Modelling the expulsion of baryons from haloes from first principles: the role of feedback and of the cosmological constant

Abstract

The extent to which galactic-scale astrophysical processes conspire with the underlying cosmological model to expel baryons from haloes remains a central question in galaxy formation. We present an analytical model for the gas distribution within and beyond haloes, based on the balance between gravitational collapse, hydrostatic pressure, and cosmic expansion. Our model predicts, from first principles, the halo-centric distance enclosing a baryon mass fraction equal to the cosmic value $f_{\rm b} = Ω_{\rm b}/Ω_{\rm m}$ (`closure radius') in an arbitrary $Λ$CDM cosmology. We compare the predictions with the results of six variants of the EAGLE cosmological, hydrodynamical simulation, encompassing values of the cosmological constant ranging from 0 to 100 times its observed value in our Universe, $Λ_0$. Despite its simplicity, our model exhibits excellent agreement with the simulations for haloes with mass $M_{\rm 200c} > 10^{11} M_\odot$ in the redshift range $0<z<3$, suggesting that it captures the key astrophysical processes and highlighting its robustness to the cosmological parameters. Thus, it provides the first physical explanation for the empirical closure radius-halo mass relation previously observed in simulations. Furthermore, we find that dark energy plays a non-negligible role in baryon evacuation: the simulations reveal that in the fiducial cosmological model, the closure radius at $z<2$ is $\sim 30\%$ larger than in an Einstein-de Sitter universe. In cosmologies with $Λ\geq 10 Λ_0$, dark energy emerges as the dominant factor in this process -- suggesting that, as our Universe transitions towards $Λ$-domination, dark energy eventually becomes the primary driver of baryon evacuation from massive haloes.

Figures (12)

• Figure 1: Plot of equation (\ref{['eq:timeevolution']}) showing the evolution of cosmological redshift over elapsed cosmic time, highlighting differences in time evolution among universes with varying dark energy. Five cosmologies are shown, including an Einstein-de Sitter universe (EdS) with zero dark energy, a universe with dark energy density corresponding to what is measured in our Universe, $\Lambda_0$, and cosmologies where this density is scaled by factors of 10, 30, and 100. Dashed lines mark the epoch of matter-dark energy equality in each model universe. It is important to bear in mind the different mapping between cosmic time and redshift when comparing results across different cosmological models.
• Figure 2: Analytical linear-theory growing-mode evolution for universes with different dark energy contents, showing how the growth of initial matter-density perturbations varies. Dotted lines mark the epoch of matter-dark energy equality in each model universe. In cosmologies with $\Lambda >0$, the linear growth factor asymptotically reaches a plateau as the scale factor increases. In an EdS universe, it grows indefinitely.
• Figure 3: Radial profile of the average enclosed baryon fraction for haloes of different masses in the 50 Mpc simulation at $z$ = 0. The yellow band shows the 5$\%$ error range meaning that the average closure radius of haloes in each mass range would be taken as the point each line intersects the lower bound of the yellow band. The closure radius error is then the difference between that and where the line intersects the purple dashed line at exactly $f_{\text{b-cosmic}}$. The closure radius is generally smaller in larger haloes, owing to the deeper potential wells retaining baryons.
• Figure 4: Distribution of baryons in and around a halo in the EAGLE L0050N0752 ($\Lambda_0$) simulation at $z = 0$. Orange and blue regions indicate locations where the baryon fraction is above or below the cosmic value respectively. The halo's characteristic radial scales, $R_{200}$ and $R_{\rm closure}$, are marked by the dashed and solid circles. The figure illustrates how feedback processes evacuate baryons from the central halo region, producing a baryon deficit within $R_{200}$, while redistributing baryons to much larger distances. As a result, the radius at which the enclosed baryon fraction returns to the cosmic value, $R_{\rm closure}$, lies several times beyond $R_{200}$.
• Figure 5: $R_{\text{closure}}/R_{200}$ against $f_{\text{b-halo}}/f_{\text{b-cosmic}}$ for every halo with $M_{200} > 10^{12} \mathrm{M}_{\odot}$ in the 50 Mpc $\Lambda_0$ simulation at $z = 0$. Each halo is colour coded by its mass and has error bars denoting the 5% error range on its closure radius calculation (see main text for details). As expected, more massive haloes have higher enclosed baryon fractions and smaller relative closure radii on average due to their larger gravitational potential wells making trapping baryons within $R_{200}$ easier. Moreover, haloes with larger $f_{\text{b-halo}}$ tend to have smaller $R_{\text{closure}}/R_{200}$ as they are less void of baryons within $R_{200}$.