Narrowing the discovery space of the cosmological 21-cm signal using multi-wavelength constraints

TL;DR

This work integrates multi-wavelength constraints to narrow the cosmological 21-cm discovery space, tying UV-luminosity-backed star formation to X-ray and radio heating while using SARAS 3 and HERA limits to bound the global signal and fluctuations. Using 21cmSPACE with $30{,}000$ simulations and a Bayesian, emulator-based framework, the authors infer IGM temperatures $T_K(z)$ and radio background $T_{rad}(z)$, establishing the first robust lower bound on the 21-cm absorption trough: ${-201~\mathrm{mK}\lesssim T_{21,\min}\lesssim -68~\mathrm{mK}}$ at $z_{\min}\approx 10-16$, and a non-zero power spectrum at $z=15$ with ${8.7~\mathrm{mK}^2 < \Delta_{21}^2(z=15) < 197~\mathrm{mK}^2}$ at $k=0.35\,h\mathrm{Mpc}^{-1}$. Key parameters include a constrained X-ray heating efficiency $f_X$ around $0.8$ (with wide uncertainties) and an upper limit on radio efficiency $f_r$, all anchored by UVLFs from HST/JWST and CXB/CRB data. The results depend on fixed high-$z$ Pop II/III modeling assumptions, particularly the X-ray SFR scaling and lack of flexible Pop III treatments; nevertheless, the study demonstrates the power of joint analyses in constraining the early IGM and guiding upcoming 21-cm experiments toward a realistically constrained observational window.

Abstract

The cosmic 21-cm signal is a promising probe of the early Universe, owing to its sensitivity to the thermal state of the neutral intergalactic medium (IGM) and properties of the first luminous sources. Here, we constrain the 21-cm signal and infer IGM properties using the Population II galaxy parameters derived in a previous study through multi-wavelength synergies. This includes high-redshift UV luminosity functions (UVLFs) from Hubble Space Telescope (HST) and James Webb Space Telescope (JWST), cosmic X-ray and radio backgrounds (CXB and CRB), the SARAS 3 global 21-cm signal non-detection, and HERA 21-cm power spectrum upper limits. From CXB and HERA data, we infer the IGM kinetic temperature to be $T_\text{K}(z=15)\lesssim 7.7~\text{K}$, $2.5~\text{K} \lesssim T_\text{K}(z=10) \lesssim 66~\text{K}$, and $20~\text{K}\lesssim T_\text{K}(z=6) \lesssim 2078~\text{K}$ at 95% credible interval (C.I.). Similarly, CRB and HERA data limit the radio emission efficiency of galaxies, giving $T_\text{rad}(z=15) \lesssim 47~\text{K}$, $T_\text{rad}(z=10)\lesssim 51~\text{K}$, and $T_\text{rad}(z=6)\lesssim 101~\text{K}$. These constraints, strengthened by UVLFs from HST and JWST, enable the first $\textit{lower bound}$ on the cosmic 21-cm signal. We infer an absorption trough of depth ${-201~\text{mK}\lesssim T_\text{21,min} \lesssim -68~\text{mK}}$ at $z_\text{min}\approx10-16$, and a power spectrum of $8.7~\text{mK}^2 < Δ_{21}^2(z=15) < 197~\text{mK}^2$ at $k=0.35~h\text{Mpc}^{-1}$. Our results highlight the power of multi-wavelength synergies in constraining the early Universe. While promising for upcoming 21-cm experiments, the results depend on our assumption of a redshift-independent X-ray and radio efficiency of galaxies, and the exclusion of a flexible model for Population III stars.

Figures (9)

• Figure 1: 1D marginal posterior probability distributions (PDFs) of the seven astrophysical parameters (mariginalizing over $\tau_\text{CMB}$ since it remains prior-dominated) from the individual and joint analysis. The constraints shown here are the same as in 2025MNRAS.542.2292D, except for the case of CXB+UVLF and CRB+UVLF which are new to this work. In case of $\alpha_\star$ and $\beta_\star$, all datasets containing UVLF lie on top of each other. The vertical black dashed line and grey shaded region show the weighted posterior mean and the 68% credible interval (CI), respectively, for the joint analysis. For the special cases of the joint analysis, see Figure \ref{['fig:param_constraints_joint']}.
• Figure 2: Constraints on the X-ray luminosity per unit SFR, $L_X/\text{SFR}$, from Chandra observations of star-forming galaxies in the local Universe 2012MNRAS.419.2095M2016MNRAS.457.4081B and at low-redshifts 2016ApJ...825....7L2019ApJ...885...65F, and 21-cm experiment inferred limits at high-redshifts 2023ApJ...945..124H2025ApJ...989...57N. We put constraints at $\log_{10}(L_X/\text{SFR}/erg~s^{-1}~M_\odot^{-1}~yr) = 40.4^{+1.1}_{-0.3}$ (68% CI) in this work from CXB contributions at $z\gtrsim6$ and 21-cm power spectrum limits from HERA at $z\lesssim10.35$ (hence the grey shaded region). The arrows towards high-$z$ reflect our assumption of a fixed $L_X/\text{SFR}$ relation during the early epochs. Since different works assume different SEDs (e.g. the energy range considered) which can change our constraints from CXB, a direct comparison is non-trivial but we convert the luminosity in the full X-ray band, $\SIrange{0.2}{95}{keV}$, to $\SIrange{2}{10}{keV}$ and $<2keV$ for a relative comparison of the luminosity in the different energy bands.
• Figure 3: Evolution of various quantities related to the IGM and star-formation in the redshift range $z\approx6-30$. The panels from top-left to bottom-right show the kinetic temperature of neutral IGM ($T_\text{K}$), the radio background temperature at the rest-frame 21-cm wavelength ($T_\text{rad}$), the spin temperature ($T_\text{S}$), the ratio of spin to radio background temperature ($T_\text{S}/T_\text{rad}$), the Pop II star-formation rate density (SFRD, $\dot{\rho}_{\star,\mathrm{II}}$), and the neutral IGM fraction ($x_\text{HI}$) at the bottom. The grey regions show the priors in this functional space, while the solid lines are $N\sim500$ samples from the joint posterior distribution. In the top panels, we also show the latest constraints on neutral IGM $T_\text{K}$ from PAPER, 2015ApJ...809...62P2016MNRAS.455.4295G, HERA+23 2023ApJ...945..124H, LOFAR 2025AA...699A.109G, MWA 2025ApJ...989...57N. In case of the HERA+23 constraints, we plot the results from their 21cmMC model 2011MNRAS.411..955M for $T_\text{K}$ and excess radio model (generated using 21cmSPACE) for $T_\text{S}/T_\text{rad}$. We also plot the same constraints for $T_\text{S}$, assuming $T_\text{S}=T_\text{K}$ for MWA (although not stated explicitly in their work, it is reasonable to assume saturated WF coupling at $z\lesssim 7$). In the panel for the SFRD $\dot{\rho}_{\star,\mathrm{II}}$, we show various inferences from literature using HST/JWST UVLFs 2015ApJ...803...34B2023ApJS..265....5H2024MNRAS.533.3222D2024ApJ...969L...2F2025ApJ...992...63W2025ApJ...991..179P, and gamma-ray bursts 2013arXiv1305.1630K. Finally, in the bottom panel for neutral fraction $x_\text{HI}$, we show constraints from dark gaps in Ly$\alpha/\beta$ forest 2015MNRAS.447..499M2023ApJ...942...59J, from Ly$\alpha$ damping wings 2017MNRAS.466.4239G2019MNRAS.484.5094G2018ApJ...864..142D2018Natur.553..473B2020ApJ...896...23W2020ApJ...897L..14Y2024ApJ...969..162D2024ApJ...971..124U, fraction of Lyman-break galaxies showing Ly$\alpha$ emission 2018ApJ...856....2M2019MNRAS.485.3947M2019ApJ...878...12H2022MNRAS.517.3263B, from Ly$\alpha$ luminosity functions 2021ApJ...919..120M2022ApJ...926..230N, and from Ly$\alpha$ equivalent width distributions 2024ApJ...967...28N. In this work, we do not constrain $x_\text{HI}$ anymore than the flat $3\sigma$ prior on $\tau_\text{CMB}$ from $\textit{Planck 2018}$, hence the overlap of grey shaded region and blue lines, but we show a variety of constraints from literature for completeness and to highlight the uncertainty in EoR evolution.
• Figure 4: PDFs of the IGM kinetic temperature $T_\text{K}$ (top row) and spin temperature $T_\text{S}$ (bottom row) at $z=6,8,10$ and $z=15$ in the joint analysis. Note that the histograms are not from one simulation, but denote many realizations of the Universe with different astrophysical parameters sampled from the posterior. The blue region denotes the adiabatic cooling limit, while the grey and black histograms are the prior and joint posteriors from our models and analysis respectively. The constraints on $T_\text{K}$ are driven by a combination of UVLF + CXB data disfavouring high $f_\text{X}$ values (shown in solid yellow histogram), and HERA disfavouring low $f_\text{X}$ values (shown in hatched orange histograms). It can be seen that we only get marginal heating at $z\gtrsim 15$, while it is guaranteed at $z\lesssim 8$.
• Figure 5: Constraints on the 21-cm global signal $T_{21}$ and power spectrum $\Delta_{21}^2$ from the individual datasets (top row) and the joint analysis (bottom row). The grey regions show the prior space, while the solid lines are $N\sim500$ samples from the respective posterior distributions. In the joint constraint panels, we highlight qualitatively regions of the prior space (as the filled coloured regions) that are disfavoured by the different datasets. The global signal panel also show histograms of the redshift/timing (along $x$-axis) and depth (along $y$-axis) of the absorption trough minima, while the power spectrum panel shows the 21-cm power spectrum limits from HERA 2023ApJ...945..124H. Most notably, via the constraints on heating efficiency $f_\text{X}$ and IGM temperature $T_\text{K}$ from the UVLF + CXB data, we find a non-vanishing global signal and power spectrum at $z\sim 10-15$ (see Section \ref{['sec:21cm_signal_constraints']} for quantified constraints). For the special cases of joint analysis where we exclude certain datasets, see Figure \ref{['fig:21cm_constraints_joint']}.