I/THE OVERCOOLING PROBLEM

Rasera, Y., Teyssier, R., The history of the baryon budget. Cosmic logistics in a hierarchical universe, 2006, A&A, 445, 1

Devriendt, J., et al., The dusty, albeit ultraviolet bright, infancy of galaxies, 2010, MNRAS, 403, L84

Horizon Project

Galaxy formation

All the ingredients of the cosmic energy budget (see here) are at play in the process of large scale structure formation (galaxies, cluster of galaxies, filaments, voids...). In the framework of the hierarchical model of galaxy formation, small primordial density fluctuations observed on the cosmological microwave background are amplified by gravitational instability at a rate governed by the amount of dark energy. They lead to the formation of larger and larger halos through hierarchical merging. Gas collapses and cools in these dark matter potential wells and forms cold centrifugally supported gas discs. These discs are then converted into stellar discs that is to say galaxies. Metals are produced by these stellar populations and further enhance cooling and star formation rate. The main problem in this scenario is the so-called ``overcooling problem'': the resulting amount of stars plus interstellar medium is greater than the observed one by a factor of order four.  What is(are) the heat source(s) that is(are) able to balance or quench cooling? Supernovae feedback? AGN feedback? Others?

Numerical cosmology: cosmological simulations and analytical models

In order to model with a high level of details the evolution of dark energy, dark matter, baryons and metals, we have run a suite of large cosmological simulations (see image above) that reproduces the different steps of galaxy formation with very large spatial dynamics (from 140 Mpc to 170 pc). We have used the RAMSES code (Romain Teyssier) which is a parallel hydrodynamics plus n-body Adaptive Mesh Refinement (AMR) code. In these simulations, we have included zero-metalicity cooling,  heating from UV ionizing background, star formation assuming Kennicut law but no feedback. The goal was to understand how bad is the overcooling problem. We have then measured the evolution of the cosmic and halo baryon budget by considering 4 phases: diffuse cold gas in the intergalactic medium, hot gas in galaxy halos, cold dense gas in galaxies and stars. To understand and predict the evolution of the various phases, we have developped a simple analytical model (see link for download below) based on the halo model, that computes the flux between the various phases. The main ingredient is the minimum mass for star forming halo (minimum between the filtering mass and the minimum cooling mass) which together with the halo mass function, and the universal baryon fraction, control the amount of new fresh gas available for further cooling and star formation. Although very simple, this analytical model turns out to be surprisingly accurate.

Comparison to observations: winds efficiency and star formation time scale

Once calibrated on the simulations for various redshift, halo masses, star formation time scale, galactic wind efficiencies, and simulation mass resolution, the analytical model allow to extrapolate very quickly (1s on a PC instead of 1 month on supercalculator for typical large cosmological simulation) the history of the baryon budget for any of the parameters. We were therefore able to explore the parameter space and to compare to the observation of the cosmic star formation rate and cosmic gas density in damped Lyman alpha systems. The goal is to find the feedback intensity and the star formation efficiency required to reproduce the observed baryon budget. Without any feedback the amount of cold dense gas plus stars is too high by a factor four. On the countrary, with the favored parameters such as an average formation time scale of order 3 Gyr and a galactic wind of about 1.5 times the star formation rate (on average), we can recover the observed value. The present-day baryon budget is

It is worth noting that, according to our analytical model, most of nowadays cosmological simulations do not resolve the bulk of star forming halos by a large factor.  Inspired by this point, collaborators from the Horizon Project have run the largest cosmological simulation to date: the Mare Nostrum run.  This is the first attempt to resolve the bulk of the cosmic star formation down to low redshift. Interestingly it gives good agreement with the observed high-redshift UV luminosity function as long as dust extinction is taken into account and cosmological parameters are set to their currently favored values.

IDL routine: evolution of the baryon budget and star formation history

mysfh.tar.gz

II/THE COOLING-FLOW PROBLEM

Rasera, Y., Chandran, B. 2008, Numerical Simulations of Buoyancy Instabilities in Galaxy Cluster Plasmas with Cosmic Rays and Anisotropic Thermal Conduction,  ApJ, 685, 105

Chandran, B., Rasera, Y., Convection and AGN Feedback in Clusters of Galaxies,  2007, ApJ, 671, 1413

Galaxy cluster internal profile

The overcooling problem (see previous part) is particularly critical in clusters of galaxies, and even supernovae driven galactic winds are not strong enough to solve it. This is because the dark matter potential well is to deep and such winds have little effect (for instance the escape velocity is several thousands kilometers per second). The cooling time scale (typical time to cool down the hot intracluster plasma) near the center of the cluster is often much shorter than the age of the cluster. Without any thermal support, one would expect strong flows of cold gas converging towards the center of the cluster. However star formation in cluster cores is ten to one hundred time below expection and no emission lines below the Virial temperature of the cluster divided by three are observed. This absence of cooling flow against expectation is the “cooling-flow problem”. What could prevent thousands of solar masses per year of hot plasma from cooling and converging towards the center? Is it AGN feedback? But in this case how is energy transferred from supermassive black holes to the surrounding intracluster medium?

MHD simulation with anisotropic transport and cosmic rays

A “realistic” simulation of AGN feedback should include all the physics at play such as gravity, hydrodynamics, cooling, and energy injection by AGN but also the (often-ignored!) magnetic fields dynamics (MHD), anisotropic thermal conduction, cosmic-ray dynamics (multifluid), and cosmic-ray anisotropic transport. At least, it is important to understand the role of these non-thermal components which are present but usually neglected. Most of my work was to include all these ingredients in an already existing MHD code (TVD MHD from Ue-Li Pen). Anisotropic transport and conduction along the magnetic field lines play a central role and is the most challenging to implement. Standard discretization can lead to negative temperature which are unphysical. Adding too much diffusion can break some physical instabilities that depend on the anisotropy of the transport. We therefore develop our own method, the flux-tube method. Instead of solving the equation using the grid geometry, we solve it directly along the magnetic field.

AGN-driven convection

There are many hypotheses for the transfer of energy from AGN to plasma (jets, hot bubbles, cosmic rays, etc...). However, it is not easy to control the density and temperature profile in a way that is both self-regulating and consistent with observations. Ben Chandran has proposed an interesting possibility: part of the AGN energy is injected as cosmic rays (because of the relativistic jets) and produces negative gradients of cosmic-ray pressure. Together with anisotropic transport, these negative cosmic-ray pressure gradients, make the intracluster medium convectively unstable. As a result, convection heats the intracluster medium and regulates the density and temperature profile. Ben has developped a simple stationnary analytical model to capture these effects. By adjusting a single parameter (the size of the cosmic-ray injection) he was able to reproduce observed density and temperature profiles for our sample of eight clusters.  On the other hand, we have run simulations of 2D atmosphere that confirm the theoretical expectation for the development of the instability. The next ongoing step is to run 3D cluster simulations!