[Paper Review] Modelling the expulsion of baryons from haloes from first principles: the role of feedback and of the cosmological constant

Oscar Veenema, Daniele Sorini+1 more|arXiv (Cornell University)|Mar 13, 2026

Galaxies: Formation, Evolution, Phenomena0 citations

TL;DR

The paper develops a first-principles analytical model for the closure radius of haloes, predicting the baryon fraction return to cosmic value and validating it against EAGLE simulations across varied cosmologies including different values of Lambda.

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 $f_{ m b} = Ω_{ m b}/Ω_{ m m}$ (`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 $M_{ m 200c} > 10^{11} M_\odot$ in the redshift range $0

Motivation & Objective

• Motivate understanding of how baryons are expelled from haloes by feedback and cosmology within a LCDM framework.
• Develop a first-principles analytical model for gas distribution around haloes linking hydrostatic balance, gravity, and cosmic expansion.
• Derive a physically motivated relation between closure radius and halo properties.
• Compare the analytical predictions to EAGLE simulations with varying cosmological constant to test robustness across cosmologies.

Proposed method

• Assume spherical symmetry and balance gas pressure, gravity, and Lambda-driven repulsion to derive a governing equation for rho(r).
• Adopt a polytropic gas equation of state P(r) = w_n rho(r)^{n+1} and solve the resulting ODE in limiting regimes.
• Derive a power-law density profile rho(r) ~ r^{-eta} in the far-field (rho << rho_crit) and relate eta to the polytropic index n.
• Compute the closure radius R_closure by equating the integrated baryon mass to f_b-cosmic M_200 via an analytic integral dependent on halo mass, gas fraction, and cosmology.
• Express the closure radius in terms of M_200, R_200, f_b-cosmic, f_b-halo, and gas thermodynamic parameters, yielding a practical formula (Eq. 21).
• Relate the thermodynamic constant w_n to halo properties such as virial temperature and gas fraction to close the system (Eq. 20).

Figure 1: Plot of equation ( 2 ) 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

Experimental results

Research questions

• RQ1 How does the closure radius depend on halo mass and redshift in a LCDM cosmology?
• RQ2 What is the impact of varying the cosmological constant on baryon evacuation from haloes?
• RQ3 Can a first-principles analytical model reproduce the empirical closure radius–halo mass relation seen in simulations?
• RQ4 How robust is the predicted closure radius to changes in feedback and gas physics across cosmologies?

Key findings

• The model predicts a closure radius greater than R_200, linking baryon depletion to cosmology and halo properties (Eq. 21).
• The closure radius increases with higher dark energy (Lambda) and lower gas fraction, consistent with baryon evacuation expectations.
• The derived analytic framework shows excellent agreement with six EAGLE-like simulations across 0<z<3 for M_200 > 1e11 Msun, spanning Lambda from 0 to 100 Lambda_0.
• Dark energy plays a non-negligible role: closure radius at z<2 is ~30% larger in the fiducial Lambda_0 cosmology than in an Einstein-de Sitter universe.
• For Lambda >= 10 Lambda_0, dark energy becomes the dominant factor in baryon evacuation, suggesting its increasing importance as the universe approaches Lambda-domination.
• The model generalizes the empirical closure radius–halo mass relation, reducing to Ayromlou et al. (2023) form under appropriate limits and extending to broader parameter ranges.

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