AC belt idler

I replaced a recessed bearing like that in a transmission part. As I recall, it stuck out enough to grab hold of with a bearing puller clamp. I can't figure how that pulley installs. Presumably your photo shows it off the bracket. There is no thru hole for a bolt, nor a thread on the backside. I prefer changing bearings on idlers, even when a new part is available (mostly on my newer cars), because the new parts come w/ Chinese no-name bearings and I'd rather keep the pulley and install a better German or Jap bearing (ebay). Bearings come in standard sizes.