Validating Posteriors Obtained by an Emulator When Jointly Fitting Mock Data of the Global 21 cm Signal and High-z Galaxy UV Luminosity Function

Abstract

Although neural-network-based emulators enable efficient parameter estimation in 21 cm cosmology, the accuracy of such constraints is poorly understood. We employ nested sampling to fit mock data of the global 21 cm signal and high- z galaxy ultraviolet luminosity function (UVLF) and compare for the first time the emulated posteriors obtained using the global signal emulator globalemu to the “true” posteriors obtained using the full model on which the emulator is trained using ARES . Of the eight model parameters we employ, four control the star formation efficiency (SFE) and thus can be constrained by UVLF data, while the remaining four control UV and X-ray photon production and the minimum virial temperature of star-forming halos ( ${T}_{\min }$ ) and thus are uniquely probed by reionization and 21 cm measurements. For noise levels of 50 and 250 mK in the 21 cm data being jointly fit, the emulated and “true” posteriors are consistent to within 1 σ . However, at lower noise levels of 10 and 25 mK, globalemu overpredicts ${T}_{\min }$ and underpredicts γ _lo , an SFE parameter, by ≈3 σ –4 σ , while the “true” ARES posteriors capture their fiducial values within 1 σ . We find that jointly fitting the mock UVLF and 21 cm data significantly improves constraints on the SFE parameters by breaking degeneracies in the ARES parameter space. Our results demonstrate the astrophysical constraints that can be expected for global 21 cm experiments for a range of noise levels from pessimistic to optimistic, as well as the potential for probing redshift evolution of SFE parameters by including UVLF data.

Keywords

• Nested sampling
• Reionization
• Luminosity function
• Neural networks
• Posterior distribution
• Radio astronomy