| . | Selection . | ||||||
|---|---|---|---|---|---|---|---|
| Characteristic . | Full . | Low-z . | Mid-z . | High-z . | Low-N . | Mid-N . | High-N . |
| z cl, min | 0.1 | 0.1 | 0.4 | 0.7 | 0.1 | 0.1 | 0.1 |
| z cl, max | 1.0 | 0.4 | 0.7 | 1.0 | 1.0 | 1.0 | 1.0 |
| 〈zcl〉 | 0.57 | 0.26 | 0.55 | 0.83 | 0.60 | 0.54 | 0.49 |
| N min | 15 | 15 | 15 | 15 | 15 | 20 | 30 |
| N max | 200 | 200 | 200 | 200 | 20 | 30 | 200 |
| 〈N〉 | 23 | 25 | 22 | 21 | 17 | 24 | 40 |
| Number of clusters | 3316 | 968 | 1140 | 1208 | 1774 | 1067 | 475 |
| 〈M200m〉 [h−11014 M⨀] | |$1.72^{+0.08}_{-0.07}$| | |$1.71^{+0.07}_{-0.07}$| | |$1.93^{+0.09}_{-0.08}$| | |$1.51^{+0.13}_{-0.13}$| | |$1.23^{+0.06}_{-0.06}$| | |$1.78^{+0.08}_{-0.08}$| | |$3.32^{+0.14}_{-0.15}$| |
| 〈R200m〉 [h−1 Mpc] | |$1.33^{+0.02}_{-0.02}$| | |$1.33^{+0.02}_{-0.02}$| | |$1.38^{+0.02}_{-0.02}$| | |$1.27^{+0.04}_{-0.04}$| | |$1.19^{+0.02}_{-0.02}$| | |$1.34^{+0.02}_{-0.02}$| | |$1.65^{+0.02}_{-0.03}$| |
| |$r_{\rm sp, model}^{\rm 3D}\ [h^{-1}\:\mbox{Mpc}]$| | |$1.61^{+0.01}_{-0.01}$| | |$1.61^{+0.01}_{-0.01}$| | |$1.63^{+0.01}_{-0.01}$| | |$1.45^{+0.03}_{-0.02}$| | |$1.41^{+0.01}_{-0.01}$| | |$1.62^{+0.01}_{-0.01}$| | |$1.92^{+0.01}_{-0.01}$| |
| |$\frac{ {d}\ln \xi _{\rm 3D} }{ {d}\ln r }|_{r=r_{\rm sp}^{\rm 3D}, {\rm model}}$| | |$-3.20^{+0.03}_{-0.03}$| | |$-3.11^{+0.03}_{-0.03}$| | |$-3.25^{+0.03}_{-0.03}$| | |$-3.27^{+0.05}_{-0.05}$| | |$-3.21^{+0.04}_{-0.04}$| | |$-3.28^{+0.03}_{-0.03}$| | |$-3.34^{+0.03}_{-0.03}$| |
| |$R_{\rm sp, model}^{\rm 2D}\ [h^{-1}\:\mbox{Mpc}]$| | |$1.12^{+0.01}_{-0.02}$| | |$1.07^{+0.03}_{-0.02}$| | |$1.16^{+0.01}_{-0.01}$| | |$1.07^{+0.04}_{-0.03}$| | |$0.99^{+0.01}_{-0.01}$| | |$1.13^{+0.01}_{-0.02}$| | |$1.39^{+0.02}_{-0.01}$| |
| |$\frac{ {d}\ln \xi _{\rm 2D} }{ {d}\ln R }|_{R=R_{\rm sp}^{\rm 2D}, {\rm model}}$| | |$-1.72^{+0.02}_{-0.02}$| | |$-1.67^{+0.01}_{-0.01}$| | |$-1.75^{+0.01}_{-0.01}$| | |$-1.75^{+0.03}_{-0.03}$| | |$-1.69^{+0.02}_{-0.02}$| | |$-1.75^{+0.02}_{-0.02}$| | |$-1.82^{+0.01}_{-0.01}$| |
| . | Selection . | ||||||
|---|---|---|---|---|---|---|---|
| Characteristic . | Full . | Low-z . | Mid-z . | High-z . | Low-N . | Mid-N . | High-N . |
| z cl, min | 0.1 | 0.1 | 0.4 | 0.7 | 0.1 | 0.1 | 0.1 |
| z cl, max | 1.0 | 0.4 | 0.7 | 1.0 | 1.0 | 1.0 | 1.0 |
| 〈zcl〉 | 0.57 | 0.26 | 0.55 | 0.83 | 0.60 | 0.54 | 0.49 |
| N min | 15 | 15 | 15 | 15 | 15 | 20 | 30 |
| N max | 200 | 200 | 200 | 200 | 20 | 30 | 200 |
| 〈N〉 | 23 | 25 | 22 | 21 | 17 | 24 | 40 |
| Number of clusters | 3316 | 968 | 1140 | 1208 | 1774 | 1067 | 475 |
| 〈M200m〉 [h−11014 M⨀] | |$1.72^{+0.08}_{-0.07}$| | |$1.71^{+0.07}_{-0.07}$| | |$1.93^{+0.09}_{-0.08}$| | |$1.51^{+0.13}_{-0.13}$| | |$1.23^{+0.06}_{-0.06}$| | |$1.78^{+0.08}_{-0.08}$| | |$3.32^{+0.14}_{-0.15}$| |
| 〈R200m〉 [h−1 Mpc] | |$1.33^{+0.02}_{-0.02}$| | |$1.33^{+0.02}_{-0.02}$| | |$1.38^{+0.02}_{-0.02}$| | |$1.27^{+0.04}_{-0.04}$| | |$1.19^{+0.02}_{-0.02}$| | |$1.34^{+0.02}_{-0.02}$| | |$1.65^{+0.02}_{-0.03}$| |
| |$r_{\rm sp, model}^{\rm 3D}\ [h^{-1}\:\mbox{Mpc}]$| | |$1.61^{+0.01}_{-0.01}$| | |$1.61^{+0.01}_{-0.01}$| | |$1.63^{+0.01}_{-0.01}$| | |$1.45^{+0.03}_{-0.02}$| | |$1.41^{+0.01}_{-0.01}$| | |$1.62^{+0.01}_{-0.01}$| | |$1.92^{+0.01}_{-0.01}$| |
| |$\frac{ {d}\ln \xi _{\rm 3D} }{ {d}\ln r }|_{r=r_{\rm sp}^{\rm 3D}, {\rm model}}$| | |$-3.20^{+0.03}_{-0.03}$| | |$-3.11^{+0.03}_{-0.03}$| | |$-3.25^{+0.03}_{-0.03}$| | |$-3.27^{+0.05}_{-0.05}$| | |$-3.21^{+0.04}_{-0.04}$| | |$-3.28^{+0.03}_{-0.03}$| | |$-3.34^{+0.03}_{-0.03}$| |
| |$R_{\rm sp, model}^{\rm 2D}\ [h^{-1}\:\mbox{Mpc}]$| | |$1.12^{+0.01}_{-0.02}$| | |$1.07^{+0.03}_{-0.02}$| | |$1.16^{+0.01}_{-0.01}$| | |$1.07^{+0.04}_{-0.03}$| | |$0.99^{+0.01}_{-0.01}$| | |$1.13^{+0.01}_{-0.02}$| | |$1.39^{+0.02}_{-0.01}$| |
| |$\frac{ {d}\ln \xi _{\rm 2D} }{ {d}\ln R }|_{R=R_{\rm sp}^{\rm 2D}, {\rm model}}$| | |$-1.72^{+0.02}_{-0.02}$| | |$-1.67^{+0.01}_{-0.01}$| | |$-1.75^{+0.01}_{-0.01}$| | |$-1.75^{+0.03}_{-0.03}$| | |$-1.69^{+0.02}_{-0.02}$| | |$-1.75^{+0.02}_{-0.02}$| | |$-1.82^{+0.01}_{-0.01}$| |
*We define each cluster sample by zcl, min, zcl, max, Nmin, and Nmax, and 〈zcl〉 and 〈N〉 give the mean values of cluster redshift and richness. We show the constraints for each sample on mean mass and R200m values, and the model predictions for the splashback feature from the mass–richness relation in Murata et al. (2019) and the halo emulator in Nishimichi et al. (2019) as described in appendix 1. We note that we use the halo–matter cross-correlation function for these model predictions and we compare our model predictions with model calculation methods in the literature in appendix 2. We show the median and the 16th and 84th percentiles of the model predictions using the fiducial results of the mass–richness relation in Murata et al. (2019) with the Planck cosmology.
| . | Selection . | ||||||
|---|---|---|---|---|---|---|---|
| Characteristic . | Full . | Low-z . | Mid-z . | High-z . | Low-N . | Mid-N . | High-N . |
| z cl, min | 0.1 | 0.1 | 0.4 | 0.7 | 0.1 | 0.1 | 0.1 |
| z cl, max | 1.0 | 0.4 | 0.7 | 1.0 | 1.0 | 1.0 | 1.0 |
| 〈zcl〉 | 0.57 | 0.26 | 0.55 | 0.83 | 0.60 | 0.54 | 0.49 |
| N min | 15 | 15 | 15 | 15 | 15 | 20 | 30 |
| N max | 200 | 200 | 200 | 200 | 20 | 30 | 200 |
| 〈N〉 | 23 | 25 | 22 | 21 | 17 | 24 | 40 |
| Number of clusters | 3316 | 968 | 1140 | 1208 | 1774 | 1067 | 475 |
| 〈M200m〉 [h−11014 M⨀] | |$1.72^{+0.08}_{-0.07}$| | |$1.71^{+0.07}_{-0.07}$| | |$1.93^{+0.09}_{-0.08}$| | |$1.51^{+0.13}_{-0.13}$| | |$1.23^{+0.06}_{-0.06}$| | |$1.78^{+0.08}_{-0.08}$| | |$3.32^{+0.14}_{-0.15}$| |
| 〈R200m〉 [h−1 Mpc] | |$1.33^{+0.02}_{-0.02}$| | |$1.33^{+0.02}_{-0.02}$| | |$1.38^{+0.02}_{-0.02}$| | |$1.27^{+0.04}_{-0.04}$| | |$1.19^{+0.02}_{-0.02}$| | |$1.34^{+0.02}_{-0.02}$| | |$1.65^{+0.02}_{-0.03}$| |
| |$r_{\rm sp, model}^{\rm 3D}\ [h^{-1}\:\mbox{Mpc}]$| | |$1.61^{+0.01}_{-0.01}$| | |$1.61^{+0.01}_{-0.01}$| | |$1.63^{+0.01}_{-0.01}$| | |$1.45^{+0.03}_{-0.02}$| | |$1.41^{+0.01}_{-0.01}$| | |$1.62^{+0.01}_{-0.01}$| | |$1.92^{+0.01}_{-0.01}$| |
| |$\frac{ {d}\ln \xi _{\rm 3D} }{ {d}\ln r }|_{r=r_{\rm sp}^{\rm 3D}, {\rm model}}$| | |$-3.20^{+0.03}_{-0.03}$| | |$-3.11^{+0.03}_{-0.03}$| | |$-3.25^{+0.03}_{-0.03}$| | |$-3.27^{+0.05}_{-0.05}$| | |$-3.21^{+0.04}_{-0.04}$| | |$-3.28^{+0.03}_{-0.03}$| | |$-3.34^{+0.03}_{-0.03}$| |
| |$R_{\rm sp, model}^{\rm 2D}\ [h^{-1}\:\mbox{Mpc}]$| | |$1.12^{+0.01}_{-0.02}$| | |$1.07^{+0.03}_{-0.02}$| | |$1.16^{+0.01}_{-0.01}$| | |$1.07^{+0.04}_{-0.03}$| | |$0.99^{+0.01}_{-0.01}$| | |$1.13^{+0.01}_{-0.02}$| | |$1.39^{+0.02}_{-0.01}$| |
| |$\frac{ {d}\ln \xi _{\rm 2D} }{ {d}\ln R }|_{R=R_{\rm sp}^{\rm 2D}, {\rm model}}$| | |$-1.72^{+0.02}_{-0.02}$| | |$-1.67^{+0.01}_{-0.01}$| | |$-1.75^{+0.01}_{-0.01}$| | |$-1.75^{+0.03}_{-0.03}$| | |$-1.69^{+0.02}_{-0.02}$| | |$-1.75^{+0.02}_{-0.02}$| | |$-1.82^{+0.01}_{-0.01}$| |
| . | Selection . | ||||||
|---|---|---|---|---|---|---|---|
| Characteristic . | Full . | Low-z . | Mid-z . | High-z . | Low-N . | Mid-N . | High-N . |
| z cl, min | 0.1 | 0.1 | 0.4 | 0.7 | 0.1 | 0.1 | 0.1 |
| z cl, max | 1.0 | 0.4 | 0.7 | 1.0 | 1.0 | 1.0 | 1.0 |
| 〈zcl〉 | 0.57 | 0.26 | 0.55 | 0.83 | 0.60 | 0.54 | 0.49 |
| N min | 15 | 15 | 15 | 15 | 15 | 20 | 30 |
| N max | 200 | 200 | 200 | 200 | 20 | 30 | 200 |
| 〈N〉 | 23 | 25 | 22 | 21 | 17 | 24 | 40 |
| Number of clusters | 3316 | 968 | 1140 | 1208 | 1774 | 1067 | 475 |
| 〈M200m〉 [h−11014 M⨀] | |$1.72^{+0.08}_{-0.07}$| | |$1.71^{+0.07}_{-0.07}$| | |$1.93^{+0.09}_{-0.08}$| | |$1.51^{+0.13}_{-0.13}$| | |$1.23^{+0.06}_{-0.06}$| | |$1.78^{+0.08}_{-0.08}$| | |$3.32^{+0.14}_{-0.15}$| |
| 〈R200m〉 [h−1 Mpc] | |$1.33^{+0.02}_{-0.02}$| | |$1.33^{+0.02}_{-0.02}$| | |$1.38^{+0.02}_{-0.02}$| | |$1.27^{+0.04}_{-0.04}$| | |$1.19^{+0.02}_{-0.02}$| | |$1.34^{+0.02}_{-0.02}$| | |$1.65^{+0.02}_{-0.03}$| |
| |$r_{\rm sp, model}^{\rm 3D}\ [h^{-1}\:\mbox{Mpc}]$| | |$1.61^{+0.01}_{-0.01}$| | |$1.61^{+0.01}_{-0.01}$| | |$1.63^{+0.01}_{-0.01}$| | |$1.45^{+0.03}_{-0.02}$| | |$1.41^{+0.01}_{-0.01}$| | |$1.62^{+0.01}_{-0.01}$| | |$1.92^{+0.01}_{-0.01}$| |
| |$\frac{ {d}\ln \xi _{\rm 3D} }{ {d}\ln r }|_{r=r_{\rm sp}^{\rm 3D}, {\rm model}}$| | |$-3.20^{+0.03}_{-0.03}$| | |$-3.11^{+0.03}_{-0.03}$| | |$-3.25^{+0.03}_{-0.03}$| | |$-3.27^{+0.05}_{-0.05}$| | |$-3.21^{+0.04}_{-0.04}$| | |$-3.28^{+0.03}_{-0.03}$| | |$-3.34^{+0.03}_{-0.03}$| |
| |$R_{\rm sp, model}^{\rm 2D}\ [h^{-1}\:\mbox{Mpc}]$| | |$1.12^{+0.01}_{-0.02}$| | |$1.07^{+0.03}_{-0.02}$| | |$1.16^{+0.01}_{-0.01}$| | |$1.07^{+0.04}_{-0.03}$| | |$0.99^{+0.01}_{-0.01}$| | |$1.13^{+0.01}_{-0.02}$| | |$1.39^{+0.02}_{-0.01}$| |
| |$\frac{ {d}\ln \xi _{\rm 2D} }{ {d}\ln R }|_{R=R_{\rm sp}^{\rm 2D}, {\rm model}}$| | |$-1.72^{+0.02}_{-0.02}$| | |$-1.67^{+0.01}_{-0.01}$| | |$-1.75^{+0.01}_{-0.01}$| | |$-1.75^{+0.03}_{-0.03}$| | |$-1.69^{+0.02}_{-0.02}$| | |$-1.75^{+0.02}_{-0.02}$| | |$-1.82^{+0.01}_{-0.01}$| |
*We define each cluster sample by zcl, min, zcl, max, Nmin, and Nmax, and 〈zcl〉 and 〈N〉 give the mean values of cluster redshift and richness. We show the constraints for each sample on mean mass and R200m values, and the model predictions for the splashback feature from the mass–richness relation in Murata et al. (2019) and the halo emulator in Nishimichi et al. (2019) as described in appendix 1. We note that we use the halo–matter cross-correlation function for these model predictions and we compare our model predictions with model calculation methods in the literature in appendix 2. We show the median and the 16th and 84th percentiles of the model predictions using the fiducial results of the mass–richness relation in Murata et al. (2019) with the Planck cosmology.
This PDF is available to Subscribers Only
View Article Abstract & Purchase OptionsFor full access to this pdf, sign in to an existing account, or purchase an annual subscription.
