Context. The XXL Survey is the largest homogeneous survey carried out with XMM-Newton. Covering an area of 50 deg2, the survey contains several hundred galaxy clusters out to a redshift of ~2 above an X-ray flux limit of ~5 × 10-15 erg cm-2 s-1. This paper belongs to the first series of XXL papers focusing on the bright cluster sample. Aims. We investigate the luminosity-temperature (LT) relation for the brightest clusters detected in the XXL Survey, taking fully into account the selection biases. We investigate the form of the LT relation, placing constraints on its evolution. Methods. We have classified the 100 brightest clusters in the XXL Survey based on their measured X-ray flux. These 100 clusters have been analysed to determine their luminosity and temperature to evaluate the LT relation. We used three methods to fit the form of the LT relation, with two of these methods providing a prescription to fully take into account the selection effects of the survey. We measure the evolution of the LT relation internally using the broad redshift range of the sample. Results. Taking fully into account selection effects, we find a slope of the bolometric LT relation of BLT = 3.08 ± 0.15, steeper than the self-similar expectation (BLT = 2). Our best-fit result for the evolution factor is E(z)1.64 ± 0.77, fully consistent with “strong self-similar” evolution where clusters scale self-similarly with both mass and redshift. However, this result is marginally stronger than “weak self-similar” evolution, where clusters scale with redshift alone. We investigate the sensitivity of our results to the assumptions made in our fitting model, finding that using an external LT relation as a low-z baseline can have a profound effect on the measured evolution. However, more clusters are needed in order to break the degeneracy between the choice of likelihood model and mass-temperature relation on the derived evolution.
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