Support using the Jeans length as the star formation threshold

[hsinhaoHHuang]

Goal

• To support using the local Jeans length $\lambda_J=\sqrt{\frac{\pi c_s^2}{G\rho}}$ as the star formation threshold

Changes

• Generalize the original SF_CreateStar_AGORA() as SF_CreateStar_GeneralGalaxy() for general local star formation recipes.

  • Separate the part checking the star formation threshold to SF_CreateStar_Check.cpp
  • Separate the part deciding the star mass to SF_CreateStar_GetStarMass.cpp

• Add a new star formation scheme SF_CREATE_STAR_SCHEME = 2 to use the Jeans length as the star formation threshold.

• Add a new runtime parameter SF_CREATE_STAR_MAX_GAS_JEANSL, where the star will only form when the local Jeans length is less than dh*SF_CREATE_STAR_MAX_GAS_JEANSL.

• Add a new test problem, Hydro/StarFormationThreshold, to test the implementation of star formation.

  • With varying temperature and density in the initial conditions.
  • Both particles and fluid are frozen and reset to initial conditions. Only stars keep forming.

Verifications

• With the modifications, we can still reproduce the results of the original Hydro/AGORA_IsolatedGalaxy test problem (tested with BITWISE_REPRODUCIBILITY on).

• In the new Hydro/StarFormationThreshold test problem, the star forms in the expected region with the expected star mass and star formation rate.

  • Setups

    • BoxSize: 8 kpc
    • Grids: 128x128x32
    • MAX_LEVEL 0
    • No initial particle
    • OPT__FREEZE_PAR 1
    • OPT__FREEZE_FLUID 1
    • OPT__RESET_FLUID 1
    • SF_CREATE_STAR_MASS_EFF 1.0e-2
    • SF_CREATE_STAR_MIN_STAR_MASS 1.0e3 (Msun)
    • SF_CREATE_STAR_MAX_STAR_MFRAC 0.5

  • Initial conditions

    • T-rho phase diagram = x-y spatial distribution
      

  • SF_CREATE_STAR_SCHEME = 1, which uses density = 8.37e-24 g cm^-3 as the threshold

    • Star formation threshold
      
      
    • Star formation mass distribution
      
    • Star formation rate
      

  • SF_CREATE_STAR_SCHEME = 2, which uses Jeans length = 1 dh as the threshold

    • Star formation threshold
      
      
    • Star formation mass distribution
      
    • Star formation rate
      
      • The periodic pattern in the star formation rate seems related to the smaller time step close to the timing of Output_DumpData and the number of bins in the calculation. Due to (1) the large number of star-forming cells and (2) the total star masses dominated by the high-density cells, the variance due to the stochastic star formation is probably unobservable. For the cells (8~9th grids from the right) that will form a star with 50% probability, the theoretical sigma/mean = 1/sqrt(~32*96) < 2%.
    Test with `OPT__RESET_FLUID = 0`, fluid was removed every step

    

    

    

[ChunYen-Chen]

@hsinhaoHHuang Thanks for the contribution. I have left some comments including some bugs. Also, please update your branch to solve the conflict.

[hsinhaoHHuang]

@ChunYen-Chen
Thank you so much for your review. I have modified the code accordingly.

About adding the new runtime parameter in the doc/wiki, I plan to wait for #431 and update it (or I will update that PR if this PR is merged earlier), since all the star formation runtime parameters are completed there.