We present a detailed investigation of the X-ray luminosity ( L _ { \mathrm { X } } ) -gas temperature ( T _ { \mathrm { vir } } ) relation of the complete X-ray flux-limited sample of the 64 brightest galaxy clusters in the sky ( HIFLUGCS ) .
We study the influence of two astrophysical processes , active galactic nuclei ( AGN ) heating and intracluster medium ( ICM ) cooling , on the L _ { \mathrm { X } } { \mathrm { - } } T _ { \mathrm { vir } } relation , simultaneously for the first time .
We employ homogeneously determined gas temperatures and central cooling times , measured with Chandra , and information about a central radio source from Mittal and collaborators .
We determine best-fit relations for different subsamples using the cool-core strength and the presence of central radio activity as selection criteria .
We find the strong cool-core clusters ( SCCs ) with short cooling times ( < 1 Gyr ) to display the steepest relation ( L _ { \mathrm { X } } \propto T _ { \mathrm { vir } } ^ { 3.33 \pm 0.15 } ) and the non-cool-core clusters ( NCCs ) with long cooling times ( > 7.7 Gyr ) to display the shallowest ( L _ { \mathrm { X } } \propto T _ { \mathrm { vir } } ^ { 2.42 \pm 0.21 } ) .
This has the simple implication that on the high-mass scale ( T _ { \mathrm { vir } } > 2.5 ~ { } keV ) the steepening of the L _ { \mathrm { X } } { \mathrm { - } } T _ { \mathrm { vir } } relation is mainly due to the cooling of the intracluster medium gas .
We propose that ICM cooling and AGN heating are both important in shaping the L _ { \mathrm { X } } { \mathrm { - } } T _ { \mathrm { vir } } relation but on different length-scales .
While our study indicates that ICM cooling dominates on cluster scales ( T _ { \mathrm { vir } } > 2.5 keV ) , we speculate that AGN heating dominates the scaling relation in poor clusters and groups ( T _ { \mathrm { vir } } < 2.5 keV ) .

The intrinsic scatter about the L _ { \mathrm { X } } { \mathrm { - } } T _ { \mathrm { vir } } relation in X-ray luminosity for the whole sample is 45.4 \% and varies from a minimum of 34.8 \% for weak cool-core clusters to a maximum of 59.4 \% for clusters with no central radio source .
The scatter does not decrease if SCC clusters are excluded from the full sample .
We find that the contribution of core luminosities within the cooling radius r _ { \mathrm { cool } } , where the cooling time is 7.7 Gyr and gas cooling may be important , to the total X-ray luminosities amounts to 44 \% and 15 \% for the SCC and WCC clusters , respectively .
We find that after excising the cooling region , the scatter in the L _ { \mathrm { X } } { \mathrm { - } } T _ { \mathrm { vir } } relation drops from 45.4 \% to 39.1 \% , implying that the cooling region contributes \sim 27 \% to the overall scatter .
The remaining scatter is largely due to the NCCs .

Lastly , the statistical completeness of the sample allows us to quantify and correct for selection effects individually for the subsamples .
We find the true SCC fraction to be 25 % lower than the observed one and the true normalizations of the L _ { \mathrm { X } } { \mathrm { - } } T _ { \mathrm { vir } } relations to be lower by 12 \% , 7 \% , and 17 \% for SCC , WCC , and NCC clusters , respectively .