Virial shocks in galactic haloes?

Yuval Birnboim*, Avishai Dekel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

850 Scopus citations


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 with the infall rate, the post-shock gas becomes unstable; it collapses inwards and cannot support the shock. We find for a monatomic gas that the shock is stable when the post-shock pressure and density obey γeff ≡ (d ln P/dt)/(d ln ρ/dt) > 10/7. When expressed in terms of the pre-shock gas properties at radius r it reads as ρrΛ(T)/u3 < 0.0126, where ρ is the gas density, u is the infall velocity and Λ(T) is the cooling function, with the post-shock temperature T ∝ u2. 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 1011 M. In such haloes, the infalling gas is not heated to the virial temperature until it hits the disc, thus avoiding the cooling-dominated quasi-static contraction phase. The direct collapse of the cold gas into the disc should have non-trivial effects on the star formation rate and on outflows. The soft X-ray produced by the shock-heated gas in the disc is expected to ionize the dense disc environment, and the subsequent recombination would result in a high flux of Lα emission. This may explain both the puzzling low flux of soft X-ray background and the Lα emitters observed at high redshift.

Original languageAmerican English
Pages (from-to)349-364
Number of pages16
JournalMonthly Notices of the Royal Astronomical Society
Issue number1
StatePublished - 11 Oct 2003


  • Cooling flows
  • Dark matter
  • Galaxies: ISM
  • Galaxies: formation
  • Hydrodynamics
  • Shock waves


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