The strong lenses we’ve discussed so far have just a single lens galaxy responsible for the lensing, with a single source galaxy observed to be lensed. A strong lensing group is a system where there are multiple lens galaxies, deflecting the one or more background sources:
The Source’s ring is much larger than other examples (> 5.0”) and there are clearly additional galaxies in and around the main lens galaxy.
Modeling group scale lenses is challenging, because each individual galaxy must be included in the overall lens model. For this simple overview, we will therefore model the system as a point source, which reduces the complexity of the model and reduces the computational run-time of the model-fit.
point_dict = al.PointDict.from_json( file_path=path.join(dataset_path, "point_dict.json") ) point_solver = al.PointSolver(grid=grid_2d, pixel_scale_precision=0.025)
Model via JSON#
We now compose the lens model. For groups there could be many hundreds of galaxies in the model. Whereas previous examples explicitly wrote the model out via Python code, for group modeling we opt to write the model in .json files, which is loaded as follows:
model_path = path.join("scripts", "group", "models") model_file = path.join(model_path, "lens_x3__source_x1.json") lenses_file = path.join(model_path, "lenses.json") lenses = af.Collection.from_json(file=lenses_file) sources_file = path.join(model_path, "sources.json") sources = af.Collection.from_json(file=sources_file) galaxies = lenses + sources model = af.Collection(galaxies=galaxies)
This .json file contains all the information on this particular lens’s model, including priors which adjust their centre to the centre of light of each lens galaxy. The script used to make the model can be viewed at the following link.
We are now able to model this dataset as a point source, using the exact same tools we used in the point source overview.
search = af.DynestyStatic(name="overview_groups") analysis = al.AnalysisPoint( point_dict=point_dict, solver=point_solver ) result = search.fit(model=model, analysis=analysis)
The result contains information on every galaxy in our lens model:
print(result.max_log_likelihood_instance.galaxies.lens_0.mass) print(result.max_log_likelihood_instance.galaxies.lens_1.mass) print(result.max_log_likelihood_instance.galaxies.lens_2.mass)
Extended Source Fitting#
For group-scale lenses like this one, with a modest number of lens and source galaxies, PyAutoLens has all the tools you need to perform extended surface-brightness fitting to the source’s extended emission, including the use of a pixelized source reconstruction.
This will extract a lot more information from the data than the point-source model and the source reconstruction means that you can study the properties of the highly magnified source galaxy. Here is what the fit looks like:
This type of modeling uses a lot of PyAutoLens’s advanced model-fitting features which are described in chapters 3 and 4 of the HowToLens tutorials. An example performing this analysis to the lens above can be found at this link.