Table 1
Best fitting parameters for a Schechter function and alternative functions to the REFLEX II X-ray luminosity function.
| Method | Lx–range | α |
|
n0 | q | η | No. cl. |
|
|
|||||||
| A | ≥0.003 | 1.74 | 3.02 | 5.0 × 10-7 | − | 2.3 | 802 |
| A | ≥0.01 | 1.76 | 3.10 | 4.7 × 10-7 | − | 2.5 | 798 |
| A | ≥0.03 | 1.78 | 3.19 | 4.5 × 10-7 | − | 2.9 | 779 |
| A | ≥0.1 | 1.93 | 3.99 | 2.8 × 10-7 | − | 9.9 | 741 |
| A | ≥0.3 | 2.03 | 4.67 | 2.0 × 10-7 | − | 24.3 | 623 |
|
|
|||||||
| B | ≥0.003 | 1.54 | 1.08 | 1.8 × 10-6 | 1.39 | 1.4 | 802 |
| B | ≥0.01 | 1.53 | 1.03 | 2.0 × 10-6 | 1.39 | 1.4 | 802 |
| B | ≥0.1 | 1.60 | 1.17 | 1.6 × 10-6 | 1.39 | 2.5 | 802 |
|
|
|||||||
| C | ≥0.003 | 2.19 | 5.7 | 1.3 × 10-7 | − | 1.6 | 802 |
| C | ≥0.01 | 2.18 | 5.5 | 1.4 × 10-7 | − | 1.6 | 798 |
| C | ≥0.03 | 2.13 | 5.0 | 1.7 × 10-7 | − | 1.4 | 779 |
| C | ≥0.1 | 2.18 | 5.4 | 1.4 × 10-7 | − | 1.7 | 741 |
| C | ≥0.3 | 2.17 | 5.4 | 1.4 × 10-7 | − | 1.6 | 623 |
Notes. The method code A is for the Schechter function (Eq. (2)), B for the q-exponential (Eq. (5)) and C for the modified Schechter function (Eq. (6)). The X-ray luminosity range used in the fit and the parameter are given in units of 
erg s-2. α, , and n0 (in units of h
Mpc-3) are the slope, the break parameter, and the normalization of the Schechter function or its modified variants, while q is the extra parameter of the q-exponential function. η is similar to a reduced χ2 parameter determined as explained in the text and the last column gives the number of clusters involved in the fit. The typical uncertainties are ~5% for α and ~22% for Lx.
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