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Register a new userCHIPS: The Cosmological HI Power Spectrum Estimator
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Detection of the cosmological neutral hydrogen signal from the Epoch of Reionization, and estimation of its basic physical parameters, is the principal scientific aim of many current low-frequency radio telescopes. Here we describe the Cosmological HI Power Spectrum Estimator (CHIPS), an algorithm developed and implemented with data from the Murchison Widefield Array (MWA), to compute the two-dimensional and spherically-averaged power spectrum of brightness temperature fluctuations. The principal motivations for CHIPS are the application of realistic instrumental and foreground models to form the optimal estimator, thereby maximising the likelihood of unbiased signal estimation, and allowing a full covariant understanding of the outputs. CHIPS employs an inverse-covariance weighting of the data through the maximum likelihood estimator, thereby allowing use of the full parameter space for signal estimation (foreground suppression). We describe the motivation for the algorithm, implementation, application to real and simulated data, and early outputs. Upon application to a set of 3 hours of data, we set a 2$sigma$ upper limit on the EoR dimensionless power at $k=0.05$~h.Mpc$^{-1}$ of $Delta_k^2<7.6times{10^4}$~mK$^2$ in the redshift range $z=[6.2-6.6]$, consistent with previous estimates.
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HI intensity mapping is a new observational technique to survey the large-scale structure of matter using the 21 cm emission line of atomic hydrogen (HI). In this work, we simulate BINGO (BAO from Integrated Neutral Gas Observations) and SKA (Square Kilometre Array) phase-1 dish array operating in auto-correlation mode. For the optimal case of BINGO with no foregrounds, the combination of the HI angular power spectra with Planck results allows $w$ to be measured with a precision of $4%$, while the combination of the BAO acoustic scale with Planck gives a precision of $7%$. We consider a number of potentially complicating effects, including foregrounds and redshift dependent bias, which increase the uncertainty on $w$ but not dramatically; in all cases the final uncertainty is found to be $Delta w < 8%$ for BINGO. For the combination of SKA-MID in auto-correlation mode with Planck, we find that, in ideal conditions, $w$ can be measured with a precision of $4%$ for the redshift range $0.35 < z < 3$ (i.e., for the bandwidth of $Delta u = [350, 1050]$ MHz) and $2%$ for $0 < z < 0.49$ (i.e., $Delta u = [950, 1421]$ MHz). Extending the model to include the sum of neutrino masses yields a $95%$ upper limit of $sum m_ u < 0.24$ eV for BINGO and $sum m_ u < 0.08$ eV for SKA phase 1, competitive with the current best constraints in the case of BINGO and significantly better than them in the case of SKA.
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.
A tomographic method is described to quantify the three-dimensional power-spectrum of the ionospheric electron-density fluctuations based on radio-interferometric observations by a two-dimensional planar array. The method is valid to first-order Born approximation and might be applicable to correct observed visibilities for phase variations due to the imprint of the full three-dimensional ionosphere. It is shown that not the ionospheric electron density distribution is the primary structure to model in interferometry, but its autocorrelation function or equivalent its power-spectrum. An exact mathematical expression is derived that provides the three dimensional power-spectrum of the ionospheric electron-density fluctuations directly from a rescaled scattered intensity field and an incident intensity field convolved with a complex unit phasor that depends on the w-term and is defined on the full sky pupil plane. In the limit of a small field of view, the method reduces to the single phase screen approximation. Tomographic self-calibration can become important in high-dynamic range observations at low radio frequencies with wide-field antenna interferometers, because a three-dimensional ionosphere causes a spatially varying convolution of the sky, whereas a single phase screen results in a spatially invariant convolution. A thick ionosphere can therefore not be approximated by a single phase screen without introducing errors in the calibration process. By applying a Radon projection and the Fourier projection-slice theorem, it is shown that the phase-screen approach in three dimensions is identical to the tomographic method. Finally we suggest that residual speckle can cause a diffuse intensity halo around sources, due to uncorrectable ionospheric phase fluctuations in the short integrations, which could pose a fundamental limit on the dynamic range in long-integration images.
We present the 21 cm power spectrum analysis approach of the Murchison Widefield Array Epoch of Reionization project. In this paper, we compare the outputs of multiple pipelines for the purpose of validating statistical limits cosmological hydrogen at redshifts between 6 and 12. Multiple, independent, data calibration and reduction pipelines are used to make power spectrum limits on a fiducial night of data. Comparing the outputs of imaging and power spectrum stages highlights differences in calibration, foreground subtraction and power spectrum calculation. The power spectra found using these different methods span a space defined by the various tradeoffs between speed, accuracy, and systematic control. Lessons learned from comparing the pipelines range from the algorithmic to the prosaically mundane; all demonstrate the many pitfalls of neglecting reproducibility. We briefly discuss the way these different methods attempt to handle the question of evaluating a significant detection in the presence of foregrounds.
Intensity mapping (IM) with neutral hydrogen is a promising avenue to probe the large scale structure of the Universe. In this paper, we demonstrate that using the 64-dish MeerKAT radio telescope as a connected interferometer, it is possible to make a statistical detection of HI in the post-reionization Universe. With the MIGHTEE (MeerKAT International GHz Tiered Extragalactic Exploration) survey project observing in the L-band ($856 < u < 1712$ MHz, $z < 0.66$), we can achieve the required sensitivity to measure the HI IM power spectrum on quasi-linear scales, which will provide an important complementarity to the single-dish IM MeerKAT observations. We present a purpose-built simulation pipeline that emulates the MIGHTEE observations and forecast the constraints that can be achieved on the HI power spectrum at $z = 0.27$ for $k > 0.3$ $rm{Mpc}^{-1}$ using the foreground avoidance method. We present the power spectrum estimates with the current simulation on the COSMOS field that includes contributions from HI, noise and point source models constructed from the observed MIGHTEE data. The results from our textit{visibility} based pipeline are in qualitative agreement to the already available MIGHTEE data. This paper demonstrates that MeerKAT can achieve very high sensitivity to detect HI with the full MIGHTEE survey on quasi-linear scales (signal-to-noise ratio $> 7$ at $k=0.49$ $rm{Mpc}^{-1}$) which are instrumental in probing cosmological quantities such as the spectral index of fluctuation, constraints on warm dark matter, the quasi-linear redshift space distortions and the measurement of the HI content of the Universe up to $zsim 0.5$.
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