K_L-correction factor, the ratio of the luminosity in [0.1–2.4] keV energy band to that in the [0.5–2.] keV band. The theoretical variation with luminosity, for z = 0 and z = 0.5 are shown with solid and dashed lines, respectively. Here the dependence on temperature K_L(T) has been translated to a variation with luminosity via the L₅₀₀–T relation. The redshiſt dependence is a small translation in the L₅₀₀K_L plane via the E(z) factor. The horizontal lines show the value for a 10⁴⁴ erg s^–1 cluster at z = 0 (solid), ±2% (dashed) or ±10% (dotted), respectively. The points show the K_L-correction (Eq. (3)) applied to the 400SD, 160SD, NEP, SHARC, and WARPS clusters (for which the catalogue flux is given in the [0.5–2.] keV band). Each point corresponds to a cluster from these samples; the temperature being estimated from the iterative procedure described in Sect. 4.1.