resulting difference map is dominated by synchrotron and free-free foreground components, and can thus provide useful insight into the morphology and possible spectral variations of these components at high latitudes. We show examples of these difference maps obtained with currently available WMAP and Planck data and demonstrate the efficacy of CMB and dust mitigation using this method. We also use these maps, in conjunction with Haslam 408 MHz and WHAM H-alpha observations, to form an estimate of the diffuse synchrotron spectral index in temperature on degree scales. The hybrid analysis approach we describe is advantageous in situations where frequency coverage is insufficient to break spectral degeneracies between AME and synchrotron.