Could supermassive black holes be quintessential primordial black holes?

Abstract

There is growing observational evidence for a population of supermassive black holes (SMBHs) in galactic bulges. We examine in detail the conditions under which these black holes must have originated from primordial black holes (PBHs). We consider the merging and accretion history experienced by SMBHs to find that, whereas it is possible that they were formed by purely astrophysical processes, this is unlikely and most probably a populations of primordial progenitors is necessary. We identify the mass distribution and comoving density of this population and then propose a cosmological scenario producing PBHs with the right properties. Although this is not essential we consider PBHs produced at the end of a period of inflation with a blue spectrum of fluctuations. We constrain the value of the spectral tilt in order to obtain the required PBH comoving density. We then assume that PBHs grow by accreting quintessence showing that their mass scales like the horizon mass while the quintessence field itself is scaling. We find that if scaling is broken just before nucleosynthesis (as is the case with some attractive non-minimally coupled models) we obtain the appropriate PBH mass distribution. Hawking evaporation is negligible in most cases, but we also discuss situations in which the interplay of accretion and evaporation is relevant.

Figures (12)

• Figure 1: Evolution to give the present day black hole in a $5\times 10^{11}M_{\odot}$ halo with redshift for various accretion efficiency factors. From top to bottom the evolutions are for $\epsilon_{acc}=10^{-7}, 3\times 10^{-7}, 10^{-6}, 3\times 10^{-6}$,and $10^{-5}$.
• Figure 2: Evolution of mass and number density for galactic black holes for 4 different accretion efficiencies. The data points are the inferred mass density values of Chokshi and Turner. The initial mass density and number density of black holes are taken to be $1 \times 10^{4} M_{\odot}Mpc^{-3}$ and $4\times 10^{-3}Mpc^{-3}$ at $z=0$ respectively. The number density at early time reaches $9\times 10^{-3}Mpc^{-3}$ at $z=10$ for the scenario that is consistent with observations. As one views the number density evolution from high z, the increase in number density arises from the formation of astrophysical black holes due to halo matter accretion. The contribution of astrophysical black holes becomes more prevalent as the accretion efficiency is increased.
• Figure 3: Evolution of mass and number density of black holes in galaxy scale halos for 3 different limiting mass thresholds. Reading top to bottom for mass density and bottom to top for number density $M_{l}=10^{10},5\times 10^{9}$ and $10^{9}M_{\odot}$ with accretion efficiencies of $\epsilon_{acc}=1.85,1.63$ and $1.38\times 10^{-6}$ respectively chosen to be in agreement with low z QSO observations
• Figure 4: Distribution of black hole masses at redshifts preceding halo merger activity for the models in fig 3 with $M_{l}=10^{10}M_{\odot}$ (full line) and $10^{9}M_{\odot}$ (dashed line). The distributions are normalised to their peak values.
• Figure 5: The evolution of black holes ignoring evaporation.