Table 5
Best-fit values of the c200 − M200 relation.
| Dataset | c15 | A | B | σlog 10c |
|
|
||||
| All objects (44 clusters) | ||||
| Method 1 - Weighted Mean |
|
0.556 ± 0.006 | −0.1 | 0.193/0.116 |
| Method 1 - FITEXY | 3.62 ± 0.07 | 0.558 ± 0.008 | −0.451 ± 0.023 | 0.135/0.116 |
| Method 1 - BCES | 3.78 ± 0.18 | 0.577 ± 0.021 | −0.544 ± 0.071 | 0.132/0.116 |
| Method 1 - LINMIX | 3.79 ± 0.22 | 0.578 ± 0.025 | −0.444 ± 0.078 | 0.132/0.116 |
| Method 2 - Weighted Mean |
|
0.534 ± 0.004 | −0.1 | 0.203/0.119 |
| Method 2 - FITEXY | 3.21 ± 0.05 | 0.507 ± 0.006 | −0.466 ± 0.015 | 0.146/0.119 |
| Method 2 - BCES | 3.51 ± 0.16 | 0.545 ± 0.020 | −0.612 ± 0.084 | 0.133/0.119 |
| Method 2 - LINMIX | 3.73 ± 0.21 | 0.572 ± 0.024 | −0.496 ± 0.068 | 0.131/0.119 |
| Selected objects (26 clusters) | ||||
| Method 1 - Weighted Mean |
|
0.664 ± 0.008 | − 0.1 | 0.165/0.092 |
| Method 1 - FITEXY | 4.06 ± 0.17 | 0.608 ± 0.018 | − 0.321 ± 0.050 | 0.143/0.092 |
| Method 1 - BCES | 3.84 ± 0.39 | 0.584 ± 0.044 | −0.586 ± 0.115 | 0.138/0.092 |
| Method 1 - LINMIX | 4.26 ± 0.48 | 0.629 ± 0.049 | −0.365 ± 0.128 | 0.132/0.092 |
| Method 2 - Weighted Mean |
|
0.602 ± 0.005 | −0.1 | 0.181/0.079 |
| Method 2 - FITEXY | 2.87 ± 0.13 | 0.458 ± 0.020 | −0.576 ± 0.063 | 0.169/0.079 |
| Method 2 - BCES | 3.18 ± 0.56 | 0.502 ± 0.076 | −0.782 ± 0.255 | 0.150/0.079 |
| Method 2 - LINMIX | 3.92 ± 0.44 | 0.594 ± 0.048 | − 0.436 ± 0.134 | 0.130/0.079 |
| only LEC objects (11 clusters) | ||||
| Method 1 - Weighted Mean |
|
0.617 ± 0.009 | −0.1 | 0.091/0.033 |
| Method 1 - FITEXY | 3.68 ± 0.15 | 0.565 ± 0.017 | −0.297 ± 0.051 | 0.081/0.033 |
| Method 1 - BCES | 3.27 ± 0.52 | 0.514 ± 0.069 | −0.472 ± 0.229 | 0.093/0.033 |
| Method 1 - LINMIX | 3.73 ± 0.46 | 0.572 ± 0.054 | −0.282 ± 0.150 | 0.081/0.033 |
| Method 2 - Weighted Mean |
|
0.581 ± 0.005 | −0.1 | 0.096/0.046 |
| Method 2 - FITEXY | 3.13 ± 0.11 | 0.496 ± 0.015 | −0.376 ± 0.054 | 0.080/0.046 |
| Method 2 - BCES | 3.21 ± 0.75 | 0.506 ± 0.102 | −0.452 ± 0.303 | 0.074/0.046 |
| Method 2 - LINMIX | 3.38 ± 0.37 | 0.529 ± 0.047 | −0.374 ± 0.137 | 0.071/0.046 |
| Simulations | ||||
| B01 | 4.29 | 0.632 | −0.102 | |
| D04 | 4.01 | 0.603 | −0.130 | |
| S06 – all, relaxed | 4.64,4.86 | 0.667,0.687 | −0.120, −0.160 | |
| N07 – all, relaxed | 3.77,4.33 | 0.576,0.636 | −0.110, −0.100 | |
| M08 / WMAP-1 – all, relaxed | 3.47,4.18 | 0.540,0.621 | −0.119, −0.104 | |
| M08 / WMAP-3 – all, relaxed | 2.94,3.41 | 0.469,0.533 | −0.088, −0.083 | |
| M08 / WMAP-5 – all, relaxed | 2.98,3.56 | 0.474,0.551 | −0.110, −0.098 | |
Notes. The best-fit values refer to Eq. (5) and are obtained by using (i) the linear least-squares fitting
with errors in both variables (FITEXY); (ii) the linear regression
method BCES; (iii) a Bayesian linear regression method
(LINMIX). In the last column, the total (
) and statistical
(
) scatters are
quoted, where
yi = log 10(c200(1 + z)),
xi = log 10M200,
ϵyi is the
statistical error on yi and
N is the number of objects.
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