Will Nonlinear Peculiar Velocity and Inhomogeneous Reionization Spoil 21 cm Cosmology from the Epoch of Reionization?

The 21 cm background from the epoch of reionization is a promising cosmological probe: line-of-sight velocity fluctuations distort redshift, so brightness fluctuations in Fourier space depend upon angle, which linear theory shows can separate cosmological from astrophysical information. Nonlinear fluctuations in ionization, density, and velocity change this, however. The validity and accuracy of the separation scheme are tested here for the first time, by detailed reionization simulations. The scheme works reasonably well early in reionization ($\lesssim 40\%$ ionized), but not late ($\gtrsim 80\%$ ionized).

Figure 1

Top left panel: the matter density power spectrum, ${\Delta }_{\delta \delta }^2=k^3{P}_{\delta \delta }(k)/2{\pi }^2$ (unitless), from $N$-body results for total matter (solid or black) and for IGM matter (green or dot), linear total density (dashed or blue), and 3PT total density (dot-dashed or magenta), at $z=6.757$. Other panels: the total matter density power spectrum [multiplied by ${\widehat{\delta T}}_b^2(z)$] as “measured” by fitting the mock data (i.e., reionization simulation) for the 3D 21 cm power spectrum to the ${\mu }_{\mathbf{k}}$ decomposition, ${\Delta }_{{\mu }^4}^2=k^3{P}_{{\mu }^4}(k)/2{\pi }^2$ (in ${\mathrm{mK}}^2$), at different phases of reionization (${\overline{x}}_{i,m}=0$, 0.01, 0.10, 0.50, 0.68, 0.78, and 0.92, respectively). Red data points are reionization simulation results. Black data points assume homogeneously ionized IGM with same ${\overline{x}}_{i,m}$ as reionization simulation. Solid black curves are the expectation from linear scheme, $P_{{\mu }^4}^{\mathrm{linear}}$, i.e., Eq. (2) evaluated using total density power spectra from $N$-body simulation [multiplied by ${\widehat{\delta T}}_b^2(z)$]. Plotted in inset are fractional systematic errors, i.e., $(P_{{\mu }^4}^{\mathrm{best}-\mathrm{fit}}-P_{{\mu }^4}^{\mathrm{linear}})/P_{{\mu }^4}^{\mathrm{linear}}$. We also plot the sampling errors (due to the simulation volume) for the best-fit 4th moment, $\sigma (P_{{\mu }^4})$, as error bars, and the fractional sampling errors, $\sigma (P_{{\mu }^4})/P_{{\mu }^4}^{\mathrm{linear}}$, as shaded regions in inset.

Figure 2

The fractional systematic error of the separation scheme, in the inhomogeneous reionization case, as a function of ${\overline{x}}_{i,m}$, for $k=0.24$, 0.35, 0.52, 0.77, $0.94h{\mathrm{Mpc}}^{-1}$, respectively. The solid (open) dots correspond to the case where the systematic error is greater (less) than the sampling error of our simulation. The inset is a zoom-in to $0\le {\overline{x}}_{i,m}\le 0.10$.