Dongsu Bak, Jae-Weon Lee

We investigate how supermassive black hole (SMBH) seeds form in the early Universe at the centers of ultralight dark matter (ULDM) halos. Focusing on the ULDM Jeans scale, we identify the critical conditions under which high-redshift baryonic gas, strongly confined by central solitonic cores of the halos, undergoes direct and monolithic collapse. The solitonic potential naturally drives rapid inflow and shock heating, allowing the gas to exceed the critical atomic-cooling and fragmentation-suppression threshold of $\sim 3 \times 10^4 {\rm K}$ without invoking an external UV background. We derive semi-analytic relations for the halo mass, soliton mass, baryonic core radius, and thermodynamic state of the gas, including the effects of baryonic contraction. These relations simultaneously determine the minimum and maximum SMBH seed masses as functions of redshift. In this framework, pristine gas clouds that satisfy the temperature threshold collapse without fragmentation, forming SMBH seeds with characteristic masses of order $\sim 10^5M_\odot$, while systems below the threshold are expected to form compact star clusters instead. Our model also implies an upper limit on the attainable SMBH mass, predicting a maximum mass scale of order $\sim10^{10}M_\odot$, consistent with the most massive quasars observed to date. The ULDM particle mass required to reproduce the inferred seed mass scale, $m \simeq 10^{-22}{\rm eV}$, coincides with the value favored by galactic-scale observations, providing a unified explanation for the characteristic masses of both galactic cores and early SMBH seeds. Our model predicts efficient SMBH seed formation at redshifts $z \gtrsim 10$ and offers a natural interpretation of recently observed little red dots as SMBHs embedded in compact, hot, ionized gas clouds.