Fitting results for all of our cluster models, showing the parameters of scientific interest only. We report the settings for the MCMC chain and the maximum likelihood |$-2\ln {\cal {L}}$| of any step in any chain for that MCMC run. We run the emcee MCMC ensemble sampler with 100 walkers for every chain, so the total number of steps included in the plots is 100 times what is listed here (including burn-in steps). When the Gaussian priors are not important, |$-2\ln {\cal {L}}$| is equal to the χ2. We also report the median value and the 1σ error regions (the 16th–84th percentile range) for the parameters of scientific interest. All models are NFW (equation 8), some with miscentring (equation 11), some with fitted M–c relations. The last model in the table is our fiducial model used in the analysis in the main text of this work. The * symbol indicates that the mass values from the output of the MCMC chain have been corrected for model bias, as described in Section 5, and the error bar is combined statistical and systematic.
. | No. of steps . | Minimum . | . | . | . |
---|---|---|---|---|---|
Model name . | (burn-in) . | |$-2\ln {\cal {L}}$| . | d.o.f. . | |$\log _{10} M_0^{\ast }$| . | α . |
Simple | 1000 (100) | 78.41 | 75 | |$14.322^{+0.028}_{-0.029}$| | |$1.36^{+0.10}_{-0.09}$| |
Simple with M–c scatter | 1000 (100) | 78.09 | 75 | |$14.323^{+0.028}_{-0.029}$| | |$1.36^{+0.09}_{-0.10}$| |
Fitted M–c amplitude and M–c scatter | 1500 (100) | 77.64 | 74 | 14.329 ± 0.030 | |$1.38^{+0.09}_{-0.10}$| |
Miscentring and M–c scatter | 1500 (100) | 78.08 | 73 | 14.347 ± 0.030 | |$1.36^{+0.09}_{-0.10}$| |
Miscentring, fitted M–c amplitude and M–c scatter | 2250 (100) | 76.37 | 72 | 14.344 ± 0.031 | |$1.33^{+0.09}_{-0.10}$| |
. | No. of steps . | Minimum . | . | . | . |
---|---|---|---|---|---|
Model name . | (burn-in) . | |$-2\ln {\cal {L}}$| . | d.o.f. . | |$\log _{10} M_0^{\ast }$| . | α . |
Simple | 1000 (100) | 78.41 | 75 | |$14.322^{+0.028}_{-0.029}$| | |$1.36^{+0.10}_{-0.09}$| |
Simple with M–c scatter | 1000 (100) | 78.09 | 75 | |$14.323^{+0.028}_{-0.029}$| | |$1.36^{+0.09}_{-0.10}$| |
Fitted M–c amplitude and M–c scatter | 1500 (100) | 77.64 | 74 | 14.329 ± 0.030 | |$1.38^{+0.09}_{-0.10}$| |
Miscentring and M–c scatter | 1500 (100) | 78.08 | 73 | 14.347 ± 0.030 | |$1.36^{+0.09}_{-0.10}$| |
Miscentring, fitted M–c amplitude and M–c scatter | 2250 (100) | 76.37 | 72 | 14.344 ± 0.031 | |$1.33^{+0.09}_{-0.10}$| |
Fitting results for all of our cluster models, showing the parameters of scientific interest only. We report the settings for the MCMC chain and the maximum likelihood |$-2\ln {\cal {L}}$| of any step in any chain for that MCMC run. We run the emcee MCMC ensemble sampler with 100 walkers for every chain, so the total number of steps included in the plots is 100 times what is listed here (including burn-in steps). When the Gaussian priors are not important, |$-2\ln {\cal {L}}$| is equal to the χ2. We also report the median value and the 1σ error regions (the 16th–84th percentile range) for the parameters of scientific interest. All models are NFW (equation 8), some with miscentring (equation 11), some with fitted M–c relations. The last model in the table is our fiducial model used in the analysis in the main text of this work. The * symbol indicates that the mass values from the output of the MCMC chain have been corrected for model bias, as described in Section 5, and the error bar is combined statistical and systematic.
. | No. of steps . | Minimum . | . | . | . |
---|---|---|---|---|---|
Model name . | (burn-in) . | |$-2\ln {\cal {L}}$| . | d.o.f. . | |$\log _{10} M_0^{\ast }$| . | α . |
Simple | 1000 (100) | 78.41 | 75 | |$14.322^{+0.028}_{-0.029}$| | |$1.36^{+0.10}_{-0.09}$| |
Simple with M–c scatter | 1000 (100) | 78.09 | 75 | |$14.323^{+0.028}_{-0.029}$| | |$1.36^{+0.09}_{-0.10}$| |
Fitted M–c amplitude and M–c scatter | 1500 (100) | 77.64 | 74 | 14.329 ± 0.030 | |$1.38^{+0.09}_{-0.10}$| |
Miscentring and M–c scatter | 1500 (100) | 78.08 | 73 | 14.347 ± 0.030 | |$1.36^{+0.09}_{-0.10}$| |
Miscentring, fitted M–c amplitude and M–c scatter | 2250 (100) | 76.37 | 72 | 14.344 ± 0.031 | |$1.33^{+0.09}_{-0.10}$| |
. | No. of steps . | Minimum . | . | . | . |
---|---|---|---|---|---|
Model name . | (burn-in) . | |$-2\ln {\cal {L}}$| . | d.o.f. . | |$\log _{10} M_0^{\ast }$| . | α . |
Simple | 1000 (100) | 78.41 | 75 | |$14.322^{+0.028}_{-0.029}$| | |$1.36^{+0.10}_{-0.09}$| |
Simple with M–c scatter | 1000 (100) | 78.09 | 75 | |$14.323^{+0.028}_{-0.029}$| | |$1.36^{+0.09}_{-0.10}$| |
Fitted M–c amplitude and M–c scatter | 1500 (100) | 77.64 | 74 | 14.329 ± 0.030 | |$1.38^{+0.09}_{-0.10}$| |
Miscentring and M–c scatter | 1500 (100) | 78.08 | 73 | 14.347 ± 0.030 | |$1.36^{+0.09}_{-0.10}$| |
Miscentring, fitted M–c amplitude and M–c scatter | 2250 (100) | 76.37 | 72 | 14.344 ± 0.031 | |$1.33^{+0.09}_{-0.10}$| |
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