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What are commonly important astrophysical systems/models, where optical refraction is important or necessary to account for?

I would kindly ask you not to consider refraction in Earth's atmosphere or inside instrumentation in this question.

Comment: Gravitational lensing is different from optical refraction even though it affects light paths. I would like to ask the authors to avoid mentioning it in the following.

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you mean refraction in telescopes/instruments or as the light is created and travel towards us? – Francesco Montesano Dec 18 '13 at 15:42
@FrancescoMontesano: Thank you, it is relevant! I mean astrophysical, not instrumental refraction. – Alexey Bobrick Dec 18 '13 at 15:51

Optical refraction is related to the change in direction of a light ray when the refractive index changes. Excluding Earth's atmospheres and instruments, I think that refraction has little/no impact in astronomy.

The only cases that comes to my mind where we can (probably) have some important refraction is in eclipsing star binaries or near edge on planetary systems. Let's imagine a planet transiting behind his star. Some of it's light passes through the stellar atmosphere and gets refracted. As the atmosphere is curved and likely changes the refractive index with height, it acts like a lens dispersing (intuition says so) the planet light.

Edit A similar description holds in general for any object passing behind an other one that have atmosphere.

And there is Gravitational Lensing (if you allow me), which has much larger impact on observations. This is caused by gravity bending light rays when passing near galaxies/cluster of galaxies(/stars/...). One of the differences of gravitational lensing with respect to standard lenses is that there is no change in refractive index, so it's achromatic (all wavelengths get bent by the same angle).

The effective index of refraction can be described as ( source: Narayan and Bartelmann(pdf) ): $$ n = 1 + \frac{2}{c^{2}} |\Phi|$$ where $\Phi$ is the gravitational potential and is generally a function of position of the object.

Gravitational lensing is canonically divided in three groups:

  1. Strong lensing, usually observed in galaxy clusters or around massive galaxies. The gravitational potential is so strong that the the image of a background galaxy is heavily distorted into arcs and rings, like in this striking image of Abell 2218 from HST:

  2. Weak lensing. The light of a galaxy encounters matter (and a lot of dark matter) travelling to us and gets refracted. This doesn't have a dramatic effect as in strong lensing, but distorts the shape of the galaxy. And this distortion can be used to study, e.g., the dark matter distribution around some object or the content of the universe.

  3. Micro lensing. Imagine to observe a star and somehow know that a blob of dark matter is going to pass in front of the star. The blob is not big enough to distort the star shape, but for sure it will increase by a small amount the luminosity of the star.

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Thank you very much! Refraction of light from transiting planets seems like a good example to me. Gravitational lensing, however, even effectively behaving like refraction, has a different nature from optical refraction. I would guess that planets are not the only cases, though. For example, interstellar or intergalactic medium can be refractive at some wavelength. – Alexey Bobrick Dec 18 '13 at 17:27
Also, I am curious if you know of any physical reason, which could substantiate this statement "I think that refraction has little/no impact in astronomy"? – Alexey Bobrick Dec 18 '13 at 17:29
@AlexeyBobrick. I know that Gravitational lensing is not refraction (that's why I wrote if you allow me), but it's the biggest effect that looks like refraction. I'm searching for some info about interstellar/intergalactic medium refraction, so I'll likely update my answer soon. About "I think that refraction has little/no impact in astronomy": the main reason is that I don't remember any talk/paper/discussion about refraction. And if it were a problem, would be important for cosmology (my field). – Francesco Montesano Dec 19 '13 at 8:36
Frankly, I do not remember too many talk/papers mentioning refraction either. However, I believe, it would be really interesting to find a physical explanation for it. Apart from the mentioned things, there might have also been some effects in radiation transfer in AGN tori which I have heard about, but I will have to look up for that. – Alexey Bobrick Dec 19 '13 at 10:54
@astromax: thanks for editing my posts :D – Francesco Montesano Dec 20 '13 at 10:12

Here's a paper I found which talks about the index of refraction of dark matter (different from gravitational lensing) and how a signal might attenuate. The paper is entitled, "Dark Matter Constraints from a Cosmic Index of Refraction", and here is the abstract:

The dark-matter candidates of particle physics invariably possess electromagnetic interactions, if only via quantum fluctuations. Taken en masse, dark matter can thus engender an index of refraction which deviates from its vacuum value. Its presence is signaled through frequency-dependent effects in the propagation and attenuation of light. We discuss theoretical constraints on the expansion of the index of refraction with frequency, the physical interpretation of the terms, and the particular observations needed to isolate its coefficients. This, with the advent of new opportunities to view gamma-ray bursts at cosmological distance scales, gives us a new probe of dark matter and a new possibility for its direct detection. As a first application we use the time delay determined from radio afterglow observations of distant gamma-ray bursts to realize a direct limit on the electric-charge-to-mass ratio of dark matter of |varepsilon|/M < 1 x 10^{-5} eV^{-1} at 95% CL.

To be honest I don't really understand how quantum fluctuations of dark matter could produce such an effect. Aside from instrumental or atmospheric effects (and theoretical considerations), I honestly don't recall refraction ever coming up as an important effect.

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I can't say yet either. This is very interesting, thank you! – Alexey Bobrick Dec 20 '13 at 13:57

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