_\mathrm{vir}$), whereas it suddenly drops to below $10^5$ K around $0.2 R_{\rm vir}$ when metal-line cooling is included. Thus, the catastrophic cooling flow of the diffuse, hot component in the inner haloes is due to metals. Indeed, while the median hot-mode radial peculiar velocity within $0.2 R_{\rm vir}$ is positive without metal-line cooling, it becomes negative (i.e. infalling) when metal-line cooling is included.

Evolution: Milky Way-sized haloes at $z=0$ {#sec:z0}
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![image](figures/radialprop_REF_L050N512_z0p0_mass11p5to12p5_pecvel0p1.eps)

Fig. \[fig:haloradz0\] is identical to Fig. \[fig:haloradz2\] except that it shows profiles for $z=0$ rather than $z=2$. For comparison, the dotted curves in Fig. \[fig:haloradz0\] show the corresponding $z=2$ results. As we are again focusing on $10^{11.5}$ M$_\odot<M_\mathrm{halo}<10^{12.5}$ M$_\odot$, the results are directly relevant for the Milky Way galaxy.

Comparing Fig. \[fig:haloradz2\] to Fig. \[fig:haloradz0\] (or comparing solid and dotted curves in Fig. \[fig:haloradz0\]), we see that the picture for $z=0$ looks much the same as it did for $z=2$. There are, however, a few notable differences. The overdensity profiles hardly evolve, although the difference between the cold and hot modes is slightly smaller at lower redshift. However, a constant overdensity implies a strongly evolving proper density ($\rho \propto (1+z)^3$) and thus also a strongly evolving cooling rate. The large decrease in the proper density caused by the expansion of the Universe also results in a large drop in the pressure and a large increase in the entropy.

The lower cooling rate shifts the peak of the cold-mode temperature profile from about 2$R_{\rm vir}$ to about $R_{\rm vir}$. While there is only a small drop in the temperature of the hot-mode gas, consistent with the mild evolution of the virial temperature of a halo of fixed mass ($T_{\rm vir} \propto (1+z)$; eq. \[\[eqn:virialtemperature\]\]), the evolution in the median