T1: Free-fall collapse
first simulations

Before the tutorials:

As discussed in the lecture, structures in the universe collapse under their own gravity. This holds from the larges structures like galaxy clusters where dark matter dominates the potential down to star formation, where gaseous clouds collapse.

• Calculate the so-called free-fall time of a sphere with uniform density.
• Now imagine the formation of a galaxy cluster. You can start from the mean density of the universe today.
• Now, if you take the typical galaxy cluster mass it has today, how large is the spatial region which had to collapse to form it?
• Compare that time to the one you get for a typical, dense molecular cloud in a star forming region.

Units are important (and tricky). Typical units for cosmological strutures are choosen to be kpc for lengths, 10¹⁰ M_⊙ for masses and km/s for velocities. Think about what this means for the time unit in such simulations.

• Compute what the resulting time unit of such simulations is.
• What is the free-fall time for the galaxy cluster case you calculated before in this unit system of choice?

During the tutorials:

Preparing the code, as in the first tutorial, copy it over. But before compiling, change the following settings in the Config.sh file:

• PERIODIC to #PERIODIC
• NOGRAVITY to #NOGRAVITY

Do not forget the module load XXXX commands before compiling.

As in the first tutorial, copy the parameter file and modify it to be non-periodic and choose a reasonable unit system and adapt the times according to your calculated free-fall time for the galaxy cluster:

• PeriodicBoundariesOn 0
• TimeMax 50.0
• TimeBetSnapshot 0.5
• UnitLength_in_cm 3.085678e21 % 1.0 kpc /h
• UnitMass_in_g 1.989e43 % 1e10 solar masses
• UnitVelocity_in_cm_per_s 1e5 % 1 km/sec
• GravityConstantInternal 0.0 % if set to zero, the physical value 6.672e-8 is taken
• SofteningHalo 20
• SofteningHaloMaxPhys 20
• Remember: the time step is defined by the softening, so make sure you use an apropriate softening for the particles you will use (dark matter in this case)!

Extend the program which you used last time to create a sphere of particles as a representation of a collapsing cloud for the galaxy cluster case. As you treat dark matter particles this time, set the particle number in npart[1] instead of index [0] as last time. You also do not need to create a rho field for the density.

• Take the size you calculated above to imagine a base grid of say 20x20x20 particles.
• Select only the particles within a sphere with the calculated radius.
• What mass do you have to give to the individual particles?
• Remember: this time you want to simulate dark matter particles, not gas particles, so remember that you have to change Npart[0] = N to Npart[1] = N and you also can skip writing the internal energy U to the file.

Now you can run the simulation as last time and use the same tools to visualize the results.

• Measure the free-fall time and compare it to what you had calculated.
• Compare this with the age of the universe and interpret the result.
• In cosmology, the largest objects like galaxy clusters form latest (compared to galaxies), see upper left panel of Figure 2. Think about possible reasons!

Programming goals for T1:

Goal of this tutorial is that you learn better how to create initial conditions files
and how to plot the results from a simulation.

Solutions

• Example(s) for setting up the particle cloud
  • Use the example in the IDL language
    • cp $HOME/Hydro/IDL/Setup/*.pro .
    • idl -e setup_cloud
  • or the example in the C/C++ language
    • cp $HOME/Hydro/C/gadget_io.h .
    • cp $HOME/Hydro/C/setup_collapse.c .
    • icc setup_collapse.c
    • ./a.out
  • or the example in the Python language
    • cp $HOME/Hydro/Python/g3read.py .
    • cp $HOME/Hydro/Python/setup_freefall.py .
    • cp $HOME/Hydro/Python/ic_header .
    • python3 setup_freefall.py
  • or the example in the Julia language
    • cp $HOME/Hydro/Julia/setup_collapse.jl .
    • julia setup_collapse.jl
• How to run: mpirun -np 1 OpenGadget3/P-Gadget3 box.param
• Example(s) for vizualising the results
  • Use the example in the IDL language
    • idl -e show
    • xv frame_0*.jpg -wait 0.1 -wloop
  • or the example in the C/C++ language
    • cp $HOME/Hydro/C/gadget_io.h .
    • cp $HOME/Hydro/C/show_collapse.c .
    • icc show_collapse.c
    • ./a.out snap_* > data.txt
    • gnuplot show.plt
  • or the example in the Julia language
    • cp $HOME/Hydro/Julia/show_collapse.jl .
    • julia show_collapse.jl
    • firefox collapse.gif
• You should see an animation like this, with the cloud of particles collapsing as expected:
  
  Small mp4 animation.