Generating initial conditions from a distribution function

It is possible to generate initial conditions for ergodic spherical models by sampling a distribution function. To this end, pNbody provides a submodule called DF. The method is strongly inspired by the method described in Errani 2022.

For a given mass density profile provided by a python function, the corresponding distribution function is obtained using the Eddigton equation. By default, through the process, the potential, the cumulative mass, as well as the total mass are computed by numerical integration. Note that those quantities can also be given directly by the appropriate function if analytically defined as in the example given below:

# import modules
import numpy as np
from pNbody import *
from pNbody.DF import DistributionFunction
from pNbody.mass_models import plummer

# define the gravitational constant
G = 43000

# define some parameters
Mtot = 1e-5     # total Plummer mass
a    = 0.1      # Plummer scale length

Rmin = 1e-2     # minimal radius
Rmax = 10       # maximal radius

N    = 1e5      # number of particles
NR   = 1e4      # number of radius bins
NE   = 1e4      # number of energy bins
Ndraw= 1e6      # number of particles to draw at each loop


# define the density, potential, cumulative mass and total mass
fctDensity        = lambda x:plummer.Density(M=Mtot, a=a, r=x, G=G)
fctPotential      = lambda x:plummer.Potential(M=Mtot, a=a, r=x, G=G)
fctCumulativeMass = lambda x:plummer.CumulativeMass(M=Mtot, a=a, r=x, G=G)
TotalMass         = plummer.TotalMass(M=Mtot, a=a, G=G)

# create the distribution function object
DF = DistributionFunction(Rmin=Rmin,Rmax=Rmax,Rinf=np.inf,NR=NR,NE=NE,
                          fctDensity=fctDensity,
                          fctPotential=fctPotential,
                          fctCumulativeMass=fctCumulativeMass,
                          TotalMass=TotalMass,G=G)

Once the DF object is defined, we can compute it, i.e., effectively solving the Eddington equation, clean it, i.e., removing negative values and compute the maximum likelihood for a given radius:

DF.computeDF()
DF.clean()
DF.computeMaxLikelihood()

Next, we can draw N particles from the distribution and retrieve the sampled positions, velocities and masses:

DF.sample(N,Ndraw)

pos = DF.pos
vel = DF.vel
mass= DF.mass

Finally, it is possible to create an Nbody object:

nb = Nbody(status='new',p_name="plummer.hdf5",pos=pos,vel=vel,mass=mass,ftype='swift')

Scripts

ic_hernquist

usage: ic_hernquist [-h] [-o OUTPUTFILENAME] [-t FTYPE] [--irand INT]
                    [--ptype INT] [--plot] [-N INT] [-a A] [--rho0 RHO0]
                    [-b B] [--Rmin RMIN] [--Rmax RMAX] [--NE NE] [--NR NR]
                    [--Ndraw NDRAW] [--mass MASS] [-q]

generate an hernquist model at equilibrium

options:
  -h, --help         show this help message and exit
  -o OUTPUTFILENAME  Name of the output file
  -t FTYPE           Type of the output file
  --irand INT        random seed
  --ptype INT        particle type
  --plot             plot dynamical time
  -N INT             total number of particles
  -a A               a parameter
  --rho0 RHO0        density at critical radius
  -b B               b parameter
  --Rmin RMIN        Rmin
  --Rmax RMAX        Rmax
  --NE NE            number of energy bins
  --NR NR            number of radius bins
  --Ndraw NDRAW      number of particles to draw at each loop
  --mass MASS        particle mass in solar mass
  -q, --quiet        quiet mode

Examples:
--------
ic_hernquist -N 730000 --Rmin 1e-3 --Rmax 100 --rho0 0.1 -a 0.1  -t swift -o hernquist.hdf5

ic_plummer

usage: ic_plummer [-h] [-o OUTPUTFILENAME] [-t FTYPE] [--irand INT]
                  [--ptype INT] [--plot] [-N INT] [-a A] [--Mtot MTOT]
                  [--Rmin RMIN] [--Rmax RMAX] [--NE NE] [--NR NR]
                  [--Ndraw NDRAW] [--mass MASS] [-q]

generate a plummer model at equilibrium

options:
  -h, --help         show this help message and exit
  -o OUTPUTFILENAME  Name of the output file
  -t FTYPE           Type of the output file
  --irand INT        random seed
  --ptype INT        particle type
  --plot             plot dynamical time
  -N INT             total number of particles
  -a A               a parameter
  --Mtot MTOT        Total mass in 1e10 Msol
  --Rmin RMIN        Rmin
  --Rmax RMAX        Rmax
  --NE NE            number of energy bins
  --NR NR            number of radius bins
  --Ndraw NDRAW      number of particles to draw at each loop
  --mass MASS        particle mass in solar mass
  -q, --quiet        quiet mode

Examples:
--------
ic_plummer   -N 100000 --Mtot 1e-5 -a 0.1 --Rmax 10 -t swift -o plummer.hdf5

ic_nfw

usage: ic_nfw [-h] [-o OUTPUTFILENAME] [-t FTYPE] [--irand INT] [--ptype INT]
              [--plot] [-N INT] [--rs RS] [--rho0 RHO0] [--c C] [--M200 M200]
              [--Rmin RMIN] [--Rmax RMAX] [--NE NE] [--NR NR] [--Ndraw NDRAW]
              [--mass MASS] [-q]

generate an nfw model at equilibrium

options:
  -h, --help         show this help message and exit
  -o OUTPUTFILENAME  Name of the output file
  -t FTYPE           Type of the output file
  --irand INT        random seed
  --ptype INT        particle type
  --plot             plot dynamical time
  -N INT             total number of particles
  --rs RS            rs parameter
  --rho0 RHO0        density at critical radius
  --c C              concentration parameter
  --M200 M200        virial mass in Msol
  --Rmin RMIN        Rmin
  --Rmax RMAX        Rmax
  --NE NE            number of energy bins
  --NR NR            number of radius bins
  --Ndraw NDRAW      number of particles to draw at each loop
  --mass MASS        particle mass in solar mass
  -q, --quiet        quiet mode

Examples:
--------
ic_nfw       -N 730000 --Rmin 1e-3 --Rmax 100  --rho0 0.1   --rs 0.1    -t swift -o nfw.hdf5
ic_nfw       -N 730000 --Rmin 1e-3 --Rmax 100  --c    8     --M200 1e10 -t swift -o nfw.hdf5

ic_nfw+plummer

usage: ic_nfw+plummer [-h] [-o OUTPUTFILENAME] [-t FTYPE] [--irand INT]
                      [--plot] [-N INT] [--rs RS] [--rho0 RHO0] [--c C]
                      [--M200 M200] [-a A] [--Mtot MTOT] [--Rmin RMIN]
                      [--Rmax RMAX] [--NE NE] [--NR NR] [--Ndraw NDRAW]
                      [--ptype1 INT] [--ptype2 INT] [--mass1 MASS1]
                      [--mass2 MASS2] [-q]

generate an nfw+plummer model at equilibrium

options:
  -h, --help         show this help message and exit
  -o OUTPUTFILENAME  Name of the output file
  -t FTYPE           Type of the output file
  --irand INT        random seed
  --plot             plot dynamical time
  -N INT             total number of particles
  --rs RS            NFW rs parameter
  --rho0 RHO0        NFW density at critical radius
  --c C              concentration parameter
  --M200 M200        virial mass in Msol
  -a A               a parameter
  --Mtot MTOT        Total mass in solar mass
  --Rmin RMIN        Rmin
  --Rmax RMAX        Rmax
  --NE NE            number of energy bins
  --NR NR            number of radius bins
  --Ndraw NDRAW      number of particles to draw at each loop
  --ptype1 INT       particle type of component 1
  --ptype2 INT       particle type of component 2
  --mass1 MASS1      particle 1 mass in solar mass
  --mass2 MASS2      particle 2 mass in solar mass
  -q, --quiet        quiet mode

Examples:
--------
ic_nfw+plummer --Rmin 1e-3 --Rmax 30  --rho0 0.007 --rs 0.5   --Mtot 1e5 -a 0.1 --ptype1 4 --ptype2 1  --mass1 1000 --mass2 1000  -t swift -o nfw+plummer.hdf5
ic_nfw+plummer --Rmin 1e-3 --Rmax 100 --M200 1e11  --c  17    --Mtot 1e9 -a 1   --ptype1 4 --ptype2 1  -N 100000                  -t swift -o nfw+plummer.hdf5
ic_nfw+plummer --Rmin 1e-3 --Rmax 100 --M200 1e11  --c  17    --Mtot 1e9 -a 1   --ptype1 4 --ptype2 1  --mass1 1e4   --mass2 1e5  -t swift -o nfw+plummer.hdf5

ic_homogeneous_box

usage: ic_homogeneous_box [-h] [-o OUTPUTFILENAME] [-t FTYPE] [--lJ FLOAT]
                          [--irand INT] [--hydro] [--ptype INT] [-N INT] [-q]

generate initial an homogeneous box

options:
  -h, --help         show this help message and exit
  -o OUTPUTFILENAME  Name of the output file
  -t FTYPE           Type of the output file
  --lJ FLOAT         Jeans wavelength
  --irand INT        random seed
  --hydro            consider gas
  --ptype INT        particle type
  -N INT             total number of particles
  -q, --quiet        quiet mode

Examples:
--------
ic_homogeneous_box -N 1024                                             -o output.hdf5
ic_homogeneous_box -N 1024 --lJ=0.5                                    -o output.hdf5
ic_homogeneous_box -N 1024 --lJ=0.5 --hydro                            -o output.hdf5
ic_homogeneous_box -N 1024 --lJ=0.5 --hydro -t swift                   -o output.hdf5
ic_homogeneous_box -N 1024 --lJ=0.5 --hydro -t swift --hydro           -o output.hdf5
ic_homogeneous_box -N 1024 --lJ=0.5 --hydro -t swift --hydro --ptype 2 -o output.hdf5