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Hubble Space Telescope Detection of the Nucleus of Comet C/2014 UN$_{271}$ (Bernardinelli-Bernstein)

We present a high-resolution observation of distant comet C/2014 UN$_{271}$ (Bernardinelli-Bernstein) using the {\it Hubble Space Telescope} on 2022 January 8. The signal of the nucleus was successfully isolated by means of the nucleus extraction technique, with an apparent $V$-band magnitude measured to be $21.64 \pm 0.11$, corresponding to an absolute magnitude of $8.62 \pm 0.11$. The product of the visual geometric albedo with the effective radius squared is $p_V R_n^2$ = 159$\pm$16 km$^2$. If the ALMA observation by Lellouch et al. (2022) refers to a bare nucleus, we derive a visual geometric albedo of $0.034 \pm 0.008$ and an effective diameter of $137 \pm 15$ km. If dust contamination of the ALMA signal is present at the maximum allowed level (24%), we find nucleus diameter $119 \pm 13$ km and albedo of $0.044 \pm 0.011$. In either case, we confirm that C/2014 UN$_{271}$ is the largest long-period comet ever detected. Judging from the measured surface brightness profile of the coma, whose logarithmic gradient varies azimuthally between $\sim$1 and 1.7 in consequence of solar radiation pressure, the mass production is consistent with steady-state production but not with impulsive ejection, as would be produced by an outburst. Using aperture photometry we estimated an enormous (albeit uncertain) mass-loss rate of $\sim$10$^3$ kg s$^{-1}$ at a heliocentric distance of $\sim$20 au.