Time Dilation and our Perception of Galaxies

[JMBuilder]

So it's widely accepted that at the center of every galaxy is a supermassive black hole. This brings up some interesting questions about our observations of the universe.

1. I read at one point that some stars towards the edges of galaxies appear to move faster than the inner stars, contradicting what we understand about orbital velocity. Some scientists theorize that it's dark matter affecting them somehow, but I think it's a bit simpler than that. Is it possible that the central black holes dilate time enough to make it appear that the inner stars are moving slower relative to the outer stars?

2. With time dilation, light from the center of our galaxy would move slower relative to our time, so it would take longer to reach us. Does this mean that we're closer to the center of our galaxy than we realize?

3. Referring to 2, does this also mean that some outer stars and other galaxies are actually further away from us than they appear to be?

[Darvince]

1, 2, 3) The supermassive black hole's percentage mass of the galaxy is only 0.000008% at best. Therefore, this could only account for the closest stars to the black hole, i.e. the ones that are orbiting the supermassive black hole directly rather than orbiting the mass of the Milky Way in general.

(Using the highest estimate provided on Wikipedia for the mass of Sagittarius A* and the lowest estimate for the mass of the Milky Way).

[JMBuilder]

Is it possible that the mass of the galaxy as a whole would have the effect that I described?

[atomic7732]

First of all, I don't think we're sure that even every large (Milky Way-sized) galaxy has a central supermassive black hole, let alone every galaxy. There are a few significant galaxies where a central supermassive black hole has not been observed.

Nonetheless, spiral galaxies like the Milky Way have a "flat rotation curve" which means that the velocity of the stars is constant as a function of distance. So, stars at the outer edges of galaxies aren't moving faster than stars closer to the center, it's more likely they have a similar speed (so the orbital period of stars further out is still longer than stars closer to the center).

I don't think this time dilation explanation is feasible. Such a magnitude of time dilation would require a galaxy to have orders of magnitude more mass than the notion of dark matter requires. And in general, invoking special relativity for a theory is not "a bit simpler" than using Newtonian mechanics (Occam's razor and all that stuff, you know). Simply assuming the mass distribution of the galaxy is not proportional to the visible, baryonic matter (stars, gas, and dust) is a perfect explanation, which is why we believe dark matter is an abundant part of a galaxy's mass, in addition to the fact that we have observational evidence of its existence.

Also, in regards to 2, I don't think time dilation would affect the time it takes for light to reach us, since photons don't "experience" time and they always travel at the same speed, but I'm not sure. Maybe there would be funky stretching of spacetime. I haven't learned too much about relativity and stuff.