When we see multiple images of the same object because of the phenomenon of gravitational lensing, do all the images show the lensed object at the same point in time?

Does it take the same amount of time for light from the lensed object to reach us no matter what image we look at or are we watching the lensed object at different points in time and if so, how big can the difference in time typically be?


Time delays between the light received from multiple lensed images is a well known and commonly studied phenomenon. A typical example can be found in Koopmans et al. (2003) where they study a quadruple lens system formed by a forefround object at z=0.6 and a background source at z=1.4. The time delays measured are 31-77 days and this seems to be typical for the objects studied so far.

The delay depends on the difference in path length taken by the multiple images. This in turn depends on the distance to the source and the distance between the source and the lensing object and on the mass distribution around the lensing object. It also depends on the expansion rate of the universe, which gives a route to estimating the Hubble parameter.

A rule of thumb appears to be that the delay is of order $r_s/c$, where $r_s = 2GM/c^2$, where $M$ is the mass of the lens interior to the path of the light ray. $$ \tau \sim 10^{-5} \left(\frac{M}{M_{\odot}}\right)\ {\rm sec}$$ So for a $10^{12}M_{\odot}$ foreground lensing galaxy (a big spiral like the Milky Way), the delay is about 100 days.

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