Consequences of Feedback from Early Supernovae for Disk Assembly

In this letter we examine the role of the rst supernovae in proto-galaxies, their role in feedback and the consequences for disk assembly. Extending the picture proposed by Dekel & Silk (1986), we argue that energetic supernovae winds can expel baryons from all proto-galaxies with varying degrees of e ciency. The fraction of baryons retained and hence available to assemble into the baryonic disk is therefore, a function of the central velocity dispersion of the halo. Such a coupling of the baryonic component to the dark halo leads to the following interesting consequence, a prediction for a weak scaling of the zero-point of the Tully-Fisher relation or alternatively, the mass-to-light ratio with the central velocity dispersion of the halo. On applying to the case of the Milky Way halo, this feedback mechanism implies: (i) that the Milky Way halo lost 10% of its original gas content, and the gas mass lost is roughly what is estimated for the mass in our X-ray halo consistent with the X-ray background in the soft band; (ii) a range in the inferred redshift of formation zf , and the local baryon fraction fb for the Milky Way that depends on the initial spin parameter h of the halo. In a range of viable cold-dark matter cosmological models, we nd that for a low spin halo ( h 0:02) zf < 1, fb 2%; for a median spin halo ( h 0:05) zf 1 2:5, fb 5%; and for a high spin halo ( h 0:2) zf 4 8, fb 20%. The observationally determined ages for the oldest disk stars in the Milky Way seem to rule out a low value for the spin parameter. Given the shape of the spin distribution of halos obtained in N-body simulations, while a high value of the spin parameter is not very probable, it is interesting to note that if this is indeed the case for the Milky Way halo, then feedback processes can cause the local baryon fraction to di er signi cantly from the universal value. Subject headings: galaxies | formation, fundamental parameters | galaxies: ISM | galaxies: kinematics and dynamics | galaxies: stellar content