Consequences of Feedback from Early Supernovae for Disk Assembly

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Abstract
In this Letter, we examine the role of the first supernovae in protogalaxies, their role in feedback, and the consequences for disk assembly. Extending the picture proposed by Dekel & Silk in 1986, we argue that energetic supernovae winds can expel baryons from all protogalaxies with varying degrees of efficiency. 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 application to the case of the Milky Way halo, this feedback mechanism implies (1) 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 and (2) 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 λh of the halo. In a range of viable cold dark matter cosmological models, we find that for a low-spin halo (λh ~ 0.02), zf < 1 and fb ~ 2%; for a median-spin halo (λh ~ 0.05), zf ~ 1-2.5 and fb ~ 5%; and for a high-spin halo (λh ~ 0.2), zf ~ 4-8 and 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 differ significantly from the universal value.
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