Table 2
Measurements of the X-ray – WL mass bias.
| Scaling relation | Model | c NFW | Slope B | Intercept A | bMC from Monte Carlo | b = ⟨ log ξ − log η ⟩ |
|
Section |
|
|
||||||||
 – |
default | c fit |
|
|
( ;
 ) |
0.08 ± 0.09 | 0.58 | 3.1 |
| default | c B13 |
|
|
( ;
 ) |
− 0.02 ± 0.04 | 0.52 | 3.1 | |
| no dilu. corr. | c fit | − 0.53 ± 0.23 | 0.01 ± 0.08 | 
(;
 ) |
0.11 ± 0.08 | 0.57 | 4.3 | |
| no dilu. corr. | c B13 | − 0.49 ± 0.29 |
|
( ;
 ) |
0.00 ± 0.03 | 0.51 | 4.3 | |
|
|
||||||||
| Mwl(rfix)–Mhyd(rfix) | rfix = 600 kpc | c B13 |
|
− 0.11 ± 0.05 | 
( ;
 ) |
− 0.02 ± 0.04 | 0.82 | 4.2 |
| rfix = 800 kpc | c B13 |
|
− 0.02 ± 0.04 | 
( ;
 ) |
− 0.02 ± 0.04 | 0.72 | 4.2 | |
| rfix = 1000 kpc | c B13 |
|
0.01 ± 0.05 | 
( ;
 ) |
− 0.03 ± 0.03 | 0.69 | 4.2 | |
|
|
||||||||
 – |
default | c B13 |
|
0.07 ± 0.03 | 
( ;
 ) |
0.04 ± 0.06 | 1.21 | 3.2 |
 – |
default | c B13 | − 0.63 ± 0.23 | 0.04 ± 0.06 | 
( ;
 ) |
0.02 ± 0.05 | 0.88 | 3.2 |
 – |
default | c B13 |
|
|
( ;
 ) |
0.00 ± 0.07 | 2.11 | 3.2 |
Notes.We estimate a possible bias between masses ξ and η by three
estimators: First, we fit to (log ξ − log η) as a
function of η, yielding an intercept A at pivot
and slope
B
from the Monte Carlo/jackknife analysis. Second, we compute the logarithmic bias
bMC = ⟨
log ξ − log η ⟩
MC, averaged over the same realisations. Uncertainties
for the MC results are given by 1σ ensemble dispersions. In parentheses next
to bMC, we show its value for the
low-Mwl and high-Mwl
clusters. Third, we quote the logarithmic bias b = ⟨ log ξ −
log η ⟩ obtained directly from the input
masses, along with its standard error. Finally, we give the
for the
mass-mass scaling, obtained from the MC method. The “default” model denotes WL and
hydrostatic masses as described in Sect. 2.
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