Nucleus and Postperihelion Activity of Interstellar Object 3I/ATLAS Observed by Hubble Space Telescope

We report the detection of the nucleus of interstellar object 3I/ATLAS, using a nucleus extraction technique on Hubble Space Telescope (HST) observations taken between December 2025 and January 2026. The product of the V-band geometric albedo, $p_V$, with the physical cross-section of the nucleus is $0.22 \pm 0.07$ km$^{2}$, which corresponds to an effective radius of $1.3 \pm 0.2$ km if assuming a comet-like albedo $p_{V} = 0.04$. This size is in agreement with an independent estimate based on the reported nongravitational acceleration and activity of the interstellar object. If the measured photometric variations are solely due to the rotation of an aspherical nucleus, the axis ratio must be $2:1$ or greater, and the rotation period $\gtrsim\!1$ hr. Leveraging the range of covered phase angles, we identified a significant opposition surge of $\sim\!0.2$ mag with a width of $3^{\circ} \pm 1^{\circ}$, which may include concurrent contributions from orbital plane crossing and tail projection, and determined a linear phase slope of $0.026 \pm 0.006$ mag degree$^{-1}$ for the coma dust. Compared to the preperihelion brightening trend, 3I faded more rapidly on the outbound leg, following an activity index of $4.5 \pm 0.3$, not unusual in the context of solar system comets. This activity asymmetry is further corroborated by a postperihelion coma surface brightness profile that is significantly shallower than its preperihelion counterpart. From discovery statistics, we infer that multiple interstellar objects resembling 3I probably went undetected prior to the discovery of 1I/`Oumuamua, unless the overall population possesses a steep size distribution.