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ABSTRACT We revisit the question of ‘hot mode’ versus ‘cold mode’ accretion on to galaxies using steady-state cooling flow solutions and idealized 3D hydrodynamic simulations. We demonstrate that for the hot accretion mode to exist, the cooling time is required to be longer than the free-fall time near the radius where the gas is rotationally supported, Rcirc, i.e. the existence of the hot mode depends on physical conditions at the galaxy scale rather than on physical conditions at the halo scale. When allowing for the depletion of the halo baryon fraction relative to the cosmic mean, the longer cooling times imply that a virialized gaseous halo may form in halo masses below the threshold of $$\sim 10^{12}\, {\rm M_{\odot }}$$ derived for baryon-complete haloes. We show that for any halo mass there is a maximum accretion rate for which the gas is virialized throughout the halo and can accrete via the hot mode of $${\dot{M}}_{\rm crit}\approx 0.7(v_{\rm c}/100\, \rm km\ s^{-1})^{5.4}(R_{\rm circ}/10\, {\rm kpc})(Z/\, {\rm Z_{\odot }})^{-0.9}\, {\rm M_{\odot }}\, {\rm yr}^{-1}$$, where Z and vc are the metallicity and circular velocity measured at Rcirc. For accretion rates $$\gtrsim {\dot{M}}_{\rm crit}$$ the volume-filling gas phase can in principle be ‘transonic’ – virialized in the outer halo but cool and free-falling near the galaxy. We compare $${\dot{M}}_{\rm crit}$$ to the average star formation rate (SFR) in haloes at 0 < z < 10 implied by the stellar-mass–halo-mass relation. For a plausible metallicity evolution with redshift, we find that $${\rm SFR}\lesssim {\dot{M}}_{\rm crit}$$ at most masses and redshifts, suggesting that the SFR of galaxies could be primarily sustained by the hot mode in halo masses well below the classic threshold of $$\sim 10^{12}\, {\rm M_{\odot }}$$.
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Cooling flow solutions for the circumgalactic medium
ABSTRACT In several models of galaxy formation feedback occurs in cycles or mainly at high redshift. At times and in regions where feedback heating is ineffective, hot gas in the galaxy halo is expected to form a cooling flow, where the gas advects inward on a cooling timescale. Cooling flow solutions can thus be used as a benchmark for observations and simulations to constrain the timing and extent of feedback heating. Using analytic calculations and idealized 3D hydrodynamic simulations, we show that for a given halo mass and cooling function, steady-state cooling flows form a single-parameter family of solutions, while initially hydrostatic gaseous haloes converge on one of these solutions within a cooling time. The solution is thus fully determined once either the mass inflow rate $${\dot{M}}$$ or the total halo gas mass are known. In the Milky Way halo, a cooling flow with $${\dot{M}}$$ equal to the star formation rate predicts a ratio of the cooling time to the free-fall time of ∼10, similar to some feedback-regulated models. This solution also correctly predicts observed $$\rm{O\,{\small VII}}$$ and $$\rm{O\,{\small VIII}}$$ absorption columns, and the gas density profile implied by $$\rm{O\,{\small VII}}$$ and $$\rm{O\,{\small VIII}}$$ emission. These results suggest ongoing heating by feedback may be negligible in the inner Milky-Way halo. Extending similar solutions out to the cooling radius however underpredicts observed $$\rm{O\,{\small VI}}$$ columns around the Milky-Way and around other low-redshift star-forming galaxies. This can be reconciled with the successes of the cooling flow model with either a mechanism which preferentially heats the $$\rm{O\,{\small VI}}$$-bearing outer halo, or alternatively if $$\rm{O\,{\small VI}}$$ traces cool photoionized gas beyond the accretion shock. We also demonstrate that the entropy profiles of some of the most relaxed clusters are reasonably well described by a cooling flow solution.
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- Award ID(s):
- 1652522
- PAR ID:
- 10184328
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Volume:
- 488
- Issue:
- 2
- ISSN:
- 0035-8711
- Page Range / eLocation ID:
- 2549 to 2572
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1093/mnras/stz1859
