A large portion of the baryons at low redshifts are still missing from detection. Most of the missing baryons are believed to reside in large scale cosmic filaments. Understanding the distribution of baryons in filaments is crucial for the search for missing baryons. We investigate the properties of cosmic filaments since $z=4.0$ in a cosmological hydrodynamic simulation, focusing on the density and temperature profiles perpendicular to the filament spines. Our quantitative evaluation confirm the rapid growth of thick and prominent filaments after $z=2$. We find that the local linear density of filaments shows correlation with the local diameter since $z=4.0$. The averaged density profiles of both dark matter and baryonic gas in filaments of different width show self-similarity, and can be described by an isothermal single-beta model. The typical gas temperature increases as the filament width increasing, and is hotter than $10^6$ K for filaments with width $D_{fil} gtrsim 4.0 rm{Mpc}$, which would be the optimal targets for the search of missing baryons via thermal Sunyaev-Zeldovich (SZ) effect. The temperature rises significantly from the boundary to the inner core regime in filaments with $D_{fil} gtrsim 4.0 rm{Mpc}$, probably due to heating by accretion shock, while the temperature rise gently in filaments with $D_{fil}< 4.0 rm{Mpc}$.
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