# $\eta$ and $\xi$ coordinate system

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.

• 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. Jun 28, 2020 at 16:59
• Apologies, I thought I included the link - thanks for digging up the related paper Jun 29, 2020 at 17:35

$$\xi$$ 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). Thanks to @planetmaker for digging this up!

• The orientation is mentioned in other plots in the references which employ the same coordinate sytem. North is up, East is left. Jun 29, 2020 at 8:25
• @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
Jun 29, 2020 at 10:11
• reference 7 by the same author in the paper quoted in the question above: ui.adsabs.harvard.edu/abs/2012A%26A...544A..73D/abstract Jun 29, 2020 at 10:36
• @planetmaker Indeed!
– pela
Jun 29, 2020 at 13:25