lenstronomy.Analysis package¶
Submodules¶
lenstronomy.Analysis.kinematics_api module¶
- class lenstronomy.Analysis.kinematics_api.KinematicsAPI(z_lens, z_source, kwargs_model, kwargs_aperture, kwargs_seeing, anisotropy_model, cosmo=None, lens_model_kinematics_bool=None, light_model_kinematics_bool=None, multi_observations=False, kwargs_numerics_galkin=None, analytic_kinematics=False, Hernquist_approx=False, MGE_light=False, MGE_mass=False, kwargs_mge_light=None, kwargs_mge_mass=None, sampling_number=1000, num_kin_sampling=1000, num_psf_sampling=100)[source]¶
Bases:
object
this class contains routines to compute time delays, magnification ratios, line of sight velocity dispersions etc for a given lens model
- galkin_settings(kwargs_lens, kwargs_lens_light, r_eff=None, theta_E=None, gamma=None)[source]¶
- Parameters
kwargs_lens – lens model keyword argument list
kwargs_lens_light – deflector light keyword argument list
r_eff – half-light radius (optional)
theta_E – Einstein radius (optional)
gamma – local power-law slope at the Einstein radius (optional)
- Returns
Galkin() instance and mass and light profiles configured for the Galkin module
- kinematic_lens_profiles(kwargs_lens, MGE_fit=False, model_kinematics_bool=None, theta_E=None, gamma=None, kwargs_mge=None, analytic_kinematics=False)[source]¶
translates the lenstronomy lens and mass profiles into a (sub) set of profiles that are compatible with the GalKin module to compute the kinematics thereof. The requirement is that the profiles are centered at (0, 0) and that for all profile types there exists a 3d de-projected analytical representation.
- Parameters
kwargs_lens – lens model parameters
MGE_fit – bool, if true performs the MGE for the mass distribution
model_kinematics_bool – bool list of length of the lens model. Only takes a subset of all the models as part of the kinematics computation (can be used to ignore substructure, shear etc that do not describe the main deflector potential
theta_E – (optional float) estimate of the Einstein radius. If present, does not numerically compute this quantity in this routine numerically
gamma – local power-law slope at the Einstein radius (optional)
kwargs_mge – keyword arguments that go into the MGE decomposition routine
analytic_kinematics – bool, if True, solves the Jeans equation analytically for the power-law mass profile with Hernquist light profile
- Returns
mass_profile_list, keyword argument list
- kinematic_light_profile(kwargs_lens_light, r_eff=None, MGE_fit=False, model_kinematics_bool=None, Hernquist_approx=False, kwargs_mge=None, analytic_kinematics=False)[source]¶
setting up of the light profile to compute the kinematics in the GalKin module. The requirement is that the profiles are centered at (0, 0) and that for all profile types there exists a 3d de-projected analytical representation.
- Parameters
kwargs_lens_light – deflector light model keyword argument list
r_eff – (optional float, else=None) Pre-calculated projected half-light radius of the deflector profile. If not provided, numerical calculation is done in this routine if required.
MGE_fit – boolean, if True performs a Multi-Gaussian expansion of the radial light profile and returns this solution.
model_kinematics_bool – list of booleans to indicate a subset of light profiles to be part of the physical deflector light.
Hernquist_approx – boolean, if True replaces the actual light profile(s) with a Hernquist model with matched half-light radius.
kwargs_mge – keyword arguments that go into the MGE decomposition routine
analytic_kinematics – bool, if True, solves the Jeans equation analytically for the power-law mass profile with Hernquist light profile and adjust the settings accordingly
- Returns
deflector type list, keyword arguments list
- kinematics_modeling_settings(anisotropy_model, kwargs_numerics_galkin, analytic_kinematics=False, Hernquist_approx=False, MGE_light=False, MGE_mass=False, kwargs_mge_light=None, kwargs_mge_mass=None, sampling_number=1000, num_kin_sampling=1000, num_psf_sampling=100)[source]¶
- Parameters
anisotropy_model – type of stellar anisotropy model. See details in MamonLokasAnisotropy() class of lenstronomy.GalKin.anisotropy
analytic_kinematics – boolean, if True, used the analytic JAM modeling for a power-law profile on top of a Hernquist light profile ATTENTION: This may not be accurate for your specific problem!
Hernquist_approx – bool, if True, uses a Hernquist light profile matched to the half light radius of the deflector light profile to compute the kinematics
MGE_light – bool, if true performs the MGE for the light distribution
MGE_mass – bool, if true performs the MGE for the mass distribution
kwargs_numerics_galkin – numerical settings for the integrated line-of-sight velocity dispersion
kwargs_mge_mass – keyword arguments that go into the MGE decomposition routine
kwargs_mge_light – keyword arguments that go into the MGE decomposition routine
sampling_number – number of spectral rendering on a single slit
num_kin_sampling – number of kinematic renderings on a total IFU
num_psf_sampling – number of PSF displacements for each kinematic rendering on the IFU
- Returns
- static transform_kappa_ext(sigma_v, kappa_ext=0)[source]¶
- Parameters
sigma_v – velocity dispersion estimate of the lensing deflector without considering external convergence
kappa_ext – external convergence to be used in the mass-sheet degeneracy
- Returns
transformed velocity dispersion
- velocity_dispersion(kwargs_lens, kwargs_lens_light, kwargs_anisotropy, r_eff=None, theta_E=None, gamma=None, kappa_ext=0)[source]¶
API for both, analytic and numerical JAM to compute the velocity dispersion [km/s] This routine uses the galkin_setting() routine for the Galkin configurations (see there what options and input is relevant.
- Parameters
kwargs_lens – lens model keyword arguments
kwargs_lens_light – lens light model keyword arguments
kwargs_anisotropy – stellar anisotropy keyword arguments
r_eff – projected half-light radius of the stellar light associated with the deflector galaxy, optional, if set to None will be computed in this function with default settings that may not be accurate.
theta_E – Einstein radius (optional)
gamma – power-law slope (optional)
kappa_ext – external convergence (optional)
- Returns
velocity dispersion [km/s]
- velocity_dispersion_analytical(theta_E, gamma, r_eff, r_ani, kappa_ext=0)[source]¶
computes the LOS velocity dispersion of the lens within a slit of size R_slit x dR_slit and seeing psf_fwhm. The assumptions are a Hernquist light profile and the spherical power-law lens model at the first position and an Osipkov and Merritt (‘OM’) stellar anisotropy distribution.
Further information can be found in the AnalyticKinematics() class.
- Parameters
theta_E – Einstein radius
gamma – power-low slope of the mass profile (=2 corresponds to isothermal)
r_ani – anisotropy radius in units of angles
r_eff – projected half-light radius
kappa_ext – external convergence not accounted in the lens models
- Returns
velocity dispersion in units [km/s]
- velocity_dispersion_map(kwargs_lens, kwargs_lens_light, kwargs_anisotropy, r_eff=None, theta_E=None, gamma=None, kappa_ext=0)[source]¶
API for both, analytic and numerical JAM to compute the velocity dispersion map with IFU data [km/s]
- Parameters
kwargs_lens – lens model keyword arguments
kwargs_lens_light – lens light model keyword arguments
kwargs_anisotropy – stellar anisotropy keyword arguments
r_eff – projected half-light radius of the stellar light associated with the deflector galaxy, optional, if set to None will be computed in this function with default settings that may not be accurate.
theta_E – circularized Einstein radius, optional, if not provided will either be computed in this function with default settings or not required
gamma – power-law slope at the Einstein radius, optional
kappa_ext – external convergence
- Returns
velocity dispersion [km/s]
lenstronomy.Analysis.lens_profile module¶
- class lenstronomy.Analysis.lens_profile.LensProfileAnalysis(lens_model)[source]¶
Bases:
object
class with analysis routines to compute derived properties of the lens model
- convergence_peak(kwargs_lens, model_bool_list=None, grid_num=200, grid_spacing=0.01, center_x_init=0, center_y_init=0)[source]¶
computes the maximal convergence position on a grid and returns its coordinate
- Parameters
kwargs_lens – lens model keyword argument list
model_bool_list – bool list (optional) to include certain models or not
- Returns
center_x, center_y
- effective_einstein_radius(kwargs_lens, center_x=None, center_y=None, model_bool_list=None, grid_num=200, grid_spacing=0.05, get_precision=False, verbose=True)[source]¶
computes the radius with mean convergence=1
- Parameters
kwargs_lens – list of lens model keyword arguments
center_x – position of the center (if not set, is attempting to find it from the parameters kwargs_lens)
center_y – position of the center (if not set, is attempting to find it from the parameters kwargs_lens)
model_bool_list – list of booleans indicating the addition (=True) of a model component in computing the Einstein radius
grid_num – integer, number of grid points to numerically evaluate the convergence and estimate the Einstein radius
grid_spacing – spacing in angular units of the grid
get_precision – If True, return the precision of estimated Einstein radius
verbose – boolean, if True prints warning if indication of insufficient result
- Returns
estimate of the Einstein radius
- local_lensing_effect(kwargs_lens, ra_pos=0, dec_pos=0, model_list_bool=None)[source]¶
computes deflection, shear and convergence at (ra_pos,dec_pos) for those part of the lens model not included in the main deflector.
- Parameters
kwargs_lens – lens model keyword argument list
ra_pos – RA position where to compute the external effect
dec_pos – DEC position where to compute the external effect
model_list_bool – boolean list indicating which models effect to be added to the estimate
- Returns
alpha_x, alpha_y, kappa, shear1, shear2
- mass_fraction_within_radius(kwargs_lens, center_x, center_y, theta_E, numPix=100)[source]¶
computes the mean convergence of all the different lens model components within a spherical aperture
- Parameters
kwargs_lens – lens model keyword argument list
center_x – center of the aperture
center_y – center of the aperture
theta_E – radius of aperture
- Returns
list of average convergences for all the model components
- mst_invariant_differential(kwargs_lens, radius, center_x=None, center_y=None, model_list_bool=None, num_points=10)[source]¶
Average of the radial stretch differential in radial direction, divided by the radial stretch factor.
\[\xi = \frac{\partial \lambda_{\rm rad}}{\partial r} \frac{1}{\lambda_{\rm rad}}\]This quantity is invariant under the MST. The specific definition is provided by Birrer 2021. Equivalent (proportional) definitions are provided by e.g. Kochanek 2020, Sonnenfeld 2018.
- Parameters
kwargs_lens – lens model keyword argument list
radius – radius from the center where to compute the MST invariant differential
center_x – center position
center_y – center position
model_list_bool – indicate which part of the model to consider
num_points – number of estimates around the radius
- Returns
xi
- multi_gaussian_lens(kwargs_lens, center_x=None, center_y=None, model_bool_list=None, n_comp=20)[source]¶
multi-gaussian lens model in convergence space
- Parameters
kwargs_lens –
n_comp –
- Returns
- profile_slope(kwargs_lens, radius, center_x=None, center_y=None, model_list_bool=None, num_points=10)[source]¶
computes the logarithmic power-law slope of a profile. ATTENTION: this is not an observable!
- Parameters
kwargs_lens – lens model keyword argument list
radius – radius from the center where to compute the logarithmic slope (angular units
center_x – center of profile from where to compute the slope
center_y – center of profile from where to compute the slope
model_list_bool – bool list, indicate which part of the model to consider
num_points – number of estimates around the Einstein radius
- Returns
logarithmic power-law slope
- radial_lens_profile(r_list, kwargs_lens, center_x=None, center_y=None, model_bool_list=None)[source]¶
- Parameters
r_list – list of radii to compute the spherically averaged lens light profile
center_x – center of the profile
center_y – center of the profile
kwargs_lens – lens parameter keyword argument list
model_bool_list – bool list or None, indicating which profiles to sum over
- Returns
flux amplitudes at r_list radii azimuthally averaged
lenstronomy.Analysis.light2mass module¶
- lenstronomy.Analysis.light2mass.light2mass_interpol(lens_light_model_list, kwargs_lens_light, numPix=100, deltaPix=0.05, subgrid_res=5, center_x=0, center_y=0)[source]¶
takes a lens light model and turns it numerically in a lens model (with all lensmodel quantities computed on a grid). Then provides an interpolated grid for the quantities.
- Parameters
kwargs_lens_light – lens light keyword argument list
numPix – number of pixels per axis for the return interpolation
deltaPix – interpolation/pixel size
center_x – center of the grid
center_y – center of the grid
subgrid_res – subgrid for the numerical integrals
- Returns
keyword arguments for ‘INTERPOL’ lens model
lenstronomy.Analysis.light_profile module¶
- class lenstronomy.Analysis.light_profile.LightProfileAnalysis(light_model)[source]¶
Bases:
object
class with analysis routines to compute derived properties of the lens model
- ellipticity(kwargs_light, grid_spacing, grid_num, center_x=None, center_y=None, model_bool_list=None)[source]¶
make sure that the window covers all the light, otherwise the moments may give a too low answers.
- Parameters
kwargs_light – keyword argument list of profiles
center_x – center of profile, if None takes it from the first profile in kwargs_light
center_y – center of profile, if None takes it from the first profile in kwargs_light
model_bool_list – list of booleans to select subsets of the profile
grid_spacing – grid spacing over which the moments are computed
grid_num – grid size over which the moments are computed
- Returns
eccentricities e1, e2
- flux_components(kwargs_light, grid_num=400, grid_spacing=0.01)[source]¶
computes the total flux in each component of the model
- Parameters
kwargs_light –
grid_num –
grid_spacing –
- Returns
- half_light_radius(kwargs_light, grid_spacing, grid_num, center_x=None, center_y=None, model_bool_list=None)[source]¶
computes numerically the half-light-radius of the deflector light and the total photon flux
- Parameters
kwargs_light – keyword argument list of profiles
center_x – center of profile, if None takes it from the first profile in kwargs_light
center_y – center of profile, if None takes it from the first profile in kwargs_light
model_bool_list – list of booleans to select subsets of the profile
grid_spacing – grid spacing over which the moments are computed
grid_num – grid size over which the moments are computed
- Returns
half-light radius
- multi_gaussian_decomposition(kwargs_light, model_bool_list=None, n_comp=20, center_x=None, center_y=None, r_h=None, grid_spacing=0.02, grid_num=200)[source]¶
multi-gaussian decomposition of the lens light profile (in 1-dimension)
- Parameters
kwargs_light – keyword argument list of profiles
center_x – center of profile, if None takes it from the first profile in kwargs_light
center_y – center of profile, if None takes it from the first profile in kwargs_light
model_bool_list – list of booleans to select subsets of the profile
grid_spacing – grid spacing over which the moments are computed for the half-light radius
grid_num – grid size over which the moments are computed
n_comp – maximum number of Gaussian’s in the MGE
r_h – float, half light radius to be used for MGE (optional, otherwise using a numerical grid)
- Returns
amplitudes, sigmas, center_x, center_y
- multi_gaussian_decomposition_ellipse(kwargs_light, model_bool_list=None, center_x=None, center_y=None, grid_num=100, grid_spacing=0.05, n_comp=20)[source]¶
MGE with ellipticity estimate. Attention: numerical grid settings for ellipticity estimate and radial MGE may not necessarily be the same!
- Parameters
kwargs_light – keyword argument list of profiles
center_x – center of profile, if None takes it from the first profile in kwargs_light
center_y – center of profile, if None takes it from the first profile in kwargs_light
model_bool_list – list of booleans to select subsets of the profile
grid_spacing – grid spacing over which the moments are computed
grid_num – grid size over which the moments are computed
n_comp – maximum number of Gaussians in the MGE
- Returns
keyword arguments of the elliptical multi Gaussian profile in lenstronomy conventions
- radial_light_profile(r_list, kwargs_light, center_x=None, center_y=None, model_bool_list=None)[source]¶
- Parameters
r_list – list of radii to compute the spherically averaged lens light profile
center_x – center of the profile
center_y – center of the profile
kwargs_light – lens light parameter keyword argument list
model_bool_list – bool list or None, indicating which profiles to sum over
- Returns
flux amplitudes at r_list radii spherically averaged
lenstronomy.Analysis.td_cosmography module¶
- class lenstronomy.Analysis.td_cosmography.TDCosmography(z_lens, z_source, kwargs_model, cosmo_fiducial=None, lens_model_kinematics_bool=None, light_model_kinematics_bool=None, kwargs_seeing=None, kwargs_aperture=None, anisotropy_model=None, **kwargs_kin_api)[source]¶
Bases:
lenstronomy.Analysis.kinematics_api.KinematicsAPI
class equipped to perform a cosmographic analysis from a lens model with added measurements of time delays and kinematics. This class does not require any cosmological knowledge and can return angular diameter distance estimates self-consistently integrating the kinematics routines and time delay estimates in the lens modeling. This description follows Birrer et al. 2016, 2019.
- ddt_dd_from_time_delay_and_kinematics(d_fermat_model, dt_measured, sigma_v_measured, J, kappa_s=0, kappa_ds=0, kappa_d=0)[source]¶
- Parameters
d_fermat_model – relative Fermat potential in units arcsec^2
dt_measured – measured relative time delay [days]
sigma_v_measured – 1-sigma Gaussian uncertainty in the measured velocity dispersion
J – modeled dimensionless kinematic estimate
kappa_s – LOS convergence from observer to source
kappa_ds – LOS convergence from deflector to source
kappa_d – LOS convergence from observer to deflector
- Returns
D_dt, D_d
- static ddt_from_time_delay(d_fermat_model, dt_measured, kappa_s=0, kappa_ds=0, kappa_d=0)[source]¶
Time-delay distance in units of Mpc from the modeled Fermat potential and measured time delay from an image pair.
- Parameters
d_fermat_model – relative Fermat potential between two images from the same source in units arcsec^2
dt_measured – measured time delay between the same image pair in units of days
kappa_s – external convergence from observer to source
kappa_ds – external convergence from lens to source
kappa_d – external convergence form observer to lens
- Returns
D_dt, time-delay distance
- static ds_dds_from_kinematics(sigma_v, J, kappa_s=0, kappa_ds=0)[source]¶
computes the estimate of the ratio of angular diameter distances Ds/Dds from the kinematic estimate of the lens and the measured dispersion.
- Parameters
sigma_v – velocity dispersion [km/s]
J – dimensionless kinematic constraint (see Birrer et al. 2016, 2019)
- Returns
Ds/Dds
- fermat_potential(kwargs_lens, kwargs_ps, original_ps_position=False)[source]¶
Fermat potential (negative sign means earlier arrival time)
- Parameters
kwargs_lens – lens model keyword argument list
kwargs_ps – point source keyword argument list
original_ps_position – boolean (only applies when first point source model is of type ‘LENSED_POSITION’), uses the image positions in the model parameters and does not re-compute images (which might be differently ordered) in case of the lens equation solver
- Returns
Fermat potential of all the image positions in the first point source list entry
- time_delays(kwargs_lens, kwargs_ps, kappa_ext=0, original_ps_position=False)[source]¶
predicts the time delays of the image positions given the fiducial cosmology relative to a straight line without lensing. Negative values correspond to images arriving earlier, and positive signs correspond to images arriving later.
- Parameters
kwargs_lens – lens model parameters
kwargs_ps – point source parameters
kappa_ext – external convergence (optional)
original_ps_position – boolean (only applies when first point source model is of type ‘LENSED_POSITION’), uses the image positions in the model parameters and does not re-compute images (which might be differently ordered) in case of the lens equation solver
- Returns
time delays at image positions for the fixed cosmology in units of days
- velocity_dispersion_dimension_less(kwargs_lens, kwargs_lens_light, kwargs_anisotropy, r_eff=None, theta_E=None, gamma=None)[source]¶
sigma**2 = Dd/Dds * c**2 * J(kwargs_lens, kwargs_light, anisotropy) (Equation 4.11 in Birrer et al. 2016 or Equation 6 in Birrer et al. 2019) J() is a dimensionless and cosmological independent quantity only depending on angular units. This function returns J given the lens and light parameters and the anisotropy choice without an external mass sheet correction.
- Parameters
kwargs_lens – lens model keyword arguments
kwargs_lens_light – lens light model keyword arguments
kwargs_anisotropy – stellar anisotropy keyword arguments
r_eff – projected half-light radius of the stellar light associated with the deflector galaxy, optional, if set to None will be computed in this function with default settings that may not be accurate.
theta_E – pre-computed Einstein radius (optional)
gamma – pre-computed power-law slope of mass profile
- Returns
dimensionless velocity dispersion (see e.g. Birrer et al. 2016, 2019)
- velocity_dispersion_map_dimension_less(kwargs_lens, kwargs_lens_light, kwargs_anisotropy, r_eff=None, theta_E=None, gamma=None)[source]¶
sigma**2 = Dd/Dds * c**2 * J(kwargs_lens, kwargs_light, anisotropy) (Equation 4.11 in Birrer et al. 2016 or Equation 6 in Birrer et al. 2019) J() is a dimensionless and cosmological independent quantity only depending on angular units. This function returns J given the lens and light parameters and the anisotropy choice without an external mass sheet correction. This routine computes the IFU map of the kinematic quantities.
- Parameters
kwargs_lens – lens model keyword arguments
kwargs_lens_light – lens light model keyword arguments
kwargs_anisotropy – stellar anisotropy keyword arguments
r_eff – projected half-light radius of the stellar light associated with the deflector galaxy, optional, if set to None will be computed in this function with default settings that may not be accurate.
- Returns
dimensionless velocity dispersion (see e.g. Birrer et al. 2016, 2019)