Bayesian recalibration of flux scale factors in diffuse radio maps using low-resolution absolute radiometers

TL;DR

The Haslam 408 MHz map suffers from uncorrected flux-scale errors that hinder diffuse-sky modeling for CMB and 21 cm experiments. The authors develop a Bayesian, multi-resolution framework that jointly infers the true sky $\mathbf{s}$, a spatial flux-scale field $\mathbf{g}$, and spatially varying spectral indices $\boldsymbol{\beta}$ using Gibbs sampling and Gaussian constrained realisations, tested on synthetic data with ~50,000 parameters. In a fiducial scenario, flux-scale factors are recovered to within $\pm 2\%$ in most regions and the corrected sky brightness within roughly $5$ K of the true sky, demonstrating the method’s viability for recalibrating Haslam maps once low-frequency radiometer data are available. The approach provides a principled, data-driven path to improved, region-specific flux calibration and a more accurate high-frequency foreground template for cosmology analyses, while highlighting degeneracies with spectral indices and the benefits and limitations of incomplete sky coverage.

Abstract

The Haslam 408 MHz all-sky map is widely used as a template to model the diffuse Galactic synchrotron emission at radio and microwave frequencies. Recent studies have suggested that there are large uncorrected flux scale errors in this map, however. We investigate the possibility of statistically recalibrating the Haslam map using absolutely-calibrated (but low angular resolution) radio experiments designed to measure the 21cm global signal at low frequencies. We construct a Gibbs sampling scheme to recover the full joint posterior distribution of $\sim 50,000$ parameters, representing the true sky brightness temperature field, as-yet uncorrected flux scale factors, and synchrotron power-law spectral indices. Using idealised full-sky simulated data, we perform a joint analysis of a $1^\circ$ resolution diffuse map at 408 MHz and multi-band 21cm global signal data with $30^\circ$ resolution under different assumptions about 1) noise levels in the maps, 2) sky coverage, and 3) synchrotron spectral index information. For our fiducial scenario in which the global signal experiment has a 50 mK noise rms per coarse pixel in each of 20 frequency bins between 50 -- 150 MHz -- the typical range for a global signal experiment,, we find that the notional Haslam flux scale factors can be recovered in most (but not all) sub-regions of the sky to an accuracy of $\pm 2 \%$. In all cases we are able to rectify the sky map to within $\sim 5$ K of the true brightness temperature. Our method can be used to correct the Haslam map once maps obtained from global experiments are available.

Figures (11)

• Figure 1: (Left): The different zones (in Galactic coordinates), corresponding to different surveys used to construct the Haslam map, taken from haslam1982AAS...47....1H. We have combined the thin strip of overlap between the Jodrell Mk-IA and Effelsburg instruments, and further subdivided each zone into 10 smaller subzones represented by the grey outline. (Right): The spectral index map used in the second part of the paper. The 'true' value of $\beta$ for each region is randomly drawn from a normal distribution i.e. $\beta \sim \mathcal{N}(\mu_\beta, 0.05)$, $\mu_\beta = [-2.5, -2.6, -2.7, -2.8, -2.9, -3]$ for each of the six zones.
• Figure 2: Clockwise from top left: the true brightness temperature map $\boldsymbol{s}$, the posterior mean of the sky temperature $\langle \boldsymbol{s}\rangle$, the standard deviation of the difference between the sample and true map, std($\Delta_{\boldsymbol{s}}$), and the fractional difference between $\langle \boldsymbol{s}\rangle$ and $\boldsymbol{s}$, $f_{\langle \boldsymbol{s}\rangle}$ for the STD case.
• Figure 4: The average difference between $\langle \boldsymbol{s} \rangle$ and $\boldsymbol{s}_{\rm true}$ in each $\boldsymbol{g}$ zone with respect to the difference between $\langle \boldsymbol{g} \rangle$ and $\boldsymbol{g}_{\rm true}$ for the STD case. The values of $\mathbfit{s}$ are in Kelvin. A total of 70 zones are plotted. The dashed line shows the line of best-fit, constrained to pass through the origin.
• Figure 5: The 'improvement factor' of the posterior mean of the temperature field, $\langle \mathbfit{s} \rangle$, compared with the prior on $\mathbfit{s}$, calculated as the ratio of the prior standard deviation (10$\%$ of $\mathbfit{s}_{\rm true}$) divided by the standard deviation of $\Delta_\mathbfit{s}$. A discrete colour map has been used to make it easier to identify the approximate improvement factor across the map, with cyan denoting the smallest improvement factor (with a value of 1 implying no improvement over the prior). The colour scale has been clipped at a value of 10, but values around 50 are achieved close to the Galactic centre.
• Figure 6: The sky map with uncorrected flux scale factors (top left) and the posterior mean (top right), along with their difference with the true sky brightness temperature field (bottom panels) for the STD case with fixed $\beta$.