The phase-space parameters of the brightest halo galaxies

The brightest galaxy in a dark matter halo is expected to reside at rest at the centre of the halo. In this paper, we test this 'Central Galaxy Paradigm' (CGP) using group catalogues extracted from the Two-Degree Field Galaxy Redshift Survey (2dFGRS) and the Sloan Digital Sky Survey (SDSS). For each group, we compute a parameter R, which is defined as the difference between the velocity of the brightest group galaxy and the average velocity of the other group members (hereafter satellites), normalized by the unbiased estimator of the velocity dispersion of the satellite galaxies. Because the redshift surveys suffer from incompleteness effects and the group selection criterion unavoidably selects interlopers, a proper comparison between data and model needs to take this into account. To this extent, we use detailed mock galaxy redshift surveys (MGRSs), which are analysed in exactly the same way as the data, thus allowing for a fair comparison. We show that the CGP is only consistent with the data in haloes with M less than or similar to 10(13) h(-1) M circle dot, while in more massive haloes the data indicate a non-zero offset between the brightest galaxy and the satellites. This indicates that either central galaxies reside at the minimum of the dark matter potential, but that the halo itself is not yet fully relaxed, or, that the halo is relaxed, but that the central galaxy oscillates in its potential well. The former is consistent with the fact that the velocity bias of the brightest halo galaxies is larger in more massive haloes, while the latter may be indicative of cored, rather than cusped, dark matter haloes. We discuss several implications of these findings, including mass estimates based on satellite kinematics, strong gravitational lensing, halo occupation models, and the frequency and longevity of lopsidedness in disc galaxies.