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

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 $7.82\sigma$ and the CMB lensing signal at $7.78\sigma$. 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 $\beta$-models with $(\alpha,\beta) = (2,2/3)$ or $(1,1)$. By jointly fitting the Compton-$y$ and $\kappa$ profiles, we constrain the central electron overdensity and temperature to be $\delta = 4.18^{+2.01}_{-1.06}$ and $T_e = 2.74^{+0.65}_{-0.53}\times 10^6 \mathrm{K}$ for the standard $\beta$-model. These results suggest that filamentary WHIM in our selected long filaments contributes a significant baryon fraction of $0.127^{+0.019}_{-0.021}\times \Omega_b$ to the cosmic baryon budget.