Recovering the Coupled Treatment of Redshift-Space Distortions and the Lightcone Effect after Diffuse Foreground Removal

TL;DR

This work tackles the problem of accurately modeling the 21 cm signal from the EoR by fully coupling lightcone evolution with redshift-space distortions, rather than treating them in sequence. The authors implement a fully coupled framework that computes voxel brightness temperature using ingredient boxes and radiative transfer (via the $T_{21}$ framework), allowing multiple coeval contributions and velocity-dependent frequency shifts along the line of sight. They demonstrate that coupling these effects changes the power spectrum across all scales, with substantial partial coeval contributions and frequency mixing, and show these differences remain recoverable after diffuse foreground removal and SKAO-like noise, especially in the Cosmic Dawn regime. The results underscore the increased physical realism of semi-numeric models and have practical implications for interpreting upcoming 21 cm observations, foreground mitigation, and data-analysis strategies, particularly regarding the cylindrical power spectrum where differences are most evident.

Abstract

The 21 cm brightness temperature during the Epoch of Reionisation is widely modelled using semi-numeric simulations, used for their computational speed and flexibility in testing astrophysical and cosmological parameters. However, it is common practice to simulate coeval brightness temperature boxes, and then apply post-processing algorithms that treat the lightcone effect and redshift-space distortions separately, assuming they can be added in sequence. We instead model them together, allowing for partial coeval cell contributions, and ensuring that velocity-induced frequency shifts are computed at the correct cosmic time for every position along the line of sight. We show that considering these effects simultaneously creates a difference in the shape of the power spectrum over all Fourier scales, and remains recoverable after semi-blind foreground removal. We show that our lightcones consist of an average of 8% and maximum of 120% of a coeval cell length. These contributions to a 21cm brightness temperature lightcone voxel are shifted from within a +/- 0.5 MHz range of the emitted frequency. The boost in the power spectrum seen over small scales (k>1.5 Mpc) of our robust 21 cm lightcone method compared to basic methods is recoverable after the addition and removal of diffuse radio foregrounds. The largest differences during the Epoch of Reionisation lie in the k-space, where the noise sensitivity for a 1000-hour SKAO-low observation is greater than the signal. However, in the cosmic dawn, we have shown that the major differences lie outside of this noise-dominated region.

Figures (14)

• Figure 1: Top: Slices of the simulated 21cm brightness lightcone at 155 MHz. Left: Our extended approach to generating a lightcone and right: the basic lightcone approach. Bottom: a slice of the extended lightcone generated between 140-180MHz. All images have been normalised to be on the same scale and saturated at the maximum value for the basic lightcone at 155MHz to better visualise the differences between the two methods. It is clear that the extended method results in brighter temperatures on small spatial scales.
• Figure 2: The voxel distribution of $21$ cm brightness temperatures ($\delta T_{\rm b}$) for our extended lightcone method (blue) and a basic lightcone method (yellow). Both distributions have been created from a 10 MHz lightcone between ( left) 80-90 MHz ($x_{\rm HII} =0.000-0.001$) and ( right) 150-160 MHz ($x_{\rm HII} =0.3-0.4$), using a bin spacing of 10 mK. In both frequency ranges, the distribution has an elongated tail of bright voxels when using our extended method.
• Figure 3: A histogram showing the number of steps which result in a contribution of 21 cm intensity, normalised by the number of steps the algorithm takes across a cell. The basic method would show all voxels to be comprised of $1.0 N_{\rm cell}$. Values above 1 indicate that there has been intensity added in addition to what the basic method would find. Values below 1 indicate the method finds only a partial contribution across the cell. This figure shows the distribution for a 10MHz lightcone between $150$ and $160$ MHz made using our extended method. With the extended method, we see an average of 8% and a maximum of 120 % of a cell per voxel.
• Figure 4: All panels show the frequency that the observed $21$ cm photon, $\nu_{\rm observed}$, appears in the lightcone versus the frequency slice of the coeval box the photon was emitted from, $\nu_{\rm emitted}$. The different panels show different frequency resolutions of lightcones (clockwise from top left) $\Delta \nu = 1, 0.5, 0.1, 0.01$. In all plots, the graphs are colour coded by the number of contributions, and normalised by the number of voxels per slice. Each plot shows a zoomed-in region of the graph. We see a smoothing out of the distribution when approaching finer frequency spacing.
• Figure 5: Both panels show coeval box redshift from which a $21$ cm contribution arises plotted against the frequency of the lightcone slice that the contribution is observed at. We have coloured coded this plot by the number of contributions per frequency, normalised by the number of voxels per slice. The basic method is shown in the top panel, and our extended method is shown in the bottom panel. We see an overlap of where more than one coeval box contributes to a lightcone slice at frequencies within $\pm 0.25$ MHz of where the basic method changes redshift box. The same colourscale is used for both panels to allow an easy comparison to be made.