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Register a new userCharting the Parameter Space of the 21-cm Power Spectrum
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The high-redshift 21-cm signal of neutral hydrogen is expected to be observed within the next decade and will reveal epochs of cosmic evolution that have been previously inaccessible. Due to the lack of observations, many of the astrophysical processes that took place at early times are poorly constrained. In recent work we explored the astrophysical parameter space and the resulting large variety of possible global (sky-averaged) 21-cm signals. Here we extend our analysis to the fluctuations in the 21-cm signal, accounting for those introduced by density and velocity, Ly$alpha$ radiation, X-ray heating, and ionization. While the radiation sources are usually highlighted, we find that in many cases the density fluctuations play a significant role at intermediate redshifts. Using both the power spectrum and its slope, we show that properties of high-redshift sources can be extracted from the observable features of the fluctuation pattern. For instance, the peak amplitude of ionization fluctuations can be used to estimate whether heating occurred early or late and, in the early case, to also deduce the cosmic mean ionized fraction at that time. The slope of the power spectrum has a more universal redshift evolution than the power spectrum itself and can thus be used more easily as a tracer of high-redshift astrophysics. Its peaks can be used, for example, to estimate the redshift of the Ly$alpha$ coupling transition and the redshift of the heating transition (and the mean gas temperature at that time). We also show that a tight correlation is predicted between features of the power spectrum and of the global signal, potentially yielding important consistency checks.
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The early star-forming Universe is still poorly constrained, with the properties of high-redshift stars, the first heating sources, and reionization highly uncertain. This leaves observers planning 21-cm experiments with little theoretical guidance. In this work we explore the possible range of high-redshift parameters including the star formation efficiency and the minimal mass of star-forming halos; the efficiency, spectral energy distribution, and redshift evolution of the first X-ray sources; and the history of reionization. These parameters are only weakly constrained by available observations, mainly the optical depth to the cosmic microwave background. We use realistic semi-numerical simulations to produce the global 21-cm signal over the redshift range $z = 6-40$ for each of 193 different combinations of the astrophysical parameters spanning the allowed range. We show that the expected signal fills a large parameter space, but with a fixed general shape for the global 21-cm curve. Even with our wide selection of models we still find clear correlations between the key features of the global 21-cm signal and underlying astrophysical properties of the high redshift Universe, namely the Ly$alpha$ intensity, the X-ray heating rate, and the production rate of ionizing photons. These correlations can be used to directly link future measurements of the global 21-cm signal to astrophysical quantities in a mostly model-independent way. We identify additional correlations that can be used as consistency checks.
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 $k < 0.15 , {rm Mpc}^{-1}$.
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 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.
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 $R_{rm mfp}$.
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