Generating realizations of distribution function and mock catalogs (WS5)

A number of problems require generating realizations of a distribution. From generating initial conditions for an N-Body simulations to generating mock catalogs, the same basic methods are deployed. The plan of this workshop is to introduce the concepts and methods for constructing mock catalogs.

Constructing Mock Galaxy Catalogs:
The galaxy luminosity function $\phi(L)$ represents the number density of galaxies with luminosities L and L+dL. Similarly we can define other distribution functions like the galaxy stellar mass function, the galaxy luminosity function in band X, the star formation rate function, the quasar luminosity function (to name a few). Such distribution functions are strongly constrained from observations, but are poorly understood theoretically. Dark matter halos and the local environment play an important role in determining the property of galaxies it hosts. Over the years a number of methods have been employed to predict the abundance and clustering of galaxies as constrained from observations. These include semi-analytical models of galaxy formation and cosmological hydrodynamical simulations, both of which employ cosmological n-body simulations, which are expensive to run. In the past decade abundance matching techniques have become popular and can be easily used to generate mock galaxy catalogs. One can use abundance matching techniques with or without halo catalogs from simulations and thereby generate mock galaxy catalogs which are homogeneous or clustered. Once mock galaxy catalogs are generated one can use it for a number of applications, we list a few which are not exhaustive:

  1. Understand how different methods estimate the survey selection function
  2. Generate mock catalogs on lightcones
  3. Generate mock catalogs in redshift space
  4. Make forecasts for upcoming and future surveys

Topics To Be Covered in the Workshop:

  1. Random numbers and probability distributions.
  2. Generating random numbers with a given distribution.
  3. Exercises:
    a: Generate a population of objects with a given luminosity function. Then generate a flux limited catalog.
    b: generating a stellar population by combining stellar evolution code, IMF
    and star formation history).
    c: Generate a position and velocity of a plummer halo.

  4. Generating random numbers with a given joint distribution.
    Exercises: Generate populations of galaxies given the colour magnitude diagram for main sequence galaxies, using this population to generate a mock catalog for a survey with a given selection function.
    • Abundance Matching the galaxy luminosity function to the halo mass function (no scatter).
    • Abundance Matching the galaxy luminosity function to the halo mass function (with scatter).
    • Abundance Matching the galaxy luminosity function to a halo catalog from a simulation.

    Exercises: large scale, scale independent halo bias and its mass dependence
    Exercises: large scale, scale independent galaxy bias and its luminosity dependence

Proposed number of Participants: 50

Method of Lectures/Hands-on Session: Zoom

Requirements from Participants:
Laptop/Desktop with knowledge of C/Python for Handson Session
Software: gcc, gsl, gnuplot, numpy, scipy, astropy
OS: Any (Linux Preferred)

Click here to download Program for Workshop 5

Resource Persons:
Jasjeet Singh Bagla, IISER Mohali (
Nishikanta Khandai, NISER Bhubaneswar (
Aseem Paranjape, IUCAA, Pune (