arXiv subjects

Jiaxin Han

Publications and source records attributed to Jiaxin Han.

At least 19 recordsLinked to original sources

arXiv2026

ELUCID-DESI II. Revealing dark matter mass, tidal, and velocity (MTV) fields using galaxy group phase information

We introduce a novel method for reconstructing the cosmic mass, tidal, and velocity (MTV) fields over the redshift range $0 < z < 0.6$ using the phase information of galaxy groups. This approach replaces the explicit theoretical bias correction typically needed to relate galaxy groups to the underlying dark matter density field with a simulation-calibrated statistical mapping, reducing a major source of systematic uncertainty and making the method directly applicable to spectroscopic redshift surveys such as the DESI Bright Galaxy Survey (BGS). We evaluate the performance of our MTV reconstruction pipeline with mock redshift surveys that include a comprehensive set of observational selection effects. The galaxy groups used as tracers are identified with an extended halo-based group finder applied to the DESI mock galaxy catalogue with an apparent magnitude limit of $m_z < 19.65$, yielding a galaxy number comparable to that of the DESI BGS faint sample ($m_r < 20.175$). Our tests show that the reconstructed velocities are accurate and unbiased, with a residual dispersion of $\sim 120\ \mathrm{km\,s^{-1}}$ across the redshift bins. The recovered velocity field allows us to shift galaxy groups to their real-space positions, thereby correcting for the Kaiser effect. By iteratively applying this Kaiser correction to the galaxy groups, we further reconstruct the tidal field and the mass-density distribution. The reconstruction is stable with respect to the grid resolution. Overall, our results demonstrate that this group-based phase-space reconstruction provides a robust pathway to recovering the dark matter MTV fields, with strong prospects for application to DESI BGS data.

astro-ph.CO↗

arXiv2026

Improved constraints on the Milky Way potential using the M68 stream and DESI spectroscopic data

We present a selection of stars belonging to the stellar stream of the M68 (NGC 4590) globular cluster, also known as Fj\"orm. This star selection is an improvement on previous ones that used only Gaia data, as it incorporates spectroscopic measurements from the DESI survey and photometric data from the DESI Legacy Surveys. The selection contains 96 stars, each with five phase-space parameters from Gaia-DR3 and radial velocity from DESI, covering the entire observed section of the stream. This constitutes the largest selection of M68 stream stars with measured radial velocities to date. The observed stream is wider than expected from N-body simulations, and the stars farthest from the centre of the stream appear to be correlated in radial velocity space. This suggests that these stars cannot have been stripped from the cluster in a static axisymmetric potential. By modelling a mock sample of stream stars created using an N-body simulation, we found that we could reliably constrain the disc mass $M_{\rm d}$ and the dark matter halo axis ratio $q_{\rm h}$ of the Milky Way. This is because the stream flows close to and almost parallel to the disc. Using the 44 stars that are consistent with having been stripped from the cluster, combined with measurements of the Milky Way's rotation curve, we constrain the Galactic potential, obtaining $M_{\rm d} = 5.34 \pm 0.57 \times 10^{10}$ M$_{\rm sun}$ and an oblate halo of $q_{\rm h} = 0.83^{+0.06}_{-0.05}$. Additionally, by fitting the stream track, we estimate the Heliocentric distance of M68 to be $r=10.55\pm0.09$ kpc.

astro-ph.GA↗

arXiv2026

What can galaxy clustering really tell us about the galaxy-halo connections?

Subhalo abundance matching (SHAM) is a commonly used framework for modeling the galaxy-halo connection. Yet, its standard implementation has difficulty reproducing the observed galaxy clustering with high accuracy (e.g., $\chi^2/\mathrm{dof} \approx 1$). To overcome this issue, we propose a novel CS-SHAM framework, in which central and satellite galaxies are independently matched to main and satellite subhalos in simulations. Within this scheme, we introduce three free parameters to explicitly characterize the satellite fraction, $f_{\mathrm{sat}}$, as a function of stellar mass or absolute magnitude. To evaluate the performance of CS-SHAM, we apply it to two sets of mock galaxy catalogs built with the conventional SHAM method but using different subhalo mass proxies, $M_{\mathrm{peak}}$ and $V_{\mathrm{peak}}$, as well as two additional galaxy samples generated from a SAM and from TNG-300. We demonstrate that CS-SHAM reliably reproduces galaxy clustering whether $M_{\mathrm{peak}}$ or $V_{\mathrm{peak}}$ is used as the subhalo mass proxy. We also find that the models are unable to place robust constraints on $f_{\mathrm{sat}}$ if different mass proxies are employed. Indeed, within the CS-SHAM framework the halo occupation distribution (HOD) and conditional luminosity or stellar mass function (CLF/CSMF) are accurately recovered. Furthermore, we demonstrate for the first time that galaxy clustering constrains the HOD and CLF/CSMF primarily for relatively massive halos. Because the halo bias is nearly constant for low-mass halos, galaxy clustering is generally not very sensitive to the satellite population residing in these low-mass systems.

astro-ph.GA↗

arXiv2026

The Sinking Statistics of Dark Matter Subhalos Across Hierarchical Levels

We investigate the mergers among subhalos in a $\Lambda$CDM simulation, focusing on two fundamental aspects overlooked by previous studies: 1) how to identify mergers robustly; 2) the statistics of mergers across the subhalo hierarchy. To this end, we make use of the HBT+ subhalo finder that tracks subhalo evolution across hierarchy levels, identifying the coalescence of subhalo cores in phase space as a "sinking" event. This coalescence marks a distinct stalled phase in orbital decay, providing a physically motivated and natural definition of a resolved merger. Moreover, the phase transition occurs over a very short timescale, making the statistics robust to numerical resolutions. Our main findings are as follows. (1) More than 90% of sinking events occur between adjacent subhalo levels, while cross-level pathways arise from tidal stripping, group accretion, and numerical constraints. (2) Resolved sinking events are predominantly major mergers (mass ratios > 1/10), whereas the contribution from minor mergers decreases with the dynamical age of the host halo. (3) Although deep-level subhalos typically have low mass ratios relative to the host halo, their mass ratios relative to their direct parents are substantially larger, significantly enhancing their sinking probability. Consequently, the satellite-satellite sinking rate can rival or even exceed the central-satellite sinking rate at lower mass thresholds. (4) Satellite-satellite sinking events are spatially biased toward the outer regions of the host halo, suggesting that the central tidal field suppresses orbital decay between satellite systems.

astro-ph.GA↗

arXiv2026

The tidal evolution of satellite galaxies in cosmological simulations: insights from COLIBRE

We investigate the co-evolution of the stellar and dark matter mass of satellite galaxies using the COLIBRE cosmological hydrodynamical simulations with subhaloes resolved by the history-based HBT-HERONS subhalo finder. We identify a universal tidal track connecting stellar mass loss to subhalo mass loss characterized by two distinct phases, which can be well described by the two-parameter model. The initial phase consists primarily of dark matter stripping, whereas stellar stripping becomes significant only after the subhalo bound mass fraction drops below a critical value ($\sim 0.057$). We find a bimodal mass loss rate distribution of subhaloes. In satellites with modest mass loss rates, the stellar mass is largely frozen. By contrast, the galaxy quickly becomes unresolved, along with the dark matter component for the extreme-mass-loss population, naturally explaining the lack of ``orphan'' galaxies in previous hydrodynamical simulations. Our model also predicts the formation condition for dark-matter-deficient galaxies (DMDGs), whose abundance peaks at $m_{*}\sim 10^{9.5}\,\rm{M}_{\odot}$. The abundance of DMDGs can be very sensitive to numerical effects, with COLIBRE resolving a much larger DMDG population than previous hydrodynamical simulations. We also estimate the influence of artificial disruption on the satellite stellar mass function, which can amount to 20 (50) per cent at $m_* \sim 10^{9} (10^{8}) \, \rm M_\odot$, given a baryonic mass resolution of $\sim 10^{6}\,\rm{M}_{\odot}$.

astro-ph.GA↗

arXiv2026

The velocity field of our Milky Way outer stellar halo based on DESI DR2

Using 64,000 halo K giants from Dark Energy Spectroscopic Instrument (DESI) second Data Release (DR2), we decompose the Milky Way (MW) stellar halo between 3 and 160 kpc into metal-rich (MR) and metal-poor (MP) components via a Gaussian mixture model (GMM). The two populations are nearly equal in number but chemically and kinematically distinct: MR stars occupy highly radial orbits with velocity anisotropy of beta ~0.94 and metallicity dispersion sigma([Fe/H]) ~0.17 dex, without obvious dependence on distance, and are mainly contributed by Gaia-Sausage/Enceladus (GSE) debris. MR component dominates the inner 30 kpc and re-emerges beyond 50 kpc, implying GSE debris can extend to ~70-80 kpc. MP stars exhibit a weaker radial bias of beta ~0.46, decreasing to -0.5 beyond 80 kpc, and with a larger metallicity dispersion of sigma([Fe/H]) ~0.46 dex, showing signatures of multiple minor mergers. Both components exhibit net prograde rotation at ~10-30 kpc with a stronger azimuthal signal in the MP population. The non-equilibrium motions of the outer halo (>50 kpc) are quantified with a dipole-plus-contraction velocity field. We find that the outer halo is simultaneously contracting (~-19 km/s, distance-independent) and subject to reflex motions (increases from -19 to -44 km/s with radius), reflecting the perturbation from the Large Magellanic Cloud (LMC). We also confirm a linear dependence of mean polar velocity for the outer stellar halo on the dipole velocity field, a direct consequence of the LMC and MW interaction. Our results provide a quantitative distance-resolved description of the MW's last major accretion event and its ongoing response to the first infall of the LMC.

astro-ph.GA↗

arXiv2026

The many boundaries of the stratified dark matter halo

We review the physics of halo collapse giving rise to various halo boundaries, as well as their identification, observation, and applications. The classical halo is typically defined as a monolithic, virialized object enclosed within its virial radius -- a definition which, however, does not account for ongoing halo growth. Continuous accretion causes the orbits of infalling particles to shrink over time, confining newly accreted material in a growing layer outside the virialized region. Several novel halo boundaries, such as the splashback and depletion radii, have recently been proposed to characterize this growth layer from different perspectives. Along with the turnaround radius, which operates on an even larger scale to enclose the entire infall region, these multiple boundaries comprise an extended view of a dark matter halo as a stratified structure. Theoretical models can largely explain the existence of various boundaries, while challenges remain in providing unified and quantitative predictions of their properties. The multiple boundaries open new avenues for observing halo growth and may substantially improve our understanding and modeling of cosmic structure formation. We provide a python package, SpheriC, implementing the key spherical collapse models.

astro-ph.CO↗

arXiv2026

Accretion history dependence of the halo depletion radius

We investigate the role of the accretion history in shaping the depletion radius of dark matter halos using a large cosmological N-body simulation. We show that the inner depletion radius, rescaled by the virial radius, depends strongly on the recent mass accretion rate (MAR) measured over a dynamical timescale, while exhibiting only weak dependence on halo mass. While this dependence mirrors that of the splashback radius and the two radii are tightly correlated, the depletion radius exhibits a more nuanced response to the detailed accretion mode. Specifically, we find that the dependence on MAR steepens at lower redshifts, aligning with self-similar spherical collapse models yet contrasting with the behavior of the splashback radius. This redshift dependence is largely driven by recent major mergers, which tend to suppress the depletion radius in stacked measurements at low redshift and high accretion rate. Furthermore, we identify a dichotomy in the drivers of the depletion radius. For slowly accreting halos, the MAR is the primary dependence, whereas for rapidly accreting halos, other properties (shape, spin, concentration, and formation time of the central subhalo) related to the anisotropic or perturbed accretion mode also play a significant role. These results establish the depletion radius as a sensitive physical probe of the detailed accretion history of dark matter halos, complementary to the splashback radius.

astro-ph.CO↗

arXiv2026

ELUCID-DESI I: A Parallel MPI Implementation of the Initial Condition Solver for Large-Scale Reconstruction Simulations

We present a highly scalable, MPI-parallelized framework for reconstructing the initial cosmic density field, designed to meet the computational demands of next-generation cosmological simulations, particularly the upcoming ELUCID-DESI simulation based on DESI BGS data. Building upon the Hamiltonian Monte Carlo approach and the FastPM solver, our code employs domain decomposition to efficiently distribute memory between nodes. Although communication overhead increases the per-step runtime of the MPI version by roughly a factor of eight relative to the shared-memory implementation, our scaling tests-spanning different particle numbers, core counts, and node layouts-show nearly linear scaling with respect to both the number of particles and the number of CPU cores. Furthermore, to significantly reduce computational costs during the initial burn-in phase, we introduce a novel ``guess'' module that rapidly generates a high-quality initial density field. The results of the simulation test confirm substantial efficiency gains: for $256^3$ particles, 53 steps ($\sim$ 54 core hours) are saved, accelerating convergence by a factor of $\sim$ 18; for $1024^3$, 106 steps ($\sim$7500 core hours), achieving a speedup factor of $\sim$ 3. The total core hour gain grows with the number of particles, rendering large-volume reconstructions computationally practical for upcoming surveys, including our planned ELUCID-DESI reconstruction simulation with $4096^3$ particles. We estimate that achieving convergence for this scale (targeting DESI-BGS data) requires about 800 HMCMC steps ($\sim$ 5 million core hours). Our initial guess module will save approximately 360 steps ($\sim$2.3 million core hours), reducing the total computational time by about 45\%.

astro-ph.GA↗

arXiv2026

First Observational Evidence for Split Infall Flow of Cosmic Filaments into Clusters

Velocity fields in the cosmic web are fundamental to structure formation but remain difficult to observe directly beyond the linear regime. Here we present observational evidence that galaxy filaments connecting pairs of galaxy clusters undergo a split infall, with opposite velocity flows toward the two clusters. Using spectroscopic galaxies from the Sloan Digital Sky Survey, we isolate the internal filament velocity field by subtracting its rigid-body background motion and Hubble flow, and detect this effect at greater than $5\sigma$ significance across a wide range of cluster and filament selections. The measured velocity profile exhibits a sign reversal near the filament midpoint and a maximum infall amplitude of $\sim30$ km/s ($\sim20$ km/s projected onto the line-of-sight) for clusters of mass $\sim10^{14.3}M_\odot$, substantially lower than expected for infall from an average cosmic environment. Multiple results on density-velocity correlation, mass-dependency, and validation with simulation indicate that filaments dynamically respond to competing gravitational potentials rather than acting as passive mass transport channels. Our results establish a new observational window on quasi-linear velocity fields in the cosmic web and provide a promising probe of mass measurement, testing gravity and velocity reconstruction with upcoming wide-field spectroscopic surveys.

astro-ph.CO↗

arXiv2025

CUBE2: A Parallel $N$-Body Simulation Code for Scalability, Accuracy, and Memory Efficiency

$N$-body simulation serves as a critical method for modeling cosmic evolution and poses a significant challenge in high-performance computing. We present CUBE2, an open-source cosmological $N$-body code emphasizing memory efficiency, computational performance, scalability and precision. The core of its algorithm utilizes multi-level Particle-Mesh (PM) method to solve the Poisson equation for matter distribution, leveraging the well-optimized Fast Fourier Transform (FFT) for computational efficiency. Precision is ensured by the optimized Green's function that seamlessly bridges gravitational interactions between multi-level PM and Particle-Particle (PP) calculations. The program design enhances per-core/node efficiency in processing $N$-body particles, while the Information Optimized Storage (IOS) addresses memory constraints for large particle counts. Using CUBE2, we run two cosmological simulations with particle counts of $6144^3$ on the Advanced Computing East China Sub-center (ACECS) to test performance and accuracy.

astro-ph.IM↗

arXiv2025

The shape-velocity alignment of satellites forged by tidal locking and dynamical friction

Utilizing the TNG50 simulation, we study two types of alignments for satellites/subhalos: 1) the alignment of their major axes with the galactocentric radial directions (radial alignment), and 2) with the motion directions (orbital alignment). We find that radial alignment is substantially stronger than orbital alignment, with both signals being consistently stronger for subhalos than for satellites. Interestingly, inward- and outward-moving satellites/subhalos show contrasting orbital alignment behaviors, which can be understood in terms of their radial alignment, orbit decay due to dynamical friction and the effect of tidal stripping. The orbital alignment is stronger in more massive halos. In the end, we explore the orbital alignment measured by a mock observer, and find that the observed alignment for MW satellites is due to projection effects, as the major axes of satellites lie within their orbital planes, approximately coplanar with the observer.

astro-ph.GA↗

arXiv2025

The Binary Fraction of Stars in the Dwarf Galaxy Ursa Minor via Dark Energy Spectroscopic Instrument

We utilize multi-epoch line-of-sight velocity measurements from the Milky Way Survey of the Dark Energy Spectroscopic Instrument to estimate the binary fraction for member stars in the dwarf spheroidal galaxy Ursa Minor. Our dataset comprises 670 distinct member stars, with a total of more than 2,000 observations collected over approximately one year. We constrain the binary fraction for UMi to be $0.61^{+0.16}_{-0.20}$ and $0.69^{+0.19}_{-0.17}$, with the binary orbital parameter distributions based on solar neighborhood observation from Duquennoy & Mayor (1991) and Moe & Di Stefano (2017), respectively. Furthermore, by dividing our data into two subsamples at the median metallicity, we identify that the binary fraction for the metal-rich ([Fe/H]>-2.14) population is slightly higher than that of the metal-poor ([Fe/H]<-2.14) population. Based on the Moe & Di Stefano model, the best-constrained binary fractions for metal-rich and metal-poor populations in UMi are $0.86^{+0.14}_{-0.24}$ and $0.48^{+0.26}_{-0.19}$, respectively. After a thorough examination, we find that this offset cannot be attributed to sample selection effects. We also divide our data into two subsamples according to their projected radius to the center of UMi, and find that the more centrally concentrated population in a denser environment has a lower binary fraction of $0.33^{+0.30}_{-0.20}$, compared with $1.00^{+0.00}_{-0.32}$ for the subsample in more outskirts.

astro-ph.SR↗

arXiv2025

BioArc: Discovering Optimal Neural Architectures for Biological Foundation Models

Foundation models have revolutionized various fields such as natural language processing (NLP) and computer vision (CV). While efforts have been made to transfer the success of the foundation models in general AI domains to biology, existing works focus on directly adopting the existing foundation model architectures from general machine learning domains without a systematic design considering the unique physicochemical and structural properties of each biological data modality. This leads to suboptimal performance, as these repurposed architectures struggle to capture the long-range dependencies, sparse information, and complex underlying ``grammars'' inherent to biological data. To address this gap, we introduce BioArc, a novel framework designed to move beyond intuition-driven architecture design towards principled, automated architecture discovery for biological foundation models. Leveraging Neural Architecture Search (NAS), BioArc systematically explores a vast architecture design space, evaluating architectures across multiple biological modalities while rigorously analyzing the interplay between architecture, tokenization, and training strategies. This large-scale analysis identifies novel, high-performance architectures, allowing us to distill a set of empirical design principles to guide future model development. Furthermore, to make the best of this set of discovered principled architectures, we propose and compare several architecture prediction methods that effectively and efficiently predict optimal architectures for new biological tasks. Overall, our work provides a foundational resource and a principled methodology to guide the creation of the next generation of task-specific and foundation models for biology.

cs.LG↗

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.

astro-ph.GA↗

arXiv2025

Modelling the M68 stellar stream with realistic mass loss and frequency distributions in angle-action coordinates

We develop a new method for simulating stellar streams generated by globular clusters using angle-action coordinates. This method reproduces the variable mass-loss and variable frequency of the stripped stars caused by the changing tidal forces acting on the cluster as it moves along an eccentric orbit. The model incorporates realistic distributions for the stripping angle and frequency of the stream stars both along and perpendicular to the stream. The stream is simulated by generating random samples of stripped stars and integrating them forward in time in angle-frequency space. Once the free parameters are calibrated, this method can be used to simulate the internal structure of stellar streams more quickly than N-body simulations, while achieving a similar level of accuracy. We use this model to study the surface density of the stellar stream produced by the globular cluster M68 (NGC 4590). We select $291$ stars from the Gaia-DR3 catalogue along the observable section that are likely to be members of the stream. We find that the width of the stream is too large to be explained by stars stripped from the cluster alone. We simulate the stream using the present method and include the Gaia selection function and observational errors, and the process of separating the stream stars from the foreground. By comparing these results with the observed data, we estimate the age of the stream, or equivalently the cluster accretion time, to be $3.04_{-0.29}^{+5.63}$ Gyr, and the mass-loss of the cluster to be $0.496 \pm 0.030$ M$_{\odot}$ Myr$^{-1}$ arm$^{-1}$.

astro-ph.GA↗

arXiv2025

The mass of the Milky Way from outer halo stars measured by DESI DR1

As a benchmark for galaxy evolution and dark matter studies, the total mass of the Milky Way is a parameter of cosmological significance, and its value at large radii from the Galactic center remains highly uncertain. Following a hierarchical Bayesian inference approach, we measure the cumulative mass of the Milky Way using full 6D phase-space information of stars from the first data release of the Dark Energy Spectroscopic Instrument (DESI). We employ 330 blue horizontal-branch stars (BHBs) and 110 RR Lyrae stars (RRLs) in DESI covering Galactocentric distances in the range $\sim$50--100 kpc. Within 100 kpc from the Galactic center, we report an enclosed mass of $M(<100\ {\rm kpc}) = 0.57^{+0.08}_{-0.07}\times10^{12}$ M$_\odot$ and $M(<100\ {\rm kpc}) = 0.55^{+0.12}_{-0.10}\times10^{12}$ M$_\odot$ when using BHBs and RRLs, respectively. Extrapolating our mass profiles beyond the extent of our data, we find the virial mass of the Galaxy to be $M_{200}=0.85^{+0.16}_{-0.14}\times10^{12}$ M$_\odot$ and $M_{200}=0.78^{+0.19}_{-0.15}\times10^{12}$ M$_\odot$, respectively. We validate the effectiveness and limitations of our method using mock BHBs and RRLs from two AuriDESI halos. These tests show that the code recovers the enclosed mass of the mock galaxy with high precision and accuracy between 50 and 200 kpc, independent of the stellar tracer used and their spatial distribution. The tests also suggest an underestimation of the galaxy's cumulative mass at a level of up to $\sim20$\% if stars close to the Galactic center are used in the models. Our mass estimates lay the groundwork for future inference of the Galactic mass with upcoming DESI data releases and spectroscopic surveys mapping the halo.

astro-ph.GA↗

arXiv2025

Dependence of halo properties on central-satellite magnitude gaps through weak lensing measurements

The magnitude gap between the central and satellite galaxies encodes information about the mass accretion history of a dark matter halo, and serves as a useful observational probe for the mass distribution in a halo. In this work, we perform the first weak lensing test of the connections between the magnitude gap and the halo profile. We measure the halo profiles of isolated central galaxies (ICGs) selected primarily from the SDSS Main Galaxy Sample. Halo mass and concentration are inferred by fitting stacked lensing profiles in bins of central luminosity, $L_\mathrm{c}$, and the central-satellite magnitude gap, $L_\mathrm{gap}$. We detect dependence on the magnitude gap in both halo properties. The dependence is the strongest in the ICG luminosity range of $10^{10.3}<L_\mathrm{c}[h^{-2}L_\odot]\leq 10^{10.7}$, where halos with smaller gaps have higher masses and lower concentrations. When $10^{10.7} <L_c[h^{-2}L_\odot] \leq 10^{11.1}$, however, no significant gap dependence is detected. In the range of $10^{9.9}<L_\mathrm{c}[h^{-2}L_\odot] \leq 10^{10.3}$, a disordering of the gap dependence is marginally observable. We compare the observational results with predictions by two lightcone catalogs built from the Illustris TNG300 and the Millennium simulations. The gap dependence in the two mock samples show overall consistency with observations, but neither matches them in all $L_\mathrm{c}$ bins to a quantitative level. We also compare the significance of the gap dependence on halo mass and concentration and find that our measurement prefers gap dependence in both parameters, while the halo mass dependence is preferred over the concentration if only one of the two dependencies is allowed.

astro-ph.CO↗