NFW Halo Shears

This is the “lensing engine” for calculating shears around an NFW halo.

class galsim.NFWHalo(mass, conc, redshift, halo_pos=galsim.PositionD(x=0.0, y=0.0), omega_m=None, omega_lam=None, cosmo=None)

Class describing NFW halos.

This class computes the lensing fields shear and convergence of a spherically symmetric NFW halo of given mass, concentration, redshift, assuming a particular cosmology. No mass-concentration relation is employed.

Based on Matthias Bartelmann’s libastro.

The cosmology to use can be set either by providing a Cosmology instance as cosmo, or by providing omega_m and/or omega_lam. If only one of the latter is provided, the other is taken to be one minus that. If no cosmology parameters are set, a default Cosmology is constructed.

Parameters:

• mass – Mass defined using a spherical overdensity of 200 times the critical density of the universe, in units of M_solar/h.

• conc – Concentration parameter, i.e., ratio of virial radius to NFW scale radius.

• redshift – Redshift of the halo.

• halo_pos – Position of halo center (in arcsec). [default: PositionD(0,0)]

• omega_m – Omega_matter to pass to Cosmology constructor. [default: None]

• omega_lam – Omega_lambda to pass to Cosmology constructor. [default: None]

• cosmo – A Cosmology instance. [default: None]

_getShear(pos_x, pos_y, z_s, reduced=True)

Equivalent to getShear, but without some sanity checks and the positions must be given as pos_x, pos_y in arcsec.

Parameters:

• pos_x – x position in arcsec (either a scalar or a numpy array)

• pos_y – y position in arcsec (either a scalar or a numpy array)

• z_s – Source redshift(s).

• reduced – Whether returned shear(s) should be reduced shears. [default: True]

Returns:

the (possibly reduced) shears as a tuple (g1,g2) (either scalars or numpy arrays)

_getConvergence(pos_x, pos_y, z_s)

Equivalent to getConvergence, but without some sanity checks and the positions must be given as pos_x, pos_y in arcsec.

Parameters:

• pos_x – x position in arcsec (either a scalar or a numpy array)

• pos_y – y position in arcsec (either a scalar or a numpy array)

• z_s – Source redshift(s).

Returns:

the convergence as either a scalar or a numpy array

_getMagnification(pos_x, pos_y, z_s)

Equivalent to getMagnification, but without some sanity checks and the positions must be given as pos_x, pos_y in arcsec.

Parameters:

• pos_x – x position in arcsec (either a scalar or a numpy array)

• pos_y – y position in arcsec (either a scalar or a numpy array)

• z_s – Source redshift(s).

Returns:

the magnification as either a scalar or a numpy array

_getLensing(pos_x, pos_y, z_s)

Equivalent to getLensing, but without some sanity checks and the positions must be given as pos_x, pos_y in arcsec.

Parameters:

• pos_x – x position in arcsec (either a scalar or a numpy array)

• pos_y – y position in arcsec (either a scalar or a numpy array)

• z_s – Source redshift(s).

Returns:

the reduced shears and magnifications as a tuple (g1,g2,mu) (each being either a scalar or a numpy array)

getConvergence(pos, z_s, units=coord.arcsec)

Calculate convergence of halo at specified positions.

Parameters:

• pos –

  Position(s) of the source(s), assumed to be post-lensing! Valid ways to input this:

  • single Position instance

  • tuple of floats: (x,y)

  • list/array of Position instances

  • tuple of lists/arrays: ( xlist, ylist )

• z_s – Source redshift(s).

• unit – Angular units of coordinates. [default: galsim.arcsec]

Returns:

the convergence, kappa

If the input pos is given a single position, kappa is the convergence value. If the input pos is given a list/array of positions, kappa is a NumPy array.

getLensing(pos, z_s, units=coord.arcsec)

Calculate lensing shear and magnification of halo at specified positions.

Parameters:

• pos –

  Position(s) of the source(s), assumed to be post-lensing! Valid ways to input this:

  • single Position instance

  • tuple of floats: (x,y)

  • list/array of Position instances

  • tuple of lists/arrays: ( xlist, ylist )

• z_s – Source redshift(s).

• units – Angular units of coordinates. [default: galsim.arcsec]

Returns:

the reduced shears and magnifications as a tuple (g1,g2,mu)

If the input pos is given a single position, the return values are the shear and magnification values at that position. If the input pos is given a list/array of positions, they are NumPy arrays.

getMagnification(pos, z_s, units=coord.arcsec)

Calculate magnification of halo at specified positions.

Parameters:

• pos –

  Position(s) of the source(s), assumed to be post-lensing! Valid ways to input this:

  • single Position instance

  • tuple of floats: (x,y)

  • list/array of Position instances

  • tuple of lists/arrays: ( xlist, ylist )

• z_s – Source redshift(s).

• units – Angular units of coordinates. [default: galsim.arcsec]

Returns:

the magnification mu

If the input pos is given a single position, mu is the magnification value. If the input pos is given a list/array of positions, mu is a NumPy array.

getShear(pos, z_s, units=coord.arcsec, reduced=True)

Calculate (reduced) shear of halo at specified positions.

Parameters:

• po –

  Position(s) of the source(s), assumed to be post-lensing! Valid ways to input this:

  • single Position instance

  • tuple of floats: (x,y)

  • list/array of Position instances

  • tuple of lists/arrays: ( xlist, ylist )

• z_s – Source redshift(s).

• units – Angular units of coordinates. [default: galsim.arcsec]

• reduced – Whether returned shear(s) should be reduced shears. [default: True]

Returns:

the (possibly reduced) shears as a tuple (g1,g2)

If the input pos is given a single position, (g1,g2) are the two shear components. If the input pos is given a list/array of positions, they are NumPy arrays.

class galsim.Cosmology(omega_m=0.3, omega_lam=0.7)

Basic cosmology calculations.

Cosmology calculates expansion function E(a) and angular diameter distances Da(z) for a LambdaCDM universe. Radiation is assumed to be zero and Dark Energy constant with w = -1 (no quintessence), but curvature is arbitrary.

Based on Matthias Bartelmann’s libastro.

Parameters:

• omega_m – Present day energy density of matter relative to critical density. [default: 0.3]

• omega_lam – Present day density of Dark Energy relative to critical density. [default: 0.7]

Da(z, z_ref=0)

Compute angular diameter distance between two redshifts in units of c/H0.

In order to get the distance in Mpc/h, multiply by c/H0~3000.

Parameters:

• z – Redshift.

• z_ref – Reference redshift, with z_ref <= z. [default: 0]

E(a)

Evaluates expansion function.

Parameters:

a – Scale factor.

a(z)

Compute scale factor.

Parameters:

z – Redshift