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

Abstract

The first stars, the chemically pristine Population III, likely played an important role in heating the intergalactic medium during the epoch of cosmic dawn. The very high effective temperatures ($\sim 10^5$ K) predicted for the most massive Population III stars could also give rise to tell-tale signatures in the emission-line spectra of early star clusters or small galaxies dominated by such stars. Important quantities in modelling their observational signatures include their photon production rates at ultraviolet energies at which photons are able to ionize hydrogen and helium, dissociate molecular hydrogen and cause Lyman-$α$ heating. Here, we model the spectral energy distributions of Population III stars to explore how these key quantities are affected by the initial mass and rotation of Population III stars given a wide range of models for the evolution of these stars. Our results indicate that rotating Population III stars that evolve to effective temperatures $\sim 2\times 10^5$ K could potentially give rise to a very strong HeII 1640 emission line in the spectra from primordial star clusters, without requiring stellar masses of $\gtrsim 100\ \mathrm{M}_\odot$ indicated by previous models for non-rotating Population III stars. The observable impact on 21-cm signatures from cosmic dawn and the epoch of reionization from our set of rotating stars that evolve to $\sim 2\times 10^5$ K is modest, except in case of high Population~III star formation efficiencies which imprint potentially detectable features in the global 21-cm signal and 21-cm power spectrum.

Figures (9)

• Figure 1: SEDs (in units of photon production rate per unit wavelength) of TLUSTY stellar atmosphere models with primordial chemical composition for $T_\mathrm{eff}= 2.05\times 10^5$ K (purple solid line), $T_\mathrm{eff} = 9.5\times 10^4$ K (blue solid line), $T_\mathrm{eff} = 5.5\times 10^4$ K (yellow solid line) and $T_\mathrm{eff} = 4.3\times 10^4$ K (red solid line), contrasted to the corresponding blackbody SEDs (purple, blue, yellow and red dashed lines). To avoid overlap, the SEDs are scaled to bolometric luminosities $\log(L_\mathrm{bol}/L_\odot)\approx 6.8$, 5.3, 4.3 and 3.3, respectively. The surface gravities of the TLUSTY SEDs has been set to $\log(g)=6.5$ for the $T_\mathrm{eff}= 2.05\times 10^5$ K model and 5.0 in the other cases. The coloured patch indicates the extent of the LW band and the arrows the extent of the Lyman band and the H-, He-, He$^{+}$-ionizing part of the SEDs. Differences between the stellar atmosphere SEDs and the blackbody SEDs are seen in all of the different bands, although the degree to which blackbody models over- or underpredict the rates depend on $T_\mathrm{eff}$. The $T_\mathrm{eff}=4.3\times 10^4$, $5.5\times 10^4$ and $9.5\times 10^4$ K SEDs are considered representative of early evolution along the $9 \ \mathrm{M}_\odot$, $15 \ \mathrm{M}_\odot$ and $120 \ \mathrm{M}_\odot$Murphy21a Pop III tracks for both rotating and non-rotating stars, whereas the $\approx 2\times 10^5$ K model is representative only for rotating Yoon12 20--150 M$_{\odot}$ stars at the very end of their lifetimes.
• Figure 2: Photon productions rates ($Q_i$) as a function of stellar age for Murphy21b non-rotating models. The top left panel is for H-ionizing photons, the top right He-ionizing, the bottom left He$^+$-ionizing, and the bottom right LW-photons. Solid lines represent predictions based on stellar atmospheres and dashed lines the corresponding predictions for black body spectra. The largest difference between photon production rates of black body and atmospheres is the over-prediction of He$^{+}$-ionizing photons for black bodies, reaching up to $\sim2.3$ dex for the less massive stars. As expected from Fig. \ref{['fig:atmos vs BB']}, the effect becomes smaller for the higher-mass stars and even inverses for the most massive, as a result of their high $T_\mathrm{eff}$ ($\approx 9.5\times 10^4$ K for the 120 M$_{\odot}$ model) close to the ZAMS. The other photon production rates are less drastically affected.
• Figure 3: Lifetime-integrated UV photon productions rates per solar mass from rotating and non-rotating models with tracks from Yoon12, Murphy21b, Volpato23, Windhorst18, Klessen23, Schaerer02, and Liu25. The top left gives the values for H-ionizing photons, the top right for He-ionizing, the bottom left for He$^{+}$-ionizing, and the bottom right for LW photons. The values from Klessen23 are based on tracks from Murphy21b and Martinet23, using black body spectra which is why they differ from the other models, especially at lower masses. Liu25 is omitted from the He$^+$ panel as they only include wavelengths above 124Å. In general, all models based on stellar atmosphere SEDs agree on the H-ionzing and He-ionizing fluxes to within $\approx$ 0.3 dex for non-rotating stars at $M\gtrsim$ 10 M$_{\odot}$ and within $\approx$ 0.7 dex when rotation is included for these masses. The use of black body spectra severely overpredict the He$^+$-ionizing fluxes compared to comparable models based on stellar atmosphere SEDs. However, models for rotating Yoon12 stars at 20--300 M$_{\odot}$ produce higher He$^+$-ionizing fluxes than all other models. In the LW-band, the Schaerer02 predictions constitute a significant outlier which we discuss further in section \ref{['subsec: LW']}.
• Figure 4: Comparison of He$^{+}$ ionizing fluxes for rotating and non-rotating tracks from Yoon12. The dashed lines show rotating models with initial velocity v = 0.4v$_k$ and the solid lines show the corresponding non-rotating models. Large differences between rotating and non-rotating stars are seen for $>10\ \mathrm{M}_{\odot}$ due to extended lifetimes for rotating stars and the very high temperatures ($\approx 2\times 10^5$ K) that 20--150 M$_{\odot}$ rotating stars evolve to at the end of their lifetimes.
• Figure 5: Equivalent widths of the HeII$\lambda$1640 line as a function of time for the Yoon12 20 and 200 M$_{\odot}$ rotating and non-rotating stars. The parameters used in the cloudy calculations are log U = -2 and n(H) = 10$^{2}$. At three points we show the equivalent widths for hydrogen density n(H) = 10$^{1}$ (circles), 10$^{3}$ (triangles), and 10$^{4}$ (squares). The 20 M$_{\odot}$ star reaches equivalent widths surpassing the maximum of the 200 M$_{\odot}$ stars at the end of its lifetime. Increasing the hydrogen density in the nebular cloud slightly increases the predicted equivalent width.