Nucleosynthetic signatures of primordial origin around supermassive black holes

If primordial black holes (PBHs) seeded the supermassive black holes (SMBHs) at the centers of high-redshift quasars, then the gas surrounding these black holes may reveal nucleosynthetic clues to their primordial origins. We present predictions of altered primordial abundances around PBHs massive enough to seed SMBHs at $z\approx 6–7.5$. We find that if PBHs with initial masses of $\sim {10}^5{\mathrm{M}}_{\odot }$ are responsible for such SMBHs, they may produce primordial deuterium and Helium fractions enhanced by $\ge 10\%$, and lithium abundance depleted by $\ge 10\%$, at distances of up to $\approx$ a comoving kiloparsec away from the black hole after decoupling. We estimate that $\sim {10}^8{\mathrm{M}}_{\odot }$ of gas is enhanced (or depleted) by at least one percent. Evidence of these modified primordial deuterium, helium, and lithium abundances could still be present if this circum-PBH gas remains unaccreted by the SMBH and in or near the host galaxies of high-redshift quasars. Measuring the abundance anomalies will be challenging, but could offer a novel way to reveal the primordial origin of such SMBH seeds.

Figure 1

Primordial abundances as a function of density in excess of the critical density as calculated from AlterBBN. The top panel shows the relative abundances of all primordial elements through lithium. The lower panel zooms in on the helium abundance.

Figure 2

Upper left panel: the primordial deuterium abundance by unit mass, ${}^2\mathrm{H}/\mathrm{H}$, at BBN as a function of distance from a ${10}^5{\mathrm{M}}_{\odot }$ PBH. The Hubble radius at BBN is $\approx 0.6\mathrm{AU}$. Lower left panel: the log of the fractional change in ${}^2\mathrm{H}/\mathrm{H}$ as seen in the upper panel. Upper middle panel: the primordial Helium abundance by unit mass, $Y_p$, at BBN in the same region. Lower middle panel: the log of the fractional change in $Y_p$ as seen in the top panel. Upper right panel: the primordial lithium abundance in the same region. Lower right panel: the log of the fractional change in ${}^7\mathrm{Li}/\mathrm{H}$ as seen in the top panel. The unperturbed abundance of deuterium is ${}^2\mathrm{H}/\mathrm{H}=2.435\times {10}^{-5}$, for Helium is $Y_p=0.2473$, and for lithium-7 is ${}^7\mathrm{Li}/\mathrm{H}=5.467\times {10}^{-10}$. In the lower panels, dotted lines represent depletion, and solid lines an enhancement in the elemental abundance.

Figure 3

Upper panel: the distribution of deuterium-enhancement fraction in the primoridal gas at BBN around our ${10}^5{\mathrm{M}}_{\odot }$ PBH. Each bin shows the mass of the gas enhanced to levels shown on the $x$ axis. Middle panel: the census of Helium-enhanced gas formed at BBN around our PBH. For clarification, the first bin represents gas that has a 1–5% percent enhancement above the standard primordial deuterium abundance. Lower panel: the census of ${}^7\mathrm{Li}$-depleted and enhanced gas. Note that most of the gas is ${}^7\mathrm{Li}$-depleted rather than enhanced. The fine bins in the lower panel represent fraction depletions of 1 to 0.5, 0.5 to 0.25, 0.25 to 0.1, and 0.1 to 0.01; and fractional enhancements of 0.01 to 0.1. Note that we have omitted all gas that is enhanced or depleted by less than one percent.

Figure 4

The upper row shows the spatial distributions of light primordial element abundances at $z=1100$ (decoupling) as a function of distance from the PBH, including the mass fractions for deuterium ${}^2\mathrm{H}/\mathrm{H}$ (left), helium $Y_p$ (middle), and lithium ${}^7\mathrm{Li}/\mathrm{H}$ (right). The bottom row shows the corresponding (logarithm) of the fractional changes relative to the global average abundance of each species. The unperturbed background abundances are ${}^2\mathrm{H}/\mathrm{H}=2.435\times {10}^{-5}$, $Y_p=0.2473$ and ${}^7\mathrm{Li}$/$\mathrm{H}=5.467\times {10}^{-10}$. The solid curves show our model with an initial density perturbation. The baryons and radiation are coupled up until this point, pushing the baryons away from the initial point perturbation at the sound speed—roughly $c/\sqrt{3}$ during radiation domination. The dashed curves show, for reference, a model where we have assumed that the gas distribution simply follows the Hubble flow with time. The dotted portion of the curves in the lower panels represent depletions rather than enhancements in helium and lithium.