Distinguishing models of reionization using future radio observations of 21-cm 1-point statistics

We explore the impact of reionization topology on 21-cm statistics. Four reionization models are presented which emulate large ionized bubbles around over-dense regions (21CMFAST/ global-inside- out), small ionized bubbles in over-dense regions (local-inside-out), large ionized bubbles around under-dense regions (global-outside-in) and small ionized bubbles around under-dense regions (local-outside-in). We show that first-generation instruments might struggle to distinguish global models using the shape of the power spectrum alone. All instruments considered are capable of breaking this degeneracy with the variance, which is higher in outside-in models. Global models can also be distinguished at small scales from a boost in the power spectrum from a positive correlation between the density and neutral-fraction fields in outside-in models. Negative skewness is found to be unique to inside-out models and we find that pre-SKA instruments could detect this feature in maps smoothed to reduce noise errors. The early, mid and late phases of reionization imprint signatures in the brightness-temperature moments, we examine their model dependence and find pre-SKA instruments capable of exploiting these timing constraints in smoothed maps. The dimensional skewness is introduced and is shown to have stronger signatures of the early and mid-phase timing if the inside-out scenario is correct.Comment: 18 pages, 13 figures, updated to agree with published versio

The impact of spin temperature fluctuations on the 21-cm moments

This paper considers the impact of Lyman-alpha coupling and X-ray heating on the 21-cm brightness-temperature one-point statistics (as predicted by semi-numerical simulations). The X-ray production efficiency is varied over four orders of magnitude and the hardness of the X-ray spectrum is varied from that predicted for high-mass X-ray binaries, to the softer spectrum expected from the hot inter-stellar medium. We find peaks in the redshift evolution of both the variance and skewness associated with the efficiency of X-ray production. The amplitude of the variance is also sensitive to the hardness of the X-ray SED. We find that the relative timing of the coupling and heating phases can be inferred from the redshift extent of a plateau that connects a peak in the variance's evolution associated with Lyman-alpha coupling to the heating peak. Importantly, we find that late X-ray heating would seriously hamper our ability to constrain reionization with the variance. Late X-ray heating also qualitatively alters the evolution of the skewness, providing a clean way to constrain such models. If foregrounds can be removed, we find that LOFAR, MWA and PAPER could constrain reionization and late X-ray heating models with the variance. We find that HERA and SKA (phase 1) will be able to constrain both reionization and heating by measuring the variance using foreground-avoidance techniques. If foregrounds can be removed they will also be able to constrain the nature of Lyman-alpha coupling.Comment: 16 pages, 13 figure, 1 table. Accepted for publication in MNRA

Epoch of reionization parameter estimation with the 21-cm bispectrum

We present the first application of the isosceles bispectrum to MCMC parameter inference from the cosmic 21-cm signal. We extend the MCMC sampler 21cmMC to use the fast bispectrum code, BiFFT, when computing the likelihood. We create mock 1000h observations with SKA1-low, using PyObs21 to account for uv-sampling and thermal noise. Assuming the spin temperature is much higher than that of the CMB, we consider two different reionization histories for our mock observations: fiducial and late-reionization. For both models we find that bias on the inferred parameter means and 1-$\sigma$ credible intervals can be substantially reduced by using the isosceles bispectrum (calculated for a wide range of scales and triangle shapes) together with the power spectrum (as opposed to just using one of the statistics). We find that making the simplifying assumption of a Gaussian likelihood with a diagonal covariance matrix does not notably bias parameter constraints for the three-parameter reionization model and basic instrumental effects considered here. This is true even if we use extreme (unlikely) initial conditions which would be expected to amplify biases. We also find that using the cosmic variance error calculated with Monte-Carlo simulations using the fiducial model parameters whilst assuming the late-reionization model for the simulated data also does not strongly bias the inference. This implies we may be able to sparsely sample and interpolate the cosmic variance error over the parameter space, substantially reducing computational costs. All codes used in this work are publicly-available.Comment: 12 pages, 11 figures (submitted to MNRAS

Quantifying the non-Gaussianity in the EoR 21-cm signal through bispectrum

The epoch of reionization (EoR) 21-cm signal is expected to be highly non-Gaussian in nature and this non-Gaussianity is also expected to evolve with the progressing state of reionization. Therefore the signal will be correlated between different Fourier modes ($k$). The power spectrum will not be able capture this correlation in the signal. We use a higher-order estimator -- the bispectrum -- to quantify this evolving non-Gaussianity. We study the bispectrum using an ensemble of simulated 21-cm signal and with a large variety of $k$ triangles. We observe two competing sources driving the non-Gaussianity in the signal: fluctuations in the neutral fraction ($x_{\rm HI}$) field and fluctuations in the matter density field. We find that the non-Gaussian contribution from these two sources vary, depending on the stage of reionization and on which $k$ modes are being studied. We show that the sign of the bispectrum works as a unique marker to identify which among these two components is driving the non-Gaussianity. We propose that the sign change in the bispectrum, when plotted as a function of triangle configuration $\cos{\theta}$ and at a certain stage of the EoR can be used as a confirmative test for the detection of the 21-cm signal. We also propose a new consolidated way to visualize the signal evolution (with evolving $\overline{x}_{\rm HI}$ or redshift), through the trajectories of the signal in a power spectrum and equilateral bispectrum i.e. $P(k)-B(k, k, k)$ space.Comment: 18 pages, 11 figures. Accepted for publication in MNRAS. Replaced to match the accepted versio

Gaussian process regression for foreground removal in hi intensity mapping experiments

We apply for the first time Gaussian Process Regression (GPR) as a foreground removal technique in the context of single-dish, low redshift H I intensity mapping, and present an open-source PYTHON toolkit for doing so. We use MeerKAT and SKA1-MID-like simulations of 21 cm foregrounds (including polarization leakage), H I cosmological signal, and instrumental noise. We find that it is possible to use GPR as a foreground removal technique in this context, and that it is better suited in some cases to recover the H I power spectrum than principal component analysis (PCA), especially on small scales

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The 21-cm bispectrum as a probe of non-Gaussianities due to X-ray heating

We present analysis of the normalized 21-cm bispectrum from fully-numerical simulations of intergalactic-medium heating by stellar sources and high-mass X-ray binaries (HMXBs) during the cosmic dawn. Ly-α coupling is assumed to be saturated, we therefore probe the nature of non-Gaussianities produced by X-ray heating processes. We find the evolution of the normalized bispectrum to be very different from that of the power spectrum. It exhibits a turnover whose peak moves from large to small scales with decreasing redshift, and corresponds to the typical separation of emission regions. This characteristic scale reduces as more and more regions move into emission with time. Ultimately, small-scale fluctuations within heated regions come to dominate the normalized bispectrum, which at the end of the simulation is almost entirely driven by fluctuations in the density field. To establish how generic the qualitative evolution of the normalized bispectrum we see in the stellar + HMXB simulation is, we examine several other simulations – two fully numerical simulations that include quasi-stellar object (QSO) sources, and two with contrasting source properties produced with the semi-numerical simulation 21CMFAST. We find the qualitative evolution of the normalized bispectrum during X-ray heating to be generic, unless the sources of X-rays are, as with QSOs, less numerous and so exhibit more distinct isolated heated profiles. Assuming mitigation of foreground and instrumental effects are ultimately effective, we find that we should be sensitive to the normalized bispectrum during the epoch of heating, so long as the spin temperature has not saturated by z≈19

Gridded and direct Epoch of Reionisation bispectrum estimates using the Murchison Widefield Array

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.Comment: 19 pages, 10 figures, accepted for publication in PAS