H1821+643: The Most X-Ray and Infrared Luminous Active Galactic Nucleus (AGN) in the Swift/BAT Survey in the Process of Rapid Stellar and Supermassive Black Hole Mass Assembly

H1821+643 is the most X-ray luminous nonbeamed active galactic nucleus (AGN) of L _{14-150 keV} = 5.2 × 10⁴⁵ erg s^-1 in the Swift/Burst Alert Telescope (BAT) ultrahard X-ray survey, and it is also a hyperluminous infrared (IR) galaxy L _IR = 10^13.2 L _⊙ residing in the center of a massive galaxy cluster, which is a unique environment achieving the rapid mass assembly of black holes (BH) and host galaxies in the local universe. We decompose the X-ray to IR spectral energy distribution (SED) into the AGN and starburst component using the SED-fitting tool CIGALE-2022.0 and show that H1821+643 consumes a large amount of cold gas ( ${\dot{M}}_{\mathrm{con}}$ ) with star formation rate of $\mathrm{log}(\mathrm{SFR}/{M}_{\odot }\,{\mathrm{yr}}^{-1})=3.01\pm 0.04$ and BH accretion rate of $\mathrm{log}({\dot{M}}_{\mathrm{BH}}/{M}_{\odot }\,{\mathrm{yr}}^{-1})=1.20\pm 0.05$ . This high ${\dot{M}}_{\mathrm{con}}$ is larger than the cooling rate ( ${\dot{M}}_{\mathrm{cool}}$ ) of the intracluster medium, ${\dot{M}}_{\mathrm{con}}/{\dot{M}}_{\mathrm{cool}}\gtrsim 1$ , which is 1 to 2 orders of magnitude higher than the typical value of other systems, indicating that H1821+643 provides the unique and extreme environment of rapid gas consumption. We also show that H1821+643 has an efficient cooling path achieving from 10⁷ to 10² K thanks to [O I] 63 μm, which is a main coolant in low temperature range (10⁴ to 10² K) with a cooling rate of ${\dot{M}}_{\mathrm{cool}}=3.2\times {10}^{5}\ {{\rm{M}}}_{\odot }\,{\mathrm{yr}}^{-1}$ , and the star-forming region extends over 40 kpc scale.