[Paper Review] The History of the Baryon Budget: Cosmic Logistics in a Hierarchical Universe

Yann Rasera, Romain Teyssier|ArXiv.org|May 23, 2005

Galaxies: Formation, Evolution, PhenomenaPhysics and Astronomy98 references137 citations

TL;DR

This paper presents a simplified analytical model for the cosmic baryon budget in a hierarchical universe, using high-resolution N-body hydrodynamical simulations to track star formation and gas phases in galactic halos. It finds that a star formation timescale of $ t_* = 3 $ Gyr and wind efficiency $ \eta_{\rm w} = 1.5 $ best reproduce the observed anti-hierarchical star formation history and baryon fractions: $ \Omega_* \simeq 0.004 $, $ \Omega_{\rm cold} \simeq 0.0004 $, $ \Omega_{\rm hot} \simeq 0.01 $, and $ \Omega_{\rm back} \simeq 0.02 $.

ABSTRACT

Using a series of high-resolution N-body hydrodynamical numerical simulations, we investigate several scenarios for the evolution of the baryon budget in galactic halos. We derive individual halo star formation history (SFH), as well as the global star formation rate in the universe. We develop a simple analytical model that allows us to compute surprisingly accurate predictions, when compared to our simulations, but also to other simulations presented in Springel & Hernquist (2003). The model depends on two main parameters: the star formation time scale t* and the wind efficiency eta_w. We also compute, for halos of a given mass, the baryon fraction in each of the following phases: cold disc gas, hot halo gas and stars. Here again, our analytical model predictions are in good agreement with simulation results, if one correctly takes into account finite resolution effect. We compare predictions of our analytical model to several observational constraints, and conclude that a very narrow range of the model parameters is allowed. The important role played by galactic winds is outlined, as well as a possible `superwind' scenario in groups and clusters. The `anti-hierarchical' behavior of observed SFH is well reproduced by our best model with t*=3Gyr and eta_w=1.5. We obtain in this case a present-day cosmic baryon budget of Omega*= 0.004, Omega_cold=0.0004, Omega_hot=0.01 and Omega_back=0.02 (diffuse background).

Motivation & Objective

• Understand the evolution of the cosmic baryon budget across different phases—stars, cold discs, hot halos, and diffuse background—within a hierarchical galaxy formation framework.
• Develop a simple analytical model that accurately predicts baryon distribution and star formation history across halo masses and redshifts.
• Calibrate the model using high-resolution N-body hydrodynamical simulations to determine key parameters: star formation timescale $ t_* $ and wind efficiency $ \eta_{\rm w} $.
• Assess the impact of galactic winds and feedback on the global star formation rate and baryon fraction in different phases.
• Constrain model parameters by comparing predictions to observational constraints on star formation history and baryon fractions.

Proposed method

• Use a series of high-resolution N-body hydrodynamical simulations to model the formation and evolution of galactic halos and their baryonic components.
• Develop an analytical model based on two free parameters: the star formation timescale $ t_* $ and the wind efficiency $ \eta_{\rm w} $, to predict baryon distribution and star formation history.
• Model gas cooling and accretion onto cold discs using two regimes: fast cooling (limited by orbital decay time $ t_{\rm orb} \simeq R_{\rm orb}/V_{\rm 200} $) and slow cooling (negligible accretion).
• Define the orbital decay timescale via $ R_{\rm orb}/R_{\rm 200} $, assumed constant across halo masses, and calibrate it against simulation results.
• Compute baryon fractions in cold discs, hot halos, stars, and the diffuse background (Lyman-alpha forest) as functions of halo mass and redshift.
• Compare model predictions to simulations (e.g., Springel & Hernquist 2003b) and observational constraints on the global star formation rate and baryon fractions.

Experimental results

Research questions

• RQ1 What is the evolution of the star formation history in the universe, and how well can it be reproduced by a simple analytical model?
• RQ2 How do the baryon fractions in cold discs, hot halos, stars, and the diffuse background evolve across halo masses and redshifts?
• RQ3 What values of the star formation timescale $ t_* $ and wind efficiency $ \eta_{\rm w} $ best match both simulation results and observational constraints?
• RQ4 How do feedback processes like galactic winds influence the global baryon budget and the anti-hierarchical behavior of the star formation history?
• RQ5 What role does the filtering mass and cooling efficiency play in determining the onset of disc formation and star formation in halos?

Key findings

• The analytical model with $ t_* = 3 $ Gyr and $ \eta_{\rm w} = 1.5 $ accurately reproduces the simulated star formation history and baryon fractions across halo masses.
• The model predicts a present-day cosmic baryon budget of $ \Omega_* \simeq 0.004 $ for stars, $ \Omega_{\rm cold} \simeq 0.0004 $ for cold discs, $ \Omega_{\rm hot} \simeq 0.01 $ for hot halos, and $ \Omega_{\rm back} \simeq 0.02 $ for the diffuse background.
• Galactic winds play a crucial role in regulating star formation, with the wind efficiency $ \eta_{\rm w} $ being tightly constrained by observations to $ \sim 1.5 $.
• The model successfully reproduces the observed anti-hierarchical star formation history, where low-mass halos form stars later than high-mass halos.
• Finite resolution effects in simulations must be carefully accounted for in order to match the analytical model predictions, particularly for cold disc and hot halo gas fractions.
• Fast cooling is limited by orbital decay time $ t_{\rm orb} \simeq R_{\rm orb}/V_{\rm 200} $, with $ R_{\rm orb}/R_{\rm 200} $ calibrated to be constant across halo masses.