lenstronomy.GalKin package¶
Submodules¶
lenstronomy.GalKin.analytic_kinematics module¶
- class lenstronomy.GalKin.analytic_kinematics.AnalyticKinematics(kwargs_cosmo, interpol_grid_num=100, log_integration=False, max_integrate=100, min_integrate=0.001)[source]¶
Bases:
lenstronomy.GalKin.anisotropy.Anisotropy
class to compute eqn 20 in Suyu+2010 with a Monte-Carlo from rendering from the light profile distribution and displacing them with a Gaussian seeing convolution
- This class assumes spherical symmetry in light and mass distribution and
a Hernquist light profile (parameterised by the half-light radius)
a power-law mass profile (parameterized by the Einstein radius and logarithmic slop)
The analytic equations for the kinematics in this approximation are presented e.g. in Suyu et al. 2010 and the spectral rendering approach to compute the seeing convolved slit measurement is presented in Birrer et al. 2016. The stellar anisotropy is parameterised based on Osipkov 1979; Merritt 1985.
all units are meant to be in angular arc seconds. The physical units are fold in through the angular diameter distances
- static draw_light(kwargs_light)[source]¶
- Parameters
kwargs_light – keyword argument (list) of the light model
- Returns
3d radius (if possible), 2d projected radius, x-projected coordinate, y-projected coordinate
- grav_potential(r, kwargs_mass)[source]¶
Gravitational potential in SI units
- Parameters
r – radius (arc seconds)
kwargs_mass –
- Returns
gravitational potential
- sigma_r2(r, kwargs_mass, kwargs_light, kwargs_anisotropy)[source]¶
equation (19) in Suyu+ 2010
- Parameters
r – 3d radius
kwargs_mass – mass profile keyword arguments
kwargs_light – light profile keyword arguments
kwargs_anisotropy – anisotropy keyword arguments
- Returns
velocity dispersion in [m/s]
- sigma_s2(r, R, kwargs_mass, kwargs_light, kwargs_anisotropy)[source]¶
returns unweighted los velocity dispersion for a specified projected radius, with weight 1
- Parameters
r – 3d radius (not needed for this calculation)
R – 2d projected radius (in angular units of arcsec)
kwargs_mass – mass model parameters (following lenstronomy lens model conventions)
kwargs_light – deflector light parameters (following lenstronomy light model conventions)
kwargs_anisotropy – anisotropy parameters, may vary according to anisotropy type chosen. We refer to the Anisotropy() class for details on the parameters.
- Returns
line-of-sight projected velocity dispersion at projected radius R from 3d radius r
lenstronomy.GalKin.anisotropy module¶
- class lenstronomy.GalKin.anisotropy.Anisotropy(anisotropy_type)[source]¶
Bases:
object
class that handles the kinematic anisotropy sources: Mamon & Lokas 2005 https://arxiv.org/pdf/astro-ph/0405491.pdf
Agnello et al. 2014 https://arxiv.org/pdf/1401.4462.pdf
- K(r, R, **kwargs)[source]¶
equation A16 im Mamon & Lokas for Osipkov&Merrit anisotropy
- Parameters
r – 3d radius
R – projected 2d radius
kwargs – parameters of the specified anisotropy model
- Returns
K(r, R)
- anisotropy_solution(r, **kwargs)[source]¶
the solution to d ln(f)/ d ln(r) = 2 beta(r)
- Parameters
r – 3d radius
kwargs – parameters of the specified anisotropy model
- Returns
f(r)
- class lenstronomy.GalKin.anisotropy.Colin[source]¶
Bases:
object
class for stellar orbits anisotropy parameter based on Colin et al. (2000) See Mamon & Lokas 2005 for details
- class lenstronomy.GalKin.anisotropy.Const[source]¶
Bases:
object
constant anisotropy model class See Mamon & Lokas 2005 for details
- static K(r, R, beta)[source]¶
equation A16 im Mamon & Lokas for constant anisotropy
- Parameters
r – 3d radius
R – projected 2d radius
beta – anisotropy
- Returns
K(r, R, beta)
- class lenstronomy.GalKin.anisotropy.GeneralizedOM[source]¶
Bases:
object
generalized Osipkov&Merrit profile see Agnello et al. 2014 https://arxiv.org/pdf/1401.4462.pdf b(r) = beta_inf * r^2 / (r^2 + r_ani^2)
- K(r, R, r_ani, beta_inf)[source]¶
equation19 in Agnello et al. 2014 for k_beta(R, r) such that K(R, r) = (sqrt(r^2 - R^2) + k_beta(R, r)) / r
- Parameters
r – 3d radius
R – projected 2d radius
r_ani – anisotropy radius
beta_inf – anisotropy at infinity
- Returns
K(r, R)
- anisotropy_solution(r, r_ani, beta_inf)[source]¶
the solution to d ln(f)/ d ln(r) = 2 beta(r) See e.g. A5 in Mamon & Lokas with a scaling (nominator of Agnello et al. 2014 Equation (12)
- Parameters
r – 3d radius
r_ani – anisotropy radius
beta_inf – anisotropy at infinity
- Returns
f(r)
- class lenstronomy.GalKin.anisotropy.Isotropic[source]¶
Bases:
object
class for isotropic (beta=0) stellar orbits See Mamon & Lokas 2005 for details
- static K(r, R)[source]¶
equation A16 im Mamon & Lokas for constant anisotropy
- Parameters
r – 3d radius
R – projected 2d radius
- Returns
K(r, R)
- class lenstronomy.GalKin.anisotropy.OsipkovMerritt[source]¶
Bases:
object
class for Osipkov&Merrit stellar orbits See Mamon & Lokas 2005 for details
- K(r, R, r_ani)[source]¶
equation A16 im Mamon & Lokas 2005 for Osipkov&Merrit anisotropy
- Parameters
r – 3d radius
R – projected 2d radius
r_ani – anisotropy radius
- Returns
K(r, R)
- class lenstronomy.GalKin.anisotropy.Radial[source]¶
Bases:
object
class for radial (beta=1) stellar orbits See Mamon & Lokas 2005 for details
- K(r, R)[source]¶
equation A16 im Mamon & Lokas for constant anisotropy
- Parameters
r – 3d radius
R – projected 2d radius
- Returns
K(r, R)
lenstronomy.GalKin.aperture module¶
- class lenstronomy.GalKin.aperture.Aperture(aperture_type, **kwargs_aperture)[source]¶
Bases:
object
defines mask(s) of spectra, can handle IFU and single slit/box type data.
- aperture_select(ra, dec)[source]¶
- Parameters
ra – angular coordinate of photon/ray
dec – angular coordinate of photon/ray
- Returns
bool, True if photon/ray is within the slit, False otherwise, int of the segment of the IFU
- property num_segments¶
lenstronomy.GalKin.aperture_types module¶
- class lenstronomy.GalKin.aperture_types.Frame(width_outer, width_inner, center_ra=0, center_dec=0, angle=0)[source]¶
Bases:
object
rectangular box with a hole in the middle (also rectangular), effectively a frame
- aperture_select(ra, dec)[source]¶
- Parameters
ra – angular coordinate of photon/ray
dec – angular coordinate of photon/ray
- Returns
bool, True if photon/ray is within the slit, False otherwise
- property num_segments¶
number of segments with separate measurements of the velocity dispersion :return: int
- class lenstronomy.GalKin.aperture_types.IFUShells(r_bins, center_ra=0, center_dec=0)[source]¶
Bases:
object
class for an Integral Field Unit spectrograph with azimuthal shells where the kinematics are measured
- aperture_select(ra, dec)[source]¶
- Parameters
ra – angular coordinate of photon/ray
dec – angular coordinate of photon/ray
- Returns
bool, True if photon/ray is within the slit, False otherwise, index of shell
- property num_segments¶
number of segments with separate measurements of the velocity dispersion :return: int
- class lenstronomy.GalKin.aperture_types.Shell(r_in, r_out, center_ra=0, center_dec=0)[source]¶
Bases:
object
Shell aperture
- aperture_select(ra, dec)[source]¶
- Parameters
ra – angular coordinate of photon/ray
dec – angular coordinate of photon/ray
- Returns
bool, True if photon/ray is within the slit, False otherwise
- property num_segments¶
number of segments with separate measurements of the velocity dispersion :return: int
- class lenstronomy.GalKin.aperture_types.Slit(length, width, center_ra=0, center_dec=0, angle=0)[source]¶
Bases:
object
Slit aperture description
- aperture_select(ra, dec)[source]¶
- Parameters
ra – angular coordinate of photon/ray
dec – angular coordinate of photon/ray
- Returns
bool, True if photon/ray is within the slit, False otherwise
- property num_segments¶
number of segments with separate measurements of the velocity dispersion :return: int
- lenstronomy.GalKin.aperture_types.frame_select(ra, dec, width_outer, width_inner, center_ra=0, center_dec=0, angle=0)[source]¶
- Parameters
ra – angular coordinate of photon/ray
dec – angular coordinate of photon/ray
width_outer – width of box to the outer parts
width_inner – width of inner removed box
center_ra – center of slit
center_dec – center of slit
angle – orientation angle of slit, angle=0 corresponds length in RA direction
- Returns
bool, True if photon/ray is within the box with a hole, False otherwise
- lenstronomy.GalKin.aperture_types.shell_ifu_select(ra, dec, r_bin, center_ra=0, center_dec=0)[source]¶
- Parameters
ra – angular coordinate of photon/ray
dec – angular coordinate of photon/ray
r_bin – array of radial bins to average the dispersion spectra in ascending order. It starts with the inner-most edge to the outermost edge.
center_ra – center of the sphere
center_dec – center of the sphere
- Returns
boolean, True if within the radial range, False otherwise
- lenstronomy.GalKin.aperture_types.shell_select(ra, dec, r_in, r_out, center_ra=0, center_dec=0)[source]¶
- Parameters
ra – angular coordinate of photon/ray
dec – angular coordinate of photon/ray
r_in – innermost radius to be selected
r_out – outermost radius to be selected
center_ra – center of the sphere
center_dec – center of the sphere
- Returns
boolean, True if within the radial range, False otherwise
- lenstronomy.GalKin.aperture_types.slit_select(ra, dec, length, width, center_ra=0, center_dec=0, angle=0)[source]¶
- Parameters
ra – angular coordinate of photon/ray
dec – angular coordinate of photon/ray
length – length of slit
width – width of slit
center_ra – center of slit
center_dec – center of slit
angle – orientation angle of slit, angle=0 corresponds length in RA direction
- Returns
bool, True if photon/ray is within the slit, False otherwise
lenstronomy.GalKin.cosmo module¶
- class lenstronomy.GalKin.cosmo.Cosmo(d_d, d_s, d_ds)[source]¶
Bases:
object
cosmological quantities
- arcsec2phys_lens(theta)[source]¶
converts are seconds to physical units on the deflector :param theta: angle observed on the sky in units of arc seconds :return: pyhsical distance of the angle in units of Mpc
- property epsilon_crit¶
returns the critical projected mass density in units of M_sun/Mpc^2 (physical units)
lenstronomy.GalKin.galkin module¶
- class lenstronomy.GalKin.galkin.Galkin(kwargs_model, kwargs_aperture, kwargs_psf, kwargs_cosmo, kwargs_numerics=None, analytic_kinematics=False)[source]¶
Bases:
lenstronomy.GalKin.galkin_model.GalkinModel
,lenstronomy.GalKin.observation.GalkinObservation
Major class to compute velocity dispersion measurements given light and mass models
The class supports any mass and light distribution (and superposition thereof) that has a 3d correspondance in their 2d lens model distribution. For models that do not have this correspondance, you may want to apply a Multi-Gaussian Expansion (MGE) on their models and use the MGE to be de-projected to 3d.
The computation follows Mamon&Lokas 2005 and performs the spectral rendering of the seeing convolved apperture with the method introduced by Birrer et al. 2016.
The class supports various types of anisotropy models (see Anisotropy class) and aperture types (see Aperture class). Solving the Jeans Equation requires a numerical integral over the 3d light and mass profile (see Mamon&Lokas 2005). This class (as well as the dedicated LightModel and MassModel classes) perform those integral numerically with an interpolated grid.
The seeing convolved integral over the aperture is computed by rendering spectra (light weighted LOS kinematics) from the light distribution.
- The cosmology assumed to compute the physical mass and distances are set via the kwargs_cosmo keyword arguments.
d_d: Angular diameter distance to the deflector (in Mpc) d_s: Angular diameter distance to the source (in Mpc) d_ds: Angular diameter distance from the deflector to the source (in Mpc)
The numerical options can be chosen through the kwargs_numerics keywords
interpol_grid_num: number of interpolation points in the light and mass profile (radially). This number should be chosen high enough to accurately describe the true light profile underneath. log_integration: bool, if True, performs the interpolation and numerical integration in log-scale.
max_integrate: maximum 3d radius to where the numerical integration of the Jeans Equation solver is made. This value should be large enough to contain most of the light and to lead to a converged result. min_integrate: minimal integration value. This value should be very close to zero but some mass and light profiles are diverging and a numerically stabel value should be chosen.
These numerical options should be chosen to allow for a converged result (within your tolerance) but not too conservative to impact too much the computational cost. Reasonable values might depend on the specific problem.
- dispersion(kwargs_mass, kwargs_light, kwargs_anisotropy, sampling_number=1000)[source]¶
computes the averaged LOS velocity dispersion in the slit (convolved)
- Parameters
kwargs_mass – mass model parameters (following lenstronomy lens model conventions)
kwargs_light – deflector light parameters (following lenstronomy light model conventions)
kwargs_anisotropy – anisotropy parameters, may vary according to anisotropy type chosen. We refer to the Anisotropy() class for details on the parameters.
sampling_number – int, number of spectral sampling of the light distribution
- Returns
integrated LOS velocity dispersion in units [km/s]
- dispersion_map(kwargs_mass, kwargs_light, kwargs_anisotropy, num_kin_sampling=1000, num_psf_sampling=100)[source]¶
computes the velocity dispersion in each Integral Field Unit
- Parameters
kwargs_mass – keyword arguments of the mass model
kwargs_light – keyword argument of the light model
kwargs_anisotropy – anisotropy keyword arguments
num_kin_sampling – int, number of draws from a kinematic prediction of a LOS
num_psf_sampling – int, number of displacements/render from a spectra to be displaced on the IFU
- Returns
ordered array of velocity dispersions [km/s] for each unit
lenstronomy.GalKin.galkin_model module¶
- class lenstronomy.GalKin.galkin_model.GalkinModel(kwargs_model, kwargs_cosmo, kwargs_numerics=None, analytic_kinematics=False)[source]¶
Bases:
object
this class handles all the kinematic modeling aspects of Galkin Excluded are observational conditions (seeing, aperture etc) Major class to compute velocity dispersion measurements given light and mass models
The class supports any mass and light distribution (and superposition thereof) that has a 3d correspondance in their 2d lens model distribution. For models that do not have this correspondence, you may want to apply a Multi-Gaussian Expansion (MGE) on their models and use the MGE to be de-projected to 3d.
The computation follows Mamon&Lokas 2005.
The class supports various types of anisotropy models (see Anisotropy class). Solving the Jeans Equation requires a numerical integral over the 3d light and mass profile (see Mamon&Lokas 2005). This class (as well as the dedicated LightModel and MassModel classes) perform those integral numerically with an interpolated grid.
- The cosmology assumed to compute the physical mass and distances are set via the kwargs_cosmo keyword arguments.
d_d: Angular diameter distance to the deflector (in Mpc) d_s: Angular diameter distance to the source (in Mpc) d_ds: Angular diameter distance from the deflector to the source (in Mpc)
The numerical options can be chosen through the kwargs_numerics keywords
interpol_grid_num: number of interpolation points in the light and mass profile (radially). This number should be chosen high enough to accurately describe the true light profile underneath. log_integration: bool, if True, performs the interpolation and numerical integration in log-scale.
max_integrate: maximum 3d radius to where the numerical integration of the Jeans Equation solver is made. This value should be large enough to contain most of the light and to lead to a converged result. min_integrate: minimal integration value. This value should be very close to zero but some mass and light profiles are diverging and a numerically stable value should be chosen.
These numerical options should be chosen to allow for a converged result (within your tolerance) but not too conservative to impact too much the computational cost. Reasonable values might depend on the specific problem.
- check_df(r, kwargs_mass, kwargs_light, kwargs_anisotropy)[source]¶
checks whether the phase space distribution function of a given anisotropy model is positive. Currently this is implemented by the relation provided by Ciotti and Morganti 2010 equation (10) https://arxiv.org/pdf/1006.2344.pdf
- Parameters
r – 3d radius to check slope-anisotropy constraint
theta_E – Einstein radius in arc seconds
gamma – power-law slope
a_ani – scaled transition radius of the OM anisotropy distribution
r_eff – half-light radius in arc seconds
- Returns
equation (10) >= 0 for physical interpretation
lenstronomy.GalKin.light_profile module¶
- class lenstronomy.GalKin.light_profile.LightProfile(profile_list, interpol_grid_num=2000, max_interpolate=1000, min_interpolate=0.001, max_draw=None)[source]¶
Bases:
object
class to deal with the light distribution for GalKin
- In particular, this class allows for:
(faster) interpolated calculation for a given profile (for a range that the Jeans equation is computed)
drawing 3d and 2d distributions from a given (spherical) profile (within bounds where the Jeans equation is expected to be accurate)
2d projected profiles within the 3d integration range (truncated)
- delete_cache()[source]¶
deletes cached interpolation function of the CDF for a specific light profile
- Returns
None
- draw_light_2d(kwargs_list, n=1, new_compute=False)[source]¶
constructs the CDF and draws from it random realizations of projected radii R CDF is constructed in logarithmic projected radius spacing
- Parameters
kwargs_list – light model keyword argument list
n – int, number of draws per functino call
new_compute – re-computes the interpolated CDF
- Returns
realization of projected radius following the distribution of the light model
- draw_light_2d_linear(kwargs_list, n=1, new_compute=False)[source]¶
constructs the CDF and draws from it random realizations of projected radii R The interpolation of the CDF is done in linear projected radius space
- Parameters
kwargs_list – list of keyword arguments of light profiles (see LightModule)
n – int; number of draws
new_compute – boolean, if True, re-computes the interpolation (becomes valid with updated kwargs_list argument)
- Returns
draw of projected radius for the given light profile distribution
- draw_light_3d(kwargs_list, n=1, new_compute=False)[source]¶
constructs the CDF and draws from it random realizations of 3D radii r
- Parameters
kwargs_list – light model keyword argument list
n – int, number of draws per function call
new_compute – re-computes the interpolated CDF
- Returns
realization of projected radius following the distribution of the light model
- light_2d(R, kwargs_list)[source]¶
projected light profile (integrated to infinity in the projected axis)
- Parameters
R – projected 2d radius
kwargs_list – list of keyword arguments of light profiles (see LightModule)
- Returns
projected surface brightness
- light_2d_finite(R, kwargs_list)[source]¶
projected light profile (integrated to FINITE 3d boundaries from the max_interpolate)
- Parameters
R – projected 2d radius (between min_interpolate and max_interpolate
kwargs_list – list of keyword arguments of light profiles (see LightModule)
- Returns
projected surface brightness
- light_3d(r, kwargs_list)[source]¶
three-dimensional light profile
- Parameters
r – 3d radius
kwargs_list – list of keyword arguments of light profiles (see LightModule)
- Returns
flux per 3d volume at radius r
- light_3d_interp(r, kwargs_list, new_compute=False)[source]¶
interpolated three-dimensional light profile within bounds [min_interpolate, max_interpolate] in logarithmic units with interpol_grid_num numbers of interpolation steps
- Parameters
r – 3d radius
kwargs_list – list of keyword arguments of light profiles (see LightModule)
new_compute – boolean, if True, re-computes the interpolation (becomes valid with updated kwargs_list argument)
- Returns
flux per 3d volume at radius r
lenstronomy.GalKin.numeric_kinematics module¶
- class lenstronomy.GalKin.numeric_kinematics.NumericKinematics(kwargs_model, kwargs_cosmo, interpol_grid_num=1000, log_integration=True, max_integrate=1000, min_integrate=0.0001, max_light_draw=None, lum_weight_int_method=True)[source]¶
Bases:
lenstronomy.GalKin.anisotropy.Anisotropy
- delete_cache()[source]¶
delete interpolation function for a specific mass and light profile as well as for a specific anisotropy model
- Returns
- draw_light(kwargs_light)[source]¶
- Parameters
kwargs_light – keyword argument (list) of the light model
- Returns
3d radius (if possible), 2d projected radius, x-projected coordinate, y-projected coordinate
- grav_potential(r, kwargs_mass)[source]¶
Gravitational potential in SI units
- Parameters
r – radius (arc seconds)
kwargs_mass –
- Returns
gravitational potential
- mass_3d(r, kwargs)[source]¶
mass enclosed a 3d radius
- Parameters
r – in arc seconds
kwargs – lens model parameters in arc seconds
- Returns
mass enclosed physical radius in kg
- sigma_r2(r, kwargs_mass, kwargs_light, kwargs_anisotropy)[source]¶
computes numerically the solution of the Jeans equation for a specific 3d radius E.g. Equation (A1) of Mamon & Lokas https://arxiv.org/pdf/astro-ph/0405491.pdf l(r) sigma_r(r) ^ 2 = 1/f(r) int_r^{infty} f(s) l(s) G M(s) / s^2 ds where l(r) is the 3d light profile M(s) is the enclosed 3d mass f is the solution to d ln(f)/ d ln(r) = 2 beta(r)
- Parameters
r – 3d radius
kwargs_mass – mass model parameters (following lenstronomy lens model conventions)
kwargs_light – deflector light parameters (following lenstronomy light model conventions)
kwargs_anisotropy – anisotropy parameters, may vary according to anisotropy type chosen. We refer to the Anisotropy() class for details on the parameters.
- Returns
sigma_r**2
- sigma_s2(r, R, kwargs_mass, kwargs_light, kwargs_anisotropy)[source]¶
returns unweighted los velocity dispersion for a specified 3d and projected radius (if lum_weight_int_method=True then the 3d radius is not required and the function directly performs the luminosity weighted integral in projection at R)
- Parameters
r – 3d radius (not needed for this calculation)
R – 2d projected radius (in angular units of arcsec)
kwargs_mass – mass model parameters (following lenstronomy lens model conventions)
kwargs_light – deflector light parameters (following lenstronomy light model conventions)
kwargs_anisotropy – anisotropy parameters, may vary according to anisotropy type chosen. We refer to the Anisotropy() class for details on the parameters.
- Returns
weighted line-of-sight projected velocity dispersion at projected radius R with weights I
- sigma_s2_project(R, kwargs_mass, kwargs_light, kwargs_anisotropy)[source]¶
returns luminosity-weighted los velocity dispersion for a specified projected radius R and weight
- Parameters
R – 2d projected radius (in angular units of arcsec)
kwargs_mass – mass model parameters (following lenstronomy lens model conventions)
kwargs_light – deflector light parameters (following lenstronomy light model conventions)
kwargs_anisotropy – anisotropy parameters, may vary according to anisotropy type chosen. We refer to the Anisotropy() class for details on the parameters.
- Returns
line-of-sight projected velocity dispersion at projected radius R
- sigma_s2_r(r, R, kwargs_mass, kwargs_light, kwargs_anisotropy)[source]¶
returns unweighted los velocity dispersion for a specified 3d radius r at projected radius R
- Parameters
r – 3d radius (not needed for this calculation)
R – 2d projected radius (in angular units of arcsec)
kwargs_mass – mass model parameters (following lenstronomy lens model conventions)
kwargs_light – deflector light parameters (following lenstronomy light model conventions)
kwargs_anisotropy – anisotropy parameters, may vary according to anisotropy type chosen. We refer to the Anisotropy() class for details on the parameters.
- Returns
line-of-sight projected velocity dispersion at projected radius R from 3d radius r
lenstronomy.GalKin.observation module¶
- class lenstronomy.GalKin.observation.GalkinObservation(kwargs_aperture, kwargs_psf)[source]¶
Bases:
lenstronomy.GalKin.psf.PSF
,lenstronomy.GalKin.aperture.Aperture
this class sets the base for the observational properties (aperture and seeing condition)
lenstronomy.GalKin.psf module¶
- class lenstronomy.GalKin.psf.PSF(psf_type, **kwargs_psf)[source]¶
Bases:
object
general class to handle the PSF in the GalKin module for rendering the displacement of photons/spectro
lenstronomy.GalKin.velocity_util module¶
- lenstronomy.GalKin.velocity_util.displace_PSF_gaussian(x, y, FWHM)[source]¶
- Parameters
x – x-coord (arc sec)
y – y-coord (arc sec)
FWHM – psf size (arc sec)
- Returns
x’, y’ random displaced according to psf
- lenstronomy.GalKin.velocity_util.displace_PSF_moffat(x, y, FWHM, beta)[source]¶
- Parameters
x – x-coordinate of light ray
y – y-coordinate of light ray
FWHM – full width at half maximum
beta – Moffat beta parameter
- Returns
displaced ray by PSF
- lenstronomy.GalKin.velocity_util.draw_cdf_Y(beta)[source]¶
Draw c.d.f for Moffat function according to Berge et al. Ufig paper, equation B2 cdf(Y) = 1-Y**(1-beta)
- Returns
- lenstronomy.GalKin.velocity_util.draw_hernquist(a)[source]¶
- Parameters
a – 0.551*r_eff
- Returns
realisation of radius of Hernquist luminosity weighting in 3d
- lenstronomy.GalKin.velocity_util.draw_moffat_r(FWHM, beta)[source]¶
- Parameters
FWHM – full width at half maximum
beta – Moffat beta parameter
- Returns
draw from radial Moffat distribution
- lenstronomy.GalKin.velocity_util.hyp_2F1(a, b, c, z)[source]¶
http://docs.sympy.org/0.7.1/modules/mpmath/functions/hypergeometric.html
- lenstronomy.GalKin.velocity_util.moffat_fwhm_alpha(FWHM, beta)[source]¶
computes alpha parameter from FWHM and beta for a Moffat profile
- Parameters
FWHM – full width at half maximum
beta – beta parameter of Moffat profile
- Returns
alpha parameter of Moffat profile