The fluorescence occurs because electrons within molecules in the linseed oil are ‘excited’ to higher energy states by absorbing energy from the UV light. This excited state is temporary, and when the electrons return to their original energy state, they release energy in the form of light as they do so. This light is usually at a longer wavelength than the energy absorbed - hence why we see it in the visible spectrum, as fluorescence. The diagram below, from this page, illustrates this:
As for the specific compound responsible for this fluorescence, I have to admit I’ve drawn a blank. The major compounds in linseed oil are fatty acids, and I suppose it’s possible that one of these could be the culprit, but that’s a bit of a stab in the dark. Any other chemists out there who just so happen to be experts in linseed oil fluorescence? :)
After a bit of article searching, no one (from the search I did, anyway) talked about if there was an individual molecule in particular that was responsible for fluorescence. It’s likely a combination. Since there are a lot of fatty acids, some with several pi bonds which are great at absorbing and emitting light, it is no surprise that linseed oil will fluoresce! However, since there aren’t any conjugated pi systems (double bonds which alternate with single bonds), the degree to which it fluoresces is not terribly great, that is, we don’t see any visible light emission. Fatty acids aren’t usually conjugated. And, furthermore, the reason the light emitted is of longer wavelength (weaker energy) than that absorbed is something known as Stokes’ Shift. Where a molecule will absorb light, get excited, and relax a bit (releasing a bit of that initial energy) and then it will release energy in the form of a weaker photon to get back to the ground state. …In case anyone was wondering.
Excellent further explanation!