. The virial radius is 264 $h^{-1}$ comoving kpc and is indicated by the white circles.

![image](figures/radialprop_REF_L050N512_z2p0_mass11p5to12p5_pecvel0p1.eps)

In Fig. \[fig:haloradz2\] we show the same quantities as in Fig. \[fig:halo\] as a function of radius for the haloes with $10^{11.5}$ M$_\odot<M_\mathrm{halo}<10^{12.5}$ M$_\odot$ at $z=2$ in simulation *REF\_L050N512*. The black curves show the median values for all gas, except for the last two panels which show the mean values. The red (blue) curves show the median or mean values for hot- (cold-)mode gas, i.e. gas with maximum past temperatures above (below) $10^{5.5}$ K. The shaded regions show values within the 16th and 84th percentiles. Hot-mode gas at radii larger than $2R_\mathrm{vir}$ is dominated by gas associated with other haloes and/or large-scale filaments.

All the results we show are weighted by mass. In other words, we stacked all 518 haloes in the selected mass range using $R/R_{\rm vir}$ as the radial coordinate. The black curves in Fig. \[fig:haloradz2\] (except for the last two panels) then show the values of the corresponding property (e.g. the gas overdensity in the top-left panel) that divide the total mass in each radial bin in half, i.e. half the mass lies above the curve. We have done the same analysis for volume-weighted quantities by computing, as a function of radius, the values of each property that divides the total volume, i.e. the sum of $m_\mathrm{gas}/\rho$, in half but we do not show the results. The volume is completely dominated by hot-mode gas out to twice the virial radius, reaching 50 per cent at $3R_\mathrm{vir}$. Even though the volume-weighted hot fraction is very different, the properties of the gas and the differences between the properties of hot- and cold-mode gas are similar if we weigh by volume rather than mass.

We find that the median density of cold-mode gas is higher, by up to 1 dex, than that of hot-mode gas and that its current temperature is lower, by up to 2 dex, at least beyond 