Topological Signatures of Heating and Dark Matter in the 21 cm Forest

TL;DR

This paper demonstrates that topological data analysis of the 21 cm forest provides unique, robust insights into Cosmic Dawn, complementing traditional methods by capturing non-Gaussian features related to heating and dark matter effects.

Contribution

It introduces persistence-based topological descriptors for 21 cm forest spectra, revealing new sensitivities to heating efficiency and dark matter properties during Cosmic Dawn.

Findings

Persistence-based descriptors effectively track absorption trough hierarchy.

Descriptors show strong sensitivity to heating efficiency and dark matter mass.

Topology remains robust against thermal noise after applying persistence cuts.

Abstract

We show that persistence-based topology of the 21 cm forest encodes information about Cosmic Dawn that is complementary to traditional amplitude- or correlation-based statistics. Applying topological data analysis to simulated one-dimensional forest spectra over a grid of X-ray heating efficiencies $f_X$ and warm-dark-matter masses $m_{\rm WDM}$ (which set the free-streaming scale), we construct persistence diagrams and Betti-0 curves that track the birth-merger hierarchy of absorption troughs under sublevel filtrations. From these summaries we define three interpretable descriptors: the trough line density $\lambda(t_\star)$, the total squared persistence $M_2=\sum_{j\in I_{\rm long}}\tau_j^2$, and the Betti-curve asymmetry $A_{\rm skew}$. In a Fisher forecast around a fiducial WDM model, $\lambda(t_\star)$ and $A_{\rm skew}$ provide strong local leverage on the heating axis, while $M_2$ retains appreciable sensitivity to the free-streaming scale and supplies an inclined constraint direction that reduces the remaining degeneracy in the $(f_X,m_{\rm WDM})$ plane. We further demonstrate that, under an SKA1-Low-like uncorrelated thermal-noise model, noise predominantly produces short-lived fluctuations that are removed by a uniform persistence cut, leaving the topology of long-lived troughs and the gross Betti-curve morphology largely intact. These results establish persistence-based descriptors as a robust non-Gaussian probe of small-scale structure and heating during Cosmic Dawn, naturally complementing power-spectrum and wavelet-based analyses.