Formation of supermassive primordial black holes by Affleck-Dine mechanism

We study the supermassive black holes (SMBHs) observed in the galactic centers. Although the origin of SMBHs is not well understood yet, previous studies suggest that seed black holes (BHs) with masses $10^{4-5}{M}_{\odot }$ exist at a high redshift ($z\sim 10$). We examine whether primordial black holes (PBHs) produced by inhomogeneous baryogenesis can explain those seed black holes. Inhomogeneous baryogenesis is realized in the modified Affleck-Dine mechanism. In this scenario, there is no stringent constraint from cosmic microwave background $\mu$-distortion in contrast to the scenario where Gaussian fluctuations collapse into PBHs. It is found that the model can account for the origin of the seed BHs of the SMBHs.

Figure 1

The schematic view of the dynamics of the AD field during and after inflation. Upper side: During inflation, the coarse-grained AD field diffuses in the complex plain and takes different values in different Hubble patches. Lower side: Just after inflation, the multivacuum structure appears due to the thermal potential and the negative Hubble induced mass. In the patches with $|\varphi |>{\varphi }_c$, the AD field rolls down to the vacuum B. On the other hand, the patches with $|\varphi |<{\varphi }_c$, the AD field rolls down to the vacuum A.

Figure 2

The evolutions of the volume fraction of HBBs $f_B(N)$ (left) and the production rate of HBBs at ${\beta }_B(N)$ (right) for various $c_I^{\prime }$. $\mathrm{\Delta }$ is adjusted for each plot so that $f_B(N=60)$ takes the same value.

Figure 3

The PBH abundance. The left panel is the case with $M_c={10}^4{M}_{\odot }$ and the right panel is the case with $M_c={10}^5{M}_{\odot }$. In each panel, three lines correspond to $N_{\mathrm{gal}}=0.1,0.01,0.001{\mathrm{Mpc}}^{-3}$ from top to bottom if $M_c\ge M_b$.

Figure 4

The number density of PBHs assuming $M_c\ge M_b$. Each plot is normalized by its maximum value. If $M_c<M_b$, the cutoff below which there is no PBH appears at $M_{\mathrm{PBH}}=M_b$.

Figure 5

The PBH abundance. The left panel is the case with $M_c={10}^4{M}_{\odot }$ and the right panel is the case with $M_c={10}^5{M}_{\odot }$. In each panel, three lines correspond to $N_{\mathrm{gal}}=0.1,0.01,0.001{\mathrm{Mpc}}^{-3}$ from top to bottom if $M_c\ge M_b$.