I recently saw this answers where it was suggested that the galactic core could illuminate a planet suffiently to make sure it is always summer on one side of the planet. This got me curious and after some research I came across this.
Astronomers have estimated that the total luminosity of the central dozen or so light-years of our galaxy is equal to about 10 million suns. That sounds big and bright – until you recall that the center of our galaxy is 25,000 light-years away. At that distance, if interstellar dust weren’t in the way, our unaided eyes would see the central part of our Milky Way galaxy as a central glow no bigger than the planet Venus, and no brighter than one of the stars of the Big Dipper. Interesting … but not blazingly bright. But wait. There’s more. The fact is that interstellar dust obscures more than just this central region. It also dims the light of billions of foreground stars, as well as stars surrounding the core itself. If there were no dust between us and the galactic center, the light of all the stars located toward the galaxy’s core would easily exceed that of a full moon. If you looked in that direction, you wouldn’t see much else but the combined glow of billions of stars.
While the first part of the article gives a value of luminosity, the second part points out why one should ignore it.
So given the fact that the galactic center is quite bright, yet itself a terrible place for planets due to gravitational interaction between stars, is there a habitable zone around the galactic centre in which a planet on an orbit inclined enough that it won't be shadowed by the discs dust clouds could be habitable?
I know that when the planet will invariably cross the galactic disc it will receive much less light and have an ice-age, but this is beyond the scope of the question. I would actually prefer if formulas were given in the answers instead of a simple yes or no.