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Table 1.
Regression analysis for X-ray luminosity vs. richness scaling relation ln(LxEz−1 erg−1 s) = α + βln(λ/27.9 ⋅ Ez)+N(0, σ).
| Sample | Intercept α | Slope β | Intrinsic scatter σ | N clusters |
|---|---|---|---|---|
| λ ≥ 20 (updated λ estimates) | 100.094 ± 0.020 | 1.463 ± 0.025 | 0.613 ± 0.009 | 2951 |
| λ ≥ 20 (redMaPPer λ) | 100.403 ± 0.017 | 1.140 ± 0.022 | 0.659 ± 0.010 | 2951 |
| Substructure λ ≥ 20 | 100.492 ± 0.035 | 1.168 ± 0.036 | 0.586 ± 0.013 | 1352 |
| No-substructure λ ≥ 20 | 99.957 ± 0.024 | 1.497 ± 0.042 | 0.592 ± 0.013 | 1599 |
| Substructure λ ≥ 40 | 100.497 ± 0.060 | 1.160 ± 0.054 | 0.564 ± 0.015 | 1015 |
| No-substructure λ ≥ 40 | 99.899 ± 0.086 | 1.505 ± 0.102 | 0.555 ± 0.019 | 616 |
| Substructure 20 ≤ λ < 40 | 100.399 ± 0.066 | 1.660 ± 0.240 | 0.653 ± 0.030 | 337 |
| No-substructure 20 ≤ λ < 40 | 99.904 ± 0.028 | 2.134 ± 0.132 | 0.609 ± 0.017 | 983 |
| Substructure λ ≥ 40, z ≥ 0.2 | 100.642 ± 0.064 | 1.061 ± 0.055 | 0.523 ± 0.015 | 897 |
| Substructure λ ≥ 40, z < 0.2 | 100.046 ± 0.238 | 1.457 ± 0.303 | 0.752 ± 0.056 | 118 |
| No-substructure λ ≥ 40, z ≥ 0.2 | 100.186 ± 0.101 | 1.239 ± 0.112 | 0.526 ± 0.021 | 463 |
| No-substructure λ ≥ 40, z < 0.2 | 99.181 ± 0.253 | 2.406 ± 0.387 | 0.570 ± 0.040 | 153 |
| Substructure 20 ≤ λ < 40, z ≥ 0.2 | 100.707 ± 0.122 | 0.969 ± 0.367 | 0.554 ± 0.034 | 195 |
| Substructure 20 ≤ λ < 40, z < 0.2 | 100.305 ± 0.083 | 1.436 ± 0.464 | 0.751 ± 0.051 | 142 |
| No-substructure 20 ≤ λ < 40, z ≥ 0.2 | 100.066 ± 0.066 | 2.031 ± 0.237 | 0.497 ± 0.025 | 396 |
| No-substructure 20 ≤ λ < 40, z < 0.2 | 99.850 ± 0.032 | 1.733 ± 0.190 | 0.653 ± 0.023 | 587 |
| No-substructure 10 ≤ λ < 20, z < 0.2 | 100.727 ± 0.234 | 3.149 ± 0.440 | 0.721 ± 0.037 | 396 |
| Multiple X-rays subsample | 100.457 ± 0.154 | 1.277 ± 0.333 | 0.905 ± 0.127 | 41 |
| Multiple opticals subsample (λ ≥ 20) | 100.432 ± 0.097 | 1.181 ± 0.087 | 0.709 ± 0.033 | 270 |
Notes. Uncertainties are quoted for the 68% confidence interval.
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