Spatial clustering and mass function of dark matter halos:
My main contribution here is the development of an analytical model for
the spatial clustering of dark haloes. The results are published in
Mo and White (1996).
This model has been used extensively to study the
clustering properties of galaxies and clusters of galaxies. Together
with the model for the high-order moments of the halo distribution
developed by
Mo, Jing & White (1997), it provides the basis for what
is now known as the `halo occupation model' for galaxy clustering.
Sheth, Mo & Tormen (2001) extended the widely-used
Press-Schechter formalism by incorporating ellipsoidal collapse, and
showed that the resulting mass function and halo bias are much more
accurate than the original Press-Schechter formalism. This extension
not only provides a more accurate model for the mass
and correlation functions of dark matter halos, but also allows
one to model how the formation of dark matter halos depends on the
large-scale environments.
Formation, structure of CDM halos and their environmental dependence:
In Zhao et al. (2003a;b), we found that the build-up of
dark halos in current CDM models generally consists of an early
phase of fast accretion followed by a phase of slow accretion.
Halos in the two accretion phases show systematically different
properties. Subsequently, in Lu, Mo, Katz \& Weinberg (2006),
it is shown that such formation histories may play an important role
in generating the universal halo density profile observed in
cosmological $N$-body simulations. The results obtained by Lu et al.
may provide important clue about the origin of the CDM dark matter halo profiles.
Zhao et al. (2009) constructed accurate models for the formation
histories and structure of dark matter halos. In Wang et al. (2007;
2011), we used simulations to study how the in internal properties
of dark matter haloes are affected by environmental effects, and we
found that the large-scale tidal field is driving factor of many
environmental effects seen in the simulations. A more thorough
analysis along the line was carried out by Shi et al. (2015) which
includes also flow patterns around halos.
Formation and structure of galaxies:
My main contribution here is the development of a model of disk
galaxy formation in a cosmological context. The results were published
in Mo, Mao & White (1998), and the model has been widely adopted
to study galaxy formation and evolution. In Shen et al. (2003) we used the
SDSS galaxies to study how the sizes of disk and elliptical galaxies
depend on galaxy luminosity/stellar mass, and a theoretical model is
constructed to interpret the observational results. More recently,
Lu, Mo & Wechsler (2015) investigated how galaxy disks grow their sizes
in dark matter halos due to radiative cooling and feedback.
Galaxy groups and the properties of galaxies in dark matter halos:
During the last ten years, my collaborators and I have embarked on a research program
to understand how galaxies form in dark matter halos as represented
by galaxy groups selected from large redshift surveys. We developed
a very successful group finder which can group galaxies together
according to their common halos (Yang et al. 2005), and
have applied the group finder to
the 2-degree Galaxy Redshift Survey (2dFGRS) and the Sloan Digital
Sky Survey (SDSS) (Yang et al. 2007). These catalogs allowed us to
carry out systematic analyses about how the properties
of galaxies are affected by their host halos. So far, this program has
produced more than 20 published papers.
Galaxy-halo connection:
According to the current paradigm of structure formation,
galaxies form and reside inside extended cold dark matter
(CDM) halos. One of the ultimate challenges
in astrophysics is to obtain a detailed understanding of how
galaxies with different properties are linked to
halos of different masses and in different environments.
This link between galaxies and dark matter halos is an
imprint of various complicated physical process related to galaxy
formation (such as gravitational instability, gas cooling, star formation,
merging, tidal stripping and heating, and a variety of feedback
processes), and its establishment is pivotal for the understanding
of galaxy formation and evolution.
In the past 10 years, my colleagues and I have worked on various
aspect of the problem. In Yang et al. (2003) we developed a
conditional luminosity function (CLF) model to link galaxies of
different luminosities/stellar masses to dark matter halos of
different masses. Later, we extended our model to the modeling of how
star formation and stellar mass assembly histories of galaxies are
related to the growth of their host halos (Yang et al. 2012; 2013).
In Lu Z. et al. (2014; 2015), we used observations at both low and high
redshifts to constrain various aspects of the halo-galaxy connection.
Reconstructing current and initial cosmic density fields:
A key step in understanding the galaxy formation processes
throughout the cosmic density field is to study the distribution
and properties of galaxies and the intergalactic medium (IGM),
and their interactions both with each other as well as with the
dark matter. Thus, a synthesized investigation of the different
components of the cosmic web is necessary. To this end,
we have developed a method to accurately reconstruct
the current cosmological density field using galaxy groups
(halos) as mass tracers (Wang et al. 2009), and to reconstruct
the initial conditions that are responsible for the underlying density
field at the present day (Wang et al. 2013; 2014). We have used the
reconstructed current mass density field from SDSS to obtain the
cosmic velocity and tidal fields
(Wang et al. 2012). These results have been used to
show the flow patterns in different regions and to
study the alignments of galaxy shapes with the large-scale tidal fields
(Zhang et al. 2013; 2015). We are now carrying out detailed
constrained simulations in various volumes of the Universe to study
their formation histories.
Semi-analytical model of galaxy formation
In the semi-analytic approach one starts with a catalog of merger
trees that describe the assembly of individual dark matter halos.
For the current cold dark matter cosmogony, accurate merger trees can be
generated straightforwardly either using Monte-Carlo methods
or using dark matter-only N-body simulations.
All the additional physical processes,
including gas cooling and accretion, galaxy mergers, star formation,
supernova and AGN feedback, metal enrichment, etc., are included
through parameterized functions.
The widespread appeal of SAMs is their promise to constrain
the space of plausible physical mechanisms and, in the end, to understand
the importance of particular mechanisms and scenarios based on the prescriptive
input physics. We have created a general SAM framework for the
BIE (a Bayesian Inference Engine) and have explored prior
sensitivity and multi-modalities in the parameter estimation.
(Lu Y. et al. 2011). We have used our model to infer model constraints
from a number of observations (Lu Y. et al. 2012; 2014).
We anticipate this will become
a widely used theoretical tool, because for the first time one will be able
to use the real power of the semi-analytical approach to rigorously
constrain galaxy formation physics.
Galaxy formation and preheating
The cold dark matter (CDM) model of structure formation has proven a very
successful paradigm for understanding the large-scale structure
of the Universe. However, as far as galaxy formation is concerned,
a number of important issues still remain. CDM models in general
predict too many low-mass dark matter halos compared to the observed
number density of galaxies. In any CDM model, including the standard
Lambda-CDM model, the mass function of dark matter halos, n(M),
goes roughly as the inverse of mass squared at the low-mass end. This is in
strong contrast with the observed luminosity function of galaxies,
which has a rather shallow faint end slope. The efficiency of star formation
in dark matter halos must therefore be a strongly nonlinear function of
halo mass. One of the most challenging problems in galaxy formation today
is to explain the origin of such a relationship and more generally to
understand the relationship between dark halos and star formation.
A number of physical processes have been proposed to suppress the star
formation efficiency in halos with relatively low masses.
These include photoionization heating by the UV
background and energy feedback from supernovae. However,
the models considered so far fail to provide a satisfactory solution,
particularly when one considers the observed HI mass function.
In Mo & Mao (2002; 2014), we proposed a promising alternative, a model
in which the medium around low-mass halos is preheated by early
starbursts and AGN activities. Such a model seems to match many
observed properties of low-mass galaxies, as shown in
Lu, Mo & Wechsler (2015), Lu Y., Mo & Lu Z. (2015) and
Lu Z., Mo & Lu Y. (2015).
Galaxy-galaxy lensing:
Observations of the image distortions of background
galaxies by the gravitational lensing effect of foreground
galaxies can be used to infer the mass distribution
of dark halos around individual galaxies in a statistical
way. Currently the best observational results
are from the SDSS, and it is now well established that
the mass of dark halo depends significantly both on galaxy
luminosity and on morphological type.
With the completion of the the SDSS, and observations from
forthcoming surveys, such as the CFHTLS, PFS, LSST, etc, a great
wealth of data will be available to probe the properties of
dark halos around different galaxies, and one expects to learn a
great deal about the galaxy-halo connection from such observations.
If lensing galaxies are assigned to groups faithfully according to
common dark halo, one can divide galaxies not only according to their
intrinsic properties, such as luminosity, color and type, but also
according to the masses of their host halos and their locations in the host
halos. By studying the lensing effects separately for
galaxies in different divisions, one will be able to
infer the properties of dark halos around isolated
central galaxies, as well as the properties of the subhalos
associated with satellite galaxies at different
radii in the host halos. Some promising results have already
been obtained (Li et al. 2014; 2015). In addition we can combine
galaxy-galaxy lensing observations and other statistical properties
of galaxies to constrain cosmology (e.g. Cacciato et al. 2013).
Galaxy clustering:
I have been interested in using different statistical methods to
characterize galaxy clustering in space.
Mo, Jing and Boerner (1993) were the first to find that the pairwise
velocity dispersion (PVD) of galaxies (for which earlier analysis
gave a very low value, which was the main reason for
the introduction of a high level of bias in the CDM cosmogony)
is very sensitive to the presence (or absence) of rich clusters in a
sample and the samples used in earlier studies were too small to give a fair
estimate of this quantity. This conclusion has since been confirmed
by many other authors. Jing, Mo & Boerner (1998) were the first to
obtain a reliable value of the PVD from the Las Campanas
Redshift Survey and show that the prediction of the current
Lambda-CDM model is consistent with observational data. These
results were subsequently confirmed by recent results based on
the 2dFGRS and the SDSS. More recently, we have used SDSS
samples to study how galaxy clustering depends on various intrinsic properties
of galaxies (e.g. Wang et al. 2007; 2008).
Mo & Fukugita (1996) was the first to predict that the Lyman-break
galaxies observed at redshift z~3 should be highly biased
relative to the underlying mass. These results have been confirmed
by various recent observations and theoretical modeling.
Mo, Mao & White (1999) proposed that
the observed number density and clustering strength
of galaxies can be used to infer the masses of their host halos.
Ths idea, called Halo Abundance Matching, has been widely adopted in
establishing the links between galaxies and dark matter halos.
Gaseous galaxy halos and QSO absorption line systems:
Mo (1994) and Mo & Miralda-Escude (1996) developed a model for the
gaseous structure of halos, and applied it to understand
QSO absorption line systems associated with galaxies.
More recently, a number of numerical simulations show that
this model may also describe how galaxies accrete the cooling gas
from their dark matter halos.
Mo & Miralda-Escude (1994) were the first to find that the total
HI mass associated with QSO damped Lyman alpha absorption line
systems can put stringent constraints on models of structure
formation. In particular, they found that the mixed
dark matter (MDM) model does not have enough clustering power on small
scale to match the observations. This triggered a series of
re-investigations of the original MDM model.