Diffuse Galactic Foregrounds

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) 

Our interests lie in the characterisation of diffuse Cosmological foregrounds, for the purposes of their accurate removal but without the loss of astrophysical information. The premise algorithm is a parametric modelling fitting technique - for a given set of frequency measurements, if there in existing idea of how to model the various emissions present then premise can determine the model parameters. premise automatically identifies regions within the data with common properties, makes fast, initial parameter estimates and then refines these regional estimates to provide the global solution through a least squares optimisation which favours sparsity (see our methodology paper for further details). The key being that the various diffuse foreground emission are sparsely represented within the wavelet domain as they have strong spatial patterns which repeat across whole frequency ranges (e.g. the Galactic plane), while cosmological signals do not.   

Diffuse thermal dust emission 

The first problem premise was set to work on was that of obtaining pure thermal dust maps from the Planck HFI data. Thermal dust emission, due to the UV radiation of dust particles, is ubiquitous throughout the ISM and the dominant diffuse Galactic foreground between 100 and 900 GHz. Despite it’s prominence, presenting maps of pure thermal dust emission is still a formidable task due to the existence of the cosmic infrared background (CIB): the unresolved infrared emission from extra-Galactic point sources. The Planck 353, 545 and 857 observational data are a mixture of thermal dust emission, CIB, CMB, resolved point sources and instrumental noise. 

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):

Iν = τ353 B(T, ν) (ν / 353)β
making the model parameters the MBB temperature (T), spectral index (β) and optical depth at 353 GHz (τ353 ). 

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:

The maps can be downloaded for use from this page.