Diffuse Galactic Foregrounds
Observational data generally contains both cosmological information pertaining to the formation and evolution of the Universe itself, as well as astrophysical information describing the Universe’s key constituents. The late-time/low-redshift components are referred to as ‘foregrounds’ when the high-redshift cosmological signal is the signal of interest. These foregrounds can be subtracted blindly; this removes the need for an understanding of their distinct emission mechanisms but also prevents any further probing of the interstellar medium (ISM). For example, the Cosmic Microwave Background (CMB) is measured in the presence of diffuse Galactic emissions which reveal information about star formation, the chemical composition of our Galaxy and the Galactic magnetic field. The Epoch of Re-ionisation (EoR) signal is dwarfed by diffuse Galactic synchrotron emission which, despite presenting a difficult foreground challenge, exposes how cosmic rays propagate through our Galaxy.
premise (parameter recovery exploiting model informed sparse estimates)
Diffuse thermal dust emission
Using a combination of the Planck 353, 545, 857 GHz data and the IRIS map at 3000 GHz, we chose to model and fit the thermal dust emission as a modified black body (MBB):
A typical, and demonstrably successful, way to deal with the contamination from instrumental noise as well as the Gaussian-like CIB is through smoothing. However convolving observational data with a Gaussian beam will smooth over signal as well noise. By using sparsity, premise can pick out the wavelet coefficients associated with the pure thermal dust emission as these coefficients will be larger than the coefficients of the Gaussian-like components within the total signal. A threshold value is defined using the mean absolute deviation of the coefficients and any coefficient lower than this threshold is removed from the observational data. This threshold value is key; using a value too large will result in the loss of thermal dust information, conversely using too low a value will result in observational data which is still contaminated by the CIB and instrumental noise.
As there is no smoothing involved premise can present parameter maps at the full resolution of the accompanying observational data. However for noise dominated regions premise will not be able to salvage any thermal dust information, as all the wavelet coefficients will be removed through thresholding. A detailed description of how we use premise to determine the MBB parameters of thermal dust emission between 353 and 3000 GHz is given in ‘Determining thermal dust emission from Planck HFI data’. Below are the MBB parameter maps calculated by premise from 353, 545, 857 and 3000 GHz observational data: