Supermassive black holes from inflation constrained by dark matter substructure

TL;DR

This work investigates whether the universe's supermassive black holes could originate from primordial black holes formed by enhanced inflationary curvature perturbations, allowing for non-Gaussian statistics that relax CMB $\mu$-distortion constraints. The authors couple a peaked small-scale power spectrum with non-Gaussian perturbation distributions to compute PBH abundances, then propagate these perturbations into the dark-matter subhalo population using an extended Press–Schechter framework and tidal evolution. They derive current bounds on the perturbation amplitude from dwarf-satellite counts, stellar streams, and gravitational lensing, finding that these DM-substructure observations can probe SMBH-seed scenarios in a region overlapping with the required parameter space, especially for non-Gaussian cases, and offer competitive reach with future $\mu$-distortion probes. The results indicate that, with forthcoming data from surveys like LSST and future spectral-distortion missions, one can test SMBH-seed models down to seed masses as low as $\sim 10^5$–$10^7\,M_⊙$ for certain non-Gaussian shapes, highlighting the complementary role of small-scale structure in constraining inflationary physics and SMBH formation. The study emphasizes the importance of non-Gaussian tails in shaping both PBH abundances and DM subhalo demographics, and discusses avenues for refining the analysis by incorporating detailed subhalo density profiles and additional observational probes.

Abstract

Recent James Webb Space Telescope observations of high-redshift massive galaxy candidates have initiated renewed interest in the important mystery around the formation and evolution of our Universe's largest supermassive black holes (SMBHs). We consider the possibility that some of them were seeded by the direct collapse of primordial density perturbations from inflation into primordial black holes and analyze the consequences of this on current dark matter substructures assuming non-Gaussian primordial curvature perturbation distributions. We derive bounds on the enhanced curvature perturbation amplitude from the number of dwarf spheroidal galaxies in our Galaxy, observations of stellar streams and gravitational lensing. We find this bound region significantly overlaps with that required for SMBH seed formation and enables us to probe Gaussian and non-Gaussian curvature perturbations corresponding to the SMBH seeds in the range ${\cal O}(10^5$\text{--}$10^{12}) M_\odot$.

Figures (6)

• Figure 1: The primordial power spectrum against the comoving-to-peak wavenumber ratio. The Planck prediction with no enhancement is shown in black-solid, while we show other combination of peak amplitude and slopes in other colors and line styles as depicted in the legend.
• Figure 2: Dependence of the initial fraction of causal horizons $\beta$ as a function of the primordial power spectrum amplitude. The Gaussian case is shown as a cyan (dot-dashed), the $\chi^2$ case as a dark cyan (dashed), and the ${\rm G}^3$ case as a blue (solid) line. The plots are corresponding to the case assuming $\mathcal{K}=2$, $\zeta_c=\delta_c=0.45$
• Figure 3: The subhalo mass function $dN_{\rm sh}/d \log_{10} m$ within 300 kpc volume of the Milky-Way halo. The data points are a combination of the stellar-stream and lensing measurements Banik:2019czaBanik:2019smi. The curves are predicted subhalo mass functions for $k_p = 32\,h$ Mpc$^{-1}$ and smaller to larger values of $A$ (from top to bottom). The left and right panels are for $n_b = 4$ and $n_b = 8$, respectively. The dotted line in each panel corresponds to the prediction without a bump feature. Note that the peak amplitude in the legend is simply $A_\textrm{peak}=A\, n_b$.
• Figure 4: Constraints from current observations on the amplitude of the primordial power spectrum $A$ as a function of the peak wavenumber $k_p$ and PBH seed mass. The left panel assumes $n_b=4$ and the right panel does $n_b=8$. The light and dark solid purple lines represent constraints on the power spectrum from the satellite counts, and combined stream and lensing analysis at the 95% confidence level, respectively. The solid gray line corresponds to COBE/FIRAS $\mu$-distortion bounds. The black region is excluded by Lyman-$\alpha$ data Bird_2011. The solid cyan, dark cyan, and blue regions correspond to the magnitude of Gaussian, $\chi^2$, and ${\rm G}^3$ distributions which would give rise to an SMBH density of $\Omega_\textrm{SMBH}=10^{-10}$, respectively. The upper and lower boundary of these three bands correspond to the accretion factors $\mathcal{A}=1$ and $\mathcal{A}=10^5$.
• Figure 5: Future prospects on the sensitivity to the amplitude of the primordial power spectrum $A$. Projected constraints from galaxy stream observations are plotted in solid magenta lines corresponding to less than a 100% increase in subhalos ($\frac{N_{\rm sh}(A,k_p,n_b)}{N_{\rm sh}(A=0)}< 2$) in four subhalo mass ranges, $10^5$--$10^6$, $10^6$--$10^7$, $10^7$--$10^8$, and $10^8$--$10^9 M_\odot$, denoted using the lightest to darkest magenta colours respectively. Here we assume no uncertainty in the subhalo mass function for the scale-invariant power spectrum. Prospects with future $\mu$-distortion measurements with PIXIE Unal:2020mts are shown with gray-dashed lines. See Fig. \ref{['fig:sbs1']} for the Lyman-$\alpha$ bounds and expected amplitude for curvature perturbations to generate SMBH seeds.