21cmSPACE

21-cm Semi-numerical Predictions Across Cosmic Epochs or 21cmSPACE (since 2011) is an actively developed, semi-numerical code written (mostly) in MATLAB that models the 21-cm signal and other high-redshift observables from before the Cosmic Dawn (z~50) to the end of Epoch of Reionization (z~6). It is a versatile tool that can be used to study the 21-cm signal affected by a wide range of astrophysical processes, including the formation and properties of the first stars and galaxies, the impact of X-ray binaries, exotic scenarios of excess radio background, and more! Due to its semi-numerical nature, each simulation takes a few hours to run, making it ideal for parameter space exploration.

Development publications

A number of papers have been published on the development of 21cmSPACE over the years. Here is a list of them:

• Wasserman et al. (2025) - Impact of various Pop III SEDs on ionization, HeII emission and the 21-cm signal. Version as in the CHE paper (Liu et al. 2025). Adds stellar SEDs from Yoon et al. 2012.

• Gessey-Jones et al. (2025) - Prospects to determine Pop III IMF using REACH and/or SKA. 

• Liu et al. (2025) - PopIII CHE stars, including ionization effects (zeta_II and zeta_III); f_XII and f_XIII; collapsed fraction as an integral of SFR for Pop III (Thomas) and Pop II (Jiten). No photoheating feedback on PopIII stars (f_coll_III = f_coll\times x_HI). 

• Dhandha et al. (2025) — UVLF observable and flexible PopII SFE model

• Sikder et al. (2024) — Line of sight radio effect

• Gessey-Jones et al. (2023) — Cosmic ray heating model

• Gessey-Jones et al. (2022) — PopIII stars and IMF variation, including Lyman band effects only: WF effect, LW feedback, Ly-a heating.

• Magg et al. (2022) — PopIII star formation and PopIII to PopII transition

• Reis et al. (2022) — Poisson fluctuations in star-forming halos; stochastic star formation efficiency

• Reis et al. (2021) — Lyman-alpha multiple scattering, Ly-a heating

• Reis et al. (2020) — Inhomogeneous radio background from galaxies, astrophysical interpretation of EDGES Low-Band  detection

• Fialkov & Barkana (2019) — Uniform excess radio background and CMB heating, astrophysical interpretation of EDGES Low-Band  detection

• Cohen et al. (2018) —21-cm parameter space exploration using power spectra

• Cohen et al. (2017) — 21-cm parameter space exploration using global signal 

• Fialkov et al. (2017) — Miniquasars vs X-ray binaries (soft/hard SEDs). First unresolved X-ray background constraints

• Cohen et al. (2016) — Photo-heating feedback

• Fialkov et al. (2014c) — Comparison between the signatures of soft and hard X-ray SEDs, and inhomogeneous X-ray heating.

• Fialkov et al. (2014b) — Realistic X-ray SED from high-mass X-ray binaries, and implementation of the excursion set formalism for reionization. 

• Fialkov et al. (2014a) — Inhomogeneous Lyman-alpha coupling (the WF effect)

• Fialkov et al. (2013) — Impact of Lyman-Werner feedback w/o vbc

• Fialkov et al. (2012) — Impact of baryon-dark matter streaming velocity (vbc), semi-analytic prescription.

• Visbal et al. (2012) — 3D simulations of the 21-cm signal from Cosmic Dawn (X-ray heating and vbc).

Apart from the above, the code has been used in a number of other publications, using it for inference, forecasting, and more which are listed below.  

Inference with 21cmSPACE

A number of papers have been published on data interpretation, inference and parameter estimation using 21cmSPACE:

• Dhandha et al. (2025b) - Limits on gas temperature and the range of the 21-cm signal for the model constrained by the joint analysis including the JWST and HST UVLFs, HERA, SARAS3, CXB and CRB (Dhandha et al., 2025a). Same 30,000 models of 21-cm signals as in Dhandha et al. 2025a.

• Gessey-Jones et al. (2025) - Inference of Pop III IMF using REACH and/or SKA. We created 60,000 signals for a 7 parameter-model: Pop III IMF (6 values, 10,000 signals per IMF), Vc, tdelay, f*III, f*II, fXII, fradIII=fradII. fXIII is calculated from the IMF.  

• Dhandha et al. (2025a) — Inference of mass- and redshift-dependent SFE of PopII, along with other model parameters, using JWST and HST UVLFs, HERA, SARAS3, upper limits on X-ray and radio background limits, CMB optical depth. A set of 30,000 models was created with 8 free parameters Vc, f*II, M0, alpha*, beta*, tau, fX, fR.  

• Sims et al. (2025) - Astro constraints using joint analysis of CMB, IGM neutral fraction measurements from Lyman-line-based data, HERA, LOFAR and MWA. Same 21cm models as in HERA2022 were used. 

• Pochinda et al. (2024) - First (weak) limits on Pop III SFE using HERA, SARAS3 and upper limits on X-ray and radio background limits. Evidence of high-z heating. For this publication a new dataset of 109,525 models was created varying 9 parameters: Vc, f*III, f*II, tdelay (3 values), fX (same for Pop II and Pop III), alphaX (X-ray SED slope, 3 values), Emin (X-ray SED cutoff, descrete 17 values), CMB optical depth (ionizing efficiency zeta is same for Pop II and Pop III), fr (same for Pop II and Pop III).  

• Gessey-Jones et al. (2024) - Constraints on superconducting cosmic strings using HERA, SARAS3 and upper limits on X-ray and radio background limits. For this publication a new dataset of 44,836 models was created varying 9 parameters: Vc, f*III, f*II, tdelay (3 values), fX (same for Pop II and Pop III), alphaX (X-ray SED slope, 3 values), Emin (X-ray SED cutoff, descrete 17 values), CMB optical depth (ionizing efficiency zeta is same for Pop II and Pop III), uniform excess radio background of intensity Ar and the exponent of its redshift evolution Br=2.25.  

• Bevins et al. (2024) - First joint analysis of a radiometer (SARAS3) and interferometer (HERA) data. We used the dataset with radio galaxies (physics from Reis et al. 2020; 2021) - five parameters varied including Vc, fX, f*, tau and fR; 10,700 models. Same model as in HERA2022.

• Abdurashidova et al. (2023) — HERA collaboration: improved constraints from HERA. A new (?) dataset of XXX models with 8 free parameters was used: Vc, f*, fX, alphaX, Emin, CMB optical depth, fr, Rmfp.  

• Abdurashidova et al. (2022) — HERA collaboration: Early constraints from HERA using radio background models. We used three scenarios: (1) Radio galaxy (physics from Reis et al. 2020; 2021) - five parameters varied including Vc, fX, f*, tau and fR; 10,700 models. (2) Uniform excess radio background (physics from Fialkov and Barkana, 2019) - five parameters varied including Vc, fX, f*, tau and AR; 10,300 models. (3) CMB-only case, 4 parameters and ~2000 models.  

• Bye et al. (2022) — 21cmVAE - emulator based on variational autoencoder trained and tested using 21cmGEM dataset. Same dataset as used for 21cmGEM and GLOBALEMU. 28,996 models with 7 free parameters was used: Vc, f*, fX, alphaX, Emin, CMB optical depth, Rmfp.  

• Bevins et al. (2022a) —A Bayesian reanalysis of SARAS 2 data.

• Bevins et al. (2022b) —Astrophysical constraints from SARAS 3 non-detections.

• Bevins et al. (2021) — GLOBALEMU. Emulator with a new architecture using 21cmGEM dataset. Same dataset as used for 21cmGEM and 21cmVAE. ~30,000 models with 7 free parameters was used: Vc, f*, fX, alphaX, Emin, CMB optical depth, Rmfp.  

• Mondal et al. (2020) — LOFAR constraints with an excess radio background.

• Cohen et al. (2020) — First global signal emulator (21cmGEM) created using the first large set of 21-cm models (~30,000 signals produced on Harvard's Odyssey cluster). The original dataset can be found here https://zenodo.org/records/4541500 . Same dataset as later used for GLOBALEMU and 21cmVAE. ~30,000 models with 7 free parameters was used: Vc, f*, fX, alphaX, Emin, CMB optical depth, Rmfp.  

• Monsalve et al. (2019) — Analysis of EDGES High-Band.

• Singh et al. (2018) — Reanalysis of SARAS2 data.

• Singh et al. (2017) — First results from SARAS2.

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