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

TL;DR

This study directly detects quasi-linear velocity fields in the cosmic web by targeting filaments between cluster pairs in SDSS data and removing the Hubble flow and rigid-body background to reveal internal filament infall. The authors observe a split infall toward the two end clusters with a significant slope in redshift space, a maximum deprojected inflow of $v_{\max}\approx30$ km s$^{-1}$ ($v_{z,\max}\approx20$ km s$^{-1}$) for $M_c\sim10^{14.3}M_\odot$, and a depletion boundary near $0.15$–$0.2$ of the filament length. The signal grows with mass imbalance and anti-correlates with filament density, and matches an emulator-based halo–filament–halo model, supporting a gravity-driven inflow rather than passive transport. These results open a new observational window on quasi-linear velocity fields in the cosmic web and offer a promising avenue for mass measurements and gravity tests with future wide-field spectroscopic surveys.

Abstract

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 $5σ$ 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.

Figures (12)

• Figure 1: Distribution of the excess redshift of galaxies $\Delta z$ after linearly subtracting rigid-body background redshift of the filament, representing the flow motion on the filament. The top-left panel shows the excess redshift $\Delta z$ v.s. location on the filament, with each (blue) point representing a galaxy. We fit a line (red) to the points and get a slope that deviates from 0 at $5.5\sigma$ significance, providing strong evidence that the filament is flowing from the center to the two sides. The top-right two panels show how the galaxies distribute on different locations and $\Delta z$. The non-uniform galaxy-line-density is not only due to selection effect, but also due to filament dynamics, see Fig. \ref{['Fig RSD cylinder']}. The two bottom panels in green show the residual distribution after subtracting the linear fit.
• Figure 2: Mean velocity flow measurement along the filament. This figure uses the same data as Fig. \ref{['Fig linear_fit']}, but divides into 10 bins to illustrate the spatial variation of the flow. The blue circle corresponds to the closer cluster (with mass $\sim10^{14.3}M_\odot$) and the red circle represents the more distant cluster (with mass $\sim10^{14.32}M_\odot$). The dotted line represents no velocity flow with respect to the "rigid-body" frame of the filament. The (black) data reject the null hypothesis at $5.6\sigma$ significance, suggesting the filament is flowing from the center toward the two ends, reaching a maximum velocity at $\sim20$ km/s. The deprojected velocity profile along the filament direction and its comparisons with N-body simulation are shown in Fig. \ref{['Fig flow data sim']}.
• Figure 3: How unbalanced mass affects velocity flow (top) and galaxy distribution (bottom) on the filament. When we further divide the sample into unbalanced mass samples, whether the more massive cluster is at the near end (blue) or at the far end (orange), the filament is generally flowing towards it. Meanwhile, a larger peak velocity ($\sim50$ to $75$ km/s) appears at a larger distance ($\sim0.2$) to the cluster center compared to Fig.\ref{['Fig flow']}. Significant dips can be found at the maximum infall place in the galaxy distribution.
• Figure 4: Filament properties (length, width, mass, alignment) of the results in Fig. \ref{['Fig linear_fit']} and \ref{['Fig flow']}, with the fiducial selections discribed in Sec. \ref{['Sec method']}. By stacking the galaxies in each cluster-filament-cluster system, we find the mean length (cluster-cluster distance, top-left panel) is 4.7 Mpc, mean width (galaxy-filament axis distance, top-right panel) is 1.6 Mpc, mean filament mass is an order smaller than the cluster mass (bottom-left panel), and mean alignment angle between filament ($\hat{f}$, pointing from the low-z cluster to the high-z cluster) and line-of-sight direction ($\hat{z}$) is $\sim60\deg$ (bottom-right panel).
• Figure 5: Comparison of different selections for the clusters. We see that pure richness selection (orange) can still yield a relatively strong S/N; however, the fitted slope (similar to that in Fig. \ref{['Fig linear_fit']}) has only $2\sigma$ significance, due to the limited number of galaxies. Thus it is not an ideal selection for understanding detailed flow behavior.