Clustering and averaging the images of Sagittarius A* and M87*

The two supermassive black holes that have been observed by the EHT have considerable differences in mass. M87* is more than a thousand times larger than the black hole at the centre of our galaxy, Sgr A*, which means that the gas goes around the latter much faster (on the timescale of minutes) than it goes around the former (on the timescale of days to weeks). When using the Dolomites as an analogy, observing the mountain range would correspond to a whole day for Sgr A* but only to a few minutes for M87*, while keeping the observing time on Earth the same. The animation starts by showing precisely these different timescales, illustrating the process of image clustering and averaging used to image Sgr A* (left) and M87* (right). The video showcases why, in a long-exposure observation of a changing subject, we can recover multiple possible images of the same mountain range. The various images produced are sorted into four different categories—known as clusters—according to their main features. Each cluster is accompanied by a vertical bar that indicates how often an image of that cluster is recovered from the total set of images. The images in each cluster are then averaged in the bottom panels and a final average image is constructed in the top part as a a weighted average of the various cluster averages (a cluster with a higher vertical bar has more weight in the final average image). The second part of the video then shows this process applied to the actual images of Sgr A* and M87* recovered from the Event Horizon Telescope observations of the two black holes. Clearly, many more images can be produced of Sgr A* and the statistics is more diversified than for M87*, where the averages are very similar. Finally, note that the different images of Sgr A* represent equally good fits of the observational data and do not refer to different instants in time as in the time-lapse movie.