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The radiations from the first luminous sources drive the fluctuations in the HI 21-cm signal at Cosmic Dawn (CD) via two dominant astrophysical processes i.e. the Ly$\alpha$ coupling and X-ray heating, making this signal highly non-Gaussian. The impact of these processes on the 21-cm signal and its non-Gaussianity vary depending on the properties of these first sources of light. Considering different CD scenarios by varying two major CD source parameters i.e. the minimum halo mass $M_{h,min}$ and X-ray photon production efficiency $f_X$ in a 1D radiative transfer code GRIZZLY, we study their impact on the large scale 21-cm bispectrum for all possible unique $k$ triangles in the Fourier domain. Our detailed and comparative analysis of the power spectrum and bispectrum shows that the shape, sign and magnitude of the bispectrum combinedly provide the best measure of the signal fluctuations and its non-Gaussianity compared to the power spectrum. We also conclude that it is important to study the sequence of sign changes along with the variations in the shape and magnitude of the bispectrum throughout the CD history to arrive at a robust conclusion about the dominant IGM processes at different cosmic times. We further observe that among all the possible unique k-triangles, the large-scale non-Gaussianity in signal is best probed by the small k-triangles in the squeezed limit and by triangles of similar shapes. This opens up the possibility of constraining the source parameters during the CD using the 21-cm bispectrum.
We next extend our analysis to the Epoch of Reionization (EoR), where the fluctuations in the HI 21-cm signal are mostly driven by the ionization of the HI in the IGM by these first sources of light. We study the 21-cm bispectrum for different reionization scenarios assuming different simulated models for the sources of reionization. We demonstrate how well the 21-cm bispectrum can distinguish between different EoR 21-cm signal topologies (defined by the size and distribution of ionized regions), which will help us shed light on the nature of the sources of ionizing photons. Our estimated large-scale bispectrum for all unique $k$-triangle shapes show a significant difference in their magnitude and sign, as one goes from one reionization scenario to the other. Additionally, our focused analysis of bispectrum for a few specific $k-\text{triangle}$ shapes (e.g. squeezed limit, linear and shapes in the vicinity of the squeezed limit) show that the large scale 21-cm bispectrum can distinguish between reionization scenarios that show inside-out, outside-in and a combination of inside-out and outside-in topologies. These results highlight the potential of using the 21-cm bispectrum for constraining different reionization scenarios. Finally, we establish the richer information content of the EoR 21-cm bispectrum compared to the power spectrum through a Fisher information matrix analysis.