The effect of Primordial Black Holes and streaming motions on structure formation

Primordial Black Holes could be an important component of the dark matter in the Universe. If they exist, they would add a Poisson component to the matter power spectrum. The extra power would speed up the emergence of dark matter halos that seed the formation of first stars and galaxies. Kashlinsky (2021) suggested that the additional velocity fluctuations would accelerate the infall of baryons onto the dark matter potential wells. We analyze the effect of Primordial Black Holes on the baryon infall from recombination to reionization and find the correction to be a few percent of the power suppression first identified by Tseliakhovich \& Hirata (2010). However, the dynamical effect of this correction in addition to the extra power speeds up the formation of halos in the mass range of $10^4-10^{5-6}$M$_\odot$, while slightly decreasing the formation of those in the range $10^6-10^8$M$_\odot$ confirming earlier analytic estimates and recent results of numerical simulations.