Simulation based inference of the ionization history from the 2D 21 cm power spectrum

Abstract

The 21 cm signal contains a wealth of information about the formation of the first stars and the reionization of the intergalactic medium during the Cosmic Dawn (CD) and Epoch of Reionization (EoR). The timing of these important milestones has only roughly been constrained through indirect measurements, such as from the cosmic microwave background (CMB) optical depth, and Lyman-$α$ forest. Therefore, inferring the neutral fraction over cosmic time is a goal of upcoming 21 cm experiments, such as the Square Kilometer Array (SKA). We contrast two approaches to infer astrophysical parameters and ionization history from 21 cm 2D power spectra (2DPS). We develop an emulator of the 21 cm 2DPS, trained on 21cmFAST simulations, taking into account the expected instrumental noise from the SKA and sample variance. We then perform simulation based inference (SBI) using neural posterior estimation (NPE). We compare training on datasets of noisy 2DPS obtained from 21cmFAST simulations and an emulator, to infer astrophysical parameters of interest. Using an emulator of the ionization history, which has been trained on simulations from the same astrophysical parameters, we then obtain posterior distributions of the ionization history over the redshift range z $\sim$ 5-12. We demonstrate that both methods are capable of accurately recovering the ionization history and astrophysical parameters. However, coverage tests indicate that adding emulated samples does not improve predictions. This work suggests that due to the stochastic nature of the 2DPS, using an emulator of this summary statistic may result in poorer inference.

Figures (17)

• Figure 1: Visualization of the sample variance. Standard deviation of each bin for a 100 simulations of differing initial conditions at z = 7.8 for a fixed parameter sample of: [$\zeta$: 17.99, $\mathrm{log}_{\mathrm{10}}T_{\mathrm{vir}}$(K): 4.82, $R_{\mathrm{mfp}}$(Mpc): 25.96]. This plot is represented in log space.
• Figure 2: Training loss (black solid line) and validation loss (red solid line) over the training epochs for the emulator of the 2DPS. The learning rate changes are also shown as the dashed blue line. The plot has been clipped to 250 epochs, as training reached convergence.
• Figure 3: Example prediction from the 2D power spectrum emulator at the fiducial point [$\zeta$: 17.99, $\mathrm{log}_{\mathrm{10}}T_{\mathrm{vir}}$(K): 4.82, $R_{\mathrm{mfp}}$(Mpc): 25.96]. The top row shows the emulator predicted 2DPS, the middle row shows the truth 2DPS, and the bottom row shows the error relative to the spread of the noise. The error is calculated as shown in Equation \ref{['noise_weighted_error']}. The emulator was trained on data with the three bottom left hand corner pixels removed, which are represented above with the white masking. For conciseness, only 3 out of the 8 redshifts are shown. The power spectra are given in the signal-to-noise ratio with k$_\perp$ bins on the bottom x axis and k$_\parallel$ bins on the y axis.
• Figure 4: Plot of the three measures of mean error. The top row shows the accuracy, the middle row shows the noise weighted error, and the bottom row shows the sample variance and noise weighted error. For conciseness and consistency, only three out of the eight redshifts are shown, matching those in Fig. \ref{['fig:square_emu_pred_truth']}. Each of the errors are calculated as shown in Section \ref{['sec:eval_metrics']} and are each represented as log$_{10}$ of the fractional error.
• Figure 5: Plot of the standard deviation of the three error metrics. The top, middle, and bottom row show the standard deviation of the accuracy, noise, and noise and SV error, respectively. Each error is calculated as shown in Section \ref{['sec:eval_metrics']} and are each represented as log$_{10}$ of the fractional error. All of these errors are dimensionless quantities.