This is a question which spun of this Can the Sun / Earth have a dark matter core?
I have argued that it is possible to pretty accurately estimate how much mass of Sun is in the regular matter, so comparing this estimate to the gravitational effect of Sun could rule out any significant esoteric mass sources.
A couple of points brought in there:
What do you mean by "visible mass"? We can only see the first ~100km of the Sun. The gravitational effects of dark matter are identical to those of normal matter. There is no debate about what the mass of the Sun is; only what it consists of. - Rob Jeffries
While we may know the Sun's total mass pretty accurately from the masses and velocities of orbiting objects, I think we cannot know how much of that mass may be dark matter. (We may be able to give an upper bound above which the Sun wouldn't work as it does now. But apart from that, I'm confident that a couple of percent of DM inside the Sun wouldn't be observable.) – JimmyB
By visible mass I mean attributed to "regular" matter as opposed to dark matter. I agree with Jimmy. The gravitational effects are the same, precisely, but other's are not, so judging from its radius, color, dynamics (solar seismology is also a thing) etc. I would bet that we could calculate how much regular matter there is, and how well it fits the total mass as observed by gravitational effects.
Are there such estimates and how precise they are, a couple of %? Could there be a discrepancy between Sun's gravitational effect and mass attributed to it's regular matter?
Edit: To avoid confusion I guess the answer I'm looking for is
x% of Hydrogene,
y% of Helium,
z% of heavier elements,
w% neutrinos etc. to fit Standard model and star physics we know and
a% of possibly dark matter, because it seems to pull planets stronger than all the regular matter constituants that we know of.