Cosmological Advection Flows in the Presence of Primordial Black Holes as Dark Matter and Formation of First Sources

In the inflation-based cosmology the dark matter (DM) density component starts moving with respect to the universal expansion at z_{eq}∼3200 while baryons remain frozen until z_{rec}∼1100. It has been suggested that in this case postlinear corrections to the evolution of small fluctuations would result, for the standard Λ-dominated cold DM (CDM) model, in delayed formation of early objects as supersonic advection flows develop after recombination, so baryons are not immediately captured by the DM gravity on small scales. We develop the hydrodynamical description of such two-component advection and show that, in the supersonic regime, the advection within irrotational fluids is governed by the gradient of the difference of the kinetic energies of the two (DM and baryonic here) components. We then apply this formalism to the case where DM is made up of LIGO-type black holes (BHs) and show that there the advection process on scales relevant for early structure collapse will differ significantly from the earlier discussed (CDM) case because of the additional granulation component to the density field produced during inflation. The advection here will lead efficiently to the common motion of the DM and baryon components on scales relevant for collapse and formation of first luminous sources. This leads to early collapse, making it easier to explain the existence of supermassive BHs observed in quasars at high z>7. The resultant net advection rate reaches minimum around ≲10^{9}  M_{⊙} and subsequently rises to a secondary maximum near the typical mass of ∼10^{12}  M_{⊙}, which may be an important consideration for formation of galaxies at z≲(a few).