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We studied physical properties of matter in 24,544 filaments ranging from 30to 100 Mpc in length, identified in the Sloan Digital Sky Survey (SDSS). Westacked the Comptonization y map produced by the Planck Collaboration aroundthe filaments, excluding the resolved galaxy groups and clusters above a massof ~3*10^13 Msun. We detected the thermal Sunyaev-Zel'dovich signal for thefirst time at a significance of 4.4 sigma in filamentary structures on such alarge scale. We also stacked the Planck cosmic microwave background (CMB)lensing convergence map in the same manner and detected the lensing signal at asignificance of 8.1 sigma. To estimate physical properties of the matter, weconsidered an isothermal cylindrical filament model with a density distributionfollowing a beta-model (beta=2/3). Assuming that the gas distribution followsthe dark matter distribution, we estimate that the central gas and matteroverdensity and gas temperature are overdensity = (19.0 +27.3 -12.1) andtemperature = (1.2 +- 0.4)*10^6 K, which results in a measured baryon fractionof (0.080 +0.116 -0.051) * Omega_b.

Density and temperature of cosmic-web filaments on scales of tens of megaparsecs