H1821+643: The most X-ray and infrared luminous 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 non-beamed AGN of $L_\mathrm{14-150 keV}= 5.2\times 10^{45}$ erg s$^{-1}$ in the Swift/BAT ultra-hard X-ray survey and it is also a hyper-luminous infrared (IR) galaxy $L_\mathrm{IR} = 10^{13.2} L_\odot$ 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 $\log ( \mathrm{SFR}/M_{\odot}~\mathrm{yr}^{-1}) = 3.01 \pm 0.04$ and BH accretion rate of $\log (\dot{M}_\mathrm{BH}/M_{\odot}~\mathrm{yr}^{-1}) = 1.20 \pm 0.05$. This high $\dot{M}_\mathrm{con}$ is larger than the cooling rate ($\dot{M}_\mathrm{cool}$) of the intra-cluster medium (ICM), $\dot{M}_\mathrm{con}/\dot{M}_\mathrm{cool} \gtrsim 1$, which is one to two order magnitude higher than the typical value of other systems, indicating that H1821 provides the unique and extreme environment of rapid gas consumption. We also show that H1821+643 has an efficient cooling path achieving from $10^7$ K to $10^2$ K thanks to [OIII] 63 $\mu \mathrm{m}$, which is a main coolant in low temperature range ($10^4$ K to $10^2$ K) with a cooling rate of $\dot{M}_{\mathrm{cool}}=3.2\times 10^5\ M_{\odot}\mathrm{~yr^{-1}}$, and the star-forming region extends over 40 kpc scale.