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

TL;DR

The paper addresses the challenge of disentangling X-ray heating and dark-matter free-streaming effects in the 21 cm forest by applying topological data analysis to one-dimensional spectra. Using persistence diagrams and Betti-0 curves, the authors derive three interpretable descriptors—trough line density $\lambda(t_\star)$, lifetime second moment $M_2$, and lifetime skewness $A_{\rm skew}$—which respond in orthogonal directions to the heating efficiency $f_X$ and dark-matter mass $m_{\rm DM}$, thereby reducing degeneracies. Their results show distinct topological signatures for heating versus WDM and demonstrate robustness to SKA-like thermal noise, suggesting topology as a stable, non-Gaussian probe of small-scale physics during Cosmic Dawn. The framework is generalizable to other one-dimensional absorption fields and complements traditional amplitude- and correlation-based statistics, offering a geometry-aware avenue for early-universe inference.

Abstract

We show that the topology of the 21 cm forest carries cosmological information that is inaccessible to traditional amplitude- or correlation-based statistics. Applying topological data analysis to simulated spectra spanning a range of X-ray heating efficiencies and dark-matter free-streaming scales, we compute persistence diagrams and Betti-0 curves that describe the formation and merger hierarchy of absorption troughs. A small set of interpretable descriptors (trough-line density, lifetime variance, and lifetime skewness) respond in nearly orthogonal directions across the (f_X, m_WDM) parameter space, enabling a substantial reduction of the degeneracy between heating and dark-matter suppression. These topological signatures remain detectable under SKA1-Low-like thermal noise, demonstrating that topology provides a stable and non-Gaussian probe of small-scale physics during Cosmic Dawn.

Figures (4)

• Figure 1: Distributions of persistence lifetimes(Death-Birth) Panels compare CDM with $f_X=0$ and $0.5$ and CDM ($f_X=0$) versus WDM ($m_{\rm WDM}=3$ keV, $f_X=0$).
• Figure 2: Top: Mean Betti--0 curves $\langle\beta_0(t)\rangle$ at $\Delta\nu=1$ kHz without persistence filtering. CDM with low $f_X$ shows a broad, high peak; stronger heating and WDM reduce small-scale troughs and hasten mergers. Bottom: Same, with 68% LOS bands after applying a persistence cut $\tau\ge0.411$, which suppresses short-lived features and clarifies model differences.
• Figure 3: Topological sensitivity for CDM ($f_X=0$). A common cut $\tau\ge0.411$ is used throughout. Left: Resolution dependence (1, 5, 10 kHz): coarser channels merge narrow troughs, lowering and narrowing the $\beta_0(t)$ peak. Right: Thermal noise at 1 kHz for 0, 100, 1000 h: longer integration suppresses noise-induced components, shrinking LOS scatter and driving the curves toward the noiseless topology.
• Figure 4: Topological degeneracy maps: signed Z--difference of three descriptors relative to the baseline (CDM, $f_X{=}0$). Columns show the trough line density $\lambda(t_\star)$, lifetime second moment $M_2$, and skewness $A_{\rm skew}$; rows compare noiseless (top) and 1000 h thermal noise (bottom). Axes span X--ray heating $f_X$ (vertical) and dark--matter mass $m_{\rm DM}$ (horizontal; INF$\equiv$CDM, decreasing to 3 keV to the right). Large--scale color gradients persist under noise, especially for $\lambda$ and $A_{\rm skew}$.