lenstronomy.Cosmo package

Submodules

lenstronomy.Cosmo._cosmo_interp_astropy_v4 module

class CosmoInterp(cosmo)

Bases: object

Class which interpolates the comoving transfer distance and then computes angular diameter distances from it This class is modifying the astropy.cosmology routines.

__init__(cosmo)

Parameters:

cosmo – astropy.cosmology instance (version 4.0 as private functions need to be supported)

lenstronomy.Cosmo._cosmo_interp_astropy_v5 module

class CosmoInterp(cosmo)

Bases: object

Class which interpolates the comoving transfer distance and then computes angular diameter distances from it This class is modifying the astropy.cosmology routines.

__init__(cosmo)

Parameters:

cosmo – astropy.cosmology instance (version 4.0 as private functions need to be supported)

lenstronomy.Cosmo.background module

class Background(cosmo=None, interp=False, **kwargs_interp)

Bases: object

Class to compute cosmological distances.

__init__(cosmo=None, interp=False, **kwargs_interp)

Parameters:

• cosmo – instance of astropy.cosmology

• interp – boolean, if True, uses interpolated cosmology to evaluate specific redshifts

• kwargs_interp – keyword arguments of CosmoInterp specifying the interpolation interval and maximum redshift

Returns:

Background class with instance of astropy.cosmology

static a_z(z)

Returns scale factor (a_0 = 1) for given redshift.

Parameters:

z – redshift

Returns:

scale factor

d_xy(z_observer, z_source)

Parameters:

• z_observer – observer redshift

• z_source – source redshift

Returns:

angular diameter distance in units of Mpc

ddt(z_lens, z_source)

Time-delay distance.

Parameters:

• z_lens – redshift of lens

• z_source – redshift of source

Returns:

time-delay distance in units of proper Mpc

T_xy(z_observer, z_source)

Parameters:

• z_observer – observer

• z_source – source

Returns:

transverse comoving distance in units of Mpc

property rho_crit

Critical density.

Returns:

value in M_sol/Mpc^3

rho_crit_z(z)

Critical density of the universe at given redshift.

Parameters:

z – redshift

Returns:

critical densith in physical [M_sun/Mpc^3]

beta_double_source_plane(z_lens, z_source_1, z_source_2)

Model prediction of ratio of scaled deflection angles.

\[\beta = \frac{\alpha_{z1}}{\alpha_{z2}}\]

Parameters:

• z_lens – lens redshift

• z_source_1 – source_1 redshift

• z_source_2 – source_2 redshift

• cosmo – ~astropy.cosmology instance

Returns:

beta

ddt_scaling(z_lens, z_source_1, z_source_2)

Scales the time-delay distance Ddt when given for one source redshift to a second source redshift.

Parameters:

• z_lens – deflector redshift

• z_source_1 – source redshift of original Ddt

• z_source_2 – new source redshift

Returns:

Ddt to z_source_2

lenstronomy.Cosmo.cosmo_interp module

class CosmoInterp(cosmo=None, z_stop=None, num_interp=None, ang_dist_list=None, z_list=None, Ok0=None, K=None)

Bases: object

Class which interpolates the comoving transfer distance and then computes angular diameter distances from it This class is modifying the astropy.cosmology routines.

__init__(cosmo=None, z_stop=None, num_interp=None, ang_dist_list=None, z_list=None, Ok0=None, K=None)

Parameters:

• cosmo – astropy.cosmology instance (version 4.0 as private functions need to be supported)

• z_stop – maximum redshift for the interpolation

• num_interp – int, number of interpolating steps

• ang_dist_list – array of angular diameter distances in Mpc to be interpolated (optional)

• z_list – list of redshifts corresponding to ang_dist_list (optional)

• Ok0 – Omega_k(z=0)

• K – Omega_k / (hubble distance)^2 in Mpc^-2

angular_diameter_distance(z, z2=None)

Angular diameter distance in Mpc at a given redshift.

This gives the proper (sometimes called ‘physical’) transverse distance corresponding to an angle of 1 radian for an object at redshift z.

Weinberg, 1972, pp 421-424; Weedman, 1986, pp 65-67; Peebles, 1993, pp 325-327.

Parameters

zarray_like

Input redshifts. Must be 1D or scalar.

z2: array_like or None

Redshift of end (optional)

Returns

d~astropy.units.Quantity

Angular diameter distance in Mpc at each input redshift.

angular_diameter_distance_z1z2(z1, z2)

Angular diameter distance between objects at 2 redshifts. Useful for gravitational lensing.

Parameters

z1, z2array_like, shape (N,)

Input redshifts. z2 must be large than z1.

Returns

d~astropy.units.Quantity, shape (N,) or single if input scalar

The angular diameter distance between each input redshift pair.

comoving_transverse_distance(z)

Comoving transverse distance in Mpc at a given redshift.

This value is the transverse comoving distance at redshift z corresponding to an angular separation of 1 radian. This is the same as the comoving distance if omega_k is zero (as in the current concordance lambda CDM model).

Parameters

zarray_like

Input redshifts. Must be 1D or scalar.

Returns

d~astropy.units.Quantity

Comoving transverse distance in Mpc at each input redshift.

Notes

This quantity also called the ‘proper motion distance’ in some texts.

lenstronomy.Cosmo.cosmo_solver module

cosmo2angular_diameter_distances(H_0, omega_m, z_lens, z_source)

Parameters:

• H_0 – Hubble constant [km/s/Mpc]

• omega_m – dimensionless matter density at z=0

• z_lens – deflector redshift

• z_source – source redshift

Returns:

angular diameter distances Dd and Ds/Dds

ddt2h0(ddt, z_lens, z_source, cosmo)

Converts time-delay distance to H0 for a given expansion history.

Parameters:

• ddt – time-delay distance in Mpc

• z_lens – deflector redshift

• z_source – source redshift

• cosmo – astropy.cosmology class instance

Returns:

h0 value which matches the cosmology class effectively replacing the h0 value used in the creation of this class

class SolverFlatLCDM(z_d, z_s)

Bases: object

Class to solve multidimensional non-linear equations to determine the cosmological parameters H0 and omega_m given the angular diameter distance relations.

__init__(z_d, z_s)

F(x, Dd, Ds_Dds)

Parameters:

x – array of parameters (H_0, omega_m)

Returns:

solve(init, dd, ds_dds)

class InvertCosmo(z_d, z_s, H0_range=None, omega_m_range=None)

Bases: object

Class to do an interpolation and call the inverse of this interpolation to get H_0 and omega_m.

__init__(z_d, z_s, H0_range=None, omega_m_range=None)

get_cosmo(Dd, Ds_Dds)

Return the values of H0 and omega_m computed with an interpolation.

Parameters:

• Dd – flat

• Ds_Dds – float

Returns:

lenstronomy.Cosmo.gnfw_param module

class GNFWParam(cosmo=None)

Bases: object

Class which contains a halo model parameters dependent on cosmology for gNFW profile. All distances are given in physical units.

Mass definitions are relative to 200 crit including redshift evolution. The redshift evolution is cosmology dependent (dark energy). The H0 dependence is propagated into the input and return units.

rhoc = 277536627000.0

__init__(cosmo=None)

Parameters:

cosmo (astropy.cosmology instance) – astropy.cosmology instance

rhoc_z(z)

Compute the critical density of the universe at redshift z in physical units [h^2 M_sun Mpc^-3].

Parameters:

z (float) – redshift

Returns:

critical density of the universe at redshift z in physical units [h^2 M_sun Mpc^-3]

Return type:

float

static M200(rs, rho0, c, gamma_in)

Calculation of the mass enclosed r_200 for gNFW profile defined as.

\[M_{200} = 4 \pi \rho_0^{3} r_{\rm s}^{3} \frac{c^{3 - \gamma_{\rm in}}} {3 - \gamma_{\rm in}} {}_2F_1(3 - \gamma_{\rm in}, 3 - \gamma_{\rm in}; 4 - \gamma_{\rm in}; -c)\]

Parameters:

• rs (float) – scale radius

• rho0 (float) – density normalization (characteristic density) in units mass/[distance unit of rs]^3

• c (float [4,40]) – concentration

• gamma_in (float) – inner slope of the gNFW profile

Returns:

M(R_200) mass in units of rho0 * rs^3

Return type:

float

r200_M(M, z)

Compute the radius R_200 crit of a halo of mass M in physical mass M/h.

Parameters:

• M (float or numpy array) – halo mass in M_sun/h

• z (float) – redshift

Returns:

radius R_200 in physical Mpc/h

Return type:

float or numpy array

M_r200(r200, z)

Compute the mass M_200 of a halo of radius r_200 in physical Mpc/h.

Parameters:

• r200 (float) – r200 in physical Mpc/h

• z (float) – redshift

Returns:

M200 in M_sun/h

Return type:

float

rho0_c(c, z, gamma_in)

Computes density normalization as a function of concentration parameter.

Parameters:

• c (float) – concentration

• z (float) – redshift

• gamma_in (float) – inner slope of the gNFW profile

Returns:

density normalization in h^2/Mpc^3 (physical)

Return type:

float

c_rho0(rho0, z, gamma_in)

Computes the concentration given density normalization rho_0 in h^2/Mpc^3 (physical) (inverse of function rho0_c)

Parameters:

• rho0 (float) – density normalization in h^2/Mpc^3 (physical)

• z (float) – redshift

• gamma_in (float) – inner slope of the gNFW profile

Returns:

concentration parameter c

Return type:

float

c_M_z(M, z)

Fitting function of http://moriond.in2p3.fr/J08/proceedings/duffy.pdf for the mass and redshift dependence of the concentration parameter. Here, assuming the NFW M-c relation for the gNFW profile.

Parameters:

• M (float or numpy array) – halo mass in M_sun/h

• z (float >0) – redshift

Returns:

concentration parameter as float

Return type:

float

gnfw_Mz(M, z, gamma_in)

Returns all needed parameter (in physical units modulo h) to draw the profile of the main halo r200 in physical Mpc/h rho_s in h^2/Mpc^3 (physical) Rs in Mpc/h physical c unit less.

Parameters:

• M (float) – Mass in physical M_sun/h

• z (float) – redshift

• gamma_in (float) – inner slope of the gNFW profile

Returns:

r200, rho0, c, Rs

Return type:

float, float, float, float

lenstronomy.Cosmo.kde_likelihood module

class KDELikelihood(D_d_sample, D_delta_t_sample, kde_type='scipy_gaussian', bandwidth=1)

Bases: object

Class that samples the cosmographic likelihood given a distribution of points in the 2-dimensional distribution of D_d and D_delta_t.

__init__(D_d_sample, D_delta_t_sample, kde_type='scipy_gaussian', bandwidth=1)

Parameters:

• D_d_sample – 1-d numpy array of angular diameter distances to the lens plane

• D_delta_t_sample – 1-d numpy array of time-delay distances

• kde_type (string) – The kernel to use. Valid kernels are ‘scipy_gaussian’ or [‘gaussian’|’tophat’|’epanechnikov’|’exponential’|’linear’|’cosine’] Default is ‘gaussian’.

• bandwidth – width of kernel (in same units as the angular diameter quantities)

log_likelihood(D_d, D_delta_t)

Likelihood of the data (represented in the distribution of this class) given a model with predicted angular diameter distances.

Parameters:

• D_d – model predicted angular diameter distance

• D_delta_t – model predicted time-delay distance

Returns:

log likelihood (log of KDE value)

lenstronomy.Cosmo.micro_lensing module

einstein_radius(mass, d_l, d_s)

Einstein radius for a given point mass and distances to lens and source.

Parameters:

• mass – point source mass [M_sun]

• d_l – distance to lens [pc]

• d_s – distance to source [pc]

Returns:

Einstein radius [arc seconds]

source_size(diameter, d_s)

Parameters:

• diameter – diameter of the source in units of the solar diameter

• d_s – distance to the source in [pc]

Returns:

diameter in [arc seconds]

lenstronomy.Cosmo.lcdm module

class LCDM(z_lens, z_source, flat=True)

Bases: object

Flat LCDM cosmology background with free Hubble parameter and Omega_m at fixed lens redshift configuration.

__init__(z_lens, z_source, flat=True)

Parameters:

• z_lens – redshift of lens

• z_source – redshift of source

• flat – bool, if True, flat universe is assumed

D_d(H_0, Om0, Ode0=None)

Angular diameter to deflector.

Parameters:

• H_0 – Hubble parameter [km/s/Mpc]

• Om0 – normalized matter density at present time

Returns:

float [Mpc]

D_s(H_0, Om0, Ode0=None)

Angular diameter to source.

Parameters:

• H_0 – Hubble parameter [km/s/Mpc]

• Om0 – normalized matter density at present time

Returns:

float [Mpc]

D_ds(H_0, Om0, Ode0=None)

Angular diameter from deflector to source.

Parameters:

• H_0 – Hubble parameter [km/s/Mpc]

• Om0 – normalized matter density at present time

Returns:

float [Mpc]

D_dt(H_0, Om0, Ode0=None)

Time-delay distance.

Parameters:

• H_0 – Hubble parameter [km/s/Mpc]

• Om0 – normalized matter density at present time

Returns:

float [Mpc]

lenstronomy.Cosmo.lens_cosmo module

class LensCosmo(z_lens, z_source, cosmo=None)

Bases: object

Class to manage the physical units and distances present in a single plane lens with fixed input cosmology.

__init__(z_lens, z_source, cosmo=None)

Parameters:

• z_lens – redshift of lens

• z_source – redshift of source

• cosmo – ~astropy.cosmology instance

property h

property dd

Returns:

angular diameter distance to the deflector [Mpc]

property ds

Returns:

angular diameter distance to the source [Mpc]

property dds

Returns:

angular diameter distance from deflector to source [Mpc]

property ddt

Returns:

time delay distance [Mpc]

property sigma_crit

Returns the critical projected lensing mass density in units of M_sun/Mpc^2.

Returns:

critical projected lensing mass density

property sigma_crit_angle

Returns the critical surface density in units of M_sun/arcsec^2 (in physical solar mass units) when provided a physical mass per physical Mpc^2.

Returns:

critical projected mass density

phys2arcsec_lens(phys)

Convert physical Mpc into arc seconds.

Parameters:

phys – physical distance [Mpc]

Returns:

angular diameter [arcsec]

arcsec2phys_lens(arcsec)

Convert angular to physical quantities for lens plane.

Parameters:

arcsec – angular size at lens plane [arcsec]

Returns:

physical size at lens plane [Mpc]

arcsec2phys_source(arcsec)

Convert angular to physical quantities for source plane.

Parameters:

arcsec – angular size at source plane [arcsec]

Returns:

physical size at source plane [Mpc]

kappa2proj_mass(kappa)

Convert convergence to projected mass M_sun/Mpc^2.

Parameters:

kappa – lensing convergence

Returns:

projected mass [M_sun/Mpc^2]

mass_in_theta_E(theta_E)

Mass within Einstein radius (area * epsilon crit) [M_sun]

Parameters:

theta_E – Einstein radius [arcsec]

Returns:

mass within Einstein radius [M_sun]

mass_in_coin(theta_E)

Parameters:

theta_E – Einstein radius [arcsec]

Returns:

mass in coin calculated in mean density of the universe

time_delay_units(fermat_pot, kappa_ext=0)

Parameters:

• fermat_pot – in units of arcsec^2 (e.g. Fermat potential)

• kappa_ext – unit-less external shear not accounted for in the Fermat potential

Returns:

time delay in days

time_delay2fermat_pot(dt)

Parameters:

dt – time delay in units of days

Returns:

Fermat potential in units arcsec**2 for a given cosmology

nfw_angle2physical(Rs_angle, alpha_Rs)

Converts the angular parameters into the physical ones for an NFW profile.

Parameters:

• alpha_Rs – observed bending angle at the scale radius in units of arcsec

• Rs_angle – scale radius in units of arcsec

Returns:

rho0 [Msun/Mpc^3], Rs [Mpc], c, r200 [Mpc], M200 [Msun]

gnfw_angle2physical(Rs_angle, alpha_Rs, gamma_in)

Converts the angular parameters into the physical ones for a gNFW profile.

Parameters:

• alpha_Rs – observed bending angle at the scale radius in units of arcsec

• Rs_angle – scale radius in units of arcsec

• gamma_in – inner slope of the gNFW profile

Returns:

rho0 [Msun/Mpc^3], Rs [Mpc], c, r200 [Mpc], M200 [Msun]

nfw_physical2angle(M, c)

Converts the physical mass and concentration parameter of an NFW profile into the lensing quantities.

Parameters:

• M – mass enclosed 200 rho_crit in units of M_sun (physical units, meaning no little h)

• c – NFW concentration parameter (r200/r_s)

Returns:

Rs_angle (angle at scale radius) (in units of arcsec), alpha_Rs (observed bending angle at the scale radius)

gnfw_physical2angle(M, c, gamma_in)

Converts the physical mass and concentration parameter of a gNFW profile into the lensing quantities.

Parameters:

• M – mass enclosed 200 rho_crit in units of M_sun (physical units, meaning no little h)

• c – NFW concentration parameter (r200/r_s)

Returns:

Rs_angle (angle at scale radius) (in units of arcsec), alpha_Rs (observed bending angle at the scale radius

nfwParam_physical(M, c)

Returns the NFW parameters in physical units.

Parameters:

• M – physical mass in M_sun in definition m200

• c – concentration

Returns:

rho0 [Msun/Mpc^3], Rs [Mpc], r200 [Mpc]

gnfwParam_physical(M, c, gamma_in)

Returns the gNFW parameters in physical units.

Parameters:

• M – physical mass in M_sun in definition m200

• c – concentration

Returns:

rho0 [Msun/Mpc^3], Rs [Mpc], r200 [Mpc]

nfw_M_theta_r200(M)

Returns r200 radius in angular units of arc seconds on the sky.

Parameters:

M – physical mass in M_sun

Returns:

angle (in arc seconds) of the r200 radius

gnfw_M_theta_r200(M)

Returns r200 radius in angular units of arc seconds on the sky.

Parameters:

M – physical mass in M_sun

Returns:

angle (in arc seconds) of the r200 radius

sis_theta_E2sigma_v(theta_E)

Converts the lensing Einstein radius into a physical velocity dispersion.

Parameters:

theta_E – Einstein radius (in arcsec)

Returns:

velocity dispersion in units (km/s)

sis_sigma_v2theta_E(v_sigma)

Converts the velocity dispersion into an Einstein radius for a SIS profile.

Parameters:

v_sigma – velocity dispersion (km/s)

Returns:

theta_E (arcsec)

hernquist_phys2angular(mass, rs)

Translates physical mass definitions of the Hernquist profile to the angular units used in the Hernquist lens profile of lenstronomy.

‘sigma0’ is defined such that the deflection at projected RS leads to alpha = 2./3 * Rs * sigma0

Parameters:

• mass – A spherical overdensity mass in M_sun corresponding to the mass definition mdef at redshift z

• rs – rs in units of physical Mpc

Returns:

sigma0, Rs_angle

hernquist_angular2phys(sigma0, rs_angle)

‘sigma0’ is defined such that the deflection at projected RS leads to alpha = 2./3 * Rs * sigma0.

Parameters:

• sigma0 – convergence normalization

• rs_angle – rs in angular units [arcseconds]

Returns:

mass [M_sun], rs [Mpc]

uldm_angular2phys(kappa_0, theta_c)

Converts the anguar parameters entering the LensModel Uldm() (Ultra Light Dark Matter) class in physical masses, i.e. the total soliton mass and the mass of the particle.

Parameters:

• kappa_0 – central convergence of profile

• theta_c – core radius (in arcseconds)

Returns:

m_eV_log10, M_sol_log10, the log10 of the masses, m in eV and M in M_sun

uldm_mphys2angular(m_log10, M_log10)

Converts physical ULDM mass in the ones, in angular units, that enter the LensModel Uldm() class.

Parameters:

• m_log10 – exponent of ULDM mass in eV

• M_log10 – exponent of soliton mass in M_sun

Returns:

kappa_0, theta_c, the central convergence and core radius (in arcseconds)

sersic_m_star2k_eff(m_star, R_sersic, n_sersic)

Translates a total stellar mass into ‘k_eff’, the convergence at ‘R_sersic’ (effective radius or half-light radius) for a Sersic profile.

Parameters:

• m_star – total stellar mass in physical Msun

• R_sersic – half-light radius in arc seconds

• n_sersic – Sersic index

Returns:

k_eff

vel_disp_dPIED_sigma0(vel_disp, Ra, Rs)

Sigma0 value in the convention of the lenstronomy pseudo_jaffe lens model.

lenstronomy conventions:

\[\Sigma(R) = \Sigma_0 \frac{Ra Rs}{Rs-Ra}\left(\frac{1}{\sqrt{Ra^2+R^2}} - \frac{1}{\sqrt{Rs^2+R^2}} \right)\]

with

\[\Sigma_0 = \pi \rho_0 \frac{Ra Rs}{Rs + Ra}\]

In the lensing parameterization,

\[\sigma_0 = \frac{\Sigma_0}{\Sigma_{\rm crit}}\]

SIS profile:

\[\theta_{\rm E, SIS} = 4\pi \frac{D_{\rm LS}}{D_{\rm S}} \left(\frac{\sigma_v}{c} \right)^2\]

\[\kappa_{\rm SIS} = \frac{1}{2} \frac{\theta_E}{R}\]

\[\kappa_{\rm dPIED} \approx \sigma_0 \frac{R_s R_a}{R_s - R_a} \left(\sim \frac{1}{R} \right))\]

relation then between velocity dispersion and sigma0:

\[\sigma_v = c \sqrt{\sigma_0 \frac{R_s R_a}{R_s - R_a} \frac{D_{\rm S}}{D_{\rm LS}} \frac{1}{2\pi} }\]

Parameters:

vel_disp – SIS equivalent velocity dispersion (km/s)

Returns:

sigma0 value in the convention of the lenstronomy pseudo_jaffe lens model

sersic_k_eff2m_star(k_eff, R_sersic, n_sersic)

Translates convergence at half-light radius to total integrated physical stellar mass for a Sersic profile.

Parameters:

• k_eff – lensing convergence at half-light radius

• R_sersic – half-light radius in arc seconds

• n_sersic – Sersic index

Returns:

stellar mass in physical Msun

beta_double_source_plane(z_lens, z_source_1, z_source_2)

Model prediction of ratio of scaled deflection angles.

Parameters:

• z_lens – lens redshift

• z_source_1 – source_1 redshift

• z_source_2 – source_2 redshift

• cosmo – ~astropy.cosmology instance

Returns:

beta

theta_E_power_law_scaling(theta_E_convention, kappa_ext_convention, gamma_pl, z_lens, z_source_convention, z_source)

Maps Einstein radius of a power-law profile with external convergence to different source redshifts.

Parameters:

• theta_E_convention – Einstein radius for the lens when a source is at z_source_conventions coming from the main deflector (excluding external convergence)

• kappa_ext_convention – external convergence for z_source_convention

• gamma_pl – power-law slope of the deflector

• z_lens – lens redshift

• z_source_convention – source redshift for lens model conventions

• z_source – source redshift

Returns:

Einstein radius for a source at redshift z_source

lenstronomy.Cosmo.nfw_param module

class NFWParam(cosmo=None)

Bases: object

Class which contains a halo model parameters dependent on cosmology for NFW profile All distances are given in physical units.

Mass definitions are relative to 200 crit including redshift evolution. The redshift evolution is cosmology dependent (dark energy). The H0 dependence is propagated into the input and return units.

rhoc = 277536627000.0

__init__(cosmo=None)

Parameters:

cosmo (astropy.cosmology) – astropy.cosmology instance

rhoc_z(z)

Compute the critical density of the universe at redshift z in physical units [h^2 M_sun Mpc^-3].

Parameters:

z (float) – redshift

Returns:

critical density of the universe at redshift z in physical units [h^2 M_sun Mpc^-3]

Return type:

float

static M200(rs, rho0, c)

Calculation of the mass enclosed r_200 for NFW profile defined as.

\[M_{200} = 4 \pi \rho_0^{3} r_{\rm s}^3 \left(\log(1+c) - \frac {c}{1 + c} \right)\]

Parameters:

• rs (float) – scale radius

• rho0 (float) – density normalization (characteristic density) in units mass/[distance unit of rs]^3

• c (float [4,40]) – concentration

Returns:

M(R_200) mass in units of rho0 * rs^3

r200_M(M, z)

Computes the radius R_200 crit of a halo of mass M in physical mass M/h.

Parameters:

• M (float or numpy array) – halo mass in M_sun/h

• z (float) – redshift

Returns:

radius R_200 in physical Mpc/h

Return type:

float or numpy array

M_r200(r200, z)

Parameters:

• r200 (float) – r200 in physical Mpc/h

• z (float) – redshift

Returns:

M200 in M_sun/h

Return type:

float

rho0_c(c, z)

Computes density normalization as a function of concentration parameter.

Parameters:

• c (float [4,40]) – concentration

• z (float) – redshift

Returns:

density normalization in h^2/Mpc^3 (physical)

Return type:

float

c_rho0(rho0, z)

Computes the concentration given density normalization rho_0 in h^2/Mpc^3 (physical) (inverse of function rho0_c)

Parameters:

• rho0 (float) – density normalization in h^2/Mpc^3 (physical)

• z (float) – redshift

Returns:

concentration parameter c

Return type:

float

static c_M_z(M, z)

Fitting function of http://moriond.in2p3.fr/J08/proceedings/duffy.pdf for the mass and redshift dependence of the concentration parameter

Parameters:

• M (float or numpy array) – halo mass in M_sun/h

• z (float >0) – redshift

Returns:

concentration parameter as float

Return type:

float

nfw_Mz(M, z)

Returns all needed parameter (in physical units modulo h) to draw the profile of the main halo r200 in physical Mpc/h rho_s in h^2/Mpc^3 (physical) Rs in Mpc/h physical c unit less.

Parameters:

• M (float) – Mass in physical M_sun/h

• z (float) – redshift

Returns:

r200, rho0, c, Rs

Return type:

tuple

Module contents