New Relationships between Galaxy Properties and Host Halo Mass, and the Role of Feedbacks in Galaxy Formation

We present new relationships between halo masses ( M h ) and several galaxy properties, including r *-band luminosities ( L r ), stellar ( M star ) and baryonic masses, stellar velocity dispersions (σ), and black hole masses ( M BH ). Approximate analytic expressions are given. In the galaxy halo mass range 3 × 10 10 M ☉ ≤ M h ≤ 3 × 10 13 M ☉ the M h - L r , M star - M h , and M BH - M h relations are well represented by a double power law, with a break at M h ,break ≈ 3 × 10 11 M ☉ , corresponding to a mass in stars M star ~ 1.2 × 10 10 M ☉ , to an r *-band luminosity L r ~ 5 × 10 9 L ☉ , to a stellar velocity dispersion σ ≃ 88 km s -1 , and to a black hole mass M BH ~ 9 × 10 6 M ☉ . The σ- M h relation can be approximated by a single power law, although a double power law is a better representation. Although there are significant systematic errors associated with our method, the derived relationships are in good agreement with the available observational data and have comparable uncertainties. We interpret these relations in terms of the effect of feedback from supernovae and from the active nucleus on the interstellar medium. We argue that the break of the power laws occurs at a mass that marks the transition between the dominance of the stellar and the AGN feedback.