Some discussions (like here) indicate that it is not real.
It does not actually exist. It was made from visual effects. Of course Lucas did base the VFX on several galaxial pictures. Also note
that Empire Strikes Back was released in 1980, five years before the
launch of Hubble in 1985. And if you think about it, Return of the
Jedi (1983) was released two years before the launch of the Hubble.
I was in the Navy when ESB came out, thus I never saw ESB until 1991
when I mustered out. I even thought it was a Hubble picture or Hubble
based until I read the book Star Wars: Empire Strikes Back: Behind the
Scenes. It was then that I realized the image was done through VFX.
Amazing what VFX can do, even back then, 30+ years ago.
The Empire Strikes Back debate
At the end of The Empire Strikes Back, characters aboard the Rebel
fleet see a celestial object from some distance away. Some fans have
said that it rotates too fast to be a galaxy and at that distance a
galaxy would not emit as much light as is portrayed in the film.
Some sources have said that the fleet spent some time hiding
outside the galactic disk, probably intending to refer to this scene.
According to the 1996 Tales of the Bounty Hunters story Of Possible
Futures: The Tale of Zuckuss and 4-LOM, the object in the film is the
galaxy, and the Rebel fleet had journeyed to a point in space far
removed from the galactic plane. This point was not outside of the
galactic plane, per se, but rather above the galactic plane.
Since the release of Tales of the Bounty Hunters, the object has been
inconsistently identified. The Complete Star Wars Trilogy Scrapbook,
first released in 1997, identifies the object as a spinning star
formation. In 2002, the Episode II DVD-ROM Exclusive Content stated
that the bright object may be the cluster known as the Rishi Maze. In
2003, Leland Chee confirmed on the StarWars.com Message Boards that
the object was indeed the Star Wars galaxy. The film's director,
Irvin Kershner, refers to the object as simply "a galaxy" on the Audio
Commentary of the 2004 DVD release.