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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 (sigma), and black hole masses (M_BH). Approximate analytic expressions are given. In the galaxy halo mass range 3*10^(10) M_sun <= M_h <= 3*10^(13) M_sun the M_h-L_r, M_star-M_h, and M_BH-M_h are well represented by a double power law, with a break at M_h_break~3*10^(11) M_sun, corresponding to a mass in stars M_star~ 1.2*10^(10) M_sun, to a r*-band luminosity L_r~ 5*10^9 L_sun, to a stellar velocity dispersion sigma ~ 88 km/s, and to a black hole mass M_BH~ 9*10^(6) M_sun. The sigma-M_h relation can be approximated by a single power law, though a double power law is a better representation. 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 which marks the transition between the dominance of the stellar and the AGN feedback.