Anything related to Viincent van Gogh's life as Jack the Ripper had meaning to him, even the hat he wore, and because it had meaning, Van Gogh painted it hidden in the Irises painting.
It's a clearly defined, fedora-like hat, which is facing the viewer. The brim around the bottom can be seen, and the crease on the top is defined with a dark line. This was likely the style of hat Van Gogh wore on the night he murdered Mary Kelly.