arXiv subjects

Wenxiang Pei

Publications and source records attributed to Wenxiang Pei.

At least 19 recordsLinked to original sources

arXiv2026

Exploring Primordial Non-Gaussianity Measurements in the CSST Spectroscopic Survey

Primordial non-Gaussianity (PNG) is a fundamental probe of the physics of the early Universe and inflation. Here we present a comprehensive study of the constraints on the local-type PNG parameter, $f_{\rm NL}$, for the spectroscopic galaxy survey of the upcoming Chinese Space-station Survey Telescope (CSST). Utilizing the high-resolution Jiutian N-body simulation suite, we construct realistic mock catalogs for emission line galaxies (ELGs) at three representative redshifts $z=0.3$, 0.6, and 0.9. The expected CSST observational characteristics are also considered, including redshift uncertainties and selection functions based on signal-to-noise ratios of emission lines. We develop a robust analysis framework for the redshift-space galaxy power spectrum and bispectrum that accounts for redshift-space distortions, scale-dependent bias, and nonlinear effects. Through a joint Markov Chain Monte Carlo (MCMC) analysis, we find that the power spectrum alone provides competitive constraints, while the inclusion of the bispectrum, specifically targeting the squeezed-limit configurations, improves the $f_{\rm NL}$ constraint precision by approximately 5%-6%. Our joint analysis yields a constraint result of $f_{\rm NL}=-20\pm52$ for the mock data in the 1~($h^{-1}$Gpc)$^3$ comoving volume at the three redshifts, and the constraint accuracy is expected to be improved by several times or even one order of magnitude for the CSST full spectroscopic survey. This work demonstrates the potential of the Stage~IV surveys like CSST to probe inflationary physics, and highlights the importance of higher-order statistics in extracting information from large-scale structure surveys.

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arXiv2026

Cross-Comparison of Galaxies Detected in the CSST Spectroscopic Survey and the SKA HI Survey

We present a forward-modeling framework to forecast the galaxies detected in the Chinese Space Station Survey Telescope (CSST) spectroscopic survey and the Square Kilometre Array (SKA) HI survey. Starting from the L-Galaxies 2020 semi-analytic model run on the Millennium-II N-body simulation (MS-II), the cold gas in galaxies is partitioned into atomic and molecular components self-consistently within the model. We further model the emission-lines (H $α$, H $β$, O III) relevant for the slitless spectrograph of the CSST in a post-processing step. We construct mock lightcones using the Mock Map Facility (MoMaF) approach, simulating the neutral hydrogen (HI) data cubes representing a 2000 hour SKA-Mid spectral line observation from redshifts 0.25--0.5, and employ the Source Finding Application 2(SOFIA-2) source-finding package to generate an HI galaxy catalog. In parallel, we apply the CSST selection function and noise model to obtain a realistic catalog of emission-line galaxies; the emission-line signal is proportional to the star formation rate. These products allow us to cross compare the galaxy samples and assess the synergy between CSST and SKA. We study the correlations of the HI and the emission-line signal with the halo mass, HI mass, and the stellar mass, and the baryonic Tully-Fisher relation (BTFR). We also perform stacking analysis of the HI signal from the CSST-selected sample, which probes the HI content in galaxies with low HI mass. Finally, we derive the optical-HI cross-correlation power spectrum of the galaxies, and measure the bias of these galaxies. These results can provide useful insight on the cold gas and stellar content of the galaxies.

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arXiv2026

Modeling the Spectral Energy Distribution of Active Galactic Nuclei: Implications for Cosmological Simulations of Galaxy Formation

Modeling the spectral energy distribution (SED) of active galactic nuclei (AGN) plays a very important role in constraining modern cosmological simulations of galaxy formation. Here, we utilize an advanced supermassive black hole (SMBH) accretion disk model to compute the accretion flow structure and AGN SED across a wide range of black hole mass ($M_{\rm SMBH}$) and dimensionless accretion rates $\dot{m}(\equiv \dot{M}_{\rm acc}/\dot{M}_\mathrm{Edd})$, where $\dot{M}_{\rm acc}$ is the mass flow rate through the disk and $\dot{M}_\mathrm{Edd}$ is the Eddington mass accretion rate. We find that the radiative efficiency is mainly influenced by $\dot m$, while contributions of $M_{\rm SMBH}$ and $\dot{m}$ to the bolometric luminosity are comparably important. We have developed new scaling relationships that relate the bolometric luminosity of an AGN to its luminosities in the hard X-ray, soft X-ray, and optical bands. Our results align with existing literature at high luminosities but suggest lower luminosities in the hard and soft X-ray bands for AGNs with low bolometric luminosities than commonly reported values. Combining with the semi-analytical model of galaxy formation \textsc{L-Galaxies} and Millennium dark matter simulation for the distribution of ($M_{\rm SMBH}, \dot{m}$) at different redshift, we find the model predictions align well with observational data at redshifts below 1 but deviates for higher redshifts regarding AGN detection fraction and luminosity functions. This deviation may arise from improper treatment of SMBH growth at high redshifts in the model or bias from limited observational data. This AGN SED calculation can be readily applied in other cosmological simulations.

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arXiv2026

Reproducing Abell 2744 with the HyperMillennium Simulation

We present the Hyper Millennium (HM) simulation, an extremely large cosmological simulation designed to support next-generation galaxy surveys. The simulation follows 4.2 trillion dark matter particles in a comoving box of $2.5\ h^{-1}{\rm Gpc}$, with a mass resolution of $3.2 \times 10^8\, {h^{-1}\rm M_{\odot}}$ and a force resolution of $3.0\ h^{-1}{\rm kpc}$. Its combination of scale and resolution is ideal for studying large-scale structures and rare cosmic objects. In this first paper of the HM project, we explore whether the massive galaxy cluster Abell~2744 (A2744) can be reproduced in detail in the simulation. Pixel-based statistics of galaxy number density $N_{\rm gal}$, luminosity density $L_{\rm gal}$, and projected mass density $κ$ show excellent agreement between A2744 and its analogues down to $\sim 50$ kpc, once field-selection biases toward high galaxy surface density are accounted for. This concordance, achieved in one of the most extreme known galaxy environments, is a validation of the underlying $Λ{\rm CDM}$ model in the extreme regime of A2744. It also showcases the robustness and accuracy of the HM simulation, which, when coupled with a sophisticated semi-analytic galaxy formation model, is capable of producing galaxy and mass catalogues of comparable quality out to high redshift across its full comoving volume of 50.4 ${\rm Gpc^3}$.

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arXiv2026

Cosmological Prediction from the joint observation of MeerKAT and CSST at $z$ = 0.4 $\sim$ 1.2

Cross-correlating neutral hydrogen (HI) 21cm intensity mapping with galaxy surveys provides an effective probe of astrophysical and cosmological information. This work presents a cross-correlation analysis between MeerKAT single-dish HI intensity mapping and Chinese Space Station Survey Telescope (CSST) spectroscopic galaxy surveys in $z=0.4\sim1.2$, which will share a survey area of several thousand square degrees. Utilizing Jiutian-1G cosmological simulation, we simulate the observational data of MeerKAT and CSST with survey areas from $\sim1600$ to $600$ deg$^2$ at $z=0.5$, 0.7, and 1. The effects of beam pattern, polarization leakage, and different foregrounds in the MeerKAT HI intensity mapping are considered in the simulation. After employing foreground removal with the principal component analysis (PCA) method and performing signal compensation, we derive the cross-power spectra of MeerKAT and CSST. We perform the joint constraint using the CSST galaxy auto-power spectra and MeerKAT-CSST cross-power spectra with the least-squares fitting method. The constraint results show that, in the simulated survey area, the relative accuracy can achieve $6\%\sim 8\%$ for the parameter products $Ω_{\rm HI}b_{\rm HI}b_{g}r_{\mathrm{HI},g}$ and $Ω_{\rm HI}b_{\rm HI}r_{\mathrm{HI},g}$ at the three redshifts, which is $3\sim4$ times smaller than the current result. These findings indicate that the full MeerKAT-CSST joint observation with thousands of square degrees overlapping survey area can be a powerful probe of large-scale structure, and has the ability to provide information of cosmic evolution of HI and galaxies in a wide redshift range.

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arXiv2026

Exploring Cosmological Constraints of the Void-Lensing Cross-Correlation in the CSST Photometric Survey

We investigate the cosmological constraints from the void-lensing cross-correlation assuming the $w$CDM model for the Chinese Space Station Survey Telescope (CSST) photometric survey. Using Jiutian simulations, we construct a mock galaxy catalog to $z=3$ covering 100 deg$^2$, which incorporates the instrumental and observational effects of the CSST. We divide the galaxy sample into seven photometric-redshift (photo-$z$) tomographic bins and identify 2D voids within each bin using the Voronoi tessellation and watershed algorithm. We measure the angular cross-power spectrum between the void distribution and the weak lensing signal, and estimate the covariance matrix via jackknife resampling combined with pseudo-$C_{\ell}$ approach to account for the partial sky correction. We employ the Halo Void Dust Model (HVDM) to model the void-matter cross-power spectrum and adopt the Markov Chain Monte Carlo (MCMC) technique to implement the constraints on the cosmological and void parameters. We find that our method can accurately extract the cosmological information, and the constraint accuracies of some cosmological parameters from the void-lensing analysis are comparable or even tighter than the weak lensing only case. This demonstrates that the void-lensing serves as an effective cosmological probe and a valuable complement to galaxy photometric surveys, particularly for the Stage-IV surveys targeting the high-redshift Universe.

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arXiv2026

Revised AGN Spectral Model Reveals a More Significant Role in Cosmic Reionization

Reionization marks one of the most important phase transitions in the history of the Universe, during which neutral baryonic matter was transformed into ionized plasma. While star-forming galaxies are widely regarded as the primary drivers of this process, the extent to which active galactic nuclei (AGNs) contribute remains a subject of ongoing investigation. In this study, we integrate a physically motivated AGN spectral energy distribution (SED) model with state-of-the-art observations to reassess the contribution of AGNs to cosmic reionization. Our findings indicate that adopting a more sophisticated AGN SED model could substantially increase the predicted ionizing photon output by a factor of 3$\sim$4, elevating AGNs to a more significant role ($\approx$20\%) in maintaining reionization than previously estimated. The inclusion of abundant faint AGNs further amplifies this contribution by a factor of a few. These conclusions remain robust across a wide range of accretion rates and ionizing photon escape fractions. Collectively, our results suggest that AGNs may have played a more prominent and previously underestimated role in the reionization of the Universe.

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arXiv2025

Forecasting the Constraint on the Hu-Sawicki $f(R)$ Modified Gravity in the CSST $3\times2$pt Photometric Survey

We forecast the constraint on the Hu-Sawicki $f(R)$ model from the photometric survey operated by the Chinese Space Station Survey Telescope (CSST). The simulated $3\times2$pt data of galaxy clustering, weak lensing, and galaxy-galaxy lensing measurements within 100 deg$^{2}$ are used in the analysis. The mock observational maps are constructed from a light cone, redshift sampling and noise. The angular power spectra are measured with pseudo-$C_\ell$ estimators and compared to theory in the same basis using validated weighting functions and an analytic covariance matrix that includes Gaussian, connected non-Gaussian, and super-sample terms. We model the theoretical spectra using two methods. The first one uses MGCAMB to compute the linear modified-gravity clustering power spectra, and the second one adopts the FREmu emulator with a baseline of nonlinear $Λ$CDM prescription. Parameter inference is performed with Cobaya, and the cosmological and modified-gravity parameters are sampled within the emulator training domain, which is jointly fitted with the systematic parameters. We find that the predictions from the two methods are in good agreement at the overlapping large scales, and the emulator method can correctly provide additional high-$\ell$ information. The $1σ$ upper bounds of $\log_{10}|f_{R0}|$ are found to be $<-5.42$ for cosmic shear only case and $<-5.29$ for the 100 deg$^2$ CSST $3\times2$pt probe. The full CSST photometric survey with 17,500 deg$^2$ survey area is expected to further improve the constraint precision by about one order of magnitude. Our results demonstrate that the CSST $3\times2$pt survey can deliver strict tests on $f(R)$ gravity.

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arXiv2025

A semi-analytical mock galaxy catalog for the CSST extragalactic surveys from the Jiutian simulations

We introduce a mock galaxy catalog built for the CSST extragalactic surveys using the primary runs of the Jiutian $N$-body simulation suites. The catalogs are built by coupling the GAlaxy Evolution and Assembly (GAEA) semi-analytical model of galaxy formation with merger trees extracted from the simulations using the Hierarchical Bound-Tracing (HBT+) algorithm. The spectral energy distributions (SEDs) and broadband magnitudes are computed using the neural-network-based stellar population synthesizer StarDuster, which is trained on radiative transfer simulations to account for detailed galaxy geometry in modeling dust obscuration. Galaxy light-cones up to $z=5$ are subsequently generated with the BLiC light-cone builder which interpolates the properties of galaxies over time using an optimized interpolation scheme. The resulting catalogs exhibit good convergence in many statistical properties of the galaxy population produced from two different resolution simulations. The catalogs reproduce a number of observed galaxy properties across a range of galaxy mass and redshift, including the stellar mass functions, the luminosity function, gas mass fraction, galaxy size-mass relation and galaxy clustering. We also present the photometric and redshift distributions of galaxies expected to be observed in the CSST surveys.

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arXiv2025

Identifying Dust-lane Spheroidal Galaxies in DESI Legacy Imaging Surveys Using Semi-Supervised Methods

Dust-lane spheroidal galaxies (DLSGs) are unique astrophysical systems that exhibit the morphology of early-type galaxies (ETGs) but are distinguished by prominent dust lanes. Recent studies propose that they form through minor mergers between ETGs and gas-rich dwarf galaxies, offering a window into the interstellar medium (ISM) of ETGs and star formation triggered by small-scale interactions. However, their rarity poses a challenge for assembling large, statistically robust samples via manual selection. To overcome this limitation, we employ GC-SWGAN, a semi-supervised learning method developed by \citet{2025ApJS..279...17L}, to systematically identify DLSGs within the DESI Legacy Imaging Surveys (DESI-LS). The methodology involves training a generative adversarial network (GAN) on unlabeled galaxy images to extract morphological features, followed by fine-tuning the model using a small dataset of labeled DLSGs. In our experiments, despite DLSGs constituting only $\sim$ 3.7\% of the test set, GC-SWGAN achieves remarkable performance, with an 87\% recall rate, 84\% accuracy, and an F1 score of 86\%, underscoring its efficacy for DLSG detection. Applying this model to $\sim$ 310,000 DESI-LS galaxies that meet the criteria $m_r < 17.0$ and $0.01 < z < 0.07$ we compile the largest catalog of DLSG candidates to date, identifying 9,482 dust-lane ETGs. A preliminary analysis reveals that these DLSGs exhibit significantly redder $g-r$ colors and higher specific star formation rates compared to non-DLSGs. This catalog enables future studies of ISM properties in ETGs and the role of minor mergers in driving star formation in the nearby universe.

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arXiv2025

The Jiutian simulations for the CSST extra-galactic surveys

We provide an overview of the Jiutian simulations, a hybrid simulation suite for the China Space Survey Telescope (CSST) extragalactic surveys. It consists of four complementary modules: the primary runs with high resolutions with the fiducial concordance cosmology, the emulator runs exploring the parameter uncertainties around the fiducial cosmology, the reconstruction runs intended for recovering the observed Universe position by position, and the extension runs employing extended cosmologies beyond the standard model. For the primary runs, two independent pipelines are adopted to construct subhaloes and merger trees. On top of them, four sets of mock galaxy light-cone catalogs are produced from semi-analytical models and subhalo abundance matching, providing a variety of observational properties including galaxy SED, emission lines, lensing distortions, and mock images. The 129 emulator runs are used to train the CSST emulator, achieving one percent accuracy in predicting the matter power spectrum over $k\leq 10h{\rm Mpc}^{-1}$ and $z\leq 2$. The reconstruction runs employ a number of subgrid baryonic models to predict the evolution and galaxy population resembling certain regions in the real Universe with constrained initial conditions, enabling controlled investigation of galaxy formation on top of structure formation. The extension runs cover models with warm dark matter, $f(R)$ gravity, interacting dark energy, and nonzero neutrino masses, revealing differences in the cosmic structure under alternative cosmological models. We introduce the specifications for each run, the data products derived from them, the corresponding pipeline developments, and present some main tests. Using the primary runs, we also show that the subhalo peak mass functions of different levels are approximately universal. These simulations form a comprehensive and open library for CSST surveys and beyond.

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arXiv2025

Exploring cosmological constraints of the weak gravitational lensing and galaxy clustering joint analysis in the CSST photometric survey

We explore the joint weak lensing and galaxy clustering analysis from the photometric survey operated by the China Space Station Telescope (CSST), and study the strength of the cosmological constraints. We employ a high-resolution JiuTian-1G simulation to construct a partial-sky light cone to $z=3$ covering 100 deg$^2$, and obtain the CSST galaxy mock samples based on an improved semi-analytical model. We perform a multi-lens-plane algorithm to generate corresponding synthetic weak lensing maps and catalogs. Then we generate the mock data based on these catalogs considering the instrumental and observational effects of the CSST, and use the Markov Chain Monte Carlo (MCMC) method to perform the constraints. The covariance matrix includes non-Gaussian contributions and super-sample covariance terms, and the systematics from intrinsic alignments, galaxy bias, photometric redshift uncertainties, shear calibration, and non-linear effects are considered in the analysis. We find that the constraint result is comparable to that from Stage III surveys, and it can be significantly improved further in the full CSST survey with 17500 deg$^2$. This indicates the CSST photometric survey is powerful for exploring the Universe.

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arXiv2025

2D watershed void clustering for probing the cosmic large-scale structure

Cosmic void has been proven to be an effective cosmological probe of the large-scale structure (LSS). However, since voids are usually identified in spectroscopic galaxy surveys, they are generally limited to low number density and redshift. We propose to utilize the clustering of two-dimensional (2D) voids identified using Voronoi tessellation and watershed algorithm without any shape assumption to explore the LSS. We generate mock galaxy and void catalogs for the next-generation Stage IV photometric surveys in $z = 0.8-2.0$ from simulations, develop the 2D void identification method, and construct the theoretical model to fit the 2D watershed void and galaxy angular power spectra. We find that our method can accurately extract the cosmological information, and the constraint accuracies of some cosmological parameters from the 2D watershed void clustering are even comparable to the galaxy angular clustering case, which can be further improved by as large as $\sim30\%$ in the void and galaxy joint constraints. This indicates that the 2D void clustering is a good complement to galaxy angular clustering measurements, especially for the forthcoming Stage IV surveys that detect high-redshift universe.

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arXiv2024

Cosmological Prediction of the Void and Galaxy Clustering Measurements in the CSST Spectroscopic Survey

The void power spectrum is related to the clustering of low-density regions in the large-scale structure (LSS) of the Universe, and can be used as an effective cosmological probe to extract the information of the LSS. We generate the galaxy mock catalogs from Jiutian simulation, and identify voids using the watershed algorithm for studying the cosmological constraint strength of the China Space Station Telescope (CSST) spectroscopic survey. The galaxy and void auto power spectra and void-galaxy cross power spectra at $z=0.3$, 0.6, and 0.9 are derived from the mock catalogs. To fit the full power spectra, we propose to use the void average effective radius at a given redshift to simplify the theoretical model, and adopt the Markov Chain Monte Carlo (MCMC) technique to implement the constraints on the cosmological and void parameters. The systematical parameters, such as galaxy and void biases, and noise terms in the power spectra are also included in the fitting process. We find that our theoretical model can correctly extract the cosmological information from the galaxy and void power spectra, which demonstrates its feasibility and effectivity. The joint constraint accuracy of the cosmological parameters can be improved by $\sim20\%$ compared to that from the galaxy power spectrum only. The fitting results of the void density profile and systematical parameters are also well constrained and consistent with the expectation. This indicates that the void clustering measurement can be an effective complement to the galaxy clustering probe, especially for the next generation galaxy surveys.

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arXiv2024

Void Number Counts as a Cosmological Probe for the Large-Scale Structure

Void number counts (VNC) indicates the number of low-density regions in the large-scale structure (LSS) of the Universe, and we propose to use it as an effective cosmological probe. By generating the galaxy mock catalog based on Jiutian simulations and considering the spectroscopic survey strategy and instrumental design of the China Space Station Telescope (CSST), which can reach a magnitude limit $\sim$23 AB mag and spectral resolution $R\gtrsim200$ with a sky coverage 17,500 deg$^2$, we identify voids using the watershed algorithm without any assumption of void shape, and obtain the mock void catalog and data of the VNC in six redshift bins from $z=0.3$ to1.3. We use the Markov Chain Monte Carlo (MCMC) method to constrain the cosmological and VNC parameters. The void linear underdensity threshold $δ_{\rm v}$ in the theoretical model is set to be a free parameter at a given redshift to fit the VNC data and explore its redshift evolution. We find that, the VNC can correctly derive the cosmological information, and the constraint strength on the cosmological parameters is comparable to that from the void size function (VSF) method, which can reach a few percentage levels in the CSST full spectroscopic survey. This is because that, since the VNC is not sensitive to void shape, the modified theoretical model can match the data better by integrating over void features, and more voids could be included in the VNC analysis by applying simpler selection criteria, which will improve the statistical significance. It indicates that the VNC can be an effective cosmological probe for exploring the LSS.

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arXiv2024

Photometric properties of classical bulge and pseudo-bulge galaxies at $0.5\le z<1.0$

We compare the photometric properties and specific star formation rate (sSFR) of classical and pseudo-bulge galaxies with $M_* \ge 10^{9.5} \rm M_{\odot}$ at $0.5\le z<1.0$, selected from all five CANDELS fields. We also compare these properties of bulge galaxies at lower redshift selected from MaNGA survey (Hu et al. 2024). This paper aims to study the properties of galaxies with classical and pseudo-bulges at intermediate redshift, to compare the differences between different bulge types, and to understand the evolution of bulges with redshift. Galaxies are classified into classical bulge and pseudo-bulge samples according to the S$\mathrm{\acute{e}}$rsic index n of the bulge component based on results of two-component decomposition of galaxies, as well as the position of bulges on the Kormendy diagram. For the 105 classical bulge and 86 pseudo-bulge galaxies selected, we compare their size, luminosity, and sSFR of various components. At given stellar mass, most classical bulge galaxies have smaller effective radii, larger $B/T$, brighter and relatively larger bulges, and less active star formation than pseudo-bulge galaxies. Besides, the two types of galaxies have larger differences in sSFR at large radii than at the central region at both low and mid-redshifts. The differences between properties of the two types of bulge galaxies are in general smaller at mid-redshift than at low redshift, indicating that they are evolving to more distinct populations towards the local universe. Bulge type is correlated with the properties of their outer disks, and the correlation is already present at redshift as high as $0.5<z<1$.

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arXiv2024

Cosmological Forecast of the Void Size Function Measurement from the CSST Spectroscopic Survey

Void size function (VSF) contains information of the cosmic large-scale structure (LSS), and can be used to derive the properties of dark energy and dark matter. We predict the VSFs measured from the spectroscopic galaxy survey operated by the China Space Station Telescope (CSST), and study the strength of cosmological constraint. We employ a high-resolution Jiutian simulation to get CSST galaxy mock samples based on an improved semi-analytical model. We identify voids from this galaxy catalog using the watershed algorithm without assuming a spherical shape, and estimate the VSFs at different redshift bins from $z=0.5$ to 1.1. We propose a void selection method based on the ellipticity, and assume the void linear underdensity threshold $δ_{\rm v}$ in the theoretical model is redshift-dependent and set it as a free parameter in each redshift bin. The Markov Chain Monte Carlo (MCMC) method is adopted to implement the constraints on the cosmological and void parameters. We find that the CSST VSF measurement can constrain the cosmological parameters to a few percent level. The best-fit values of $δ_{\rm v}$ are ranging from $\sim-0.4$ to $-0.1$ as the redshift increases from 0.5 to 1.1, which has a distinct difference from the theoretical calculation with $δ_{\rm v}\simeq-2.7$ assuming the spherical evolution and using particles as tracer. Our method can provide a good reference for void identification and selection in the VSF analysis of the spectroscopic galaxy surveys.

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arXiv2024

Effectiveness of halo and galaxy properties in reducing the scatter in the stellar-to-halo mass relation

The stellar-to-halo mass relation (SHMR) is a fundamental relationship between galaxies and their host dark matter haloes. In this study, we examine the scatter in this relation for primary galaxies in the semi-analytic L-Galaxies model and two cosmological hydrodynamical simulations, \eagle{} and \tng{}. We find that in low-mass haloes, more massive galaxies tend to reside in haloes with higher concentration, earlier formation time, greater environmental density, earlier major mergers, and, to have older stellar populations, which is consistent with findings in various studies. Quantitative analysis reveals the varying significance of halo and galaxy properties in determining SHMR scatter across simulations and models. In \eagle{} and \tng{}, halo concentration and formation time primarily influence SHMR scatter for haloes with $M_{\rm h}<10^{12}~\rm M_\odot$, but the influence diminishes at high mass. Baryonic processes play a more significant role in \lgal{}. For halos with $M_{\rm h} <10^{11}~\rm M_\odot$ and $10^{12}~\rm M_\odot 10^{13}~\rm M_\odot$, supermassive black hole mass becomes more important. Interestingly, it is found that AGN feedback may increase the amplitude of the scatter and decrease the dependence on halo properties at high masses.

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