[danbruc]

No, it happened 1795 years ago. There is only one frame of reference involved here, one we can attach to the Milky Way neglecting the relatively small movements of earth and KIC 9832227 within it. And two events are simultaneous in a given frame of reference if light emitted from both events reaches a point midway between the locations of the two events at the same time.

So you position your space ship in the middle between were earth and KIC 9832227 were 1795 years ago, about 900 light years away from each and sometime about the year 1122 you will see the stars colliding and at the same time, with a good enough telescope, what was happing on earth in the year 222 which establishes that the the collision of KIC 9832227 and the year 222 on earth were simultaneous in the frame of reference attached to the Milky Way.

[dsqrt]

Please see my other reply below. Reference frames are local constructs. There is no such a thing as a (unique) reference frame of the entire galaxy that can be used to define simultaneity. In fact there are infinitely many of them.

[danbruc]

I have seen that your profiles says theoretical astrophysicist so you certainly know a lot more than me about the topic. Nonetheless I can not see why we can not have a reference frame extending over 100,000 light years or at least over 1,800 light years. That seem relatively small distance, the relative velocities are relatively small, space is relatively flat, expansion of space is, I guess, not really relevant within galaxies.

So naively I would expect that you can attach a reference frame to almost all objects in the Milky Way and they would agree on simultaneity to within hours or maybe days. There are certainly some notable exceptions like the central black hole or particles traveling at an appreciable fraction of the speed of light and you can certainly just invent a reference frame with huge relative velocity changing simultaneity a lot.

But are there really places within the Milky Way so that simultaneity would be off by hundreds and thousands of years over a distance of just 1,800 light years? If yes, what is the cause of that, as far as I can tell it would have to be an effect of general relativity because, again as far as I can tell, there is no problem of defining simultaneity across extended distances in special relativity and the involved velocities are not large enough to have an appreciable effect to begin with.

EDIT: Just calculated an example Lorentz transformation, 500 km/s relative velocity and 1,800 light years distance, and the time difference comes out at almost exactly 3 years. That is certainly more than I expected and adds up to 166 years across the entire Milky Way, on the other hand 500 km/s is probably quite a bit above common relative velocities within the Milky Way.

So I am still not convinced that picking a reference frame for the entire Milky Way, say with the origin at the center of mass, one axis coinciding with the axis of rotation and rotating with the Milky Way so that the angular momentum vanishes, could not provide a good enough reference frame for the entire Milky Way for back of the napkin calculations.

[dsqrt]

I agree that you can make such a construction in theory. However, in practice there is no way we can synchronize our clocks with an observer at the location of that binary star system. There is also no reason to do it: the precise time of the star merger does not have any physical meaning, it is just a label. Saying that some astronomical event took place on the date we observe it, is equally valid and free from ambiguities.