add_gammat_point_mass
================================================

Add point mass contributions to galaxy-galaxy lensing (gamma_t) signal

+-------------+-------------------------------------------+
| File        | shear/point_mass/add_gammat_point_mass.py |
+-------------+-------------------------------------------+
| Attribution | Shivam Pandey                             |
+-------------+-------------------------------------------+
| URL         |                                           |
+-------------+-------------------------------------------+
| Citations   | https://doi.org/10.1093/mnras/stz2761     |
+-------------+-------------------------------------------+

This module adds point mass contributions to the galaxy-galaxy lensing 
tangential shear signal gamma_t. Point masses around lenses contribute 
a 1/theta^2 term to the lensing signal.

The module computes the critical surface density inverse (sigma_crit^-1)
for each lens-source bin combination and uses bias parameters to scale
the point mass contribution. It can use either the cosmological parameters
from the pipeline or a fiducial cosmology for distance calculations.


Assumptions
-----------

 - Point mass contributions follow 1/theta^2 angular dependence
 - Critical surface density can be computed from geometry or fiducial cosmology



Setup Parameters
----------------

.. list-table::
   :header-rows: 1

   * - Name
     - Type
     - Default
     - Description

   * - bias_section
     - str
     - add_pm
     - Section name containing point mass bias parameters
   * - bias_prefix
     - str
     - b_
     - Prefix for bias parameter names
   * - add_togammat
     - bool
     - False
     - Whether to add point mass term to existing gamma_t
   * - use_fiducial
     - bool
     - False
     - Whether to use fiducial cosmology for distance calculations
   * - Omega_m_fid
     - real
     - 0.3
     - Fiducial matter density parameter
   * - H0_fid
     - real
     - 69.0
     - Fiducial Hubble parameter in km/s/Mpc
   * - lens_nz_section
     - str
     - nz_lens
     - Section name for lens n(z) data
   * - source_nz_section
     - str
     - nz_source
     - Section name for source n(z) data
   * - gammat_section
     - str
     - galaxy_shear_xi
     - Section name for gamma_t measurements
   * - sigcrit_inv_section
     - str
     - sigma_crit_inv_lens_source
     - Section name for critical surface density inverse output


Input values
----------------

.. list-table::
   :header-rows: 1

   * - Section
     - Name
     - Type
     - Default
     - Description

   * - bias_section
     - bias_parameter
     - real
     - 
     - Point mass bias parameter for lens bins
   * - lens_nz_section
     - nbin
     - int
     - 
     - Number of lens redshift bins
   * - 
     - z
     - real 1d
     - 
     - Redshift sample values for lenses
   * - 
     - bin_i
     - real 1d
     - 
     - Lens n(z) for bin i
   * - source_nz_section
     - nbin
     - int
     - 
     - Number of source redshift bins
   * - 
     - z
     - real 1d
     - 
     - Redshift sample values for sources
   * - 
     - bin_i
     - real 1d
     - 
     - Source n(z) for bin i
   * - gammat_section
     - theta
     - real 1d
     - 
     - Angular separation values (if add_togammat=true)
   * - 
     - bin_i_j
     - real 1d
     - 
     - Galaxy-galaxy lensing signal for lens bin i, source bin j
   * - cosmological_parameters
     - hubble
     - real
     - 
     - Hubble parameter H0 in km/s/Mpc (if use_fiducial=false)
   * - 
     - omega_m
     - real
     - 
     - Matter density parameter (if use_fiducial=false)
   * - distances
     - z
     - real 1d
     - 
     - Redshift values for distance measurements (if use_fiducial=false)
   * - 
     - d_m
     - real 1d
     - 
     - Comoving distance in Mpc (if use_fiducial=false)


Output values
----------------


.. list-table:: Output values
   :header-rows: 1

   * - Section
     - Name
     - Type
     - Description

   * - gammat_section
     - bin_i_j
     - real 1d
     - Modified gamma_t with point mass contribution (if add_togammat=true)
   * - point_mass
     - bin_i_j
     - real
     - Point mass contribution coefficient for lens bin i, source bin j
   * - sigcrit_inv_section
     - sigma_crit_inv_i_j
     - real
     - Critical surface density inverse for lens bin i, source bin j