<p><span class="math-container">$\xi$</span> and <span class="math-container">$\eta$</span> are just arbitrary names of coordinates, used because the actual position on the sky doesn't matter in this context, i.e. only the relative position in the plot is important. An analogue would be to label the coordinates of your living room <span class="math-container">$x$</span> and <span class="math-container">$y$</span>, instead of using Earth's longitude and latitude.</p>
<p>If you really want to transform, you can use the information given by the authors that an &quot;over-dense feature&quot; is located at <span class="math-container">$(\xi,\eta) = (0.25,0.06)\,\mathrm{deg}$</span>, which they say corresponds to <span class="math-container">$(\mathrm{RA},\mathrm{dec}) = (2^\mathrm{h}21^\mathrm{m}2.2^\mathrm{s}, -34^\circ 27'17.6'')$</span>.</p>
<p>This transformation requires that positive <span class="math-container">$\xi$</span> and <span class="math-container">$\eta$</span> values point toward east and north, respectively. This is not explicitly written in the reference you give, but is seen to be the case in the paper they quote (<a href="https://ui.adsabs.harvard.edu/abs/2012A%26A...544A..73D" rel="nofollow noreferrer">de Boer et al. 2012</a>). Thanks to @planetmaker for digging this up!</p>

CC BY-SA 4.0
2020-06-29T08:25:05.897Z
The orientation is mentioned in other plots in the references which employ the same coordinate sytem. North is up, East is left.
planetmaker
CC BY-SA 4.0
2020-06-29T10:11:40.483Z
@planetmaker I can't seem to see that, can you tell me? (I'm sure you're right; it would be the natural choice)
pela
CC BY-SA 4.0
2020-06-29T10:36:59.597Z
reference 7 by the same author in the paper quoted in the question above:  https://ui.adsabs.harvard.edu/abs/2012A%26A...544A..73D/abstract
planetmaker
CC BY-SA 4.0
2020-06-29T13:25:23.820Z
@planetmaker Indeed!
pela
CC BY-SA 4.0
2020-06-29T07:29:57.020Z
2020-07-14T20:45:23.463Z
2020-07-14T20:45:23.463Z
pela
<p>Is there a standard definition for <span class="math-container">$\eta$</span> and <span class="math-container">$\xi$</span> in terms of Ra and Dec, as used in an astronomical coordinate system? I'm used to working with Ra and Dec, and am not sure how to precisely interpret this spatial graph from <a href="https://ui.adsabs.harvard.edu/abs/2013A%26A...551A.103D/abstract" rel="nofollow noreferrer">de Boer et al. 2013</a>.
<a href="https://i.sstatic.net/1HQRY.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/1HQRY.png" alt="stellar density from de Boer et al. 2013" /></a></p>

CC BY-SA 4.0
2020-06-28T16:59:18.797Z
What is eta and xi supposed to mean? Without context it might be a choice of an arbitrarily-aligned coordinate system, names chosen such to be not confused with other common choices. Discussing oddities, it always helps to link the sources of what you wonder about instead of just pasting without reference and credits a figure you did not create.
planetmaker
CC BY-SA 4.0
2020-06-29T17:35:06.760Z
Apologies, I thought I included the link - thanks for digging up the related paper
Elias
<coordinate>
$\eta$ and $\xi$ coordinate system
Elias
# $\eta$ and $\xi$ coordinate system

(Asked by: username_0 on 2020-06-28)

Is there a standard definition for $\eta$ and $\xi$ in terms of Ra and Dec, as used in an astronomical coordinate system? I'm used to working with Ra and Dec, and am not sure how to precisely interpret this spatial graph from [de Boer et al. 2013](https://ui.adsabs.harvard.edu/abs/2013A%26A...551A.103D/abstract).
[![stellar density from de Boer et al. 2013](https://i.sstatic.net/1HQRY.png)](https://i.sstatic.net/1HQRY.png)

**Tags:** coordinate

> **Comments:**
> **username_1**: What is eta and xi supposed to mean? Without context it might be a choice of an arbitrarily-aligned coordinate system, names chosen such to be not confused with other common choices. Discussing oddities, it always helps to link the sources of what you wonder about instead of just pasting without reference and credits a figure you did not create.  
> **username_0**: Apologies, I thought I included the link - thanks for digging up the related paper  

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## 1 answers

### Answer by username_2 on 2020-06-29. Score: 6 | Accepted answer

$\xi$ and $\eta$ are just arbitrary names of coordinates, used because the actual position on the sky doesn't matter in this context, i.e. only the relative position in the plot is important. An analogue would be to label the coordinates of your living room $x$ and $y$, instead of using Earth's longitude and latitude.

If you really want to transform, you can use the information given by the authors that an "over-dense feature" is located at $(\xi,\eta) = (0.25,0.06)\,\mathrm{deg}$, which they say corresponds to $(\mathrm{RA},\mathrm{dec}) = (2^\mathrm{h}21^\mathrm{m}2.2^\mathrm{s}, -34^\circ 27'17.6'')$.

This transformation requires that positive $\xi$ and $\eta$ values point toward east and north, respectively. This is not explicitly written in the reference you give, but is seen to be the case in the paper they quote ([de Boer et al. 2012](https://ui.adsabs.harvard.edu/abs/2012A%26A...544A..73D)). Thanks to @username_1 for digging this up!

> **Comments:**
> **username_1**: The orientation is mentioned in other plots in the references which employ the same coordinate sytem. North is up, East is left.  
> **username_2**: @username_1 I can't seem to see that, can you tell me? (I'm sure you're right; it would be the natural choice)  
> **username_1**: reference 7 by the same author in the paper quoted in the question above:  https://ui.adsabs.harvard.edu/abs/2012A%26A...544A..73D/abstract  
> **username_2**: @username_1 Indeed!  

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