/Quad-configurations-solver

Primary LanguageC++

Quad Quasar Configuration Solver

This is a simple program that solves the quadruple image configurations of source lensed by Singular Isothermal Elliptical Potential with parallel eXternal Shear (SIEP+XS $_{||}$). It outputs the image positions, magnifications, and all the derivatives with respect to the input parameters.

Requirements

  • Python 3.6 or later
  • pytorch 2.0 or later

Usage

To utilize the code, one needs to import the SIEP_plus_XS class from potentials.py. Then, one can create an object of this class by passing the lens parameters: b, x_g, y_g, eps, eps_theta, gamma, gamma_theta. Here, eps_theta and gamma_theta are in degrees and they should be equal to each other.

Then, from this object, one can call the function get_image_configuration by passing the source position: x_s, y_s. This will return the image positions and magnifications. One can also call the function get_all_derivations with source position to get the derivatives of the image positions and magnifications with respect to the lens parameters and source position. The output of these functions will be dictionary objects. The keys of the dictionary are the names of the parameters and the values are the corresponding values of the parameters.

The main.py script gives the skeleton code to run the program. The potential parameters and source position can be modified in the main.py script. The output is a dictionary containing the image positions, magnifications, and all the derivatives with respect to the input parameters.

SIEP+XS $_{||}$ potential

The SIEP+XS $_{||}$ potential is given by the following equation: $$ \psi(x,y) = b\sqrt{(x-x_g)^2 + \frac{(y-y_g)^2}{(1-\epsilon)^2}} - \frac{\gamma}{2}\left((x-x_g)^2 - (y-y_g)^2\right) $$ where $b$ is the Einstein radius, $(x_g, y_g)$ is the lens center, $\epsilon$ is the ellipticity, and $\gamma$ is the external shear which is parallel to the ellipticity and aligned along the x-axis.

Code structure

The code is organized as follows:

  • quartic_solver.py: This file contains the function to solve the ACLE quartic equation. The function _get_quartic_solution takes in a complex parameter $W$ and returns the angular image configuration.
  • potentials.py: This file contains the base class Potential. It contains the main class SIEP_plus_XS which inherits from Potential and is specific to the SIEP+XS potential. It has the functions get_image_configuration and get_all_derivations.
  • main.py: This script uses the class SIEP_plus_XS from potentials.py to compute the image positions and magnifications from the lens parameters and source position.

TODO

  • Known issues:
    • Currently, the code always outputs four images even when the potential might just produce two images. This will be fixed by checking if the solutions of the ACLE quartic lie on the unit circle.
    • The code needs non-zero ellipticity or shear and crashes for asymptotically spherical potential. This can be fixed by interpolation for small eccentricity.