Ultraviolet photon production rates of the first stars: Impact on the He II $λ$ 1640 � emission line from primordial star clusters and the 21-cm signal from cosmic dawn

This paper models the spectral energy distributions of rotating Population III stars to demonstrate that they can produce strong He II $\lambda$1640 emission lines without requiring extremely high stellar masses, while also assessing their modest but potentially detectable impact on the global 21-cm signal and power spectrum during cosmic dawn.

The Gist

The Cosmic "First Light" Mystery

Imagine the universe as a giant, dark room just after a power outage. For millions of years, it was pitch black, filled only with cold gas. Then, the "First Stars" (called Population III) flickered on. These weren't like our sun; they were chemically pure, massive, and incredibly hot. They were the universe's first lightbulbs, and they had a huge job to do: they had to heat up the cold gas and strip electrons off atoms to turn the universe from a dark fog into a transparent, glowing place.

This paper is like a technical manual for those first lightbulbs. The authors are asking: How bright are they really? What color are they? And how much "heat" do they actually put out?

The Big Misunderstanding: Blackbody vs. Real Stars

For a long time, scientists modeled these stars using a simple math trick called a "Blackbody."

• The Analogy: Imagine trying to describe the sound of a violin by just playing a single, perfect sine wave on a synthesizer. It's a smooth, simple tone. It's close, but it misses all the complex overtones, the scratch of the bow, and the resonance of the wood.
• The Reality: Real stars are like violins. They have complex atmospheres with specific chemical layers that block or boost certain colors of light.

The authors of this paper say: "We've been using the simple sine wave (Blackbody) to predict how these stars work, but we need to use the real violin (Stellar Atmosphere Models)."

The Result?
When they switched to the "real violin" models, they found a massive difference in how much Helium-ionizing light (super-energetic UV light) the stars produced.

• Old Model (Blackbody): "Oh, these stars are blasting out a ton of Helium-busting light!"
• New Model (Real Atmosphere): "Actually, for most stars, they produce much less of that specific light than we thought. The atmosphere acts like a filter, blocking some of it."

The "Super-Runner" Twist: Rotation

Here is the plot twist. The paper looks at stars that are spinning (rotating).

• The Analogy: Imagine a figure skater. If they pull their arms in and spin fast, they spin faster and generate more heat due to friction.
• The Science: When these first stars spin really fast, it mixes their fuel. It's like stirring a pot of soup so thoroughly that the fresh ingredients get to the bottom and the old stuff gets to the top. This allows the star to burn longer and get much hotter at the end of its life.

The Discovery:
The authors found that a spinning star that is only about 20 times the mass of our Sun can get so hot at the end of its life that it starts acting like a 100-solar-mass monster.

• Why does this matter? There is a specific color of light (He II 1640 Å) that is a "smoking gun" for these massive stars. Previously, scientists thought you needed a 100+ solar mass star to produce this light.
• The New View: You might not need a monster. You just need a normal-sized star that is spinning like a top. It can produce the same "smoking gun" light without needing to be a giant.

The "Cosmic Radio" Signal (21-cm)

The paper also looks at how these stars affect the 21-cm signal.

• The Analogy: Imagine the universe is a giant radio station. The "static" on the radio is the neutral hydrogen gas. When the first stars turn on, they change the "tuning" of the radio, creating a dip in the signal (an absorption trough).
• The Finding: The authors ran simulations to see if the "spinning" stars change the radio signal differently than the "non-spinning" ones.
  • If there are only a few of these stars (low efficiency), the radio signal looks almost the same. It's hard to tell the difference.
  • If there are lots of these stars (high efficiency), the spinning ones create a distinctly different radio pattern. They heat up the gas faster and ionize it differently.

The Takeaway: If we build a giant radio telescope (like the Square Kilometre Array or SKA) and listen to the early universe, we might be able to tell if those first stars were spinning or not, just by listening to the "static" of the cosmos.

Summary of the "Aha!" Moments

1. Stop using the simple math: Don't treat stars like perfect black spheres. Use the complex "atmosphere" models, or you'll get the numbers wrong (especially for Helium).
2. Spin is key: A medium-sized star spinning fast can do the work of a giant star. This changes how we interpret the light we see from the early universe.
3. The "Smoking Gun" Light: That specific bright line (He II 1640) doesn't necessarily mean we found a 500-solar-mass monster; it might just be a 20-solar-mass star doing a backflip (spinning).
4. Listening to the Universe: If we listen carefully to the 21-cm radio signal, we might be able to detect these spinning stars, but only if there were many of them.

Why should you care?

This paper helps us rewrite the history of the universe's "childhood." It tells us that the first stars were more dynamic, more complex, and perhaps more "spinny" than we thought. It suggests that the universe might have been lit up by a crowd of medium-sized, fast-spinning stars rather than just a few giant monsters. And soon, our new radio telescopes might finally let us "hear" the proof.

Technical Summary

1. Problem Statement

The first generation of stars (Population III or Pop III) played a critical role in heating the intergalactic medium (IGM) and driving cosmic reionization. However, modeling their observational signatures relies heavily on accurate estimates of their ultraviolet (UV) photon production rates. Previous studies often relied on blackbody approximations for stellar spectral energy distributions (SEDs), which may fail to capture the complex physics of hot, metal-free stellar atmospheres. Furthermore, the impact of stellar rotation on the evolution and UV output of Pop III stars remains a significant source of uncertainty. Specifically, there is a need to determine:

• How much do stellar atmosphere models deviate from blackbody models in predicting ionizing photon rates (H, He, He$^+$) and Lyman-Werner (LW) fluxes?
• Can rotating Pop III stars produce strong He II $\lambda$1640 Å emission lines without requiring extremely massive ($\gtrsim 100 M_\odot$) stars?
• How do these differences in UV output affect the global 21-cm signal and power spectrum during the Cosmic Dawn and Epoch of Reionization?

2. Methodology

The authors utilized the Muspelheim framework (Zackrisson et al. 2024) to generate SEDs for Pop III stars.

• Stellar Models: They coupled stellar evolutionary tracks from five different sources (Yoon et al. 2012, Windhorst et al. 2018, Murphy et al. 2021a, Volpato et al. 2023, Costa et al. 2025) with a grid of TLUSTY stellar atmosphere models. This approach replaces the standard blackbody assumption with realistic atmospheric physics.
• Rotation: The study specifically compared non-rotating models against rotating models (e.g., Yoon et al. 2012 tracks with $v = 0.4 v_K$), which include effects like rotational mixing and magnetic fields.
• Photon Rate Calculations: The authors calculated instantaneous and lifetime-integrated photon production rates ($Q$) for:
  • Hydrogen-ionizing ($Q_H$, $\lambda < 912$ Å)
  • Helium-ionizing ($Q_{He}$, $\lambda < 504$ Å)
  • Helium II-ionizing ($Q_{He^+}$, $\lambda < 228$ Å)
  • Lyman-Werner ($Q_{LW}$, $912 < \lambda < 1107$ Å)
  • Lyman-band ($Q_{Ly}$, $912 < \lambda < 1216$ Å)
• He II Emission Modeling: Using the photoionization code Cloudy, they simulated the He II $\lambda$1640 Å equivalent width (EW) for gas clouds surrounding single stars, varying ionization parameters ($U$) and gas densities.
• 21-cm Cosmology Simulations: The authors employed the semi-numerical code 21cmSPACE to simulate the global 21-cm signal and the spherically averaged power spectrum ($\Delta^2_{21}$). They tested two scenarios with different Pop III star formation efficiencies ($f_{\star, III} = 0.1\%$ and $1%$) using single-mass IMFs (20$M_\odot$and 200$M_\odot$) based on the various stellar models.

3. Key Contributions

• Systematic Comparison of SEDs: A rigorous comparison between blackbody and TLUSTY stellar atmosphere SEDs across a wide mass range ($1.7 - 1000 M_\odot$), highlighting where blackbody approximations fail.
• Rotation-Induced Evolution: Detailed analysis of how rotation alters the late-stage evolution of Pop III stars, specifically the ability of rotating stars to reach extreme effective temperatures ($T_{eff} \sim 2 \times 10^5$ K) at the end of their lives.
• Revised LW Rates: A correction to the literature values for Lyman-Werner photon production per baryon, challenging the widely used values of $\sim 4800$ and $\sim 10^5$.
• Public Data Release: The provision of updated Muspelheim model grids, including lifetime-integrated and average photon production rates for rotating and non-rotating tracks.

4. Key Results

A. Stellar Atmosphere vs. Blackbody

• He$^+$ Ionization: Blackbody models significantly overpredict He$^+$ ionizing rates for stars with $M \lesssim 100 M_\odot$ (by up to $\sim 6$ dex at low masses) due to the absence of continuum breaks present in real stellar atmospheres.
• H and He Ionization: For $M \gtrsim 10 M_\odot$, H and He ionizing rates agree within $\sim 0.3$ dex between atmosphere and blackbody models, though blackbodies generally overpredict H-ionizing rates slightly.
• LW Flux: Blackbody models overpredict LW flux at high masses but underpredict it at low masses compared to stellar atmosphere models.

B. Impact of Rotation on He II $\lambda$1640 Å

• Extreme Temperatures: Rotating Yoon et al. (2012) models ($20-150 M_\odot$) evolve to$T_{eff} \approx 2 \times 10^5$ K at the end of their lives, a state not reached by non-rotating models of similar mass.
• Strong Emission Lines: This high temperature allows rotating $\sim 20 M_\odot$ stars to produce He II $\lambda$1640 Å equivalent widths ($EW \gtrsim 30$ Å) comparable to those produced by non-rotating stars with $M \gtrsim 100 M_\odot$.
• Implication: A strong He II line in a high-redshift galaxy does not necessarily imply a top-heavy IMF dominated by $>100 M_\odot$ stars; it could instead indicate a population of rapidly rotating $\sim 20 M_\odot$ stars. This could reduce the total Pop III stellar mass required to explain observed line luminosities (e.g., in the GNz-11 halo) by a factor of $\sim 2$.

C. 21-cm Signal Signatures

• Global Signal: Differences in the global 21-cm signal between models are modest for low star formation efficiency ($f_{\star, III} = 0.1\%$). However, for high efficiency ($f_{\star, III} = 1\%$), differences become observable ($\sim 20$ mK at $z \approx 15$).
• Power Spectrum: The ionization peak in the power spectrum at $z \approx 12.5$ shows a factor of 2–3 difference between rotating and non-rotating models in the high-efficiency scenario. Rotating stars, due to their extreme ionizing flux, suppress the 21-cm absorption signal more rapidly.
• Detectability: The Square Kilometre Array (SKA) could potentially distinguish between these scenarios if Pop III star formation efficiency is high ($\sim 1\%$).

D. Lyman-Werner (LW) Rates

• The authors recommend a lifetime-integrated LW photon production rate of $\sim 8 \times 10^3$ to $3 \times 10^4$ photons per stellar baryon.
• This corrects the literature's reliance on two disparate values ($\sim 4800$ and $\sim 10^5$), attributing the higher value to integration errors (integrating to infinity rather than the Lyman limit).

5. Significance

This paper fundamentally refines the theoretical inputs for modeling the Cosmic Dawn and Epoch of Reionization.

1. Observational Interpretation: It provides a new physical mechanism (rotation) to explain strong He II emission lines in high-redshift galaxies without invoking the existence of extremely massive ($>100 M_\odot$) stars, which are difficult to form and short-lived.
2. 21-cm Cosmology: It demonstrates that the 21-cm signal is sensitive to the rotation state of Pop III stars, offering a potential new probe to constrain the initial mass function and rotation rates of the first stars using future SKA observations.
3. Modeling Accuracy: It establishes that blackbody approximations are inadequate for calculating He$^+$ ionizing fluxes and LW rates, urging the community to adopt stellar atmosphere models for precision cosmology.
4. Data Availability: The release of these updated models allows for immediate integration into large-scale cosmological simulations and observational analysis pipelines.