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Register a new userThe effect of non-Gaussianity on error predictions for the Epoch of Reionization (EoR) 21-cm power spectrum
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Rajesh Mondal
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The Epoch of Reionization (EoR) 21-cm signal is expected to become increasingly non-Gaussian as reionization proceeds. We have used semi-numerical simulations to study how this affects the error predictions for the EoR 21-cm power spectrum. We expect $SNR=sqrt{N_k}$ for a Gaussian random field where $N_k$ is the number of Fourier modes in each $k$ bin. We find that non-Gaussianity is important at high $SNR$ where it imposes an upper limit $[SNR]_l$. For a fixed volume $V$, it is not possible to achieve $SNR > [SNR]_l$ even if $N_k$ is increased. The value of $[SNR]_l$ falls as reionization proceeds, dropping from $sim 500$ at $bar{x}_{HI} = 0.8-0.9$ to $sim 10$ at $bar{x}_{HI} = 0.15 $ for a $[150.08, {rm Mpc}]^3$ simulation. We show that it is possible to interpret $[SNR]_l$ in terms of the trispectrum, and we expect $[SNR]_l propto sqrt{V}$ if the volume is increased. For $SNR ll [SNR]_l$ we find $SNR = sqrt{N_k}/A $ with $A sim 0.95 - 1.75$, roughly consistent with the Gaussian prediction. We present a fitting formula for the $SNR$ as a function of $N_k$, with two parameters $A$ and $[SNR]_l$ that have to be determined using simulations. Our results are relevant for predicting the sensitivity of different instruments to measure the EoR 21-cm power spectrum, which till date have been largely based on the Gaussian assumption.
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The EoR 21-cm signal is expected to become highly non-Gaussian as reionization progresses. This severely affects the error-covariance of the EoR 21-cm power spectrum which is important for predicting the prospects of a detection with ongoing and future experiments. Most earlier works have assumed that the EoR 21-cm signal is a Gaussian random field where (1) the error variance depends only on the power spectrum and the number of Fourier modes in the particular $k$ bin, and (2) the errors in the different $k$ bins are uncorrelated. Here we use an ensemble of simulated 21-cm maps to analyze the error-covariance at various stages of reionization. We find that even at the very early stages of reionization ($bar{x}_{rm HI} sim 0.9 $) the error variance significantly exceeds the Gaussian predictions at small length-scales ($k > 0.5 ,{rm Mpc}^{-1}$) while they are consistent at larger scales. The errors in most $k$ bins (both large and small scales), are however found to be correlated. Considering the later stages ($bar{x}_{rm HI} = 0.15$), the error variance shows an excess in all $k$ bins within $k ge 0.1 , {rm Mpc}^{-1}$, and it is around $200$ times larger than the Gaussian prediction at $k sim 1 , {rm Mpc}^{-1}$. The errors in the different $k$ bins are all also highly correlated, barring the two smallest $k$ bins which are anti-correlated with the other bins. Our results imply that the predictions for different 21-cm experiments based on the Gaussian assumption underestimate the errors, and it is necessary to incorporate the non-Gaussianity for more realistic predictions.
Measurements of the Epoch of Reionization (EoR) 21-cm signal hold the potential to constrain models of reionization. In this paper we consider a reionization model with three astrophysical parameters namely (1) the minimum halo mass which can host ionizing sources, $M_{rm min}$, (2) the number of ionizing photons escaping into the IGM per baryon within the halo, $N_{rm ion}$ and (3) the mean free path of the ionizing photons within the IGM, $R_{rm mfp}$. We predict the accuracy with which these parameters can be measured from future observations of the 21-cm power spectrum (PS) using the upcoming SKA-Low. Unlike several earlier works, we account for the non-Gaussianity of the inherent EoR 21-cm signal. Considering cosmic variance only and assuming that foregrounds are completely removed, we find that non-Gaussianity increases the volume of the $1 sigma$ error ellipsoid of the parameters by a factor of $133$ relative to the Gaussian predictions, the orientation is also different. The ratio of the volume of error ellipsoids is $1.65$ and $2.67$ for observation times of $1024$ and $10000$ hours respectively, when all the $mathbf{k}$ modes within the foreground wedge are excluded. With foreground wedge excluded and for $1024$ hours, the 1D marginalized errors are $(Delta M_{rm min}/M_{rm min},Delta N_{rm ion}/N_{rm ion},Delta R_{rm mfp}/R_{rm mfp})=(6.54, 2.71, 7.75) times 10^{-2}$ which are respectively $2 %$, $5 %$ and $23 %$ larger than the respective Gaussian predictions. The impact of non-Gaussianity increases for longer observations, and it is particularly important for $R_{rm mfp}$.
The non-Gaussian nature of the epoch of reionization (EoR) 21-cm signal has a significant impact on the error variance of its power spectrum $P({bf textit{k}})$. We have used a large ensemble of semi-numerical simulations and an analytical model to estimate the effect of this non-Gaussianity on the entire error-covariance matrix ${mathcal{C}}_{ij}$. Our analytical model shows that ${mathcal{C}}_{ij}$ has contributions from two sources. One is the usual variance for a Gaussian random field which scales inversely of the number of modes that goes into the estimation of $P({bf textit{k}})$. The other is the trispectrum of the signal. Using the simulated 21-cm signal ensemble, an ensemble of the randomized signal and ensembles of Gaussian random ensembles we have quantified the effect of the trispectrum on the error variance ${mathcal{C}}_{ij}$. We find that its relative contribution is comparable to or larger than that of the Gaussian term for the $k$ range $0.3 leq k leq 1.0 ,{rm Mpc}^{-1}$, and can be even $sim 200$ times larger at $k sim 5, {rm Mpc}^{-1}$. We also establish that the off-diagonal terms of ${mathcal{C}}_{ij}$ have statistically significant non-zero values which arise purely from the trispectrum. This further signifies that the error in different $k$ modes are not independent. We find a strong correlation between the errors at large $k$ values ($ge 0.5 ,{rm Mpc}^{-1}$), and a weak correlation between the smallest and largest $k$ values. There is also a small anti-correlation between the errors in the smallest and intermediate $k$ values. These results are relevant for the $k$ range that will be probed by the current and upcoming EoR 21-cm experiments.
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.
Measuring the small primordial nonGaussianity (PNG) predicted by cosmic inflation theories may help diagnose them. The detectability of PNG by its imprint on the 21cm power spectrum from the epoch of reionization is reassessed here in terms of $f_{NL}$, the local nonlinearity parameter. We find that an optimum, multi-frequency observation by SKA can achieve $Delta f_{NL} sim 3$ (comparable to recent Planck CMB limits), while a cosmic-variance-limited array of this size like Omniscope can even detect $Delta f_{NL} sim 0.2$. This substantially revises the methods and results of previous work.
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