| 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. |
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.
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.
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.
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?
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:
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.
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:
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.
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.
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.
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