Preamble

Vol. 43, No. 3

September 2025

Progress in Astronomy Vol. 43, No. 3 Sept., 2025 doi: 10.3969/j.issn.1000-8349.2025.03.02

Recent Advances in the Study of Effects of Cosmic Filaments on Star Formation Activities

YANG Sirui¹,²

(1. Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China;
2. School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China)

Abstract

Large-scale structures composed of galaxies and extending up to hundreds of megaparsecs are known as the cosmic web. Based on morphology and galaxy density, the cosmic web is classified into nodes, filaments, walls, and voids. Galaxies near filaments typically have higher masses and a greater proportion of early-type red galaxies compared to those in voids. Observational and simulation results indicate that star formation activity in galaxies weakens as they approach filaments. Several factors may introduce uncertainties into these results: (1) filament structures identified by different algorithms may differ; (2) various methods exist for measuring the geometric properties of filaments; and (3) galaxies near filaments usually have larger stellar masses, higher local environmental densities, and more massive host dark matter halos, all of which can also affect star formation activity. This review examines algorithms for studying the cosmic web and explores the influence of filaments on star formation activity while controlling for factors such as stellar mass, galaxy density, and halo mass, aiming to understand how galactic star formation is affected by the filament environment.

Keywords: cosmic filament; galaxy quenching; star formation

1 Introduction

The cosmic web represents the largest-scale structure in the observed universe, exhibiting fractal self-similarity and allowing classification of different structures across various scales. Regions with low galaxy number density are typically called "voids," while high-density regions are termed "nodes." Sparse structures, or "voids" completely devoid of galaxies, occupy nearly 95% of cosmic space [1, 2]. "Filaments" and "walls" represent structures of intermediate density, with lengths ranging from tens to hundreds of Mpc. Direct observations of wall structures are relatively rare, with notable examples including the CfA2 Great Wall [3], the Sloan Great Wall [4], and the Hercules-Corona Borealis Great Wall [5]. Cosmic filament structures at low redshift have substantial observational evidence from surveys such as the Sloan Digital Sky Survey (SDSS) [6]. Through Lyman-α radiation, astronomers can also map the morphology and physical properties of cosmic filaments at high redshift. Wang et al. [7] discovered filament structures existing just 830 million years after the Big Bang, identified by bright quasars, composed of 10 galaxies extending 3 million light-years.

Studying large-scale cosmic structures aids in understanding fundamental questions such as the Big Bang and in establishing and refining cosmological models. Cosmic inflation is generally believed to have generated tiny primordial perturbations that collapsed under gravity to form large-scale filaments. Filament structures formed in different cosmological models, such as cold dark matter and warm dark matter scenarios, would exhibit distinct morphologies. Investigating large-scale structures through observations and simulations helps constrain cosmological parameters including dark matter density, dark energy density, and the Hubble constant. The diverse large-scale environments also provide testbeds for studying galaxy formation and evolution processes. Filaments—elongated structures composed of dark matter and baryonic matter (galaxies, gas, etc.) that connect galaxies and galaxy clusters—exhibit several characteristics that distinguish galaxies near them from field galaxies: (1) Galaxies in filaments have higher masses than those outside filaments. Laigle et al. [8] used data from the COSMOS survey [9] to study galaxy mass profile curves, finding that massive galaxies are distributed closer to filament centers than low-mass galaxies. Galaxies may gradually increase their mass through mergers as they travel along cosmic filaments into galaxy clusters [10]. (2) The proportion of early-type galaxies is higher near filaments, and galaxies appear redder. Kuutma et al. [11] found that the elliptical-to-spiral galaxy ratio (E/S) increases near filaments, synchronized with changes in $g-i$ color. Salerno et al. [12] discovered that the proportion of red galaxies is highest in clusters, intermediate in filaments, and lowest in the field. How far does the filament environment influence star formation within galaxies? Does the filament transport baryonic matter? Is filament growth and evolution synchronized with galaxy mergers and evolution? Answering these questions will not only advance galaxy evolution studies but also deepen our understanding of the properties and formation processes of large-scale structures.

Section 2 lists several algorithms for finding filament structures. Section 3 reviews research progress on the influence of filament environments on galactic star formation activity, where Section 3.1 summarizes observations and simulations of decreased star formation activity near filaments; Section 3.2 discusses studies of filament quenching mechanisms after controlling for variables such as halo mass and local galaxy density fields, as well as the importance ranking of different variables using random forests; and Section 3.3 explores the possibility that the cosmic web may promote star formation activity through gas transport. Section 4 provides a summary and outlook.

2 Introduction to Several Algorithms for Identifying Cosmic Web Structures

Libeskind [13] summarized several algorithms for finding cosmic web structures in their research. As a supplement, this review examines the most commonly used DisPerSE (Discrete Persistent Structures Extractor) algorithm and also discusses Sconce, MCPM, the Bisous model, and simple connection network algorithms, comparing their advantages and disadvantages with a summary provided in Table 1 [TABLE:1].

2.1 DisPerSE

The widely used structure finder DisPerSE can extract persistent topological features such as peaks, voids, and walls, and trace filaments connecting them [14]. DisPerSE begins with field data—a set of discrete points that may come from galaxy coordinates, halo positions, or dark matter particles in simulations. DisPerSE then tessellates the field using DTFE (Delaunay Tessellation Field Estimator) [15] and computes the average of neighboring values (taking the two nearest vertices) at each tessellation vertex to obtain a smoothed density field. Structures in the density field are identified as functions on a Morse-Smale complex. Points where the density function gradient equals zero are critical points, comprising maxima, minima, and saddle points. In DisPerSE, filaments are one-dimensional structures—one-manifolds of ascending or descending gradient—composed of two integral lines (curves tangent to the gradient field at each point) emanating from a given saddle point and connecting to two maxima.

Topological structures in data may be unstable. For instance, data noise can create temporary structures, while smoothing at different scales may cause these structures to disappear. DisPerSE identifies and quantifies the significance of these structures by measuring their topological persistence [16]. It calculates the persistence ratio between pairs of critical points (e.g., maxima and saddle points) and removes points with occurrence probabilities below a set threshold in random fields. By setting a lower threshold, more filament structures can be discovered.

2.2 Sconce

For two- and three-dimensional discrete point coordinates, Zhang et al. [17] developed two Python packages (DirSCMS, DirLinSCMS) to find filament structures. The Sconce algorithm operates through two processes: (1) computing the density field on a regularly spaced grid using a directional kernel density estimator in spherical coordinates [18, 19] with corresponding smoothing bandwidth parameters (larger bandwidth yields smoother density fields); and (2) directly locating density ridges—composed of local density maxima in the normal direction defined by the Hessian matrix—through an iterative process similar to gradient ascent. The Sconce algorithm effectively avoids spurious filament structures caused by the "fingers-of-God" effect [20] when converting redshift to comoving distance and can simultaneously construct filaments parallel and perpendicular to the line-of-sight direction in three-dimensional space.

Zhang et al. [17] compared filament structures identified by Sconce and DisPerSE in their Figure 4 [FIGURE:4]. They found that in high declination regions of the celestial sphere, filaments identified by DisPerSE are irregular and may contain many spurious components, though DisPerSE has advantages in finding short filament structures and can be used to identify "tendrils." In contrast, Sconce offers higher recovery precision for filaments and shows clear advantages in locating long filaments, avoiding errors that may arise from reconnecting short filament structures.

2.3 MCPM

The Monte Carlo Physarum Machine (MCPM) [21] was inspired by Jones [22] and references the efficient network-forming behavior of the slime mold Physarum polycephalum when foraging for food [23]. In the algorithm, "slime mold" moves along "chemoattractant" paths, depositing its own trail at each time step to find optimal transport networks. MCPM adapts this model to three dimensions, sampling possible paths probabilistically so that paths leading to smaller deposits may still be traversed. This algorithm's advantage is its ability to reasonably interpolate low-density regions of the cosmic web. MCPM has been applied to analyze galaxy and fast radio burst data [21, 24], advancing research on intergalactic neutral hydrogen and thermally ionized gas in the cosmic web.

2.4 Bisous Model and Connection Network Algorithms

Some algorithms identify cosmic web structures using the geometric connectivity properties of the cosmic web itself, combined with statistical methods, without requiring density field interpolation, smoothing, or estimation. The Bisous model proposed by Tempel et al. [25] assumes that galaxies cluster in small cylinders. If adjacent cylinders align in similar directions, they can be combined into filaments. Each small cylinder can be marked by four parameters: center coordinates, height, base radius, and direction vector. The model then calculates a probability density field based on the Poisson distribution probability density function, with system energy as the primary parameter (equivalent to total Gibbs energy in physics, determined here by cylinder positions, alignment, and connectivity in the galaxy field), and finally extracts filament structures in regions with high probability density. The Bisous model can accurately extract filaments while considering network connectivity, though implementation is relatively complex.

Hong and Dey [26] proposed that when the distance between two galaxies is smaller than a given "linking length," they are considered connected. First, large random networks are known to exhibit Poisson distribution characteristics [27]. Each random process is a binomial trial, and calculating the distribution of $n$ points in spherical space with radius $l$ yields a Poisson-like formula whose mean can be expressed in terms of $l$ and $n$. Therefore, linking length can be determined by constructing a Poisson distribution and used to find connectivity between galaxies. Structures are then classified by connectivity at each point: voids (lowest connectivity), walls, and nodes (highest connectivity).

Martínez et al. [28] proposed first identifying "node pairs" connected by filaments, then screening filaments by calculating galaxy overdensity. Specifically, node pairs must satisfy given thresholds for both projected distance and line-of-sight distance, with projected distance exceeding the sum of the virial radii of the two halos to ensure clear structures are found. Subsequently, rectangular prisms (height along line-of-sight, base in projection plane) are constructed between node pairs, and galaxy overdensity is calculated (by counting galaxies within the prism and comparing with field galaxy counts in the same spatial and redshift range). Overdensity greater than 1 is classified as a filament structure. Both methods are fast, intuitive, and consume minimal computational resources. However, Hong and Dey's method is highly dependent on the linking length parameter and cannot directly construct filament networks. Martínez et al.'s method relies on threshold parameters for line-of-sight and projected distances and requires high-precision galaxy position and redshift data, as measurement errors may affect results. It is currently mainly applied to distinguishing cosmic web environments where galaxies reside.

3 Studies of Galaxy Quenching in Cosmic Web Environments

The evolution from star-forming "blue galaxies" to star-formation-quenched "red galaxies" occurs over relatively short cosmological timescales. The transitional stage between them is called the "green valley," appearing as a narrow distribution in color-magnitude diagrams [29]. Galaxy star formation and quenching mechanisms are complex, influenced by both intrinsic properties such as mass and morphology, and external environments such as dark matter halos, local galaxy density, and large-scale structure. Dressler [30] proposed the famous relationship between environmental density and galaxy morphology: cluster galaxies are more likely to be elliptical, while field galaxies are typically spiral. Jaffé et al. [31] studied the ram pressure stripping mechanism of neutral hydrogen gas in galaxy clusters by plotting observed galaxies on velocity-phase diagrams, classified by neutral hydrogen detection and red/blue color. Lotz et al. [33] simulated galaxy orbits "pre-processed" in clusters, finding that most satellite galaxies with radial velocity directions are rapidly quenched by gas stripping effects [34] during their first infall. As structures with density lower than clusters but higher than voids, whether cosmic filaments contain similar galaxy quenching processes remains to be tested.

3.1 Galaxy Quenching in Filaments: Observational and Simulation Results

Various observations and simulations have studied changes in galaxy star formation activity when approaching filaments. Several statistical indicators are commonly used to measure changes in galaxy formation activity: (1) calculating galaxy colors, such as $u-r > 1.8$ for red galaxies [36], or making divisions on $g-r/u-g$ diagrams like $(g-r) > 0.234(u-g) + 1.03$ [37]; (2) calculating $sSFR$ (the ratio of star formation rate to stellar mass), which shows a bimodal distribution highly consistent with color diagrams [38] and thus provides a quick diagnostic for quenching; and (3) calculating the quenched fraction after sample division as a statistic. Here we introduce several studies applying different statistical indicators that observed changes in galaxy formation activity across different cosmic environments.

Kuutma et al. [11] used data from SDSS Release 10 [39] and classified galaxies using Galaxy Zoo. Their Figure 3 [FIGURE:3] statistics show the elliptical-to-spiral ratio (E/S) and galaxy $g-i$ color varying from 10 Mpc·h$^{-1}$ to 0.1 Mpc·h$^{-1}$ from filaments. They found that brighter galaxies tend to become redder when approaching filaments, while fainter galaxies show no significant change beyond error bars. The elliptical-to-spiral ratio increases with proximity to filaments, synchronized with $g-i$ value changes. They proposed that morphological transformation might cause the color index changes. However, after distinguishing galaxy morphology in the brighter galaxy sample, the trend of galaxies becoming redder near filaments persists, being more significant for spiral galaxies.

Malavasi et al. [35] used IllustrisTNG [40–42] simulation data at redshift 0 to study the dependence of galaxy stellar mass, star formation rate ($SFR$), and $sSFR$ on distance to filaments, as shown in Figure 1a [FIGURE:1]. They identified the cosmic web (including filament segment positions and node locations) using the DisPerSE algorithm and considered three distance variables: (1) distance to the nearest node on the cosmic web (density function maxima and bifurcation points identified by DisPerSE) ($d_{cp}$); (2) distance to the nearest filament segment midpoint ($d_{fil}$); and (3) distance from the nearest filament point (the projection position of the galaxy onto its nearest filament) to one of the two critical points connected by that filament ($d_{skel}$). Regardless of the calculation method, all three galaxy properties show strong dependence on cosmic web distance variables.

Similarly, Hasan et al. [43, 44] analyzed the relationship between galaxy $sSFR$ and distance to filaments using IllustrisTNG data, extending the redshift range to 4 and distinguishing between central and satellite galaxies. Their study shows that cosmic web influence on $sSFR$ only begins at redshift 2, being almost absent at higher redshifts. Moreover, environmental quenching primarily affects satellite galaxies, with central galaxies experiencing only minimal effects.

Observational evidence exists for cosmic environmental influence on galaxy quenching at higher redshifts. Salerno et al. [12] selected galaxies from the VIMOS Extragalactic Survey [45] in the redshift range 0.43–0.89, classified them by cosmic environment, and compared how quenched fractions vary with galaxy mass. They found that galaxy quenched fractions are lowest in field and infall regions, intermediate in filament environments, and highest in groups, as shown in Figure 2 [FIGURE:2]. However, Salerno et al. did not calculate galaxy distances to filaments nor statistically account for other potential quenching factors.

In both observational results and theoretical simulations, multiple parameters characterizing galaxy star formation activity show declining trends from 10 Mpc·h$^{-1}$ to 0.1 Mpc·h$^{-1}$ from filaments. Simulation studies extend this influence to redshifts 1–2. Simulations indicate this trend is dominated by satellite galaxies, while observations find it mainly appears in lower-luminosity galaxies (central galaxies are typically brighter than satellites). Satellite galaxies have smaller stellar masses and reside closer to halo edges, making them more susceptible to environmental influences. However, since star formation rate variations are more significant in low-luminosity galaxies, observational biases may exist, requiring further evidence to investigate the scope and mechanisms of large-scale environmental quenching.

3.2 Research Results on Environmental Quenching After Controlling Influence Variables

Galaxy stellar mass, local environment (i.e., halo mass), and the underlying local galaxy density field all influence star formation activity, and these parameters exhibit some degeneracy. Proximity to filaments typically corresponds to larger stellar mass, more massive halos, and higher galaxy density, making it crucial to separate variable influences in research.

Galaxy star formation rate and stellar mass are tightly correlated [46]. Hydrodynamic simulations generally agree that feedback from supermassive black holes (SMBH) or active galactic nuclei (AGN) is key to quenching massive galaxies [47, 48]. AGN feedback can be triggered under various conditions, such as black hole accretion and galaxy mergers [49, 50], heating gas through powerful jets and causing galaxy quenching. Most environmental quenching studies (including those in Section 3.1) control for galaxy mass as an influence variable.

Researchers have found in both observational data [51–53] and theoretical simulations [54, 55] that galaxies may become redder or quenched in massive dark matter halos. The mechanism by which halo mass affects galaxy quenching is that in halos above a critical mass of $10^{12} M_\odot$, virial shock heating of infalling gas from the intergalactic medium prevents accreted gas from directly fueling star formation [56]. Additionally, AGN feedback efficiency correlates with halo mass. Lin et al. [57] used SDSS-IV MaNGA survey [58] data to classify galaxy quenching as inside-out or outside-in. External mechanisms such as ram pressure stripping or gas exhaustion typically cause outside-in quenching, while AGN feedback produces the opposite trend (inside-out). They found inside-out quenching dominates, with its fraction increasing with both stellar mass (at fixed halo mass) and halo mass (at fixed stellar mass). Some studies control for halo mass to determine whether filament environments have independent effects on galaxy formation beyond local environments. Perez et al. [59] used TNG300-1 data, divided galaxies into red and blue, and plotted their distributions in three halo mass bins ($M_{halo}<10^{11.5} M_\odot \cdot h^{-1}$, $10^{11.5} M_\odot \cdot h^{-1}<M_{halo}<10^{12.5} M_\odot \cdot h^{-1}$, $M_{halo}>10^{12.5} M_\odot \cdot h^{-1}$), as shown in Figure 3. They found that in low-mass halos, more blue galaxies appear in filament peripheries (galaxy-to-filament distances of 1.2–2 Mpc·h$^{-1}$). In massive halos, this trend reverses: more blue galaxies appear near filament centers (galaxy-to-filament distances of 0–0.1 Mpc·h$^{-1}$), with red galaxies dominating filament peripheries—still reflecting local halo effects.

O'Kane et al. [60] used SDSS DR8 data to study the scatter of $SFR$ around the star formation main sequence (MS) as a measure of star formation suppression. After matching galaxy stellar masses across different environments, they found higher suppression of star formation activity in filament galaxies, demonstrating environmental influence. However, after simultaneously matching both stellar mass and local galaxy density, this effect nearly disappeared, indicating that filament environment influence is degenerate with local density field effects. As shown in Figure 1b, Malavasi et al. [35] also analyzed galaxy property dependence on the local density field: as density increases, galaxy mass increases while $SFR$ and $sSFR$ decrease, with different galaxy-to-filament distances having minor effects on results. When $\rho_{DTFE}$ is between 10–10$^3$ Mpc$^{-3}$, $sSFR$ increases slightly with density over a small range. Figure 1c shows that local density and distance to filaments are degenerate variables. To separate their effects on galaxy property distributions, they proposed a "shuffling" method: dividing the density field into many small intervals and randomly shuffling galaxy properties ($SFR$, galaxy mass, etc.) among galaxies within each interval 1,000 times while keeping galaxy-to-filament distances ($d_{cp}$, $d_{skel}$, $d_{fil}$) unchanged. This randomizes the relationship between galaxy properties and filament distance within each interval while preserving the relationship between properties and local density field when recombining intervals. They calculated differences between the shuffled average results ($H_R$) and original results ($H_0$), normalized by the root-mean-square of original errors. The differences are nearly zero at most filament distances, thus cannot rule out that filament distance effects on quenching are due to the local density field.

Song et al. [61] used HORIZON-AGN data, simultaneously considering local density field and halo mass effects. Using 0.4 times the halo virial radius as a criterion ($d_{fil} = 0.4 R_{h,vir} = d_{cut}$), they distinguished galaxies on filaments from those near filaments. At fixed local density, they found that galaxies on filaments generally have higher halo mass, galaxy mass, and $SFR$ than those near filaments, with a jump-like increase when very close to filaments (see their Figure 8 [FIGURE:8]). To remove halo effects, they fitted the $SFR$–halo mass relation and calculated residuals between $SFR$ and this primary relation (see their Figure 7 [FIGURE:7]). The $SFR$ residual increases closer to filaments but begins decreasing from approximately $10^{0.5} R_{h,vir}$, indicating galaxies experience quenching processes near filaments.

To compare the importance of different variables for galaxy quenching and identify the most predictive parameters for star formation activity, researchers can employ random forest methods. Random forest is a machine learning approach for classifying complex data. First, data are split into training and test sets, with multiple subsets constructed through random sampling from the training set. Each subset builds a decision tree to learn which feature parameters best classify the data (in galaxy quenching studies, the classes are "star-forming" and "quenched"). The probability of randomly selecting a class at each node can be used to calculate Gini impurity [62]; higher Gini impurity indicates poorer classification ability of the feature parameter. If a feature parameter effectively reduces Gini impurity, it is more important for galaxy quenching. Weighted averaging of Gini impurity changes across decision trees yields variable importance. Bluck et al. [37] analyzed MaNGA observational data and found that bulge mass is the most predictive photometric parameter (including bulge mass, disk mass, total stellar mass, and B/T morphology) for galaxy quenching, while central stellar velocity dispersion becomes more important when spectroscopic data are available. Goubert et al. [63] compared several simulation datasets and found that for central galaxies and massive satellite galaxies, central black hole mass is the best quenching predictor, while for low-mass satellite galaxies, halo mass is the best predictor. Random forest algorithms have limitations: they are significantly affected by input data quality and completeness, and may overfit training data, particularly when the number of trees is very large or the model is improperly tuned. Therefore, multiple approaches are needed to study these issues.

3.3 Phenomena and Mechanisms of Cosmic Web Promoting Galaxy Star Formation Activity

Galárraga-Espinosa et al. [64] studied the "filament connectivity" of central galaxies above $10^8 M_\odot$ in TNG50-1 simulations—defined as how many filaments a galaxy connects to. As shown in Figure 4a, to simultaneously control for stellar mass and local density field, they first divided galaxies into four groups (A, B, C, D). Figure 4b plots $sSFR$ versus filament connectivity. Groups A and B (lower stellar mass groups) show $sSFR$ significantly increasing with connectivity, indicating that more filaments enhance star formation activity. They interpret this effect through Kereš et al. [66]: the host halos of these low-mass galaxies may lack sufficient mass to maintain shock effects, allowing cold gas to flow along filaments into central galaxies. Meanwhile, groups C and D show almost no variation with connectivity, indicating that in massive galaxies, star formation is more likely regulated by internal processes independent of cold gas inflow through filaments. This may relate to Gabor and Davé [67], who found using hot gas quenching models that while red galaxies often reside in denser environments, many isolated red central galaxies exist in hot dark halos.

Kraljic et al. [65] studied filament connectivity of star-forming and inactive galaxies, finding very different results from Galárraga-Espinosa et al. [64]. Kraljic et al. found inactive galaxies have higher connectivity (see Figure 4c). Galárraga-Espinosa et al. argued that Kraljic et al.'s study only demonstrates that different galaxies inhabit different environments but cannot well explain how galaxy properties themselves vary with environment. Additionally, with improved simulation resolution, their study focused on finding fine filament structures. Both studies used DisPerSE to identify filaments: Kraljic et al. used galaxy coordinates as input, while Galárraga-Espinosa et al. used dark matter particle coordinates, which may be more advantageous for finding fine filament structures—a major distinction from previous studies.

The physical picture suggested by these studies remains worth exploring. Bulichi et al. [68] found through Simba simulations [69] that while changes in star formation activity of central galaxies near filament centers are negligible, the amount of H$2$ gas available for star formation increases. Nelson et al. [70] noted that gas transport within halos (gas flow from CGM into galaxies) is significantly affected by hydrodynamic simulation numerical schemes. However, some observational data provide potential evidence for cold gas storage in filament structures. Kleiner et al. [71] analyzed neutral hydrogen content (ratio of neutral hydrogen mass to galaxy mass) in galaxies near filament backbones in the nearby universe, finding that more massive galaxies (above $10^{11} M\odot$) show higher neutral hydrogen content. Odekon et al. [72] used neutral hydrogen data from the ALFALFA survey [73] to analyze star-forming galaxies in the mass range $10^{8.5} M_\odot$–$10^{10.5} M_\odot$, finding higher neutral hydrogen content in galaxies located in filament and tendril environments than in voids. Sinigaglia et al. [74] selected star-forming galaxies above $10^{9.6} M_\odot$ at redshift 0.37 from COSMOS survey data, finding significantly higher neutral hydrogen content in filament environment galaxies than in field and cluster galaxies. Cosmic web structures may transport cold gas to central galaxies, delaying their quenching processes under the influence of halo mass and black hole feedback [75].

4 Summary and Outlook

This review examined research on the cosmic web and galaxy quenching in filament environments. Algorithms including DisPerSE, Sconce, MCPM, and Poisson distribution-based networks are used to identify and quantify cosmic web structures. Although observations at redshifts 0–1 and simulations at redshifts 0–2 have found evidence of weakened star formation activity near filaments—manifested as redder galaxy colors, decreased $sSFR$, and increased quenched fractions—some studies show that after separating central and satellite galaxies and controlling for variables including halo mass and local (galaxy) density fields, filament effects on star formation activity are weak or uncertain. Some researchers propose alternative views: filaments may supply gas to nearby galaxies and cause $SFR$ increases. However, since numerical simulations heavily depend on specific schemes, directly simulating results regarding gas and star formation activity in large-scale structure studies remains difficult.

Future research can address several questions through new numerical simulation techniques and high-redshift observational data: (1) Filament structure formation mechanisms: With high-redshift observational projects such as the James Webb Space Telescope (JWST), wide-field surveys like the Euclid mission, and future Nancy Grace Roman Space Telescope wide-field infrared surveys, researchers can study galaxy distribution and evolution in different filament environments, further exploring the origin and formation mechanisms of filament structures and cosmic environments at high redshift. (2) Long-term connections between filament environments and galaxy evolution: Through large-scale simulations such as MillenniumTNG, researchers can study galaxy evolution processes in cosmic filaments and explore the long-term effects of different filament environments on galaxy evolution. (3) Connections between environment and internal star formation mechanisms: With high-resolution simulations like FIRE (Feedback In Realistic Environments), researchers can explore how filament environments affect internal processes such as AGN feedback and cold gas flows in circumgalactic media, investigating how cosmic filaments influence central galaxy star formation efficiency through cold gas transport.

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