Is galactic gravitational lensing self-magnification big enough to contribute noticeably to the galaxy rotation curve problem?

Question

Gravitational lenses magnifies the appearance of themselves, so in the case of a galaxy it looks bigger than it is. Thus the outer stars in a galaxy seems to have a higher tangential velocity.
For example, the Sun deflects light passing from minus infinity to us 1.75 seconds of arc. Say that half of that value is the amount it deflects its own light at its edge, then the Sun looks 200 km wider.
Does this effect noticeably contribute to the galaxy rotation curve (dark energy/matter) problem?

ProfRob · Accepted Answer

For a spherically symmetric potential, the apparent radius of an object seen from far away is
$$R_{infty} = R left(1 - frac{2GM}{Rc^2}right)^{-1/2}, $$
where $M$ is the total mass-energy and $R$ is the radius in Schwarzschild coordinates.
For a big spiral galaxy (like the Milky Way), and ignoring any contribution from dark matter, then approximate numbers would be $M sim 5times 10^{10} M_{odot}$ and $R sim 20$ kpc.
Using the equation above, $R_{infty} = 20.0000002$ kpc.
If one includes dark matter, then you might lose one of the zeroes.
So no, the effect you ask about has no significant influence on the measurement of galactic sizes or velocities.

Is galactic gravitational lensing self-magnification big enough to contribute noticeably to the galaxy rotation curve problem?

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