nfw module

NFW profiles for shear and magnification.

Surface mass density and differential surface mass density calculations for NFW dark matter halos, with and without the effects of miscentering offsets.

class clusterlensing.nfw.SurfaceMassDensity(rs, delta_c, rho_crit, offsets=None, rbins=None, numTh=200, numRoff=200, numRinner=20, factorRouter=3)

Bases: object

Calculate NFW profiles for Sigma and Delta-Sigma.

Parameters:

rs : array_like

Scale radii (in Mpc) for every halo. Should be 1D, optionally with astropy.units of Mpc.

delta_c : array_like

Characteristic overdensities for every halo. Should be 1D and have the same length as rs.

rho_crit : array_like

Critical energy density of the universe (in Msun/Mpc/pc^2) at every halo z. Should be 1D, optionally with astropy.units of Msun/Mpc/(pc**2), and have the same length as rs.

offsets : array_like, optional

Width of the Gaussian distribution of miscentering offsets (in Mpc), for every cluster halo. Should be 1D, optionally with astropy.units of Mpc, and have the same length as rs. (Note: it is common to use the same value for every halo, implying that they are drawn from the same offset distribution).

rbins : array_like, optional

Radial bins (in Mpc) at which profiles will be calculated. Should be 1D, optionally with astropy.units of Mpc.

Other Parameters:  

numTh : int, optional

Number of bins to use for integration over theta, for calculating offset profiles (no effect for offsets=None). Default 200.

numRoff : int, optional

Number of bins to use for integration over R_off, for calculating offset profiles (no effect for offsets=None). Default 200.

numRinner : int, optional

Number of bins at r < min(rbins) to use for integration over Sigma(<r), for calculating DeltaSigma (no effect for Sigma ever, and no effect for DeltaSigma if offsets=None). Default 20.

factorRouter : int, optional

Factor increase over number of rbins, at min(r) < r < max(r), of bins that will be used at for integration over Sigma(<r), for calculating DeltaSigma (no effect for Sigma, and no effect for DeltaSigma if offsets=None). Default 3.

See also

ClusterEnsemble

Parameters and profiles for a sample of clusters. This class provides an interface to SurfaceMassDensity, and tracks a DataFrame of parameters as well as nfw profiles for many clusters at once, only requiring the user to specify cluster z and richness, at a minimum.

References

Sigma and DeltaSigma are calculated using the formulas given in:

C.O. Wright and T.G. Brainerd, “Gravitational Lensing by NFW Halos,” The Astrophysical Journal, Volume 534, Issue 1, pp. 34-40 (2000).

The offset profiles are calculated using formulas given, e.g., in Equations 11-15 of:

J. Ford, L. Van Waerbeke, M. Milkeraitis, et al., “CFHTLenS: a weak lensing shear analysis of the 3D-Matched-Filter galaxy clusters,” Monthly Notices of the Royal Astronomical Society, Volume 447, Issue 2, p.1304-1318 (2015).

Methods

sigma_nfw()	Calculate surface mass density Sigma.
deltasigma_nfw()	Calculate differential surface mass density DeltaSigma.

deltasigma_nfw()

Calculate NFW differential surface mass density profile.

Generate the differential surface mass density profiles of each cluster halo, assuming a spherical NFW model. Optionally includes the effect of cluster miscentering offsets, if the parent object was initialized with offsets.

Returns:

Quantity :

Differential surface mass density profiles (ndarray, in astropy.units of Msun/pc/pc). Each row corresponds to a single cluster halo.

sigma_nfw()

Calculate NFW surface mass density profile.

Generate the surface mass density profiles of each cluster halo, assuming a spherical NFW model. Optionally includes the effect of cluster miscentering offsets, if the parent object was initialized with offsets.

Returns:

Quantity :

Surface mass density profiles (ndarray, in astropy.units of Msun/pc/pc). Each row corresponds to a single cluster halo.