def velocity_dispersion(self, kwargs_lens, r_eff, R_slit, dR_slit, psf_fwhm, aniso_param=1, psf_type='GAUSSIAN', moffat_beta=2.6, num_evaluate=1000, kappa_ext=0): """ 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. Further information can be found in the AnalyticKinematics() class. :param kwargs_lens: lens model parameters :param kwargs_lens_light: deflector light parameters :param aniso_param: scaled r_ani with respect to the half light radius :param r_eff: half light radius, if not provided, will be computed from the lens light model :param R_slit: width of the slit :param dR_slit: length of the slit :param psf_fwhm: full width at half maximum of the seeing (Gaussian form) :param psf_type: string, point spread functino type, current support for 'GAUSSIAN' and 'MOFFAT' :param moffat_beta: float, beta parameter of Moffat profile :param num_evaluate: number of spectral rendering of the light distribution that end up on the slit :param kappa_ext: external convergence not accounted in the lens models :return: velocity dispersion in units [km/s] """ gamma = kwargs_lens[0]['gamma'] theta_E = kwargs_lens[0]['theta_E'] r_ani = aniso_param * r_eff analytic_kinematics = AnalyticKinematics(fwhm=psf_fwhm, moffat_beta=moffat_beta, psf_type=psf_type, **self._kwargs_cosmo) sigma = analytic_kinematics.vel_disp(gamma, theta_E, r_eff, r_ani, R_slit, dR_slit, rendering_number=num_evaluate) sigma *= np.sqrt(1 - kappa_ext) return sigma
def test_galkin_vs_LOS_dispersion(self): """ tests whether the old and new version provide the same answer :return: """ # light profile light_profile = 'Hernquist' r_eff = 0.5 kwargs_light = {'r_eff': r_eff} # effective half light radius (2d projected) in arcsec # mass profile mass_profile = 'power_law' theta_E = 1.2 gamma = 2. kwargs_profile = {'theta_E': theta_E, 'gamma': gamma} # Einstein radius (arcsec) and power-law slope # anisotropy profile anisotropy_type = 'r_ani' r_ani = 0.5 kwargs_anisotropy = {'r_ani': r_ani} # anisotropy radius [arcsec] # aperture as shell #aperture_type = 'shell' #kwargs_aperture_inner = {'r_in': 0., 'r_out': 0.2, 'center_dec': 0, 'center_ra': 0} #kwargs_aperture_outer = {'r_in': 0., 'r_out': 1.5, 'center_dec': 0, 'center_ra': 0} # aperture as slit aperture_type = 'slit' length = 3.8 width = 0.9 kwargs_aperture = {'length': length, 'width': width, 'center_ra': 0, 'center_dec': 0, 'angle': 0} psf_fwhm = 0.1 # Gaussian FWHM psf kwargs_cosmo = {'D_d': 1000, 'D_s': 1500, 'D_ds': 800} galkin = GalKinAnalytic(aperture=aperture_type, mass_profile=mass_profile, light_profile=light_profile, anisotropy_type=anisotropy_type, psf_fwhm=psf_fwhm, kwargs_cosmo=kwargs_cosmo) sigma_v = galkin.vel_disp(kwargs_profile, kwargs_aperture, kwargs_light, kwargs_anisotropy, num=2000) los_disp = AnalyticKinematics(**kwargs_cosmo) sigma_v2 = los_disp.vel_disp(gamma, theta_E, r_eff, r_ani=r_ani, R_slit=length, dR_slit=width, FWHM=psf_fwhm, rendering_number=2000) npt.assert_almost_equal((sigma_v-sigma_v2)/sigma_v2, 0, decimal=2)
def test_compare_power_law(self): """ compare power-law profiles analytical vs. numerical :return: """ # light profile light_profile_list = ['HERNQUIST'] r_eff = 1.5 kwargs_light = [{'Rs': r_eff, 'amp': 1.}] # effective half light radius (2d projected) in arcsec # 0.551 * # mass profile mass_profile_list = ['SPP'] theta_E = 1.2 gamma = 2. kwargs_profile = [{'theta_E': theta_E, 'gamma': gamma}] # Einstein radius (arcsec) and power-law slope # anisotropy profile anisotropy_type = 'OsipkovMerritt' r_ani = 2. kwargs_anisotropy = {'r_ani': r_ani} # anisotropy radius [arcsec] # aperture as slit aperture_type = 'slit' length = 1. width = 0.3 kwargs_aperture = {'length': length, 'width': width, 'center_ra': 0, 'center_dec': 0, 'angle': 0} psf_fwhm = 1. # Gaussian FWHM psf kwargs_cosmo = {'D_d': 1000, 'D_s': 1500, 'D_ds': 800} kwargs_numerics = {'sampling_number': 1000, 'interpol_grid_num': 500, 'log_integration': True, 'max_integrate': 100} galkin = Galkin(mass_profile_list, light_profile_list, aperture_type=aperture_type, anisotropy_model=anisotropy_type, fwhm=psf_fwhm, kwargs_cosmo=kwargs_cosmo, **kwargs_numerics) sigma_v = galkin.vel_disp(kwargs_profile, kwargs_light, kwargs_anisotropy, kwargs_aperture) kwargs_numerics = {'sampling_number': 1000, 'interpol_grid_num': 500, 'log_integration': False, 'max_integrate': 10} galkin = Galkin(mass_profile_list, light_profile_list, aperture_type=aperture_type, anisotropy_model=anisotropy_type, fwhm=psf_fwhm, kwargs_cosmo=kwargs_cosmo, **kwargs_numerics) sigma_v_lin = galkin.vel_disp(kwargs_profile, kwargs_light, kwargs_anisotropy, kwargs_aperture) los_disp = AnalyticKinematics(**kwargs_cosmo) sigma_v2 = los_disp.vel_disp(gamma, theta_E, r_eff / 0.551, r_ani=r_ani, R_slit=length, dR_slit=width, FWHM=psf_fwhm, rendering_number=1000) print(sigma_v, sigma_v_lin, sigma_v2, 'sigma_v Galkin (log and linear), sigma_v los dispersion') npt.assert_almost_equal(sigma_v2/sigma_v, 1, decimal=2)
def velocity_dispersion_analytical(self, theta_E, gamma, r_eff, kwargs_aperture, kwargs_psf, r_ani, num_evaluate=1000, kappa_ext=0): """ 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 'OsipkovMerritt' stellar anisotropy distribution. Further information can be found in the AnalyticKinematics() class. :param theta_E: Einstein radius :param gamma: power-low slope of the mass profile (=2 corresponds to isothermal) :param r_ani: anisotropy radius in units of angles :param r_eff: projected half-light radius :param kwargs_aperture: aperture parameters (see Galkin module) :param num_evaluate: number of spectral rendering of the light distribution that end up on the slit :param kappa_ext: external convergence not accounted in the lens models :return: velocity dispersion in units [km/s] """ analytic_kinematics = AnalyticKinematics( kwargs_psf=kwargs_psf, kwargs_aperture=kwargs_aperture, **self._kwargs_cosmo) sigma = analytic_kinematics.vel_disp(gamma, theta_E, r_eff, r_ani, rendering_number=num_evaluate) sigma *= np.sqrt(1 - kappa_ext) return sigma
class LensProp(object): """ this class contains routines to compute time delays, magnification ratios, line of sight velocity dispersions etc for a given lens model """ def __init__(self, z_lens, z_source, kwargs_model, cosmo=None): """ :param z_lens: redshift of lens :param z_source: redshift of source :param kwargs_model: model keyword arguments :param cosmo: astropy.cosmology instance """ self.z_d = z_lens self.z_s = z_source self.lensCosmo = LensCosmo(z_lens, z_source, cosmo=cosmo) self.lens_analysis = LensAnalysis(kwargs_model) self._lensModelExt = LensModelExtensions(self.lens_analysis.LensModel) self.kwargs_options = kwargs_model kwargs_cosmo = { 'D_d': self.lensCosmo.D_d, 'D_s': self.lensCosmo.D_s, 'D_ds': self.lensCosmo.D_ds } self.analytic_kinematics = AnalyticKinematics(**kwargs_cosmo) def time_delays(self, kwargs_lens, kwargs_ps, kappa_ext=0): """ predicts the time delays of the image positions :param kwargs_lens: lens model parameters :param kwargs_ps: point source parameters :param kappa_ext: external convergence (optional) :return: time delays at image positions for the fixed cosmology """ fermat_pot = self.lens_analysis.fermat_potential( kwargs_lens, kwargs_ps) time_delay = self.lensCosmo.time_delay_units(fermat_pot, kappa_ext) return time_delay def velocity_dispersion(self, kwargs_lens, kwargs_lens_light, lens_light_model_bool_list=None, aniso_param=1, r_eff=None, R_slit=0.81, dR_slit=0.1, psf_fwhm=0.7, num_evaluate=1000): """ 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. Further information can be found in the AnalyticKinematics() class. :param kwargs_lens: lens model parameters :param kwargs_lens_light: deflector light parameters :param aniso_param: scaled r_ani with respect to the half light radius :param r_eff: half light radius, if not provided, will be computed from the lens light model :param R_slit: width of the slit :param dR_slit: length of the slit :param psf_fwhm: full width at half maximum of the seeing condition :param num_evaluate: number of spectral rendering of the light distribution that end up on the slit :return: velocity dispersion in units [km/s] """ gamma = kwargs_lens[0]['gamma'] if 'center_x' in kwargs_lens_light[0]: center_x, center_y = kwargs_lens_light[0][ 'center_x'], kwargs_lens_light[0]['center_y'] else: center_x, center_y = 0, 0 if r_eff is None: r_eff = self.lens_analysis.half_light_radius_lens( kwargs_lens_light, center_x=center_x, center_y=center_y, model_bool_list=lens_light_model_bool_list) theta_E = kwargs_lens[0]['theta_E'] r_ani = aniso_param * r_eff sigma2 = self.analytic_kinematics.vel_disp( gamma, theta_E, r_eff, r_ani, R_slit, dR_slit, FWHM=psf_fwhm, rendering_number=num_evaluate) return sigma2 def velocity_dispersion_numerical(self, kwargs_lens, kwargs_lens_light, kwargs_anisotropy, kwargs_aperture, psf_fwhm, aperture_type, anisotropy_model, r_eff=None, kwargs_numerics={}, MGE_light=False, MGE_mass=False, lens_model_kinematics_bool=None, light_model_kinematics_bool=None, Hernquist_approx=False): """ Computes the LOS velocity dispersion of the deflector galaxy with arbitrary combinations of light and mass models. For a detailed description, visit the description of the Galkin() class. Additionaly to executing the Galkin routine, it has an optional Multi-Gaussian-Expansion decomposition of lens and light models that do not have a three-dimensional distribution built in, such as Sersic profiles etc. The center of all the lens and lens light models that are part of the kinematic estimate must be centered on the same point. :param kwargs_lens: lens model parameters :param kwargs_lens_light: lens light parameters :param kwargs_anisotropy: anisotropy parameters (see Galkin module) :param kwargs_aperture: aperture parameters (see Galkin module) :param psf_fwhm: full width at half maximum of the seeing (Gaussian form) :param aperture_type: type of aperture (see Galkin module :param anisotropy_model: stellar anisotropy model (see Galkin module) :param r_eff: a rough estimate of the half light radius of the lens light in case of computing the MGE of the light profile :param kwargs_numerics: keyword arguments that contain numerical options (see Galkin module) :param MGE_light: bool, if true performs the MGE for the light distribution :param MGE_mass: bool, if true performs the MGE for the mass distribution :param lens_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 :param light_model_kinematics_bool: bool list of length of the light model. Only takes a subset of all the models as part of the kinematics computation (can be used to ignore light components that do not describe the main deflector :return: LOS velocity dispersion [km/s] """ kwargs_cosmo = { 'D_d': self.lensCosmo.D_d, 'D_s': self.lensCosmo.D_s, 'D_ds': self.lensCosmo.D_ds } mass_profile_list = [] kwargs_profile = [] if lens_model_kinematics_bool is None: lens_model_kinematics_bool = [True] * len(kwargs_lens) for i, lens_model in enumerate(self.kwargs_options['lens_model_list']): if lens_model_kinematics_bool[i] is True: mass_profile_list.append(lens_model) if lens_model in ['INTERPOL', 'INTERPOL_SCLAED']: center_x, center_y = self._lensModelExt.lens_center( kwargs_lens, k=i) kwargs_lens_i = copy.deepcopy(kwargs_lens[i]) kwargs_lens_i['grid_interp_x'] -= center_x kwargs_lens_i['grid_interp_y'] -= center_y else: kwargs_lens_i = { k: v for k, v in kwargs_lens[i].items() if not k in ['center_x', 'center_y'] } kwargs_profile.append(kwargs_lens_i) if MGE_mass is True: lensModel = LensModel(lens_model_list=mass_profile_list) massModel = LensModelExtensions(lensModel) theta_E = massModel.effective_einstein_radius(kwargs_profile) r_array = np.logspace(-4, 2, 200) * theta_E mass_r = lensModel.kappa(r_array, np.zeros_like(r_array), kwargs_profile) amps, sigmas, norm = mge.mge_1d(r_array, mass_r, N=20) mass_profile_list = ['MULTI_GAUSSIAN_KAPPA'] kwargs_profile = [{'amp': amps, 'sigma': sigmas}] light_profile_list = [] kwargs_light = [] if light_model_kinematics_bool is None: light_model_kinematics_bool = [True] * len(kwargs_lens_light) for i, light_model in enumerate( self.kwargs_options['lens_light_model_list']): if light_model_kinematics_bool[i]: light_profile_list.append(light_model) kwargs_lens_light_i = { k: v for k, v in kwargs_lens_light[i].items() if not k in ['center_x', 'center_y'] } if 'q' in kwargs_lens_light_i: kwargs_lens_light_i['q'] = 1 kwargs_light.append(kwargs_lens_light_i) if r_eff is None: lensAnalysis = LensAnalysis( {'lens_light_model_list': light_profile_list}) r_eff = lensAnalysis.half_light_radius_lens( kwargs_light, model_bool_list=light_model_kinematics_bool) if Hernquist_approx is True: light_profile_list = ['HERNQUIST'] kwargs_light = [{'Rs': r_eff, 'amp': 1.}] else: if MGE_light is True: lightModel = LightModel(light_profile_list) r_array = np.logspace(-3, 2, 200) * r_eff * 2 flux_r = lightModel.surface_brightness(r_array, 0, kwargs_light) amps, sigmas, norm = mge.mge_1d(r_array, flux_r, N=20) light_profile_list = ['MULTI_GAUSSIAN'] kwargs_light = [{'amp': amps, 'sigma': sigmas}] galkin = Galkin(mass_profile_list, light_profile_list, aperture_type=aperture_type, anisotropy_model=anisotropy_model, fwhm=psf_fwhm, kwargs_cosmo=kwargs_cosmo, **kwargs_numerics) sigma2 = galkin.vel_disp(kwargs_profile, kwargs_light, kwargs_anisotropy, kwargs_aperture) return sigma2 def angular_diameter_relations(self, sigma_v_model, sigma_v, kappa_ext, D_dt_model): """ :return: """ sigma_v2_model = sigma_v_model**2 Ds_Dds = sigma_v**2 / (1 - kappa_ext) / ( sigma_v2_model * self.lensCosmo.D_ds / self.lensCosmo.D_s) D_d = D_dt_model / (1 + self.lensCosmo.z_lens) / Ds_Dds / (1 - kappa_ext) return D_d, Ds_Dds def angular_distances(self, sigma_v_measured, time_delay_measured, kappa_ext, sigma_v_modeled, fermat_pot): """ :param sigma_v_measured: velocity dispersion measured [km/s] :param time_delay_measured: time delay measured [d] :param kappa_ext: external convergence estimated [] :param sigma_v_modeled: lens model velocity dispersion with default cosmology and without external convergence [km/s] :param fermat_pot: fermat potential of lens model, modulo MSD of kappa_ext [arcsec^2] :return: D_d and D_d*D_s/D_ds, units in Mpc physical """ Ds_Dds = (sigma_v_measured / float(sigma_v_modeled))**2 / ( self.lensCosmo.D_ds / self.lensCosmo.D_s) / (1. - kappa_ext) DdDs_Dds = 1. / (1 + self.lensCosmo.z_lens) / (1. - kappa_ext) * ( const.c * time_delay_measured * const.day_s) / (fermat_pot * const.arcsec**2) / const.Mpc return Ds_Dds, DdDs_Dds