Inferring population III star properties from the 21-cm global signal

Abstract: Investigating the properties of the first stars in the universe is essential, yet it remains an open question. One way to explore these stars is by examining their effects on the surrounding gas during the epoch of reionization. In this study, we investigate whether the 21-cm global signal can constrain the typical mass and star formation efficiency of first-generation stars. We perform semi-numerical simulations that include the escape fraction of ionizing photons, which depends on stellar and halo masses, as well as the heating structure surrounding a halo that hosts the first star, determined by radiation hydrodynamics (RHD) simulations. By applying Fisher analysis, while accounting for foreground emissions, we demonstrate that future observations with instruments such as the Radio Experiment for the Analysis of Cosmic Hydrogen (REACH) could provide meaningful constraints on these properties.

• The paper proposes a rigorous statistical framework to infer Pop III star formation efficiency and typical stellar mass using the global 21-cm signal.
• It employs detailed radiative feedback and Lyα/LW coupling models along with Fisher matrix analysis to predict observable signal variations.
• The results imply that next-generation 21-cm measurements, if foreground residuals are minimized, can constrain key Pop III parameters to within 20–25%.

Inferring Population III Star Properties from the 21-cm Global Signal

Introduction

The formation and properties of Population III (Pop III) stars fundamentally shaped the early universe. Due to their high masses, strong radiative feedback, and unique nucleosynthetic signatures, Pop III stars controlled early metal enrichment, influenced early galaxy formation, and reionized the neutral intergalactic medium (IGM). However, direct constraints on their properties, including the initial mass function (IMF) and star formation efficiency ($f_*$), remain elusive due to their occurrence at high redshift and the limited sensitivity of present-day instrumentation. This paper presents a rigorous statistical framework to constrain Pop III star properties by leveraging the global 21-cm signal, which encapsulates the collective imprint of early star formation on the thermal and ionization evolution of the IGM (2604.02814).

Methodology: Physical and Radiative Modeling

Pop III Feedback and Escape Fraction Formalism

The radiative feedback of Pop III stars is modeled through the escape fraction $\mathscr{f}_\mathrm{esc}$ of ionizing photons as a function of both host halo mass and stellar mass. Unlike previous work assuming constant $\mathscr{f}_\mathrm{esc}$, this study adopts an empirically-calibrated relation derived from one-dimensional radiation-hydrodynamics simulations. The analysis demonstrates a strong dependence: larger $M_\mathrm{h}$ leads to lower $\mathscr{f}_\mathrm{esc}$ due to increased absorption, while larger $M_\mathrm{s}$ yields higher $\mathscr{f}_\mathrm{esc}$ by facilitating more rapid ionized bubble expansion.

Figure 1: The escape fraction–halo mass relation exhibits a suppression at high $M_\mathrm{h}$ and enhancement with increasing $M_\mathrm{s}$, reflecting radiative feedback effects.

To obtain the net radiative input to the IGM, the halo-mass-averaged escape fraction is computed by integrating over the Sheth-Mo-Tormen mass function. Its decline with increasing cooling threshold $M_\mathrm{cool}$ and decreasing redshift is shown to impact the timing and amplitude of 21-cm features.

Figure 2: The halo-mass-averaged escape fraction $\mathscr{f}_\mathrm{esc}$0 declines at lower redshift and higher $\mathscr{f}_\mathrm{esc}$1, reflecting suppression of photoionization from low-mass halos.

Incorporation of Lyα and LW Feedback

The heating structure around individual halos is modeled, with the sub-grid method validated by RHD results regarding the warm neutral shell mass fraction. Importantly, Lyman–Werner (LW) radiative feedback is included by self-consistently evolving the background intensity and recalculating the minimum cooling halo mass $\mathscr{f}_\mathrm{esc}$2 in each timestep using the framework established by Visbal et al. This approach captures the non-linear suppression—and delayed resumption—of star formation in minihalos induced by the rising LW flux.

Simulated 21-cm Signal and Parameter Dependencies

The authors simulate the global 21-cm brightness temperature as a function of redshift for a multi-dimensional parameter grid in $\mathscr{f}_\mathrm{esc}$3 and $\mathscr{f}_\mathrm{esc}$4. They find the depth and shape of the absorption feature are highly sensitive to these astrophysical parameters: higher $\mathscr{f}_\mathrm{esc}$5 produces deeper absorption (through more vigorous early Lyα pumping and heating), while higher $\mathscr{f}_\mathrm{esc}$6 leads to shallower absorption via stronger LW feedback (which suppresses star formation in low-mass halos and thus Lyα production) and enhanced ionization heating.

Figure 3: The global 21-cm brightness temperature as a function of redshift, with solid, dashed, and dotted lines for varying $\mathscr{f}_\mathrm{esc}$7, and color encoding for $\mathscr{f}_\mathrm{esc}$8; deeper absorption for higher $\mathscr{f}_\mathrm{esc}$9 and shallower for higher $\mathscr{f}_\mathrm{esc}$0 is evident.

The underlying star formation rate density (SFRD), which tracks the overall collapse fraction and feedback-regulated burstiness of Pop III star formation, maps onto observable features in the signal.

Figure 4: SFRD evolution for the same parameter grid, demonstrating suppression at high $\mathscr{f}_\mathrm{esc}$1 due to feedback and amplification with high $\mathscr{f}_\mathrm{esc}$2.

These trends are driven by the interactions among escape fraction, LW feedback, SFRD, and cumulative ionized fraction and heating.

Figure 5: The mass-averaged escape fraction as a function of redshift, reflecting parameter-induced variations in radiative feedback.

Figure 6: Computed background LW intensity, indicating increased feedback at higher $\mathscr{f}_\mathrm{esc}$3.

Figure 7: Evolution of the minimum halo mass for star formation, $\mathscr{f}_\mathrm{esc}$4, as determined by feedback processes.

Figure 8: The ionized fraction as a function of redshift for several model choices, quantifying the progress of reionization and associated heating.

Fisher Matrix Analysis and Forecasting Constraints

To quantify the information content of the global 21-cm signal, a Fisher matrix analysis is performed. The likelihood incorporates both astrophysical dependencies in the mean signal and parameter-dependent covariance due to the scaling of thermal and systematic noise with total sky brightness. The foreground modeling uses the $\mathscr{f}_\mathrm{esc}$5 template relevant for low-frequency radio observations. The signal is modeled across $\mathscr{f}_\mathrm{esc}$6–30, above the expected onset of significant Pop II galaxy formation.

The derivatives of the 21-cm spectrum with respect to $\mathscr{f}_\mathrm{esc}$7 and $\mathscr{f}_\mathrm{esc}$8 are shown to be highly anti-correlated during absorption-dominated phases (deep trough becomes both deeper and shallower as $\mathscr{f}_\mathrm{esc}$9 and $M_\mathrm{h}$0, respectively, increase), but this degeneracy weakens at high $M_\mathrm{h}$1 where UV/ionization heating causes the derivative sign to flip for $M_\mathrm{h}$2, breaking the parameter degeneracy.

Figure 9: Forecasted joint $M_\mathrm{h}$3 and $M_\mathrm{h}$4 constraints for Pop III parameters in several experimental configurations; the constraints are foreground-limited as opposed to thermal-noise-limited.

Figure 10: Normalized derivatives of the global signal with respect to $M_\mathrm{h}$5 and $M_\mathrm{h}$6 across redshift, showing sign change for $M_\mathrm{h}$7 at high $M_\mathrm{h}$8 and nearly constant sign for $M_\mathrm{h}$9.

The main results include:

• For $\mathscr{f}_\mathrm{esc}$0, $\mathscr{f}_\mathrm{esc}$1, with $\mathscr{f}_\mathrm{esc}$2 hr and residual foreground $\mathscr{f}_\mathrm{esc}$3, $\mathscr{f}_\mathrm{esc}$4 and $\mathscr{f}_\mathrm{esc}$5 can be simultaneously constrained to $\mathscr{f}_\mathrm{esc}$6 and $\mathscr{f}_\mathrm{esc}$7 ($\mathscr{f}_\mathrm{esc}$8).
• All near-term constraint regimes are foreground-residual-limited; modest integration times suffice once $\mathscr{f}_\mathrm{esc}$9 is subdominant.
• The $M_\mathrm{s}$0 degeneracy is sensitive to the location of the absorption trough, and can be efficiently broken if both pre- and post-heating epochs are probed.

Noise forecasts utilizing the REACH instrument configuration indicate that instrumental sensitivities are sufficient to achieve these statistical constraints.

Figure 11: Estimated noise contours for the 21-cm global measurement as a function of redshift and integration time, compared against the model signal variation.

Implications, Limitations, and Prospects

This work demonstrates that the next generation of sky-averaged 21-cm observations (typified by REACH) can move Pop III astrophysics into a precision-constrained regime, provided foreground mitigation reaches levels of $M_\mathrm{s}$1 of total sky signal. The methodology incorporates improvements over previous efforts by explicitly modeling the stellar mass dependence of the escape fraction and including physical heating structure, expanding on earlier studies [2022MNRAS.516..841G, 2025NatAs...9.1268G, 2018MNRAS.478.5591M].

However, the analysis imposes a single-mass Pop III IMF and assumes a spatially-homogeneous LW background. Incorporating a realistic IMF (and constraining its parameters) as well as stochastic fluctuations in the background intensity is essential for robust parameter inference. Analysis of the 21-cm power spectrum—especially with interferometric data (e.g., SKA-Low)—will provide complementary constraints by distinguishing spatial scales affected by $M_\mathrm{s}$2 versus $M_\mathrm{s}$3.

Practical limitations include residuals from calibration, beam chromaticity, polarization leakage, and actual transition redshift from Pop III- to Pop II-dominated star formation, which may depend non-trivially on feedback and chemical enrichment history. Comprehensive joint inference with high-redshift galaxy surveys (JWST, Roman Space Telescope) will further constrain the Pop III star formation landscape.

Conclusion

The paper establishes a general framework for quantifying the constraint power of the global 21-cm signal on fundamental Pop III star parameters. By incorporating radiative feedback, Lyα/LW dynamical coupling, and realistic noise models, it is shown that precision measurements of the 21-cm brightness temperature across $M_\mathrm{s}$4 can statistically constrain both the star formation efficiency and typical stellar mass at the $M_\mathrm{s}$5--$M_\mathrm{s}$6 level. These results highlight that robust foreground removal, rather than thermal instrument sensitivity, is the foremost requirement for realizing the scientific potential of next-generation 21-cm cosmology experiments in the context of first star astrophysics. The extension to IMF parameter inference and high-dimensional feedback modeling remains a compelling avenue for future work.