Feedback reshapes the baryon distribution within haloes, in halo outskirts, and beyond: the closure radius from dwarfs to massive clusters

We explore three sets of cosmological hydrodynamical simulations, IllustrisTNG, EAGLE, and SIMBA, to investigate the physical processes impacting the distribution of baryons in and around haloes across an unprecedented mass range of ${10}^8<M_{200\mathrm{c}}\mathrm{/}{\mathrm{M}}_{\odot }<{10}^{15}$, from the halo centre out to scales as large as $30R_{200\mathrm{c}}$. We demonstrate that baryonic feedback mechanisms significantly redistribute gas, lowering the baryon fractions inside haloes while simultaneously accumulating this material outside the virial radius. To understand this large-scale baryonic redistribution and identify the dominant physical processes responsible, we examine several variants of TNG that selectively exclude stellar and AGN feedback, cooling, and radiation. We find that heating from the UV background in low-mass haloes, stellar feedback in intermediate-mass haloes, and AGN feedback in groups (${10}^{12}\le M_{200\mathrm{c}}\mathrm{/}{\mathrm{M}}_{\odot }<{10}^{14}$) are the dominant processes. Galaxy clusters are the least influenced by these processes on large scales. We introduce a new halo mass-dependent characteristic scale, the closure radius $R_{\mathrm{c}}$, within which all baryons associated with haloes are found. For groups and clusters, we introduce a universal relation between this scale and the halo baryon fraction: $R_{\mathrm{c}}\mathrm{/}{R}_{200\mathrm{c},500\mathrm{c}}-1=\beta (z)(1-f_{\mathrm{b}}(<R_{200\mathrm{c},500\mathrm{c}})\mathrm{/}{f}_{\mathrm{b},\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{m}\mathrm{i}\mathrm{c}})$, where $\beta (z)=\alpha (1+z{)}^{\gamma }$, and $\alpha$ and $\gamma$ are free parameters fit using the simulations. Accordingly, we predict that all baryons associated with observed X-ray haloes can be found within $R_{\mathrm{c}}\sim 1.5-2.5R_{200\mathrm{c}}$. Our results can be used to constrain theoretical models, particularly the physics of supernova and AGN feedback, as well as their interplay with environmental processes, through comparison with current and future X-ray and SZ observations.