Table A.2
Continuation of Table 2.
| Scaling relation | Model | c NFW | Slope B | Intercept A | bMC from Monte Carlo | b = ⟨ log ξ − log η ⟩ |
|
Section |
|
|
||||||||
 – |
varying ⟨ β ⟩ | c fit |
|
|
( ;
 ) |
0.07 ± 0.07 | 0.60 | 4.3 |
| varying ⟨ β ⟩ | c B13 |
|
− 0.02 ± 0.08 | 
( ;
 ) |
− 0.01 ± 0.03 | 0.50 | 4.3 | |
| S-peak centred | c fit |
|
− 0.02 ± 0.07 | 
( ;
 ) |
− 0.04 ± 0.04 | 0.59 | A.3 | |
| S-peak centred | c B13 |
|
− 0.03 ± 0.07 | 
( ;
 ) |
− 0.07 ± 0.03 | 0.60 | A.3 | |
|
|
||||||||
 – |
default | c fit |
|
0.05 ± 0.04 | 
( ;
 ) |
0.06 ± 0.07 | 1.67 | 3.2 |
| no dilu. corr. | c fit |
|
0.06 ± 0.04 | 
(;
 ) |
0.09 ± 0.06 | 1.51 | 4.3 | |
| no dilu. corr. | c B13 |
|
0.07 ± 0.03 | 
( ;
 ) |
0.06 ± 0.05 | 1.08 | 4.3 | |
|
|
||||||||
– |
default | c fit |
|
0.01 ± 0.05 | 
( ;
 ) |
0.01 ± 0.05 | 0.77 | 3.2 |
| – |
default | c B13 |
|
0.00 ± 0.05 | 
( ;
 ) |
− 0.02 ± 0.04 | 0.65 | 3.2 |
 – |
default | c B13 |
|
0.04 ± 0.05 | 
( ;
 ) |
− 0.02 ± 0.04 | 0.66 | 3.2 |
 – |
default | c B13 |
|
− 0.01 ± 0.06 | 
(;
 ) |
− 0.02 ± 0.04 | 0.62 | 3.2 |
|
|
||||||||
| – |
default | – |
|
0.07 ± 0.03 | 0.07 ± 0.05 | 0.06 ± 0.03 | 1.29 | 3.2 |
– |
default | – |
|
0.04 ± 0.05 | 0.04 ± 0.07 | 0.04 ± 0.02 | 0.79 | 3.2 |
– |
default | – |
|
|
|
0.01 ± 0.05 | 1.85 | 3.2 |
|
|
||||||||
| – |
default (MMT8) | – |
|
|
− 0.04 ± 0.05 | − 0.03 ± 0.03 | 1.27 | 4.4 |
| all 36 | – |
|
0.00 ± 0.02 | − 0.03 ± 0.02 | − 0.02 ± 0.01 | 1.32 | 4.4 | |
|
|
||||||||
| – |
default (MMT8) | – |
|
|
− 0.07 ± 0.02 | − 0.07 ± 0.04 | 3.43 | 4.4 |
| all 36 | – |
|
− 0.05 ± 0.01 | − 0.07 ± 0.01 | − 0.07 ± 0.01 | 2.32 | 4.4 | |
|
|
||||||||
| – |
default (MMT8) | – |
|
0.05 ± 0.03 |
|
− 0.04 ± 0.06 | 2.81 | 4.4 |
| all 36 | – |
|
0.02 ± 0.02 | − 0.04 ± 0.02 | − 0.05 ± 0.02 | 2.58 | 4.4 | |
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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