The impact of the WHIM on the IGM thermal state determined from the low-z Lyman forest

At z less than or similar to 1, shock heating caused by large-scale velocity flows and possibly violent feedback from galaxy formation, converts a significant fraction of the cool gas (T similar to 10(4) K) in the intergalactic medium (IGM) into warm-hot phase (WHIM) with T > 10(5) K, resulting in a significant deviation from the previously tight power-law IGM temperature-density relationship, T= T-0(rho/rho)(gamma-1). This study explores the impact of the WHIM on measurements of the low-z IGM thermal state, [T-0, gamma], based on the b-N-HI distribution of the Ly alpha forest. Exploiting a machine learning-enabled simulation-based inference method trained on Nyx hydrodynamical simulations, we demonstrate that [T-0, gamma] can still be reliably measured from the b-N-HI distribution at z = 0.1, notwithstanding the substantial WHIM in the IGM. To investigate the effects of different feedback, we apply this inference methodology to mock spectra derived from the IllustrisTNG and Illustris simulations at z = 0.1. The results suggest that the underlying [T-0, gamma] of both simulations can be recovered with biases as low as |Delta log (T-0/K)| less than or similar to 0.05 dex, |Delta gamma| less than or similar to 0.1, smaller than the precision of a typical measurement. Given the large differences in the volume-weighted WHIM fractions between the three simulations (Illustris 38 per cent, IllustrisTNG 10 per cent, and Nyx 4 per cent), we conclude that the b-N-HI distribution is not sensitive to the WHIM under realistic conditions. Finally, we investigate the physical properties of the detectable Ly alpha absorbers, and discover that although their T and Delta distributions remain mostly unaffected by feedback, they are correlated with the photoionization rate used in the simulation.