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Register a new userThe FHD/$boldsymbol{varepsilon}$ppsilon Epoch of Reionization Power Spectrum Pipeline
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Epoch of Reionization data analysis requires unprecedented levels of accuracy in radio interferometer pipelines. We have developed an imaging power spectrum analysis to meet these requirements and generate robust 21 cm EoR measurements. In this work, we build a signal path framework to mathematically describe each step in the analysis, from data reduction in the FHD package to power spectrum generation in the $varepsilon$ppsilon package. In particular, we focus on the distinguishing characteristics of FHD/$varepsilon$ppsilon: highly accurate spectral calibration, extensive data verification products, and end-to-end error propagation. We present our key data analysis products in detail to facilitate understanding of the prominent systematics in image-based power spectrum analyses. As a verification to our analysis, we also highlight a full-pipeline analysis simulation to demonstrate signal preservation and lack of signal loss. This careful treatment ensures that the FHD/$varepsilon$ppsilon power spectrum pipeline can reduce radio interferometric data to produce credible 21 cm EoR measurements.
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We describe the validation of the HERA Phase I software pipeline by a series of modular tests, building up to an end-to-end simulation. The philosophy of this approach is to validate the software and algorithms used in the Phase I upper limit analysis on wholly synthetic data satisfying the assumptions of that analysis, not addressing whether the actual data meet these assumptions. We discuss the organization of this validation approach, the specific modular tests performed, and the construction of the end-to-end simulations. We explicitly discuss the limitations in scope of the current simulation effort. With mock visibility data generated from a known analytic power spectrum and a wide range of realistic instrumental effects and foregrounds, we demonstrate that the current pipeline produces power spectrum estimates that are consistent with known analytic inputs to within thermal noise levels (at the 2 sigma level) for k > 0.2 h/Mpc for both bands and fields considered. Our input spectrum is intentionally amplified to enable a strong `detection at k ~0.2 h/Mpc -- at the level of ~25 sigma -- with foregrounds dominating on larger scales, and thermal noise dominating at smaller scales. Our pipeline is able to detect this amplified input signal after suppressing foregrounds with a dynamic range (foreground to noise ratio) of > 10^7. Our validation test suite uncovered several sources of scale-independent signal loss throughout the pipeline, whose amplitude is well-characterized and accounted for in the final estimates. We conclude with a discussion of the steps required for the next round of data analysis.
We introduce a new method for performing robust Bayesian estimation of the three-dimensional spatial power spectrum at the Epoch of Reionization (EoR), from interferometric observations. The versatility of this technique allows us to present two approaches. First, when the observations span only a small number of independent spatial frequencies ($k$-modes) we sample directly from the spherical power spectrum coefficients that describe the EoR signal realisation. Second, when the number of $k$-modes to be included in the model becomes large, we sample from the joint probability density of the spherical power spectrum and the signal coefficients, using Hamiltonian Monte Carlo methods to explore this high dimensional ($sim$ 20000) space efficiently. This approach has been successfully applied to simulated observations that include astrophysically realistic foregrounds in a companion publication (Sims et al. 2016). Here we focus on explaining the methodology in detail, and use simple foreground models to both demonstrate its efficacy, and highlight salient features. In particular, we show that including an arbitrary flat spectrum continuum foreground that is $10^8$ times greater in power than the EoR signal has no detectable impact on our parameter estimates of the EoR power spectrum recovered from the data.
Measurements of 21 cm Epoch of Reionization (EoR) structure are subject to systematics originating from both the analysis and the observation conditions. Using 2013 data from the Murchison Widefield Array (MWA), we show the importance of mitigating both sources of contamination. A direct comparison between results from Beardsley et al. 2016 and our updated analysis demonstrates new precision techniques, lowering analysis systematics by a factor of 2.8 in power. We then further lower systematics by excising observations contaminated by ultra-faint RFI, reducing by an additional factor of 3.8 in power for the zenith pointing. With this enhanced analysis precision and newly developed RFI mitigation, we calculate a noise-dominated upper limit on the EoR structure of $Delta^2 leq 3.9 times 10^3$ mK$^2$ at $k=0.20$ $textit{h}$ Mpc$^{-1}$ and $z=7$ using 21 hr of data, improving previous MWA limits by almost an order of magnitude.
The power spectrum of redshifted 21 cm emission brightness temperature fluctuations is a powerful probe of the Epoch of Reionization (EoR). However, bright foreground emission presents a significant impediment to its unbiased recovery from interferometric data. We build on the Bayesian power spectral estimation methodology introduced in Sims et al. 2016 and demonstrate that incorporating a priori knowledge of the spectral structure of foregrounds in the large spectral scale component of the data model enables significantly improved modelling of the foregrounds without increasing the model complexity. We explore two astrophysically motivated parametrisations of the large spectral scale model: (i) a constant plus power law model of the form $q_{0}+q_{1}( u/ u_{0})^{b_{1}}$ for two values of $b_{1}$: $b_{1} = <beta>_mathrm{GDSE}$ and $b_{1} = <beta>_mathrm{EGS}$, the mean spectral indices of the Galactic diffuse synchrotron emission and extragalactic source foreground emission, respectively, and (ii) a constant plus double power law model of the form $q_{0}+q_{1}( u/ u_{0})^{b_{1}}+q_{2}( u/ u_{0})^{b_{2}}$ with $b_{1} = <beta>_mathrm{GDSE}$ and $b_{2} = <beta>_mathrm{EGS}$. We estimate the EoR power spectrum from simulated interferometric data consisting of an EoR signal, Galactic diffuse synchrotron emission, extragalactic sources and diffuse free-free emission from the Galaxy. We show that, by jointly estimating a model of the EoR signal with the constant plus double power law parametrisation of the large spectral scale model, unbiased estimates of the EoR power spectrum are recoverable on all spatial scales accessible in the data set, including on the large spatial scales that were found to be contaminated in earlier work.
21 cm Epoch of Reionization observations promise to transform our understanding of galaxy formation, but these observations are impossible without unprecedented levels of instrument calibration. We present end-to-end simulations of a full EoR power spectrum analysis including all of the major components of a real data processing pipeline: models of astrophysical foregrounds and EoR signal, frequency-dependent instrument effects, sky-based antenna calibration, and the full PS analysis. This study reveals that traditional sky-based per-frequency antenna calibration can only be implemented in EoR measurement analyses if the calibration model is unrealistically accurate. For reasonable levels of catalog completeness, the calibration introduces contamination in otherwise foreground-free power spectrum modes, precluding a PS measurement. We explore the origin of this contamination and potential mitigation techniques. We show that there is a strong joint constraint on the precision of the calibration catalog and the inherent spectral smoothness of antennae, and that this has significant implications for the instrumental design of the SKA and other future EoR observatories.
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