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Register a new userExploring the evolution of Reionisation using a wavelet transform and the light cone effect
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Cathryn M. Trott
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The Cosmic Dawn and Epoch of Reionisation, during which collapsed structures produce the first ionising photons and proceed to reionise the intergalactic medium, span a large range in redshift (z~30-6) and time (t_{age} ~ 0.1-1.0~Gyr). Exploration of these epochs using the redshifted 21~cm emission line from neutral hydrogen is currently limited to statistical detection and estimation metrics (e.g., the power spectrum) due to the weakness of the signal. Brightness temperature fluctuations in the line-of-sight (LOS) dimension are probed by observing the emission line at different frequencies, and their structure is used as a primary discriminant between the cosmological signal and contaminating foreground extragalactic and Galactic continuum emission. Evolution of the signal over the observing bandwidth leads to the `line cone effect whereby the HI structures at the start and end of the observing band are not statistically consistent, yielding a biased estimate of the signal power, and potential reduction in signal detectability. We implement a wavelet transform to wide bandwidth radio interferometry experiments to probe the local statistical properties of the signal. We show that use of the wavelet transform yields estimates with improved estimation performance, compared with the standard Fourier Transform over a fixed bandwidth. With the suite of current and future large bandwidth reionisation experiments, such as with the 300~MHz instantaneous bandwidth of the Square Kilometre Array, a transform that retains local information will be important.
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We apply two methods to estimate the 21~cm bispectrum from data taken within the Epoch of Reionisation (EoR) project of the Murchison Widefield Array (MWA). Using data acquired with the Phase II compact array allows a direct bispectrum estimate to be undertaken on the multiple redundantly-spaced triangles of antenna tiles, as well as an estimate based on data gridded to the $uv$-plane. The direct and gridded bispectrum estimators are applied to 21 hours of high-band (167--197~MHz; $z$=6.2--7.5) data from the 2016 and 2017 observing seasons. Analytic predictions for the bispectrum bias and variance for point source foregrounds are derived. We compare the output of these approaches, the foreground contribution to the signal, and future prospects for measuring the bispectra with redundant and non-redundant arrays. We find that some triangle configurations yield bispectrum estimates that are consistent with the expected noise level after 10 hours, while equilateral configurations are strongly foreground-dominated. Careful choice of triangle configurations may be made to reduce foreground bias that hinders power spectrum estimators, and the 21~cm bispectrum may be accessible in less time than the 21~cm power spectrum for some wave modes, with detections in hundreds of hours.
Measurements of the HI 21-cm power spectra from the reionization epoch will be influenced by the evolution of the signal along the line-of-sight direction of any observed volume. We use numerical as well as semi-numerical simulations of reionization in a cubic volume of 607 Mpc across to study this so-called light cone effect on the HI 21-cm power spectrum. We find that the light cone effect has the largest impact at two different stages of reionization: one when reionization is $sim 20%$ and other when it is $sim 80%$ completed. We find a factor of $sim 4$ amplification of the power spectrum at the largest scale available in our simulations. We do not find any significant anisotropy in the 21-cm power spectrum due to the light cone effect. We argue that for the power spectrum to become anisotropic, the light cone effect would have to make the ionized bubbles significantly elongated or compressed along the line-of-sight, which would require extreme reionization scenarios. We also calculate the two-point correlation functions parallel and perpendicular to the line-of-sight and find them to differ. Finally, we calculate an optimum frequency bandwidth below which the light cone effect can be neglected when extracting power spectra from observations. We find that if one is willing to accept a $10 %$ error due to the light cone effect, the optimum frequency bandwidth for $k= 0.056 , rm{Mpc}^{-1}$ is $sim 7.5$ MHz. For $k = 0.15$ and $0.41 , rm{Mpc}^{-1}$ the optimum bandwidth is $sim 11$ and $sim 16$ MHz respectively.
Parameter estimation with non-Gaussian stochastic fields is a common challenge in astrophysics and cosmology. In this paper, we advocate performing this task using the scattering transform, a statistical tool sharing ideas with convolutional neural networks (CNNs) but requiring no training nor tuning. It generates a compact set of coefficients, which can be used as robust summary statistics for non-Gaussian information. It is especially suited for fields presenting localized structures and hierarchical clustering, such as the cosmological density field. To demonstrate its power, we apply this estimator to a cosmological parameter inference problem in the context of weak lensing. On simulated convergence maps with realistic noise, the scattering transform outperforms classic estimators and is on a par with state-of-the-art CNN. It retains the advantages of traditional statistical descriptors, has provable stability properties, allows to check for systematics, and importantly, the scattering coefficients are interpretable. It is a powerful and attractive estimator for observational cosmology and the study of physical fields in general.
Observations of redshifted 21-cm radiation from neutral hydrogen during the epoch of reionization (EoR) are considered to constitute the most promising tool to probe that epoch. One of the major goals of the first generation of low frequency radio telescopes is to measure the 3D 21-cm power spectrum. However, the 21-cm signal could evolve substantially along the line of sight (LOS) direction of an observed 3D volume, since the received signal from different planes transverse to the LOS originated from different look-back times and could therefore be statistically different. Using numerical simulations we investigate this so-called light cone effect on the spherically averaged 3D 21-cm power spectrum. For this version of the power spectrum, we find that the effect mostly `averages out and observe a smaller change in the power spectrum compared to the amount of evolution in the mean 21-cm signal and its rms variations along the LOS direction. Nevertheless, changes up to 50% at large scales are possible. In general the power is enhanced/suppressed at large/small scales when the effect is included. The cross-over mode below/above which the power is enhanced/suppressed moves toward larger scales as reionization proceeds. When considering the 3D power spectrum we find it to be anisotropic at the late stages of reionization and on large scales. The effect is dominated by the evolution of the ionized fraction of hydrogen during reionization and including peculiar velocities hardly changes these conclusions. We present simple analytical models which explain qualitatively all the features we see in the simulations.
We present a new statistical tool, called the triangle correlation function (TCF), inspired by the earlier work of Obreschkow et al. It is derived from the three-point correlation function and aims to probe the characteristic scale of ionized regions during the epoch of reionization from 21cm interferometric observations. Unlike most works, which focus on power spectrum, i.e. amplitude information, our statistic is based on the information we can extract from the phases of the Fourier transform of the ionization field. In this perspective, it may benefit from the well-known interferometric concept of closure phases. We find that this statistical estimator performs very well on simple ionization fields. For example, with well-defined fully ionized discs, there is a peaking scale, which we can relate to the radius of the ionized bubbles. We explore the robustness of the TCF when observational effects such as angular resolution and noise are considered. We also get interesting results on fields generated by more elaborate simulations such as 21CMFAST. Although the variety of sources and ionized morphologies in the early stages of the process make its interpretation more challenging, the nature of the signal can tell us about the stage of reionization. Finally, and in contrast to other bubble size distribution algorithms, we show that the TCF can resolve two different characteristic scales in a given map.
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