Table E.1.
Marginal constraints on all model parameters listed together with their priors, for the fiducial and extension setups considered.
| Parameter | Prior | Fiducial | Planckns prior | Poissonian satellite dist. | Mass dependent 𝒫 | ||||
|---|---|---|---|---|---|---|---|---|---|
| MMAX | MAP+PJ-HPD | MMAX | MAP+PJ-HPD | MMAX | MAP+PJ-HPD | MMAX | MAP+PJ-HPD | ||
| Ωm | [0.1, 0.6] |
 |
 |
 |
 |
0.330 ± 0.019 |
 |
 |
 |
| σ8 | [0.4, 1.2] |
 |
 |
 |
 |
 |
 |
 |
 |
| h | [0.64, 0.82] | < 0.726 | < 0.711 | < 0.716 | < 0.715 | < 0.720 | < 0.712 | < 0.720 | < 0.720 |
| Ωb | [0.01, 0.06] | > 0.01 | > 0.01 | > 0.01 | > 0.01 | > 0.01 | > 0.01 | > 0.01 | > 0.01 |
| ns | [0.92, 1.1] | < 1.004 | < 0.978 |
 |
 |
< 0.988 | < 0.979 | < 0.996 | < 0.998 |
| S8 | – |
 |
 |
 |
 |
 |
 |
 |
 |
| fh | [0.0, 1.0] | > 0.645 | > 0.939 | > 0.665 | > 0.948 | > 0.652 | > 0.938 | > 0.581 | > 0.928 |
| M0 | [7.0, 13.0] |
 |
 |
 |
 |
 |
 |
 |
 |
| M1 | [9.0, 14.0] |
 |
 |
 |
 |
 |
 |
 |
 |
| γ1 | [2.5, 15.0] |
 |
 |
 |
 |
 |
 |
 |
 |
| γ2 | [0.0, 10.0] | 0.201±0.010 | 0.201±0.009 | 0.201±0.011 | 0.211±0.010 | 0.201±0.010 | 0.207±0.007 | 0.201±0.007 | 0.203±0.004 |
| σc | [0.0, 2.0] |
 |
 |
 |
 |
 |
 |
 |
 |
| fs | [0.0, 1.0] | > 0.377 | > 0.84 | > 0.394 | > 0.858 | > 0.223 | > 0.808 | > 0.288 | > 0.757 |
| αs | [ − 5.0, 5.0] |
 |
 |
 |
 |
 |
 |
 |
 |
| b0 | [ − 5.0, 5.0] |
 |
 |
 |
 |
−0.239±0.092 |
 |
 |
 |
| b1 | [ − 5.0, 5.0] |
 |
 |
 |
 |
 |
 |
 |
 |
| 𝒫 | [0.0, 2.0] | 0.403±0.029 |
 |
0.403±0.030 |
 |
1.0 fixed | 1.0 fixed | – | – |
| Mpiv | [8.0, 15.0] | – | – | – | – | – | – |
 |
 |
| 𝒟 | [0.0, 0.3] |
 |
 |
 |
 |
 |
 |
 |
 |
 |
– | 1.07 | 1.07 | 1.25 | 1.1 | ||||
| p-value | – | 0.27 | 0.27 | 0.02 | 0.19 | ||||
Notes: This table lists all the free parameters in our model: the energy density of cold matter Ωm, the normalisation of power spectrum σ8, the dimensionless Hubble parameter h, the spectral index ns, the energy density of baryonic matter Ωb, the derived parameter S8, the normalisation of the concentration-mass relation for dark matter haloes fh, the normalisation of stellar-to-halo mass relation M0, the characteristic scale of the stellar-to-halo mass relation M1, the slope parameters of the stellar-to-halo mass relation γ1 and γ2, the scatter between stellar mass and halo mass σc, the normalisation of the concentration-mass relation for distribution of satellite galaxies fs, the power law behaviour of satellites αs, the normalisation constants of the Schechter function b0 and b1, and the Poisson parameter 𝒫. Parameter Mpiv is the location of the power law used to describe the mass dependence of the Poisson parameter 𝒫. Parameters are deemed unconstrained when the marginal probability at 2σ level exceeds 13% of the peak probability (see Appendix A of Asgari et al. 2021b). In cases where one side is constrained we report the 1σ lower/upper limit. The MMAX estimate is the marginal maximum statistic, reporting the point of maximum marginal posterior distribution to the iso-posterior levels above and below the maximal point. The MAP+PJ-HPD (maximum posterior with projected joint highest posterior density) estimates are calculated following Joachimi et al. (2021).
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