Table 5.
Best-fit scaling relations of the optically selected clusters obtained from three types of fitting codes.
| Kelly |
1D HiBRECS |
2D HiBRECS |
|||||||
|---|---|---|---|---|---|---|---|---|---|
| Relation | a | b | σ | a | b | σ | a | b | σ |
| N − T | 1.44 ± 0.10 | 0.61 ± 0.21 | 0.095 | 1.19 ± 0.02 | 1.05 (fix) | 0.24 | 1.07 ± 0.04 | 1.05 (fix) | 0.30 (fix) |
| E(z)−1L − T | 1.38 ± 0.24 | 1.87 ± 0.45 | 0.28 | 1.48 ± 0.21 | 1.70 ± 0.40 | 0.63 | 1.23 ± 0.28 | 2.08 ± 0.46 | 0.63 |
| N − E(z)M | 1.43 ± 0.19 | 0.45 ± 0.24 | 0.10 | 1.22 ± 0.03 | 0.70 (fix) | 0.25 | 1.29 ± 0.06 | 0.70 (fix) | 0.16 |
| E(z)−1L − E(z)M | 1.44 ± 0.32 | 1.22 ± 0.43 | 0.32 | 1.50 ± 0.29 | 1.27 ± 0.25 | 0.65 | 1.24 ± 0.25 | 1.52 ± 0.34 | 0.65 |
| N − T | – | – | – | – | – | – | 1.07 ± 0.03 | 1.05 (fix) | 0.30 (fix) |
| L − T | 1.45 ± 0.27 | 1.94 ± 0.50 | 0.31 | 1.57 ± 0.24 | 1.72 ± 0.44 | 0.68 | 1.41 ± 0.30 | 1.97 ± 0.50 | 0.70 |
| N − M | 1.36 ± 0.22 | 0.61 ± 0.33 | 0.094 | 1.31 ± 0.03 | 0.70 (fix) | 0.11 | 1.24 ± 0.08 | 0.70 (fix) | 0.27 |
| L − M | 1.56 ± 0.34 | 1.33 ± 0.49 | 0.33 | 1.62 ± 0.30 | 1.24 ± 0.45 | 0.72 | 1.39 ± 0.32 | 1.58 ± 0.44 | 0.64 |
Notes.T, L, M are in the units of keV, 1042 erg s−1, 1014 M⊙, respectively. The best-fit values of a, b in Eq. (10), and the intrinsic scatter of y are listed. The results with and without E(z)-correction are shown in 1–4 and 5–8 rows, respectively. The 2D HiBRECS code takes into account the correction for the selection bias and mass calibration, but the other two codes do not (Sects. 5.3 and 6.2).
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