The Bayesian Global Sky Model (B-GSM)

Abstract

Observations of the redshifted 21-cm signal of neutral hydrogen gas from the first billion years after the Big Bang have the potential to inform studies of cosmic structure formation and fundamental physics research [3, 5]. This signal is today visible at frequencies in the range 50-200~MHz. Attempts to observe this 21-cm signal suffer from foreground contamination that is 4-6 orders of magnitude greater than the expected signal [3, 5]. It is therefore essential, for 21-cm cosmology studies, that an accurate foreground model be available for the low frequency sky. In this thesis, we present a new low frequency global model of the diffuse radio sky, the Bayesian Global Sky Model (B-GSM). The novel Bayesian framework of B-GSM aims to address the limitations of previous sky models, notably the Global Sky Model (GSM), by introducing robust error quantification and calibration into the model. We use nested sampling to compute Bayesian evidence and to determine posterior distributions for the spectral behaviour and spatial amplitudes of diffuse emission components. Bayesian model comparison, using these Bayesian evidence values, is then used to select the number of emission components and their spectral parametrisation. B-GSM is based on a dataset of nine large area diffuse sky surveys covering the frequency range 45-408~MHz. Along with an independent dataset of absolute temperature measurements, used for calibration. We present a pre-processing pipeline to perform point source removal for these diffuse maps and demonstrate the effectiveness of this pipeline. B-GSM is tested using a synthetic dataset, yielding promising results. This synthetic dataset reflects the main features of the true dataset, but is created with a known set of model parameters and a known true sky signal. We find that the Bayesian evidence is able to select the correct number of components and spectral model. For the model with the highest evidence, the posterior sky predictions match the true sky within statistical error, showing B-GSM's ability to accurately model the dataset's true signal. The root-mean-square (RMS) residual relative to the true signal is significantly reduced in the posterior sky prediction, compared to the uncalibrated dataset. Additionally, the posterior calibration parameters agree with the true values within 2σ, confirming B-GSM's ability to calibrate the maps in the dataset. These results are obtained for an idealized case. We find that while the posterior components and spectra roughly match the true ones, recovering the correct spectral parameters within error is challenging. It is possible that the choice of prior influences the posterior distribution of component spectra and amplitudes. However, we find that the choice of prior has minimal effect on B-GSM's ability to accurately model the sky. We present preliminary results for the B-GSM framework applied to our real dataset. We find that the Bayesian evidence selects for a two component model with curved power-law component spectra. The two identified components appear to correspond to physically explainable emission processes. The first component appears to correspond to Galactic synchrotron emission and shows significant contribution both in the galactic plane and at higher and lower Galactic latitudes. We find that the first component follows a power-law spectrum with spectral index β = -2.6153±0.0006 with curvature γ = -0.0511±0.0004 (reference frequency ν = 180 MHz), corresponding well with previous literature. The second component appears to correspond to free-free emission, and is primarily contained in the Galactic plane. This second component follows a power-law spectrum with a spectral index of β = -1.77±0.01 with curvature γ=-1.64±0.02 (reference frequency ν = 180 MHz). The pronounced curvature of the second component may correspond to free-free absorption at low frequencies. For this highest evidence model, we find that the posterior sky predictions are indistinguishable by eye from observations. Additionally, we find that the posterior predicted sky temperature as a function of Local Sidereal Time (LST) is in reasonable agreement (within ∼ 5-10%) with the temperatures produced using EDGES [41, 40] measurements and EDGES spectral indexes. However, we find that the normalised residuals (between the posterior predicted and observed sky) do not follow a Gaussian distribution, and have a mean of -0.25 and standard deviation of 0.83. The non-Gaussian shape may indicate that the assumptions we make about the noise in the observed maps are incorrect. The non-zero mean indicates that B-GSM is systematically under-predicting the sky temperature by on average a quarter the reported observational error.