Hierarchical Bayesian CMB Component Separation with the No-U-Turn Sampler

Key to any cosmic microwave background (CMB) analysis is the separation of the CMB from foreground contaminants. In this paper we present a novel implementation of Bayesian CMB component separation. We sample from the full posterior distribution using the No-U-Turn Sampler (NUTS), a gradient based sampling algorithm. Alongside this, we introduce new foreground modelling approaches. We use the mean-shift algorithm to define regions on the sky, clustering according to naively estimated foreground spectral parameters. Over these regions we adopt a complete pooling model, where we assume constant spectral parameters, and a hierarchical model, where we model individual spectral parameters as being drawn from underlying hyper-distributions. We validate the algorithm against simulations of the LiteBIRD and C-BASS experiments, with an input tensor-to-scalar ratio of $r=5\times 10^{-3}$. Considering multipoles $32\leq\ell\leq 121$, we are able to recover estimates for $r$. With LiteBIRD only observations, and using the complete pooling model, we recover $r=(10\pm 0.6)\times 10^{-3}$. For C-BASS and LiteBIRD observations we find $r=(7.0\pm 0.6)\times 10^{-3}$ using the complete pooling model, and $r=(5.0\pm 0.4)\times 10^{-3}$ using the hierarchical model. By adopting the hierarchical model we are able to eliminate biases in our cosmological parameter estimation, and obtain lower uncertainties due to the smaller Galactic emission mask that can be adopted for power spectrum estimation. Measured by the rate of effective sample generation, NUTS offers performance improvements of $\sim10^3$ over using Metropolis-Hastings to fit the complete pooling model. The efficiency of NUTS allows us to fit the more sophisticated hierarchical foreground model, that would likely be intractable with non-gradient based sampling algorithms.Comment: 19 pages, 9 figure

C-Band All-Sky Survey (C-BASS): Simulated parametric fitting in single pixels in total intensity and polarization

The cosmic microwave background (CMB) B-mode signal is potentially weaker than the diffuse Galactic foregrounds over most of the sky at any frequency. A common method of separating the CMB from these foregrounds is via pixel-based parametric-model fitting. There are not currently enough all-sky maps to fit anything more than the most simple models of the sky. By simulating the emission in seven representative pixels, we demonstrate that the inclusion of a 5 GHz data point allows for more complex models of low-frequency foregrounds to be fitted than at present. It is shown that the inclusion of the C-BASS data will significantly reduce the uncertainties in a number of key parameters in the modelling of both the galactic foregrounds and the CMB. The extra data allow estimates of the synchrotron spectral index to be constrained much more strongly than is presently possible, with corresponding improvements in the accuracy of the recovery of the CMB amplitude. However, we show that to place good limits on models of the synchrotron spectral curvature will require additional low-frequency data

The C-Band All-Sky Survey (C-BASS): Simulated parametric fitting in single pixels in total intensity and polarization

The cosmic microwave background (CMB) B-mode signal is potentially weaker than the diffuse Galactic foregrounds over most of the sky at any frequency. A common method of separating the CMB from these foregrounds is via pixel-based parametric-model fitting. There are not currently enough all-sky maps to fit anything more than the most simple models of the sky. By simulating the emission in seven representative pixels, we demonstrate that the inclusion of a 5 GHz data point allows for more complex models of low-frequency foregrounds to be fitted than at present. It is shown that the inclusion of the C-BASS data will significantly reduce the uncertainties in a number of key parameters in the modelling of both the galactic foregrounds and the CMB. The extra data allow estimates of the synchrotron spectral index to be constrained much more strongly than is presently possible, with corresponding improvements in the accuracy of the recovery of the CMB amplitude. However, we show that to place good limits on models of the synchrotron spectral curvature will require additional low-frequency data

The C-Band All-Sky Survey: total intensity point-source detection over the northern sky

We present a point-source detection algorithm that employs the second-order Spherical Mexican Hat wavelet filter (SMHW2), and use it on C-Band All-Sky Survey (C-BASS) northern intensity data to produce a catalogue of point sources. This catalogue allows us to cross-check the C-BASS flux-density scale against existing source surveys, and provides the basis for a source mask that will be used in subsequent C-BASS and cosmic microwave background (CMB) analyses. The SMHW2 allows us to filter the entire sky at once, avoiding complications from edge effects arising when filtering small sky patches. The algorithm is validated against a set of Monte Carlo simulations, consisting of diffuse emission, instrumental noise, and various point-source populations. The simulated source populations are successfully recovered. The SMHW2 detection algorithm is used to produce a 4.76GHz northern sky source catalogue in total intensity, containing 1784 sources and covering declinations δ ≥ −10°. The C-BASS catalogue is matched with the Green Bank 6 cm (GB6) and Parkes-MIT-NRAO (PMN) catalogues over their areas of common sky coverage. From this we estimate the 90 per cent completeness level to be approximately 610mJy⁠, with a corresponding reliability of 98 per cent, when masking the brightest 30 per cent of the diffuse emission in the C-BASS northern sky map. We find the C-BASS and GB6 flux-density scales to be consistent with one another to within approximately 4 per cent

The C-Band All-Sky Survey (C-BASS):Design and capabilities

The C-Band All-Sky Survey (C-BASS) is an all-sky full-polarisation survey at a frequency of 5 GHz, designed to provide complementary data to the all-sky surveys of WMAP and Planck, and future CMB B-mode polarization imaging surveys. The observing frequency has been chosen to provide a signal that is dominated by Galactic synchrotron emission, but suffers little from Faraday rotation, so that the measured polarization directions provide a good template for higher frequency observations, and carry direct information about the Galactic magnetic field. Telescopes in both northern and southern hemispheres with matched optical performance are used to provide all-sky coverage from a ground-based experiment. A continuous-comparison radiometer and a correlation polarimeter on each telescope provide stable imaging properties such that all angular scales from the instrument resolution of 45 arcmin up to full sky are accurately measured. The northern instrument has completed its survey and the southern instrument has started observing. We expect that C-BASS data will significantly improve the component separation analysis of Planck and other CMB data, and will provide important constraints on the properties of anomalous Galactic dust and the Galactic magnetic field.Comment: 21 pages, 9 figure

Measurements of diffuse galactic emission at 5 GHz with C-BASS

The C-Band All-Sky Survey (C-BASS) is a project to produce an all-sky map in intensity and polarization at a central frequency of 5 GHz with 1 GHz bandwidth and approximately 1 degree resolution. The central frequency is low enough for the map to be dominated by synchrotron and free-free emission but high enough so that Faraday rotation and depolarization are small across most of the sky. The C-BASS map will enable a more accurate removal of contaminating foregrounds from measurements of the cosmic microwave background, particularly in polarization where the B-mode signal from inflation is likely to be orders of magnitude weaker than the diffuse Galactic foreground emission. To produce an all-sky map from the ground requires two telescopes, one in the northern and one in the southern hemisphere. This thesis focuses on analysis of C-BASS North data. The noise properties of time-ordered data are characterised by fitting a noise model to periodograms. Using simulations, the errors introduced into the C-BASS maps by a destriping mapmaker are quantified and we reduce the signal error by masking the brightest pixels during baseline offset estimation. Jackknife tests are used to test the C-BASS data for systematics and to test the accuracy of the sensitivity maps. In total intensity, the spectral index of diffuse Galactic emission between 5 GHz and 408 MHz is measured using an extended T-T plot method and the results are compared to simulations. The spectral index of polarized diffuse Galactic emission between 5 GHz and 30 GHz is estimated in 55 arcminute pixels, modelling the polarized intensity as a Rician random variable.</p

Measurements of diffuse galactic emission at 5 GHz with C-BASS

The C-Band All-Sky Survey (C-BASS) is a project to produce an all-sky map in intensity and polarization at a central frequency of 5 GHz with 1 GHz bandwidth and approximately 1 degree resolution. The central frequency is low enough for the map to be dominated by synchrotron and free-free emission but high enough so that Faraday rotation and depolarization are small across most of the sky. The C-BASS map will enable a more accurate removal of contaminating foregrounds from measurements of the cosmic microwave background, particularly in polarization where the B-mode signal from inflation is likely to be orders of magnitude weaker than the diffuse Galactic foreground emission. To produce an all-sky map from the ground requires two telescopes, one in the northern and one in the southern hemisphere. This thesis focuses on analysis of C-BASS North data. The noise properties of time-ordered data are characterised by fitting a noise model to periodograms. Using simulations, the errors introduced into the C-BASS maps by a destriping mapmaker are quantified and we reduce the signal error by masking the brightest pixels during baseline offset estimation. Jackknife tests are used to test the C-BASS data for systematics and to test the accuracy of the sensitivity maps. In total intensity, the spectral index of diffuse Galactic emission between 5 GHz and 408 MHz is measured using an extended T-T plot method and the results are compared to simulations. The spectral index of polarized diffuse Galactic emission between 5 GHz and 30 GHz is estimated in 55 arcminute pixels, modelling the polarized intensity as a Rician random variable.</p