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Register a new userPhoton number conservation and the large-scale 21 cm power spectrum in semi-numerical models of reionization
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Semi-numerical models of the reionization of neutral hydrogen (HI) based on the excursion set (ES) approach are known to violate photon number conservation at the few per cent level. In this work, we highlight a more severe, previously unrecognized shortcoming of ES models: the large-scale 21 cm power spectrum (equivalently, HI bias b_HI) is a relatively strong function of the spatial resolution used to generate ES ionization maps. We trace this problem to the fact that photon non-conservation in these models arises from a resolution-dependent mixture of spatially resolved, photon non-conserving bubbles, and partially ionized grid cells which are perfectly photon-conserving by construction. We argue that this inevitably leads to a resolution-dependence of b_HI, with the correct, converged value only emerging at very coarse resolution. Quantitatively, we find that b_HI can be non-converged by as much as ~20-25% in conservative ES implementations with grid sizes Delta x=5-10 cMpc/h, even when photon non-conservation is as small as ~3-4%. Thus, although numerically efficient, ES ionization maps coarse enough to produce a converged HI bias would wash out all topological features of the ionization field at scales k>~0.05 h/cMpc. We therefore present a new, explicitly photon conserving (PC) semi-numerical algorithm which distributes photons isotropically around sources while also accounting for anisotropic overlaps between nearby bubbles. Our PC algorithm predicts a resolution-independent value of b_HI consistent with the result of low-resolution ES maps, thus serving as a useful compromise between standard ES implementations and more expensive radiative transfer simulations.
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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.
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.
Hemispherical power asymmetry has emerged as a new challenge to cosmology in early universe. While the cosmic microwave background (CMB) measurements indicated the asymmetry amplitude $A simeq 0.07$ at the CMB scale $k_{rm CMB}simeq 0.0045,{rm Mpc}^{-1}$, the high-redshift quasar observations found no significant deviation from statistical isotropy. This conflict can be reconciled in some scale-dependent asymmetry models. We put forward a new parameterization of scale-dependent asymmetric power spectrum, inspired by a multi-speed inflation model. The 21-cm power spectrum from the epoch of reionization can be used to constrain the scale-dependent hemispherical asymmetry. We demonstrate that an optimum, multi-frequency observation by the Square Kilometre Array (SKA) Phase 2 can impose a constraint on the amplitude of the power asymmetry anomaly at the level of $Delta A simeq 0.2$ at $0.056 lesssim k_{rm 21cm} lesssim 0.15 ,{rm Mpc}^{-1}$. This limit may be further improved by an order of magnitude as $Delta A simeq 0.01$ with a cosmic variance limited experiment such as the Omniscope.
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.
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 $k < 0.15 , {rm Mpc}^{-1}$.
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