Lensing in the darkness: a Bayesian analysis of 22 Chandra sources at z ≳ 6 shows no evidence of lensing

More than 200 quasars have been detected so far at z > 6, with only one showing clear signs of strong gravitational lensing. Some studies call for a missing population of lensed high-z quasars, but their existence is still in doubt. A large fraction of high-z quasars being lensed would have a significant effect on the shape of the intrinsic quasar luminosity function (QLF). Here, we perform the first systematic search for lensed X-ray-detected quasars at z ≳ 6 employing a Bayesian analysis, with the code BAYMAX, to look for morphological evidence of multiple images that may escape a visual inspection. We analysed a sample of 22 quasars at z > 5.8 imaged by the Chandra X-ray observatory and found none with statistically significant multiple images. In the sub-sample of the eight sources with photon counts >20, we exclude multiple images with separations r > 1 arcsec and count ratios f > 0.4, or with separations as small as 0.7 arcsec and f > 0.7 at $95{{\ \rm per\ cent}}$ confidence level. Comparing this non-detection with predictions from theoretical models suggesting a high- and a low-lensed fraction, we placed upper limits on the bright-end slope, β, of the QLF. Using only the sub-sample with eight sources, we obtain, in the high-lensing model, a limit β < 3.38. Assuming no multiple source is present in the full sample of 22 sources, we obtain β < 2.89 and β < 3.53 in the high- and low-lensing models, respectively. These constraints strongly disfavour steep QLF shapes previously proposed in the literature.