Halo Concentrations and the New Baseline X-ray Luminosity-Temperature
  and Mass Relations of Galaxy Clusters
  The standard self-similar model of galaxy cluster formation predicts that the
X-ray luminosity-temperature ($L_X$-$T_X$) relation of galaxy clusters should
have been $L_X\propto T_X^2$ in absence of the baryonic physics, such as
radiative cooling and feedback from stars and black holes. However, this
baseline relation is predicted without considering the fact that the halo
concentration and the characteristic density of clusters increases as their
mass decreases, which is a consequence of hierarchical structure formation of
the universe. Here, we show that the actual baseline relation should be
$L_X\propto T_X^\alpha$, where $\alpha\sim 1.7$, instead of $\alpha=2$, given
the mass dependence of the concentration and the fundamental plane relation of
galaxy clusters. Numerical simulations show that $\alpha\sim 1.6$, which is
consistent with the prediction. We also show that the baseline luminosity-mass
($L_X$-$M_\Delta$) relation should have been $L_X\propto M_\Delta^\beta$, where
$\beta\sim 1.1$-1.2, in contrast with the conventional prediction
($\beta=4/3$). In addition, some of the scatter in the $L_X$-$M_\Delta$
relation can be attributed to the scatter in the concentration-mass ($c$-$M$)
relation. The confirmation of the shallow slope could be a proof of
hierarchical clustering. As an example, we show that the new baseline relations
could be checked by studying the temperature or mass dependence of gas mass
fraction of clusters. Moreover, the highest-temperature clusters would follow
the shallow baseline relations if the influences of cool cores and cluster
mergers are properly removed.
