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Register a new userThe wedge bias in reionization 21-cm power spectrum measurements
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A proposed method for dealing with foreground emission in upcoming 21-cm observations from the epoch of reionization is to limit observations to an uncontaminated window in Fourier space. Foreground emission can be avoided in this way, since it is limited to a wedge-shaped region in $k_{parallel}, k_{perp}$ space. However, the power spectrum is anisotropic owing to redshift-space distortions from peculiar velocities. Consequently, the 21-cm power spectrum measured in the foreground avoidance window---which samples only a limited range of angles close to the line-of-sight direction---differs from the full spherically-averaged power spectrum which requires an average over emph{all} angles. In this paper, we calculate the magnitude of this wedge bias for the first time. We find that the bias is strongest at high redshifts, where measurements using foreground avoidance will over-estimate the power spectrum by around 100 per cent, possibly obscuring the distinctive rise and fall signature that is anticipated for the spherically-averaged 21-cm power spectrum. In the later stages of reionization, the bias becomes negative, and smaller in magnitude ($lesssim 20$ per cent). The effect shows only a weak dependence on spatial scale and reionization topology.
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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.
A number of experiments are currently working towards a measurement of the 21 cm signal from the Epoch of Reionization. Whether or not these experiments deliver a detection of cosmological emission, their limited sensitivity will prevent them from providing detailed information about the astrophysics of reionization. In this work, we consider what types of measurements will be enabled by a next-generation of larger 21 cm EoR telescopes. To calculate the type of constraints that will be possible with such arrays, we use simple models for the instrument, foreground emission, and the reionization history. We focus primarily on an instrument modeled after the $sim 0.1~rm{km}^2$ collecting area Hydrogen Epoch of Reionization Array (HERA) concept design, and parameterize the uncertainties with regard to foreground emission by considering different limits to the recently described wedge footprint in k-space. Uncertainties in the reionization history are accounted for using a series of simulations which vary the ionizing efficiency and minimum virial temperature of the galaxies responsible for reionization, as well as the mean free path of ionizing photons through the IGM. Given various combinations of models, we consider the significance of the possible power spectrum detections, the ability to trace the power spectrum evolution versus redshift, the detectability of salient power spectrum features, and the achievable level of quantitative constraints on astrophysical parameters. Ultimately, we find that $0.1~rm{km}^2$ of collecting area is enough to ensure a very high significance ($gtrsim30sigma$) detection of the reionization power spectrum in even the most pessimistic scenarios. This sensitivity should allow for meaningful constraints on the reionization history and astrophysical parameters, especially if foreground subtraction techniques can be improved and successfully implemented.
The post-reionization ${rm HI}$ 21-cm signal is an excellent candidate for precision cosmology, this however requires accurate modelling of the expected signal. Sarkar et al. (2016) have simulated the real space ${rm HI}$ 21-cm signal, and have modelled the ${rm HI}$ power spectrum as $P_{{rm HI}}(k)=b^2 P(k)$ where $P(k)$ is the dark matter power spectrum and $b(k)$ is a (possibly complex) scale dependent bias for which fitting formulas have been provided. This paper extends these simulations to incorporate redshift space distortion and predict the expected redshift space ${rm HI}$ 21-cm power spectrum $P^s_{{rm HI}}(k_{perp},k_{parallel})$ using two different prescriptions for the ${rm HI}$ distributions and peculiar velocities. We model $P^s_{{rm HI}}(k_{perp},k_{parallel})$ assuming that it is the product of $P_{{rm HI}}(k)=b^2 P(k)$ with a Kaiser enhancement term and a Finger of God (FoG) damping which has $sigma_p$ the pair velocity dispersion as a free parameter. Considering several possibilities for the bias and the damping profile, we find that the models with a scale dependent bias and a Lorentzian damping profile best fit the simulated $P^s_{{rm HI}}(k_{perp},k_{parallel})$ over the entire range $1 le z le 6$. The best fit value of $sigma_p$ falls approximately as $(1+z)^{-m}$ with $m=2$ and $1.2$ respectively for the two different prescriptions. The model predictions are consistent with the simulations for $k < 0.3 , {rm Mpc}^{-1}$ over the entire $z$ range for the monopole $P^s_0(k)$, and at $z le 3$ for the quadrupole $P^s_2(k)$. At $z ge 4$ the models underpredict $P^s_2(k)$ at large $k$, and the fit is restricted to $k < 0.15 , {rm Mpc}^{-1}$.
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.
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