This research proposal was included with the application for the Tier I Canada Research Chair in March 2003. The Chair was approved in September 2003, and is scheduled to start in March 2004. In this document, "I" refers to Dr. Hugo Martel, the Chairholder.

DESCRIPTION OF THE PROPOSED RESEARCH PROGRAM

We propose to create a research chair in theoretical and computational cosmology at Université Laval. This chair will be centered on two main research areas:
  1. The formation and evolution of galaxies, and the feedback of the galaxy formation process on the evolution of the Intergalactic Medium (IGM).
  2. The formation of stars and star clusters in galaxies, and the feedback of the star formation process on the evolution of the galaxy and the subsequent formation of other stars.
The areas of cosmology/galaxy formation and star formation were traditionally regarded as distinct. However, in recent years, the astrophysical community has recognized the complex interplay between these various processes. Stellar evolution has a direct impact on galactic evolution: supernovae explosions create galactic outflows that directly affect the evolution of the host galaxies. The ejection of energy and metals into the surrounding IGM modifies the entropy content and cooling rate of the intergalactic gas, impacting the rate of formation of new galaxies. Similarly, galactic evolution can directly affect star formation: violent episodes of star formation, such as starbusts, can be triggered by large-scale interactions such as collisions between galaxies, tidal disruption, or accretion of gas from the IGM in cooling flows, while processes such as ram pressure stripping can have an inhibiting effect on star formation. In recent years, thanks to improvements in space and ground-based observations, it is now possible to measure the evolution of the star formation rate over most of the age of the universe. Such observations put serious constraints on the cosmological and galaxy formation models. Finally, a currently very active and exciting area is the formation of the first stars in the universe (Population III), a problem that is essentially cosmological in nature. The recent and spectacular release of the first results of the Wilkinson Microwave Anisotropy Probe (WMAP), indicate that the universe was reionized much earlier than what was previously believed [4]. This constitutes an enormous challenge to theoretical models of the formation of the Population III stars that are presumably responsible for reionizing the universe.

The formation of the first structures in the universe is linked to a central problem in cosmology: the nature of the dark energy. The observations of high-redshift supernovae in the late 1990's, and the recent results of WMAP indicate that about 2/3 of the energy content of the universe is in form of dark energy [4]. While the existence of dark energy is now well established, its nature remains unknown. The main candidates for dark energy are a nonzero cosmological constant, or a more complex form known as quintessence. The nature of the dark energy affects the growth of structures in the universe. Hence, by modeling the formation of the first structures in the universe and comparing the predictions of these models with high-redshift observations, we might be able to determine the nature of the dark energy.

Studying these various problems will require collaboration between observers who can provide the necessary data over a wide range of wavelengths and redshifts, and an expert in cosmology, structure formation, and numerical modelisation. The expertise in modelisation is crucial, as the problems being studied are far too complex to allow for any other approach. The astronomy group at Université Laval already has a wide expertise in observational astronomy. The purpose of this chair is to complement this existing observational strength with a theoretical cosmologist who has the proper expertise. I am an expert in numerical modeling of galaxy and large-scale structure formation in the universe, and star formation. I have pioneered the development of new and innovative numerical techniques, such as the Adaptive SPH algorithm. I also have a strong background in theoretical cosmology. I was one of the first to study dark energy (cosmological constant) and its effect on structure formation long before this was a popular idea. In retrospect, this early work can be regarded as pioneering, since the existence of the cosmological constant now seems well established. This expertise constitutes the perfect complement to the existing strengths of the astronomy group at Laval. The observers will greatly beneficiate from having a theorist around to help with the interpretation of the data, while I would greatly beneficiate from closely collaborating with observers who can provide such data. Finally, this chair fits into the Strategic Research Plan of the university, in which astrophysics and numerical simulations are identified as a priority.

In the remainder of this document, I give a brief summary of the research projects I would be conducting during the first years of this chair.

1. Formation and Evolution of X-ray Clusters in Cold Dark Matter (CDM) Models

Rich clusters of galaxies represent the largest structures in the universe to have undergone nonlinear gravitational collapse out of the expanding background universe, forming by the condensation of the matter originally within a region of radius about 10 Mpc as measured in today's universe. The richest clusters have temperatures above 10 keV, and sound speeds and galaxy velocity dispersions of order 1000 km/s. Rich clusters can be used to constrain cosmological models of large-scale structure formation in a variety of ways. Their abundance and its evolution are directly related to the shape and amplitude of the power spectrum P(k) of primordial linear density fluctuations that formed them and to the average properties of the universe as it effects the growth of these fluctuations. Observations suggest that the variance of the matter density field filtered on the scale of clusters at present is about one. This means that at earlier epochs, when the variance was smaller, such clusters were much rarer. Hence, a comparison of simulations with observations of clusters at a range of redshifts can discriminate strongly amongst models that nevertheless look similar at the present. Current simulation techniques do not yet have a sufficient resolution to yield a fully converged solution for the X- ray emitting gas inside clusters, failing to explain the luminosity function of clusters among other things [1,6,12]. I have pioneered the development of a new numerical gasdynamical algorithm called Adaptive Smoothed Particle Hydrodynamics (ASPH) [16,20], and have recently implemented into this algorithm a technique called particle splitting [9]. Particle splitting is a recent innovation that has not yet been applied to cosmological problems. I will use this ASPH code with particle splitting to study the cluster formation. This project is divided into 3 steps:
  1. Adiabatic Case. I will first perform a series of simulations of cluster formation within a cubic simulation volume 200 Mpc on a side. The advantage of using such a large volume is that several X-ray clusters will form, thus providing a good statistical sample that can be compared with observations. The drawback is that resolution is poor, but this problem will be eliminated by the use of particle splitting. I will perform several simulations with identical initial conditions but different levels of splitting, to study the convergence of the solution.
  2. Radiative Cooling and Galactic Feedback. I will redo the simulations described above, but with the inclusion of radiative cooling, a prescription for identifying galaxy formation, and the feedback of explosive energy release and heavy elements. Two particular questions I will address are: (1) what is the evolution of the distribution of metals in the intracluster gas, and how does this affect the evolution of the cluster? (2) Is the outflow from the central galaxies strong enough to stop and possibly reverse the cooling flow? This could explain why simple cooling flow models, which ignore feedback from galaxies, have problems reproducing observations.
  3. Comparison of the Properties of Simulated Clusters with Observational Data. All simulation results will be analyzed in comparison with observational data of individual X-ray clusters and the statistical properties of clusters. These include the luminosity-temperature relation for different redshifts, the gas and dark matter density, temperature, and velocity dispersion profiles.

2. Reionization of the Universe and Its Feedback Effect on Galaxy Formation

The universe was reionized before redshift z = 6 by a small fraction of the baryons in the universe, which released energy following their condensation out of the cold, dark, and neutral IGM into the earliest galaxies. The theory of this reionization is a critical missing link in the theory of galaxy formation. Its numerous observable consequences include effects on the spectrum, anisotropy, and polarization of the Cosmic Microwave Background (CMB) that affect the interpretation of measurements of cosmological parameters using current and future data. The recent release of the first results of the WMAP satellite [4] reveals that reionization occurred at a high redshift, of order z ~ 17, in conflict with the results from the Sloan Digital Sky Survey, which give a reionization redshift of z ~ 6. These results suggest that reionization might have occurred over an extended period of time, requiring a major revision of the current models.

The CDM model predicts that a large number of dark "minihalos" were present in the universe during the "dark ages" (z > 6). The presence of these minihalos can drastically affect the propagation of ionizing fronts. Previous work by my collaborators and myself [10, 11, 19] has shown that minihalos constitute an important sink of ionizing photons: these photons are used up to photoevaporate minihalos and are no longer available to reionize the diffuse IGM. The deposition of energy into the IGM by galactic outflows might also play a role in reionization, a possibility that I have investigated [13, 14, 15]. I intend to pursue this work by focusing on a few crucial problems in the theory of reionization and feedback. These include: (1) a comparison of the effects of reionization by starlight versus quasars; (2) the escape fraction of ionizing radiation from high-redshift galaxies which host stars and miniquasars; (3) the suppression of dwarf galaxies by reionization; (4) the heavy element enrichment of the IGM by SN-driven explosions and galactic winds from dwarf galaxies; and (5) the effect of feedback on the halo density profile" cuspy core" crisis of the standard CDM model.

To study these problems, I will use an Eulerian code with Adaptive Mesh Refinement that was developed by my collaborators, to simulate the photoevaporation of minihalos by the ionization fronts that reionized the IGM. Such simulations are essential to resolve the sub-kpc- scale of minihalos, which are likely to consume most of the ionizing photons during reionization. With this method, I will study the effect of radiation from stars and miniquasars inside early galaxies on their hosts, the amount and spectrum of the ionizing radiation that emerges from these hosts, and its feedback on the formation of other galaxies.

In parallel with this work, I will use my ASPH algorithm to study the effect of supernova- driven explosions during galaxy formation, in order to address 3 specific questions: (1) can the metals ejected by a galaxy travel far enough to "pollute" nearby galaxies, and eventually affect the star formation rate in these galaxies? (2) Is the amount of energy deposited into the IGM sufficiently large to completely reionize it? (3) How does the energy deposition affect the subsequent formation of other galaxies?

The results of WMAP are a major challenge to current models of reionization. This makes my recent and proposed research extremely timely, since it directly impacts the interpretation of the current models and the most up-to-date observations.

3. The Formation of Clusters and the Origin of the Initial Mass Function (IMF)

The determination of the IMF is possibly the most crucial problem in star formation. Since the IMF is the end product of the entire star formation process, predicting an IMF that reproduces observations is the critical test that any theory of star formation must pass. I have been studying this problem in recent years, and intend to pursue this work.

3.1. Part 1: High-Resolution Simulations of Cloud Fragmentation

Numerical simulations of molecular cloud fragmentation often use an isothermal equation of state, an approximation that is valid as long as the gas is optically thin. In an isothermal gas, the Jeans mass decreases with increasing density, and therefore any bound, collapsing clump is expected to fragment. The Jeans criterion [3] requires that each Jeans mass must contain a minimum number of particles to be properly resolved and prevent a spurious effect called artificial fragmentation. In standard SPH simulations, this criterion is eventually violated as the Jeans mass goes down, and the only solution to this problem is to implement particle splitting in the SPH algorithm. However, fragmentation will come to an end eventually, when the density reaches values of order 1010cm-3 and the isothermal approximation breaks down. I will use my ASPH algorithm with particle splitting to simulate the fragmentation of a molecular cloud over 10 orders of magnitudes in density, up to densities as large as 1012cm-3. The algorithm will use a two-component barotropic equation of state, isothermal at low densities and adiabatic at high densities [2,5]. These simulations will provide a critical test of the algorithm by demonstrating that it can automatically satisfy the Jeans criterion over any range of densities, and will provide the first single simulation of the fragmentation of a molecular cloud that can resolve the full mass spectrum of the IMF, down to the lowest possible Jeans masses.

The dynamical timescale of a cloud of mean density 102cm-3 is t = 2.2× 106 years. It is therefore possible to simulate, in a reasonable amount of CPU time, the evolution of the cloud over a timescale that exceeds the lifetime of the most massive stars. Such stars would eventually explode in supernovae. To simulate supernovae explosions, the algorithm will ascribe to each protostellar core a finite lifetime based on its mass. If a core reaches the end of its life before the simulation is completed, it will explode: the algorithm will remove the core, replace it by ASPH gas particles, and give an outward "kick" to these particles, adjusting their radial velocities in order to reproduce the amount of kinetic energy typically released by supernovae explosions. This modified algorithm will enable us to study two important processes: (1) the effect of supernovae feedback on the star formation history, and (2) the evolution of the metallicity inside the cloud. The release of large amounts of kinetic energy into the ISM can substantially affect the star formation rate, and the effect could go either way. On one hand, gas that is gravitationally bound inside clumps, and destined to form stars, might be blown away into low- density regions thus being prevented from forming a star or being accreted onto a preexisting clump. On the other hand, the shock wave created by the explosion will compress the surrounding gas to densities that might be large enough to trigger star formation. These simulations will enable us to assess the relative importance of these various processes.

3.2. Part 2: The Fragmentation of Dense Molecular Cloud Cores

I intend to simulate the fragmentation of a dense molecular cloud core. Observational studies of conditions in the cores forming massive clusters of stars indicate mean densities of 106cm-3 [17] and mean temperatures of about 50 K. I will simulate the evolution of these regions to form structures with densities as high as 1010cm-3, where the isothermal approximation breaks down. These simulations will extend previous work by simulating much higher densities, and by including additional physical effects. In addition, I will run simulations that test the sensitivity of the results to the cooling rate and the nature of kinetic energy injection. These simulations will allow me to address issues of how star formation would differ in gas of lower metallicity.

The most obvious form of feedback that should be included in simulations of cluster formation is the heating caused by radiation from forming stars. At early stages, the material around forming stars is highly opaque to the ultraviolet and visible photons produced by the hot stars, and they are all degraded to longer wavelengths through absorption and re-emission by dust grains. Based on detailed comparison of radiative transport codes [7,8] to observations of forming stars of various luminosities [21,22], we understand the behavior of the dust temperature profile Td(r) around a forming star quite well. For typical dust properties, Td(r) = 660K (L/Lsun)0.2(r/1 AU)0.4. At the high densities found in these simulations, the gas temperature will be equal to the dust temperature, allowing a fairly simple way to include radiative feedback. I will incorporate this heating by protostars into the algorithm, and investigate the effect of early star formation on the subsequent evolution of the rest of the core.

Incorporation of the kinetic energy feedback is less straightforward. While the jets from forming stars are quite anisotropic, we can begin to understand their effects in aggregate with some simple prescriptions for the input of turbulent energy into the core. Observational studies have established a strong correlation between the luminosity of the forming star and the kinetic energy injection rate. Theoretical arguments [18] suggest that the balance between energy injection rate and dissipation leads to a relationship in which the feedback energy scales as the 2/3 power of the star formation rate. I will experiment with various formulations of this feedback, applying the constraint that the result must match the observed conditions in cluster- forming cores. Once we include kinetic energy feedback, we must also include a more sophisticated treatment of the energetics. The kinetic energy input will create shocks, raising the gas temperature above the dust temperature temporarily. To follow the gas temperature, I will consider both gas cooling and the coupling to dust, which will act as a coolant when the gas temperature exceeds the dust temperature.

SPH simulations of outflows and jets inside molecular clouds have shown that in presence of radiative cooling, a large amount of momentum can be transferred into the ISM. I propose to use a similar approach and redo the simulations described above, "turning on" the jets whenever the density of a clump reaches a certain threshold value. Using these simulations, I will address two specific questions: (1) how does the presence of winds and jets coming out of a young stellar object affect the final mass of that object? and (2) once the first dense objects form and start emitting jets, what is the effect of these jets on the subsequent formation of stars, the overall evolution of the molecular cloud, and the final form of the IMF?

4. Training and Supervision Activities Envisaged

This research program is very labor intensive, and will provide research opportunities for several students. Each of the four projects described above (in sections 1, 2, 3.1, and 3.2) could lead to a Ph.D. dissertation. Also, various subparts of these projects would be suitable for a Master's dissertation. Overall, this program has the potential to train several graduate students, who would acquire skills and expertise in areas ranging from theoretical cosmology and theory of star formation, to high-performance numerical gasdynamical simulation and modeling of observational data. Furthermore, this research program will lead to the development of innovative numerical simulation algorithms, analysis and visualization software that will be available to future students and researchers in the department. Finally, the development of a strong basis in theoretical and computational cosmology at Université Laval will likely attract graduate students in this field.

REFERENCES