GNFW does not have potential implemented

[jhod0]

Hello - an undergrad I'm working with has run into a problem trying to run the lens equation solver with a generalized NFW profile. It fails saying that the GNFW profile has no potential implemented.

There's a comment in the docs so it looks like you're aware of it!

lenstronomy/lenstronomy/LensModel/Profiles/general_nfw.py

Line 24 in 97414b2

TODO: implement the gravitational potential for this profile

Is the problem just that it hasn't been implemented, or is there no analytic solution for it? If it's the former, I would be happy to help implement it 😄

[sibirrer]

Hi @jhod0,
to my knowledge, there is no analytical solution to it, and hence this was left as 'TODO'. There could be different approaches here, either use a numerical integration (there might be examples of other profiles), or use a multi gaussian expansion (MGE), or even an expansion with CSE (cored steep ellipse) profiles. The latter can be implemented as a 'SYNTHESIS' profile and has been done by @mattgomer . See e.g. these test functions: https://github.com/lenstronomy/lenstronomy/blob/main/test/test_LensModel/test_Profiles/test_synthesis.py
Perhaps @dangilman has another solution for it in pyhalo as well. Just tagging them here.

[dangilman]

Hi @jhod0 @sibirrer, there probably is an analytic solution for the potential, the profile is fairly simple. If you have mathematica you can probably do it fairly easily

[jhod0]

Thanks @jhod0 @sibirrer! I might try plugging into Mathematica later. (Although looking at the Munoz 2001 paper cited as the source of the profile, I assume the solution is quite messy.)

For the near-term goal of simply computing predicted image positions for a source image, is there another solver that does not require the lens potential to be implemented? The undergrad who was running this code has been using Solver.image_position_from_source with the lenstronomy solver. I might ask him to try the stochastic option.

[sibirrer]

@jhod0 , the only part where the lens potential is requested in this routine is when sorting the images according to arrival times. I.e. if you set arrival_time_sort=False, you might not get an error.