Virial shocks in galactic haloes?

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Abstract
We investigate the conditions for the existence of an expanding virial shock in the gas falling within a spherical dark-matter halo. The shock relies on pressure support by the shock-heated gas behind it. When the radiative cooling is efficient compared to the infall rate the post-shock gas becomes unstable; it collapses inwards and cannot support the shock. We find for a monoatomic gas that the shock is stable when the post-shock pressure and density obey gamma effective>10/7, with gamma effective begin the time depended equivalent to the adiabatic index. We express the effective gamma in terms of r, u and rho at the shock to obtain a simple condition for shock stability. This result is confirmed by hydrodynamical simulations, using an accurate spheri-symmetric Lagrangian code. When the stability analysis is applied in cosmology, we find that a virial shock does not develop in most haloes that form before z ~ 2, and it never forms in haloes less massive than a few 10^11 solar masses. In such haloes the infalling gas is never heated to the virial temperature, and it does not need to cool radiatively before it drops into a disc. Instead, the gas collapses at T ~ 10^4K directly into the disc. This should have nontrivial effects on the star-formation rate and on the gas removal by supernova-driven winds. Instead of radiating soft x rays, this gas would emit lyman alpha thus helping explain the low flux of soft x-ray background and the lyman alpha emitters observed at high redshift.

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