lenspack.halo.profiles module

class lenspack.halo.profiles.nfw_profile(z, c200, m200=None, r200=None, cosmology='default')

Bases: object

Navarro, Frenk, & White (1997) radial halo density profile.

rho(r; rho0, rs) = rho0 / [(r / rs) * (1 + r / rs)^2],

where rho0 can be written as the product delta_c * rho_crit. The more common (and useful) parameterization is (c200, m200) instead of (rho0, rs).

Parameters

• z (float) – Halo redshift. [dimensionless]

• c200 (float) – Halo concentration. [dimensionless]

• m200 (float, optional) – Spherical mass contained within a radius r200. [solar mass]

• r200 (float, optional) – Characteristic halo radius. [Mpc]

• cosmology ({‘default’, instance of astropy.cosmology}) – Cosmological model in which to calculate distances. The default is a FlatLambdaCDM object with parameters H0=70, Om0=0.3, Ob0=0.044, and Tcmb0=2.725. Alternatively, a custom cosmology can be provided as an instance of astropy.cosmology.

Notes

1. Either m200 or r200 must be given to fully define the profile, and m200 takes precedence over r200 if both are given.

2. The reference background density implicitly used in the definition of c200, m200, and r200 is the critical density at the redshift of the halo.

rho(r)

Density at a given distance from the halo center.

mass_enclosed(r)

Mass (3D) inside a sphere of a given radius.

sigma_crit(zs)

Critical surface mass density for a given source redshift.

Parameters

zs (float or array_like) – Redshift(s) of the source galaxies.

sigma(r, r_off=None)

Surface mass density (Sigma) at a given radial distance.

Parameters

• r (float or array_like) – Projected radial distance from the halo center.

• r_off (float, optional) – Projected radial offset of the halo center. If provided, the computed Sigma is the mean over all azimuthal angles, i.e., averaged over the circle of radius r_off centered on the halo.

Notes

The calculation is much slower when r_off is given due to the numerical integration necessary.

Value(s) are returned in units of solar mass per square parsec.

delta_sigma(r, r_off=None)

Difference between the mean Sigma within a disk and its boundary.

Parameters

• r (float or array_like) – Projected radial distance from the halo center.

• r_off (float, optional) – Projected radial offset of the halo center. If provided, the computed Delta Sigma is the mean over all azimuthal angles, i.e., averaged over the circle of radius r_off centered on the halo.

Notes

The calculation is much slower when r_off is given due to the numerical integration necessary.

Value(s) are returned in units of solar mass per square parsec.

mean_sigma_enclosed(r, r_off)

Mean surface mass density (Sigma) enclosed within a disk.

Parameters

• r (float or array_like) – Projected radial distance from the halo center.

• r_off (float, optional) – Projected radial offset of the halo center.

Notes

The calculation is much slower when r_off is given due to the numerical integration necessary.

Value(s) are returned in units of solar mass per square parsec.

gamma_t(r, zs, r_off=None)

Tangential shear magnitude experienced by a source object.

Parameters

• r (float or array_like) – Projected radial (proper) distance from the source to the halo center. Units of Mpc are assumed if r is not given an astropy quantity.

• zs (float or array_like) – Redshift of the source. If a single float is given, this value is used for each r.

• r_off (float, optional) – Projected radial offset of the halo center.

kappa(r, zs, r_off=None)

Convergence experienced by a source object.

Parameters

• r (float or array_like) – Projected radial (proper) distance from the source to the halo center. Units of Mpc are assumed if r is not given an astropy quantity.

• zs (float or array_like) – Redshift of the source. If a single float is given, this value is used for each r.

• r_off (float, optional) – Projected radial offset of the halo center.