<p><strong>tl;dr:</strong> Atmospheric refraction is different at radio frequencies than at optical frequencies due to water vapor and electrons, and needs to be though of in a different way. It can be much stronger than for optical observations, and <strong>it can indeed be non-zero at the zenith!</strong> due to ionospheric effects.</p>

<p>The quoted passage in the question should be only applied to optical observations where the refraction is very weak and doesn't vary much (on average) across the aperture of one optical telescope.</p>

<hr>

<p>Refraction happens to all electromagnetic radiation, not only just visible light.</p>

<p>At visible wavelengths the atmosphere is only very weakly absorbing/attenuating, so the refractive index is treated as a real number, with n ~ 1.0003 due to the dielectric properties of mostly N2 and O2 gas at the surface and dropping with decreasing density going up. </p>

<p>However <em>things are very different at other wavelengths!</em></p>

<p>For radio astronomy there are (at least) two more sources of refraction:</p>

<ol>
<li>water vapor </li>
<li>electrons </li>
</ol>

<p>and the interaction of radio waves with these is more complex.</p>

<h2>Water vapor</h2>

<p>Water vapor is fairly strongly absorbing in the microwave and infrared wavelengths, with a complicated distribution of vibrational and rotational states that strongly interact with electromagnetic radiation due to the molecule's strong polarization. And whenever you have absorption at one frequency (imaginary part of index of refraction), you have changes in the real index of refraction above and below.</p>

<p>Since the distribution of water vapor with altitude differs from the distribution of the other gases, refraction can vary differently than a model for visible light refraction would predict. Since the refraction can be stronger than for visible light, accuracy become much more important as well.</p>

<p>For very high resolution inteferometric radio telescope arrays like ALMA for example, there are differences in refraction seen by each dish, and so every dish is equipped with its own <em>precipital water vapor monitor</em> which I believe is some kind of broadband microwave monitor sensitive to the columnar density of water <em>in the direction that the dish is pointed</em>, but I'm not sure. So I've asked <a href="https://astronomy.stackexchange.com/q/18791/7982">What is precipitable water vapor in millimeter-wave radioastronomy and how is it measured?</a> and I'm still waiting for an authoritative reply.</p>

<h2>Electrons</h2>

<p><a href="https://i.sstatic.net/8MO2b.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/8MO2b.png" alt="enter image description here"></a> <a href="http://www.arrl.org/files/file/Technology/pdf/119962.pdf" rel="nofollow noreferrer">Source</a> from <a href="https://astronomy.stackexchange.com/a/22402/7982">here</a>.</p>

<p>The Earth's atmosphere includes a layer called the ionosphere, and for every ion there's a free electron as well. The same way that the electron "plasma" in metals block and reflect light with frequency below the metal's plasma frequency, the ionosphere blocks and reflects radio waves with frequency below the ionosphere's plasma frequency. It's more complicated because the ionosphere is modeled in layers, but you can imagine a frequency somewhere between roughly 10 and 60 MHz depending on the time of day and the mood of the Sun below which the ionosphere is opaque. </p>

<p>At higher frequency and shorter wavelengths than this, the ionosphere will be mostly transparent, but the real part of the index of refraction will still be significant because it is close to an absorption edge. </p>

<p>In this case refraction can be much larger than for optical telescopes. I'm still working on an answer to [How large does refraction become in radioastronomy?](How large does refraction become in radioastronomy?) While @RobJeffries <a href="https://astronomy.stackexchange.com/a/22411/7982">points out</a> that for GHz type frequencies and above the refraction is not much different than for optical, it can get <strong>much larger</strong> at much lower frequencies near the plasma frequency.</p>

<p>Slide #29 of <a href="http://www.phys.unm.edu/~lwa/chicago08/talks/anderson_software.pdf" rel="nofollow noreferrer">LOFAR Calibration of the Ionosphere and Other Fun Things</a> shows that refraction can be several degrees at elevations that are still very useful for radio astronomy.</p>

<p><a href="https://i.sstatic.net/gnGDu.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/gnGDu.png" alt="enter image description here"></a></p>

<p>But to address the OP's question directly, have a look at slide #21! A radio observation with an array of antennas has been fit to a simple model for the ionosphere with thin "screen" of refraction at 200 km. It shows a phase shift gradient of roughly 100 degrees over only 0.2 degrees in latitude, which is exactly the kind of refraction shown in the OP's question!</p>

<p><a href="https://i.sstatic.net/tS67Z.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/tS67Z.jpg" alt="enter image description here"></a> </p>

CC BY-SA 4.0
2019-03-06T07:29:54.150Z
2019-03-06T07:29:54.150Z
uhoh
<p>To predict the position of a star one has to account for atmospheric refraction. In a simple model, the atmosphere is treated as being composed of layers of gas with variation in density and temperature due to height, but no variation with latitude or longitude and no turbulence. In such a model, one can predict the position of a star to a great deal of accuracy (so it is a useful model), and in this model there is no refraction at the zenith (as the light doesn't pass <em>at an angle</em> through a medium of varying optical density).</p>

<p>In such a model there would be no twinkling, however modelling twinkling is not needed for positional astronomy. Large variation in optical density that could cause stars to appear significantly displaced at the zenith doesn't occur. The variation in optical density with height is much more significant for positional astronomy.</p>

CC BY-SA 4.0
2019-03-05T21:41:58.953Z
2019-03-05T21:41:58.953Z
James K
<p><a href="https://en.wikipedia.org/wiki/Atmospheric_refraction" rel="nofollow noreferrer">Wikipedia states</a>:</p>

<blockquote>
  <p>Atmospheric refraction of the light from a star is zero in the zenith</p>
</blockquote>

<p>and other sources seem to agree.</p>

<p>I don't see why this should be so. Consider a situation in which air gets warmer from left to right. Then light should curve towards the warm air, and a star at the zenith would appear refracted.</p>

<p><a href="https://i.sstatic.net/gZBGL.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/gZBGL.png" alt="Cold air - Hot air"></a></p>

<p>So why do so many sources claim there is no refraction at the zenith? What do they mean by this?</p>

CC BY-SA 4.0
2019-03-05T03:07:16.837Z
The refraction equations are based on a standard atmospheric model  which considers temperature variation in altitude only, not from one location to another. Your illustration is not a typical occurrence.
JohnHoltz
CC BY-SA 4.0
2019-03-05T06:23:02.427Z
Hmm, that kind of helps, but it's also not really true to say what I've illustrated is "not common", as the model you're describing would not predict the twinkling of stars, which is a common occurrence.
Mark Eichenlaub
CC BY-SA 4.0
2019-03-05T09:06:10.607Z
I would say that turbulence is at low scale right what you describe *and fluctuating*. In such a sense there is twinkling at zenith but not a fixed apparent displacement. @Mark Eichenlaub
Alchimista
<atmospheric-effects>
What is meant by "there is no refraction at the zenith"?
Mark Eichenlaub
# What is meant by "there is no refraction at the zenith"?

(Asked by: username_0 on 2019-03-04)

[Wikipedia states](https://en.wikipedia.org/wiki/Atmospheric_refraction):

> Atmospheric refraction of the light from a star is zero in the zenith

and other sources seem to agree.

I don't see why this should be so. Consider a situation in which air gets warmer from left to right. Then light should curve towards the warm air, and a star at the zenith would appear refracted.

[![Cold air - Hot air](https://i.sstatic.net/gZBGL.png)](https://i.sstatic.net/gZBGL.png)

So why do so many sources claim there is no refraction at the zenith? What do they mean by this?

**Tags:** atmospheric-effects
> **Comments:**
> **username_1**: The refraction equations are based on a standard atmospheric model  which considers temperature variation in altitude only, not from one location to another. Your illustration is not a typical occurrence.  
> **username_0**: Hmm, that kind of helps, but it's also not really true to say what I've illustrated is "not common", as the model you're describing would not predict the twinkling of stars, which is a common occurrence.  
> **username_2**: I would say that turbulence is at low scale right what you describe *and fluctuating*. In such a sense there is twinkling at zenith but not a fixed apparent displacement. @Mark Eichenlaub  

---

## 2 answers

### Answer by username_4 on 2019-03-05. Score: 4 | Accepted answer

To predict the position of a star one has to account for atmospheric refraction. In a simple model, the atmosphere is treated as being composed of layers of gas with variation in density and temperature due to height, but no variation with latitude or longitude and no turbulence. In such a model, one can predict the position of a star to a great deal of accuracy (so it is a useful model), and in this model there is no refraction at the zenith (as the light doesn't pass *at an angle* through a medium of varying optical density).

In such a model there would be no twinkling, however modelling twinkling is not needed for positional astronomy. Large variation in optical density that could cause stars to appear significantly displaced at the zenith doesn't occur. The variation in optical density with height is much more significant for positional astronomy.


---

### Answer by username_3 on 2019-03-06. Score: 2

**tl;dr:** Atmospheric refraction is different at radio frequencies than at optical frequencies due to water vapor and electrons, and needs to be though of in a different way. It can be much stronger than for optical observations, and **it can indeed be non-zero at the zenith!** due to ionospheric effects.

The quoted passage in the question should be only applied to optical observations where the refraction is very weak and doesn't vary much (on average) across the aperture of one optical telescope.

---

Refraction happens to all electromagnetic radiation, not only just visible light.

At visible wavelengths the atmosphere is only very weakly absorbing/attenuating, so the refractive index is treated as a real number, with n ~ 1.0003 due to the dielectric properties of mostly N2 and O2 gas at the surface and dropping with decreasing density going up.

However *things are very different at other wavelengths!*

For radio astronomy there are (at least) two more sources of refraction:

1. water vapor
2. electrons

and the interaction of radio waves with these is more complex.

## Water vapor

Water vapor is fairly strongly absorbing in the microwave and infrared wavelengths, with a complicated distribution of vibrational and rotational states that strongly interact with electromagnetic radiation due to the molecule's strong polarization. And whenever you have absorption at one frequency (imaginary part of index of refraction), you have changes in the real index of refraction above and below.

Since the distribution of water vapor with altitude differs from the distribution of the other gases, refraction can vary differently than a model for visible light refraction would predict. Since the refraction can be stronger than for visible light, accuracy become much more important as well.

For very high resolution inteferometric radio telescope arrays like ALMA for example, there are differences in refraction seen by each dish, and so every dish is equipped with its own *precipital water vapor monitor* which I believe is some kind of broadband microwave monitor sensitive to the columnar density of water *in the direction that the dish is pointed*, but I'm not sure. So I've asked [What is precipitable water vapor in millimeter-wave radioastronomy and how is it measured?](https://astronomy.stackexchange.com/q/18791/7982) and I'm still waiting for an authoritative reply.

## Electrons

[![enter image description here](https://i.sstatic.net/8MO2b.png)](https://i.sstatic.net/8MO2b.png) [Source](http://www.arrl.org/files/file/Technology/pdf/119962.pdf) from [here](https://astronomy.stackexchange.com/a/22402/7982).

The Earth's atmosphere includes a layer called the ionosphere, and for every ion there's a free electron as well. The same way that the electron "plasma" in metals block and reflect light with frequency below the metal's plasma frequency, the ionosphere blocks and reflects radio waves with frequency below the ionosphere's plasma frequency. It's more complicated because the ionosphere is modeled in layers, but you can imagine a frequency somewhere between roughly 10 and 60 MHz depending on the time of day and the mood of the Sun below which the ionosphere is opaque.

At higher frequency and shorter wavelengths than this, the ionosphere will be mostly transparent, but the real part of the index of refraction will still be significant because it is close to an absorption edge.

In this case refraction can be much larger than for optical telescopes. I'm still working on an answer to [How large does refraction become in radioastronomy?](How large does refraction become in radioastronomy?) While @RobJeffries [points out](https://astronomy.stackexchange.com/a/22411/7982) that for GHz type frequencies and above the refraction is not much different than for optical, it can get **much larger** at much lower frequencies near the plasma frequency.

Slide #29 of [LOFAR Calibration of the Ionosphere and Other Fun Things](http://www.phys.unm.edu/~lwa/chicago08/talks/anderson_software.pdf) shows that refraction can be several degrees at elevations that are still very useful for radio astronomy.

[![enter image description here](https://i.sstatic.net/gnGDu.png)](https://i.sstatic.net/gnGDu.png)

But to address the OP's question directly, have a look at slide #21! A radio observation with an array of antennas has been fit to a simple model for the ionosphere with thin "screen" of refraction at 200 km. It shows a phase shift gradient of roughly 100 degrees over only 0.2 degrees in latitude, which is exactly the kind of refraction shown in the OP's question!

[![enter image description here](https://i.sstatic.net/tS67Z.jpg)](https://i.sstatic.net/tS67Z.jpg)


---

