Tracing Missing Baryons in the Cosmic Filaments with tSZ and CMB-Lensing Stacking

TL;DR

This work targets the long-standing missing baryon problem by statistically detecting and characterizing the WHIM in cosmic filaments. By stacking Planck PR4 Compton-$y$ and CMB-lensing convergence maps around ~30,000 DisPerSE-identified filaments from SDSS, the authors jointly model gas and matter density with two $\beta$-models, obtaining $δ\approx 4.2$, $r_c\approx 5.2\,\mathrm{cMpc}$, and $T_e\approx2.7\times10^6$ K for the standard model. The inferred filamentary gas fraction is $ρ_{gas}^{\rm fil}/\Omega_b\approx0.127$ for the $30$–$100\,\mathrm{cMpc}$ subset, rising to $\approx0.232$ when including filaments of all lengths, indicating that WHIM in filaments accounts for a substantial portion of the cosmic baryon budget. The study demonstrates the power of combining tSZ and CMB lensing with filament geometry and projection corrections to probe diffuse baryons in the cosmic web and paves the way for higher-resolution follow-up with future CMB experiments.

Abstract

We investigate the distribution of missing baryons in the cosmic filaments by stacking $\sim 30,700$ filaments across the northern and southern SDSS sky regions using Planck Compton-$y$ and CMB lensing maps. Filaments are identified using the DisPerSE algorithm applied to the SDSS LOWZ-CMASS galaxy samples, selecting structures with lengths between 30-100 cMpc and redshifts in the range $0.2 < z < 0.6$. Radial profiles are extracted out to 25 cMpc from the filament spines, and galaxy clusters with halo masses above $\sim 3 \times 10^{13} M_\odot$ are masked to reduce contamination. We detect the thermal Sunyaev-Zeldovich (tSZ) signal at $7.82σ$ and the CMB lensing signal at $7.78σ$. The stacked profiles are corrected by a geometric bias correction based on filament inclination with respect to the line-of-sight, and they are portrayed assuming isothermal, cylindrically symmetric models. We explore different gas and matter density distributions, focusing on the $β$-models with $(α,β) = (2,2/3)$ or $(1,1)$. By jointly fitting the Compton-$y$ and $κ$ profiles, we constrain the central electron overdensity and temperature to be $δ= 4.18^{+2.01}_{-1.06}$ and $T_e = 2.74^{+0.65}_{-0.53}\times 10^6 \mathrm{K}$ for the standard $β$-model. These results suggest that filamentary WHIM in our selected long filaments contributes a significant baryon fraction of $0.127^{+0.019}_{-0.021}\times Ω_b$ to the cosmic baryon budget.

Figures (15)

• Figure 1: Redshift (top) and length (bottom) distributions of the selected filament sample (highlighted in red).
• Figure 2: Spatial distribution of filaments extracted by DisPerSE: northern sky (top) and southern sky (bottom).
• Figure 3: Masked Planck Compton-$y$(a) and lensing convergence (b) maps centered on the north and south Galactic poles. Regions outside the SDSS DR12 footprint are excluded, and additional masking is applied to remove galaxy clusters out to $3 \times R_{500}$.
• Figure 4: Schematic illustration of the filament stacking procedure. Black lines represent the filament spine constructed from critical points (black dots) identified by DisPerSE. The filament endpoints correspond to maxima or bifurcation points, whereas the intermediate nodes correspond to type–1 saddle points along the filamentary structure. Radial bins (colored) extend perpendicularly from the spine out to $25\,\mathrm{cMpc}$ in comoving radius. Colored dots mark the central positions of HEALPix pixels included in the analysis, while white dots indicate masked pixels excluded from the stacking.
• Figure 5: Average radial profiles of stacked filaments for Compton-$y$(a) and lensing convergence $\kappa$(b) under different cluster masking radii. Shaded bands indicate $1\sigma$ bootstrap uncertainties.