Mass Profiles

This section covers the lens mass profiles implemented in GLEE.

General Remarks

Below are important notes regarding the profiles used in GLEE.

The strength of the profiles (e.g., $\Theta_E$: the Einstein radius) corresponds to the true deflection angles ($\hat\alpha$), not the scaled deflection angles ($\alpha$).

• In single-plane lensing, the D_ds / D_s factors will be multiplied by the true deflection angles to obtain the scaled deflection angle for ray tracing via the lens equation.
• In multi-plane lensing, the redshift/distance factors are incorporated into the recursive multi-plane lens equation for ray tracing.
• If D_ds / D_s = 1 for a specific source (sources/esources in the config file), then the Einstein radius in the lens profiles corresponds directly to the observed lensed image separation for the specific lens and source redshifts.
• If D_ds / D_s is set to its actual value (e.g., 0.48, based on spectroscopic z_d and z_s measurements), then the Einstein radius in the lenses_vary section of the config file represents the Einstein radius for a source at redshift infinity, rather than the specific lens-source redshift pair.
• If D_ds / D_s ≠ 1.0, the "scale:" parameter in theta_e will correspond to the Einstein radius of a lens profile for a source at redshift infinity, since normalizations are defined before multiplying the D_ds / D_s factor.
• To avoid numerical singularities, some profiles include a softening radius (r_soft).
  • The default value is 1e-4.
  • Users can override this value in the GLEE config file using: Rsoft xyz

Profile Summary

Profile	Keyword	Description
Elliptical Power Law (EPL)	epl	Standard smooth power-law lens
External Shear	shear	Tidal shear from the lens environment
PIEMD	piemd	Pseudo-Isothermal Elliptical — cored isothermal
Mass-Follows-Light PIEMD (PIEMDMFL)	piemdmfl	PIEMD with mass-to-light ratio coupling
Dual Pseudo-Isothermal Elliptical (dPIE)	dpie	Truncated PIEMD for satellite galaxies
SPEMD	spemd	Softened Power-law Elliptical — generalized PIEMD
NFW	nfw	Navarro-Frenk-White dark matter halo
Elliptical NFW (eNFW)	enfw	NFW with ellipticity in surface density
Generalized NFW (GNFW)	gnfw	NFW with variable inner slope
Triaxial NFW (TNFW)	tnfw	Fully triaxial dark matter halo
Prolate NFW (PNFW)	pnfw	Axisymmetric cigar-shaped NFW
Point Mass	point	Point mass for compact objects
Convergence Gradient (kgrad)	kgrad	Constant external convergence gradient

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Below is a list of all detailed profile documentation:

Elliptical Power Law (EPL)

Power-law elliptical mass distribution — the standard model for galaxy-scale lenses.

External Shear

External shear component — models the tidal influence of the lens environment.

PIEMD (Mass)

Pseudo-Isothermal Elliptical Mass Distribution — a cored isothermal sphere with ellipticity.

Mass-Follows-Light PIEMD (PIEMDMFL)

PIEMD with mass-to-light ratio parameter — couples stellar light to mass distribution.

SPEMD (Mass)

Softened Power-law Elliptical Mass Distribution — a generalisation of PIEMD with a variable slope.

Dual Pseudo-Isothermal Elliptical (dPIE)

Truncated PIEMD profile with core and truncation radii — ideal for modeling satellite galaxies.

NFW (Navarro-Frenk-White)

NFW profile — the standard dark matter halo profile from N-body simulations.

eNFW (Elliptical NFW)

Elliptical Navarro–Frenk–White profile — NFW with applied ellipticity in the surface mass density.

Point Mass

Point mass lens model — useful for stellar or compact object microlensing perturbations.

Generalized NFW (GNFW)

NFW profile with variable inner slope — more flexible dark matter halo modeling.

Triaxial NFW (TNFW)

Fully triaxial dark matter halo profile — most realistic 3D halo shape.

Prolate NFW (PNFW)

Axisymmetric cigar-shaped NFW halo — simplified triaxial profile.

Convergence Gradient (kgrad)

Constant external convergence gradient — models large-scale structure effects.