# Strong Gravitational Lensing¶

When two galaxies are aligned down the line-of-sight to Earth, light rays from the background galaxy are bent by the intervening mass of one or more foreground galaxies. Its light can be fully bent around the foreground galaxies, traversing multiple paths to the Earth, meaning that the background galaxy is observed multiple times. This alignment of galaxies is called a strong gravitational lens, an example of which, SLACS1430+4105, is shown in the image below. The massive elliptical lens galaxy can be seen in the centre of the left panel, surrounded by a multiply imaged source galaxy whose light has been distorted into an Einstein ring’. The central and right panels shows reconstructions of the source’s lensed and unlensed light distributions, which are created using a model of the lens galaxy’s mass to trace backwards how the source’s light is gravitationally lensed.

Strong lensing provides astronomers with an invaluable tool to study a diverse range of topics, including the structure of galaxies, dark matter and the expansion of the Universe. The past decade has seen the discovery of many hundreds of new strong lenses, however the modeling of a strong lens is historically a time-intensive process that requires significant human intervention to perform, restricting the scope of any scientific analysis. In the next decade of order one hundred thousand strong lenses will be discovered by surveys such as Euclid, the Vera Rubin Observatory and Square Kilometer Array.

PyAutoLens is open source software aiming to automate the lens modeling process and make strong lensing accessible to the entire scientific community.

# How does PyAutoLens Work?¶

A strong lens system can be quickly assembled from abstracted objects. A Galaxy object contains one or more LightProfile’s and MassProfile’s, which represent its two dimensional distribution of starlight and mass. Galaxy’s lie at a particular distance (redshift) from the observer, and are grouped into Plane’s. Raytracing through multiple Plane’s is achieved by passing them to a Tracer with an astropy Cosmology. By passing these objects a Grid strong lens sightlines are computed, including multi-plane ray-tracing. All of these objects are extensible, making it straightforward to compose highly customized lensing system. The example code below shows this in action:

import autolens as al
import autolens.plot as aplt

"""
To describe the deflection of light by mass, two-dimensional grids of (y,x) Cartesian
coordinates are used.
"""

grid = al.Grid.uniform(
shape_2d=(50, 50),
pixel_scales=0.05,  # <- Conversion from pixel units to arc-seconds.
)

"""The lens galaxy has an EllipticalIsothermal MassProfile and is at redshift 0.5."""

sie = al.mp.EllipticalIsothermal(
)

lens_galaxy = al.Galaxy(redshift=0.5, mass=sie)

"""The source galaxy has an EllipticalExponential LightProfile and is at redshift 1.0."""

exponential = al.lp.EllipticalExponential(
centre=(0.3, 0.2),
elliptical_comps=(0.05, 0.25),
intensity=0.05,
)

source_galaxy = al.Galaxy(redshift=1.0, light=exponential)

"""
We create the strong lens using a Tracer, which uses the galaxies, their redshifts
and an input cosmology to determine how light is deflected on its path to Earth.
"""

tracer = al.Tracer.from_galaxies(
galaxies=[lens_galaxy, source_galaxy], cosmology=cosmo.Planck15
)

"""
We can use the Grid and Tracer to perform many lensing calculations, for example
plotting the image of the lensed source.
"""

aplt.Tracer.image(tracer=tracer, grid=grid)


To perform lens modeling, PyAutoLens adopts the probabilistic programming language PyAutoFit. PyAutoFit allows users to compose a lens model from LightProfile, MassProfile and Galaxy objects, customize the model parameterization and fit it to data via a NonLinearSearch (e.g. dynesty, emcee or PySwarms). The example code below shows how to setup and fit a lens model to a dataset:

import autofit as af
import autolens as al
import autolens.plot as aplt

"""In this example, we'll fit a simple lens galaxy + source galaxy system."""

dataset_path = "/path/to/dataset"
lens_name = "example_lens"

"""Use the dataset path and lens name to load the imaging data."""

imaging = al.Imaging.from_fits(
image_path=f"{dataset_path}/{lens_name}/image.fits",
noise_map_path=f"{dataset_path}/{lens_name}/noise_map.fits",
psf_path=f"{dataset_path}/{lens_name}/psf.fits",
pixel_scales=0.1,
)

"""Create a mask for the data, which we setup as a 3.0" circle."""

)

"""
We model our lens galaxy using an EllipticalIsothermal MassProfile &
our source galaxy as an EllipticalSersic LightProfile.
"""

lens_mass_profile = al.mp.EllipticalIsothermal
source_light_profile = al.lp.EllipticalSersic

"""
To setup our model galaxies, we use the GalaxyModel class, which represents a
galaxy whose parameters are free & fitted for by PyAutoLens.
"""

lens_galaxy_model = al.GalaxyModel(redshift=0.5, mass=lens_mass_profile)
source_galaxy_model = al.GalaxyModel(redshift=1.0, light=source_light_profile)

"""
To perform the analysis we set up a phase, which takes our galaxy models & fits
their parameters using a NonLinearSearch (in this case, Dynesty).
"""

phase = al.PhaseImaging(
galaxies=dict(lens=lens_galaxy_model, source=source_galaxy_model),
name="example/phase_example",
search=af.DynestyStatic(n_live_points=50),
)

"""
We pass the imaging data and mask to the phase, thereby fitting it with the lens
model & plot the resulting fit.
"""

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