Beyond21: A Global Framework for Cosmic Dawn and Reionization Within and Beyond the Standard Model

TL;DR

Beyond21, a fully open-source Python package that implements flexible prescriptions for Pop II and Pop III star formation and computes the resulting radiation backgrounds and their impact on the intergalactic medium, is presented.

Abstract

Observations of the Cosmic Dawn (CD) and Epoch of Reionization (EoR) are steadily improving, opening new opportunities to study early galaxies through complementary probes. To enable consistent interpretation of these observations, we present Beyond21, a fully open-source Python package that implements flexible prescriptions for Pop II and Pop III star formation and computes the resulting radiation backgrounds and their impact on the intergalactic medium. From this coupled evolution, Beyond21 predicts the global 21-cm signal, UV luminosity functions (UVLFs), the ionization history, and the contribution to the observed cosmic X-ray background (CXB) within a single, self-consistent pipeline. A full global evolution run executes in $\sim0.1 \ {\rm s}$ on a single CPU core, enabling broad, high-resolution parameter exploration. The modular architecture facilitates straightforward modification of astrophysical prescriptions and the incorporation of new physics. As an illustrative example, we implement a scenario in which a small fraction of dark matter is millicharged, leading to baryon cooling through elastic interactions.

Figures (5)

• Figure 1: Left (upper): Evolution of the spin (gold) and kinetic (navy) temperatures for our fiducial model (see Tab. \ref{['tab:Params']}), together with the CMB temperature (dashed). Left (lower): The resulting global 21-cm signal. At high redshifts, the CMB, kinetic, and spin temperatures are tightly coupled scaling as $T \propto (1+z)$, yielding a null 21-cm signal (see Eq. \ref{['eq:T21']}). Around $z \sim 250$, the kinetic temperature decouples from the CMB and evolves adiabatically, scaling as $T \propto (1+z)^{2}$ (see Sec. \ref{['SubSec:Tk']}). The spin temperature remains coupled to the cooling gas through collisions, producing the first 21-cm absorption trough, which peaks near $z \sim 100$ when collisional coupling weakens and induced CMB interactions drive $T_{\rm s}$ back toward $T_{\rm CMB}$. At $z \sim 30$, Ly-$\alpha$ photons from the first stars couple $T_{\rm s}$ to the effective Ly$\alpha$ temperature, generating a second, deeper absorption feature in $T_{21}$. Subsequently, X-ray heating increases the gas and Ly-$\alpha$ temperatures, driving $T_{\rm s}$ above $T_{\rm CMB}$ and producing an emission signal. Finally, as reionization progresses ($z \lesssim 10$), ionizing UV photons deplete neutral hydrogen, causing the 21-cm signal to vanish independently of $T_{\rm s}$ (Eq.\ref{['eq:T21']}). Right: Comparison between $\texttt{Beyond21}$ (solid) and 21cmFAST (dashed) global 21-cm evolutions for three benchmark models. Brown curves correspond to the fiducial two-population (Pop II and Pop III) model of Munoz:2021psm, while blue lines follow the single-population fiducial model of Park:2018ljd. The green curves show the evolution predicted by the latest 21cmFAST model Davies_2025_1, which assumes stochastic galactic properties and a continuous metallicity evolution.
• Figure 2: UVLFs produced with $\texttt{Beyond21}$. Solid curves correspond to the fiducial model, which assumes a deterministic halo–magnitude relation and is calibrated using the UVLFs observed by the HST for $M_{\rm UV} > -20\,\mathrm{mag}$ at $6 \leq z \leq 10$. Dashed curves show an extended model that includes a Gaussian scatter about the mean halo–magnitude relation and is calibrated to the HST dataset at $z\leq8$ and to JWST measurements at higher redshifts. The model parameters are given in Tab. \ref{['tab:Params']}. Red and purple data points denote HST measurements from Bouwens:2014fuaBouwens_2021, while turquoise show JWST data from donnan2024jwstprimernewmultifield
• Figure 3: The evolution of the neutral hydrogen fraction. Results for our fiducial model (Tab \ref{['tab:Params']}) is shown in grey. BluePark:2018ljd, orangeMunoz:2021psm and greenDavies_2025_1 are the $x_{\rm HI}$ evolutions for the same 21cmFAST models as in fig \ref{['fig:T21']}. Solid are ionization histories generated with $\texttt{Beyond21}$, while dashed are outputs from 21cmFAST. The electron scattering optical depth of CMB photons for each model is given in the legend.
• Figure 4: Solid curves show the thermal and global 21-cm evolution for a viable 2cDM model with $Q=2\times10^{-3}$, $m_{\rm m}=500,{\rm MeV}$, $m_{\rm C}=200,{\rm MeV}$, and $\sigma_0$ set to its maximal value consistent with Planck constraints Liu:2019knx. This parameter choice satisfies the bounds from BBN, accelerator experiments, and direct-detection searches Barkana:2018qrxMunoz:2018pzpBerlin:2018sjsCreque-Sarbinowski:2019mcmDavidson:2000hfBadertscher:2006fmPrinz:1998uaMagill:2018tbbchatrchyan2013searchArgoNeuT:2019ckqLiu:2019knxEmken:2019tni, summarized in Katz:2024ayw. The corresponding $\Lambda$CDM evolution is shown with dashed curves. Left: Temperature evolution of the CMB (grey), baryons (blue), IDM (turquoise), and CDM (brown) assuming the fiducial astrophysical parameters of this work (Tab. \ref{['tab:Params']}). Initially, the mDM is tightly coupled to the baryons. After baryon–CMB decoupling at $z\sim250$, the baryon–mDM fluid cools adiabatically until mDM–CDM interactions become efficient at $z\sim100$, leading to a coupled evolution of all three components. This coupling breaks at $z\sim20$, when X-rays by astrophysical sources reheat the baryons, and the mDM with them. Right: Evolution of the global 21-cm signal. Black curves correspond to the fiducial astrophysical model. The reduced baryonic temperature in the 2cDM scenario produces a deeper absorption feature, enhanced by a factor of $\sim3$ relative to $\Lambda$CDM. Purple curves illustrate the effect of varying the UV normalization by a factor of two around the fiducial value. A larger UV photon production rate increases the Ly-$\alpha$ background, strengthening the coupling between the spin and kinetic temperatures and resulting in a deeper absorption signal. Orange curves show the impact of varying the X-ray normalization by a factor of five. Stronger (weaker) heating produces a shallower (deeper) absorption trough, as reduced X-ray heating allows $T_{\rm k}$ to remain low at lower redshifts where the Ly-$\alpha$ intensity is larger, and the spin-kinetic coupling is tighter.
• Figure 5: Execution flow in $\texttt{Beyond21}$. Time ordering proceeds from top to bottom. The user interacts only with the GlobalWrapper object, which sets the cosmology, initializes the astrophysical history and subsequently runs the IGM evolution. During initialization, the CosmoHMF module defines the cosmological background and computes the HMF. The HMF is then passed to the IonSFR module, which determines the coupled evolution of the SFRD, UV ionized fraction, and LW photons (see Sec. \ref{['SubSec:SFR']}). These outputs are supplied to the Xrays module to compute X-ray heating, ionization rates, and Ly-$\alpha$ emissivity from secondary events. The X-ray–induced Ly-$\alpha$ emissivity is then passed to the NoIonUV object, which computes the direct stellar Ly-$\alpha$ intensity and combines both contributions to obtain the total Ly-$\alpha$ background. The resulting radiation backgrounds and ionization histories are then passed to the EvolveIGM module, which solves the coupled evolution equations for the IGM thermal and ionization state. This module also computes the 21-cm brightness temperature and the hydrogen spin temperature, the latter entering the thermal evolution when Ly-$\alpha$ heating is included (see Sec. \ref{['SubSec:Tk']}). Overall, a full execution of the pipeline typically requires $\sim 0.1 \ \mathrm{s}$. For flexability, the CXB and UVLFs are computed post-evolution on demand via the GlobalWrapper, which internally calls the Xrays and IonSFR modules.