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We investigate the potential of low-redshift Lyman alpha (Ly$\alpha$) forestfor constraining active galactic nuclei (AGN) feedback models by analyzing theIllustris and IllustrisTNG simulation at z=0.1. These simulations are ideal forstudying the impact of AGN feedback on the intergalactic medium (IGM) as theyshare initial conditions with significant differences in the feedbackprescriptions. Both simulations reveal that the IGM is significantly impactedby AGN feedback. Specifically, feedback is stronger in Illustris and results inreducing cool baryon fraction to 23% relative to 39% in IllustrisTNG. However,when comparing various statistics of Ly$\alpha$ forest such as 2D andmarginalized distributions of Doppler widths and H I column density, linedensity, and flux power spectrum with real data, we find that most of thesestatistics are largely insensitive to the differences in feedback models. Thislack of sensitivity arises because of the fundamental degeneracy between thefraction of cool baryons and the H I photoionization rate ($\Gamma_{\rm HI}$)as their product determines the optical depth of the Ly$\alpha$ forest. Sincethe $\Gamma_{\rm HI}$ cannot be precisely predicted from first principles, itneeds to be treated as a nuisance parameter adjusted to match the observedLy$\alpha$ line density. After adjusting $\Gamma_{\rm HI}$, the distinctions inthe considered statistics essentially fade away. Only the Ly$\alpha$ flux powerspectrum at small spatial scales exhibits potentially observable differences,although this may be specific to the relatively extreme feedback model employedin Illustris. Without independent constraints on either $\Gamma_{\rm HI}$ orcool baryon fraction, constraining AGN feedback with low-redshift Ly$\alpha$forest will be very challenging.

Can the Low Redshift Lyman Alpha Forest Constrain AGN Feedback Models?