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.