# Works

## Published Works

We propose an efficient and robust method to estimate the halo concentration based on the first moment of the density distribution, which is $R_1\equiv \int_0^{r_{\rm vir}}4\pi r^3\rho(r)dr/M_{\rm vir}/r_{\rm vir}$. We find that $R_1$ has a monotonic relation with the concentration parameter of the NFW profile, and that a cubic polynomial function can fit the relation with an error $\lesssim 3\%$. Tests on ideal NFW halos show that the conventional NFW profile fitting method and the $V_{\rm max}/V_{\rm vir}$ method produce biased halo concentration estimation by $\approx 10\%$ and $\approx 30\%$, respectively, for halos with 100 particles. In contrast, the systematic error for our $R_1$ method is smaller than $0.5\%$ even for halos containing only 100 particles. Convergence tests on realistic halos in $N$-body simulations show that the NFW profile fitting method underestimates the concentration parameter for halos with $\lesssim 300$ particles by $\gtrsim 20\%$, while the error for the $R_1$ method is $\lesssim 8\%$. We also show other applications of $R_1$, including estimating $V_{\rm max}$ and the Einasto concentration $c_{\rm e}\equiv r_{\rm vir}/r_{-2}$. The calculation of $R_1$ is efficient and robust, and we recommend including it as one of the halo properties in halo catalogs of cosmological simulations.

We propose a novel method to quantify the assembly histories of dark matter halos with the redshift evolution of the mass-weighted spatial variance of their progenitor halos, i.e. the protohalo size history. We find that the protohalo size history for each individual halo at z~0 can be described by a double power-law function. The amplitude of the fitting function strongly correlates to the central-to-total stellar mass ratios of descendant halos. The variation of the amplitude of the protohalo size history can induce a strong halo assembly bias effect for massive halos. This effect is detectable in observation using the central-to-total stellar mass ratio as a proxy of the protohalo size. The correlation to the descendant central-to-total stellar mass ratio and the halo assembly bias effect seen in the protohalo size are much stronger than that seen in the commonly adopted half-mass formation time derived from the mass accretion history. This indicates that the information loss caused by the compression of halo merger trees to mass accretion histories can be captured by the protohalo size history. Protohalo size thus provides a useful quantity to connect protoclusters across cosmic time and to link protoclusters with their descendant clusters in observations.

We use the most recent data release (DR9) of the DESI legacy imaging survey and SDSS galaxy groups to measure the conditional luminosity function (CLF) for groups with halo mass $M_{\rm h}\ge 10^{12}M_{\odot}$ and redshift $0.01\le z\le 0.08$, down to a limiting $r$-band magnitude of $M_{\rm r}=-10\sim-12$. For a given halo mass we measure the CLF for the total satellite population, as well as separately for the red and blue populations classified using the $(g-z)$ color. We have the following findings:

- A clear faint-end upturn is seen in the CLF of red satellites, with a slope $\alpha\approx-1.8$ which is almost independent of halo mass, This faint-end upturn is not seen for blue satellites and for the total population.
- Our stellar population synthesis modeling shows that the $(g-z)$ color provides a clean red/blue division, and that group galaxies in the red population defined by $(g-z)$ are all dominated by old stellar populations.
- The fraction of old galaxies as a function of galaxy luminosity shows a minimum at a luminosity $M_{\rm r}\sim-18$, corresponding to a stellar mass $M_\ast\sim10^{9.5}M_\odot$. This mass scale is independent of halo mass and is comparable to the characteristic luminosity at which galaxies show a dichotomy in surface brightness and size, suggesting that the dichotomy in the old fraction and in galaxy structure may have a common origin.
- The rising of the old fraction at the faint end for Milky Way (MW)-sized halos found here is in good agreement with the quenched fraction measured both for the MW/M31 system and from the ELVES survey.
- We discuss the implications of our results for the formation and evolution of low-mass galaxies, and for the stellar mass functions of low-mass galaxies to be observed at high redshift.

By employing three approaches to generate the mock HI density from an N-body simulation at low z, we check the assumption that HI gas traces the matter density distribution linearly on large scales. Our main findings are:

- The assumption of HI linearity is valid at the scale corresponding to the first BAO peak, but breaks down at $k \geq 0.1 h {\rm Mpc}^{−1}$.
- The nonlinear effects of halo clustering and HI content modulation counteract each other at small scales, and their competition results in a model-dependent “sweet-spot” redshift near z=1 where the HI bias is scale-independent down to small scales.
- The linear HI bias scales approximately linearly with redshift for z ≤ 3.

We develop an empirical model pipeline, *MAHGIC*, to populate dark matter halos with galaxies.
The main features of the model and our main results include:

- PCA and GBDT learners are used to transform halo properties to galaxy properties.
- Two sets of hydrodynamic simulations, TNG and EAGLE, are used to train the model, which is then applied to other DMO simulations.
- The model can reproduce a variety of statistical properties of galaxies. It is verified reliable, flexible and accurate.

Our study provides a framework of using hydrodynamic simulations to discover, and to motivate the use of, key ingredients to model galaxy formation using halo properties. Our findings include:

- The SFH of central galaxies are tightly related to halo MAH.
- The classification of SF and quenched populations has significant contamination.
- We propose a multi-stage halo-based empirical model for the star formation in central galaxies, which reproduces many galaxy statistics and galaxy-halo relations including assembly bias.

We build mock galaxy catalogs for high-z galaxy surveys, and we propose methods to measure GLFs, GSMFs and 2PCFs at high-z Universe. Our findings include:

- Our methods of estimating GLFs, GSMFs and 2PCFs reliably cancel the bias from target selection and sample imcompleteness.
- Mock catalogs are constructed for zCOSMOS-bright sample and PFS galaxy evolution survey.
- We quantify the cosmic variance using the mocks, and find the cosmic variance is reduced by a factor of 3-4 in PFS compared with zCOSMOS.

We develop a method to identify proto-clusters based on dark matter halos at high redshift. Our main findings include:

- The test with N-body simulations shows that our finder has completeness $\sim 85\%$, purity $\geq 90\%$, mass estimates uncertainty $ \leq 0.25 {\rm dex}$.
- Our method can recover progenitor stellar mass distribution, providing an avenue to link high-z and low-z galaxies in clusters.

We extend the halo-based group finder to use data simultaneously with either photometric or spectroscopic redshifts. The performance is evaluated with a mock from N-body simulation. Our main results include:

- For magnitude $z \leq 21 $ galaxies in DESI, $\geq 60\%$ members in $\sim 90\%$ halos with $M_{\rm h} \geq 10^{12.5} h^{-1}M_\odot$ can be identified. Detected groups with $M_{\rm h} \geq 10^{12} h^{-1}M_\odot$ has purity $\geq 90\%$.
- Group mass assignment has uncertainty from 0.2 dex (high mass end) to 0.45 dex (low mass end).
- Group with 10 members has redshift accuracy $\sim 0.08$.
- A group catalog is provided for DR8.

We use a large N-body simulation to study the relation of structural properties of dark matter halos to their assembly history and environment. Our main conclusions are:

- The complexity of individual halo assembly histories can be well described by a small number of principal components, which are preferred over formation times for several reasons.
- 60%, 10%, 20% of the variances in halo concentration, axis ratio and spin, respectively, can be explained by combining four dominating predictors $\rm PC_{MAH,1}$, $M_{\rm halo}$, $\alpha_\mathcal{T}$, $b$. Degeneracies between predictors are found and analyzed, and are still hold for mass-binned samples.
- Tidal field provides important environmental information, with $\alpha_\mathcal{T}$ shows strongest assembly bias signal.

High-z spectroscopic surveys, usually incomplete in redshift sampling, present both opportunities and challenges to identifying groups in the high-z Universe. We develop a group finder that is based on incomplete redshift samples combined with photometric data. Our main findings are:

- Mock test shows that $\geq 90\%$ of groups with $M_{\rm h}\geq 10^{12} h^{-1}{\rm M}_\odot$ are successfully identified.
- The standard deviation in the halo mass estimation is smaller than 0.25 dex at all masses.
- We apply our group finder to zCOSMOS-bright and describe basic properties of the group catalog obtained.

We propose a method based on conditional stellar mass functions to estimate global GSMF. Our findings include:

- We extend the halo merger trees from N-body simulation to a higher resolution.
- We use constrained N-body simuation and empirical approach to construct a 'real' mock catalog, which recovers the galaxy distribution in the local Universe (SDSS volume).
- The low-mass end GSMF estimated from SDSS sample can be significantly affected by the Cosmic Variance (CV).
- We propose a new method based on CGSMF, provide unbiased estimate of GSMF which show significant upture below $M_* \leq 10^{9.5} h^{-1}{\rm M}_\odot$ and is missed in many earlier works.

## Part-Time Works

Major contributor in the development of the following websites:

- LIG: the data server of the galaxy and cosmology group in Tsinghua DoA.
- Tsinghua High-z Team: the homepage of the high-z team in Tsinghua DoA.
- ELUCID-project: the data server of the ELUCID project.

Developer of the following softwares:

- HIPP: a modern C++ toolkit for HPC.
- PyHIPP: a modern Python toolkit for HPC.
- TwoPhaseGalaxyModel: A two-phase model of galaxy formation.
- HaloFactory: Semi-analytical dark matter halo generators.
- HaloProps: a calculator/predictor for halo structural properties. Python API and web application are available.
- AstroHammer: lectures on astronomical techniques for beginners.