Efficient semi-analytic modelling of Pop III star formation from Cosmic Dawn to Reionization

TL;DR

The paper develops the abcd model, a fast semi-analytic 'bathtub' framework that evolves two gas reservoirs (pristine and enriched) within dark matter halos and couples them to a surrounding CGM and the evolving IGM, to trace Pop III and Pop II star formation from cosmic dawn through reionization. It extends prior minimalist models by explicitly modeling dual ISMs, CGM dynamics, metal mixing, and environmental feedback such as reionization and IGM enrichment, enabling self-consistent forecasts of SFRDs, UV luminosity functions, transients, and the 21-cm global signal. Key findings include substantial late-time Pop III star formation restricted to the most massive halos, strong regulation by IGM enrichment, and a detectable but challenging Pop III SN signature, with the 21-cm signal showing notable sensitivity to primordial star formation physics. The framework is designed for speed and interpretability, offering a tractable platform to guide observations and parameter inference while highlighting major theoretical uncertainties in metal mixing, LW feedback, and the Pop III IMF.

Abstract

The quest to find the first stars has driven astronomers across cosmic time, from hopes to identify their signatures in their heyday at cosmic dawn to deep searches for their remnants in our local neighborhood. Such work crucially relies on robust theoretical modelling to understand when and where we expect pristine star formation to have occurred and survived. To that end, here we introduce an analytic bathtub for cosmic dawn, the abcd model, to efficiently trace the formation of the first stars from their birth through the first billion years of our universe's history, jointly following star formation out of pristine and metal-enriched gas over time. Informed by the latest theoretical developments in our understanding of star formation in molecular cooling halos, metal mixing, and early galaxies, we expand pre-existing minimal models for galaxy formation to include Population III stars and many of the processes - both internal and environmental - affecting their evolution, while remaining fast and interpretable. With this framework, we can bridge the gap between numerical simulations and previous semi-analytic models, as we self-consistently follow star formation in dark matter halos from the minihalo era through the epoch of reionization, finding that, under plausible physical conditions, pristine star formation can persist at a high level in the presence of Pop II star formation down to $z\sim 5$, but is limited to the most massive halos. We highlight areas of theoretical uncertainty in the physics underpinning Pop III star formation and demonstrate the effects of this uncertainty first on individual star formation histories and subsequently bracketing the range of global star formation levels we expect. Finally, we leverage this model to make preliminary observable predictions, generating forecasts for high-$z$ luminosity functions, transient rates, and the 21-cm global signal.

Figures (18)

• Figure 1: A schematic overview of the various components of the abcd model. As in the subsequent plots, DM reservoirs are represented in green, pristine reservoirs in red, and enriched reservoirs in blue. While in detail the model does not contain any spatial information about the star-forming and gaseous components of the different mass reservoirs, this schematic serves to illustrate the rough picture motivating the choices of the different quantities and parameterizations underpinning the model. Most of the quantities referenced in this schematic are specified in Table \ref{['tab:constants']} or in eqs. \ref{['eq:m_ism_ev']}-\ref{['eq:t_mix']}. As noted in those equations and the table, the $m$ quantities correspond to masses in different reservoirs, $t$ to the timescales over which the different processes proceed, and $\eta$ to the mass loading factors computed for feedback and metal ejection (eqs. \ref{['eq:minimalist_eta']} and \ref{['eq:eta_metal']}). A broad overview of the model is as follows: pristine material flows into the circumgalactic region of a DM halo along filaments from the IGM (red clouds). After some time ($\mathcal{O}(t_{\rm dyn})$), this gas settles into the central ISM and eventually forms stars, driving the buildup of pristine stellar mass $m_\star^{\rm pri}$. Once these stars die, they eject metal-enriched gas into the circum- and intergalactic media around that halo (with strengths characterized by the mass-loading parameters $\eta^{\rm pri}$, $\eta^{\rm metal}$), kick-starting the local and global metal enrichment process. As the enriched reservoir (blue clouds) builds up, it too settles into the ISM, from which a central disk forms and Population II stars are born ($m_\star^{\rm enr}$). These cycles proceed in both reservoirs --- enriched and pristine --- as the halo's local (and the IGM) metallicity slowly grows (which modifies $f_{\rm enr}$; Section \ref{['sec:global_enrichment']}), subject to the additional effects of reionization feedback (which alters $f_{g}$; Section \ref{['ssec:reion_feedback']}).
• Figure 2: In the absence of environmental effects, inefficient mixing of metals ejected by stellar feedback events can result in a high level of Pop III star formation out to $z\sim 5$. Evolution of a $\sim 10^{9.5}\ M_\odot$ halo from $z=35$ to $z=5$. (top) The different mass reservoirs characterizing the halo are indicated with colored lines, with pristine reservoirs identified by red, enriched by blue, and DM by green. For a given (red or blue) color, different line styles denote the different reservoirs --- dashed are the CGM gas reservoirs, thin solid are the ISM, and thick solid are the cumulative stellar mass formed over the galaxy's history. The cumulative mass that has escaped the system due to stellar feedback is shown with a purple solid line. For reference, the critical halo mass for Pop III star formation (an environmental quantity) is shown with a green dashed line and the atomic cooling threshold is indicated with a green dot-dashed line. (bottom) The corresponding fractions of baryonic mass for each of the curves in the upper panel; i.e., $X_i = m_i/f_bm_h$.
• Figure 3: The estimated evolution of $Q_{\rm IGM}$ following the framework discussed in Section \ref{['sec:global_enrichment']} for three choices of the efficiency value for the energy carried by stellar winds (1, 50, and 0.1 $\times K_w$ for the solid, dashed, and dotted curves, respectively). For reference, we also show the model estimates from liu_when_2020 and yamaguchi_extent_2023 as orange and purple dot-dashed curves, respectively.
• Figure 4: Reionization feedback and IGM enrichment can significantly influence the late time evolution of low-mass halos.(upper) Evolution of the same $\sim 10^{9.5}\ M_\odot$ halo from Figure \ref{['fig:SFH_ex']}, now with external feedback processes included. We additionally display the accretion threshold induced by reionization heating of the IGM (eq. \ref{['eq:Mcrit_acc']}) as a green dotted line. The cumulative stellar mass if the halo were in an (un)ionized region is shown with a dashed (solid) line, with the associated probability denoted by the black line (corresponding to the right vertical axis). The corresponding stellar mass curves in the absence of external feedback (i.e., the same as Figure \ref{['fig:SFH_ex']}) are shown as colored dotted curves. (lower) Star formation rate smoothed over a 30 Myr window in the pristine and enriched reservoirs for the same ionized and unionized cases, with the pristine SFR from Figure \ref{['fig:SFH_ex']} dotted again.
• Figure 5: Environmental feedback can introduce significant variations in star formation efficiency, depending on the host halo mass. Evolution of the same $\sim 10^{9.5}\ M_\odot$ halo from Figures \ref{['fig:SFH_ex']} and \ref{['fig:SFH_reionization_feedback']} (solid curves) compared with a more massive $\sim 10^{11.6}M_\odot$ halo (dashed) and a lower mass $10^{8.5}M_\odot$ halo (dotted), with their associated star formation histories (cumulative pristine stellar mass in red and enriched in blue) including all components of the model, both internal and environmental.