Lensed images ra,dec coordinates

[enricoteofilo]

Hello.

From the documentation it wasn't totally clear to me how to get from x0_image_positions and x1_image_positions values to the (effective) ra,dec coordinates of individual lensed images for each event.

Would it be possible to get clarifications on that? Thanks.

[hemantaph]

Many apologies for the delayed response. I missed your previous comment. Below I am giving you an explanation regarding the image position.

'x0_image_positions' and 'x1_image_positions' corresponds to x and y axis in the lens plane (thin lens approximation); everything wrt the lens centre.

Also, I saw some code missing in the recent versions of ler ; so I have added these code lines regarding the source position wrt to the centre of the lens. ler latest version is 0.4.2 . Now, you will see extra lens parameters [x_source, y_source].

Thanks for pointing it out. I have also added a few lines in the documentation regarding this.

Lastly, [ra,dec] corresponds to the position of the compact-binary source, i.e. source position. So, to plot the image position in the sky, you need to start from the source position [ra,dec], and the lens centre will be [-x_source, -y_source] and image positions will be [x0_image_positions - x_source, x1_image_positions - y_source]. I will add function to do this conversion in the next ler version and also to make a sky plot.

Please follow up, if you have more doubt.

[enricoteofilo]

Thank you, it's more clear. The fact that the coordinates x0,x1were defined with respect to the lens center in the lens plane was already more or less clear to me from the documentation, but there was still ambiguity in how the x0=0,x1=0 axes were oriented with respect to the zero points of the ra,dec coordinates used to characterize the source position. Moreover, the fact that the image position in the sky is [x0_image_positions - x_source, x1_image_positions - y_source] (where x0,x1 are measured in Einstein radii measured in radians?) means that we are assuming small angles approximation, I'm guessing? (The small angle being the angular distance of the image position in the sky with respect to the original source position) Please correct me if I'm wrong :)

[hemantaph]

1. Regarding orientation: x-axis should be wrt to RA and y-axis should be wrt to declination.
2. Scale: Many apologies, I should have added about units in all of my function; I will in the next update; it's a lot of work for a single person :) . The image positions are in unit of einstein radius, so does the source position wrt to the lens centre. In this code line, I set theta_E=1 for sampling source position.
3. Small angle appoximation: yes; all angles here are in the context of small angle approximation (source and image position, einstein radius), thus we can use simple algebra in the cordinate conversion. The einstein radius is in arseconds, so you can convert image positions to arcsecoonds and use the following to convert to radian. $\theta = \text{angle in arsec} \times \frac{\pi}{648000}$

[enricoteofilo]

Thank you for the clarifications!

1. Regarding orientation: x-axis should be wrt to RA and y-axis should be wrt to declination.

This was of course the most probable answer because it's the most natural choice, but I wanted to be sure.

2. Scale: Many apologies, I should have added about units in all of my function;

Yes, I remember seeing the radius being measured in Einstein radii somewhere in the documentation, but not everywhere, therefore I wanted to double-check after the latest update to the library :)

I will in the next update; it's a lot of work for a single person :) .

Don't worry, actually thank you very much for your work.

3. Small angle appoximation: yes; all angles here are in the context of small angle approximation (source and image position, einstein radius), thus we can use simple algebra in the cordinate conversion. The einstein radius is in arseconds, so you can convert image positions to arcsecoonds and use the following to convert to radian.

I guess that any error due to the use of the small angles approximation is totally obscured by the huge uncertainties in the position of the events in sky maps, so I think that small angles is totally fine. If something more precise than small angles approximation is ever needed, I guess there's always the possibility of using Astropy modules to deal with angular coordinates, even though the calculations would be slower. Anyway, if you were able to also include ra,dec coordinates of the individual lensed images in the lensed events dictionary, that would be very useful for skymaps, catalogues cross-matching...

[hemantaph]

Thanks for the suggestion. I will include a function to convert the images positions to ra and dec in the skymap.