Tutorial

A complete walkthrough of all the functionality and tools available in this project is provided in the Demo.

A simple example use case is as follows. Suppose you want the differential surface mass density \(\Delta\Sigma(r)\) profiles for a handful of galaxy clusters. Lets say they are at redshifts \(z = 0.1\), \(0.2\), and \(0.5\), and have masses of \(1 \times 10^{15}\), \(5 \times 10^{14}\), and \(2 \times 10^{14} M_{\odot}\), respectively.

After installing cluster-lensing, all we have to do is:

import numpy as np
from clusterlensing import ClusterEnsemble
z = [0.1, 0.2, 0.3]
c = ClusterEnsemble(z)
c.m200 = [1e15, 5e14, 2e14]
r = np.arange(0.5, 5, 0.5)  #radial bins
c.calc_nfw(r)

Then the attribute c.deltasigma_nfw will contain an array of \(\Delta\Sigma(r)\) profiles, one for each of the three clusters:

>>> print c.deltasigma_nfw
[[ 216.99031097  131.96892957   89.95900137   65.95785776   50.81725977
    40.57785901   33.28891018   27.89244619   23.77114581]
 [ 159.82908955   88.92279328   57.75958551   41.06296211   30.95764522
    24.32100583   19.69970451   16.33693743   13.80449899]
 [  99.4563379    49.5200608    30.40868664   20.87864071   15.36566757
    11.85760144    9.47172553    7.76726675    6.50260522]] solMass / pc2

Let’s say you are concerned about the accuracy of your clusters’ centroid estimates. We can easily calculate the miscentered \(\Delta\Sigma(r)\) profiles by passing the optional offsets parameter to the calc_nfw() function. The offsets are given in units of Mpc, just like the radius, and represent the width of a 2D Gaussian offset distribution.

>>> c.calc_nfw(r, offsets=[0.1, 0.1, 0.1])
>>> print c.deltasigma_nfw
[[ 198.81572771  129.96652087   89.16550619   65.7334123    50.65140495
    40.49991719   33.22670747   27.85454194   23.73961746]
 [ 146.78755133   88.37783273   57.34742622   40.97849669   30.88520548
    24.29289523   19.67582995   16.32416666   13.79347989]
 [  91.77806816   49.70092894   30.26422875   20.87331318   15.3514408
    11.85804354    9.47045213    7.76873388    6.50334115]] solMass / pc2

The above example illustrates a really simple use case, but cluster-lensing provides far more functionality. You can specify cosmologies and mass-concentration relations to use for the NFW calculations. Additionally, if you don’t have mass estimates at all, you can empoy a built-in (or customizeable) mass-richness scaling relation to easily convert richness estimates into masses. Be sure to check out the Demo page for all the details.