# Do we have to take gravitational lensing into consideration when measuring the size of exoplanets?

For the method of waiting for a planet to pass in front of a star. rather than just measuring the light that is blocked do we also have to take into consideration the light that may not be coming to us because of gravitational lensing caused by the planet? Is the mass of a planet large enough to cause gravitational lensing significant enough for us to see an effect?

• No, the planet mass is nowhere near great enough. A quick look at the obvious WIkipedia page shows that the mass has to be of magnitude on the order of $c^2$ for the effect to be significant. – Carl Witthoft Jun 26 '17 at 13:56

No, there is no effect here.

Why?

Gravitational lensing magnification works by increasing the observed surface area of the lensed object while preserving the surface brightness. An exoplanet angular diameter is much smaller than that of its host star (even if we can't resolve either). Hence, all the magnification happens across a uniformly lit background, for which the measured increased brightness is zero. In effect, you stretch the image of part of the star into equally bright other parts of the star, resulting in zero magnification - the Einstein radius of the lens is much smaller than the radius of the star.

You might get a negligible effect when the star moves across the edge of the stellar disk.

Why does even that not matter?

The geometry is very disadvantageous. Setting aside the small mass of the planet (which is another factor), gravitational lensing works best when the distance between source and lens is about the same as the distance between lens and observer. This is very much not the case in the scenario we look at here.

Summary

• Gravitational lensing has no effect on a background of uniform brightness.
• The geometry of the lensing system makes any leftover effects tiny.
• The mass of the lens is small to begin with.

Also, there will be other effects that will completely dominate any lensing going on.

Edit to emphasize the size argument

In this image you can see a small source in red, and the resulting lensed image in green. Note that the increase in brightness is purely an effect of the size of the lensed image, not more flux per area. If we assume that the blue circle is the size of the star, we can see that any lensing happening while the planet transits its star will simply stretch parts of a bright uniform background into other parts of the same bright uniform background. Of course, the extent of the lensed image here is greatly exaggerated in order to be able to show any lensing features at all. With a planet in front of a star you would not even get multiple images.

• Wouldn't distance from the observed system play a roll in how much of an effect g-lensing would make? – Joe Jun 27 '17 at 15:52
• @Joe: I added an image to hopefully clarify what I meant in the first paragraph. As to your question, yes, the distance from observer (us) to lens and source (planet and star) enters into the equation. In the case of exoplanets, it will not affect whether we can observe anything or not, for reasons detailed in the answer. – Alex Jul 5 '17 at 12:10