Hubble Study of the Proper Motion of HST-1 in the Jet of M87
The radio galaxy M87 is well known for its jet, which features a series of bright knots observable from radio to X-ray wavelengths. The most famous of these, HST-1, exhibits superluminal motion, and our analysis of {\it Chandra} data \citep{Thimmappa24} reveals a correlation between the X-ray flux of HST-1 and its separation from the core. This correlation likely arises from moving shocks in the jet, allowing measurement of the internal structure of HST-1 in the X-ray band. To follow up on these results, we use observations from the {\it Hubble} Space Telescope Advanced Camera for Surveys HRC/WFC/SBC channel and the Wide Field Camera 3 (WFC3)'s UVIS to analyze the image and flux variability of HST-1. Our analysis includes 245 ACS and 120 WFC3 observations from 2002-2022, with a total exposure time of $\sim345$ ks. We study the brightness profile of the optical jet and measure the relative separation between the core and HST-1 for comparison to the X-ray. We find that the X-ray and the UV/optical emission could arise from physically distinct regions. The measured proper motion of the knot HST-1 is 1.04$\pm$0.04 c from 2002-2005 and around 2.1$\pm$0.05 c from 2005-2022. We discuss the acceleration of the jet and the flaring synchrotron emission from HST-1 from optical to X-rays.