n thus dominates the growth of galaxies.

Dependence on halo mass {#sec:mass}
=======================

![image](figures/massprop_REF_L050N512_z2p0_pecvel0p1.eps)

In Fig. \[fig:halomassz2\] we plot the same properties as in Fig. \[fig:haloradz2\] as a function of halo mass for gas at radii $0.8R_\mathrm{vir}<R<R_\mathrm{vir}$, where differences between hot- and cold-mode gas are large. Grey, dashed lines show analytic estimates and are discussed below. The dotted, grey line in the top-left panel indicates the star formation threshold, i.e. $n_{\rm H}=0.1~{\rm cm}^{-3}$. The differences between the density and temperature of the hot- and cold-mode gas increase with the mass of the halo. The average temperature, maximum past temperature, pressure, entropy, metallicity, absolute radial peculiar velocity, absolute accretion rate, and the hot fraction all increase with halo mass.

We can compare the gas overdensity at the virial radius to the density that we would expect if baryons were to trace the dark matter, $\rho_\mathrm{vir}$. We assume an NFW profile [@Navarro1996], take the mean internal density relative to the critical density at redshift $z$, $\Delta_c\langle\rho\rangle$, from spherical collapse calculations [@Bryan1998] and the halo mass-concentration relation from @Duffy2008 and calculate the mean overdensity at $R_\mathrm{vir}$. This is plotted as the dashed, grey line in the top-left panel of Fig. \[fig:halomassz2\]. It varies very weakly with halo mass, because the concentration depends on halo mass, but this is invisible on the scale of the plot. For all halo masses the median density is indeed close to this analytic estimate. While the same is true for the hot-mode gas, for high-mass haloes ($M_\mathrm{halo}\gtrsim10^{12}$ M$_\odot$) the median density of cold-mode gas is significantly higher than the estimated density and the difference reaches two orders of magnitude for $M_\mathrm{halo}\sim10^{13}$ M$_\odot$. A significant fraction of the cold-mode gas in these most massive haloes is star for