3D MHD models

This notebook explains how to use cubic results of 3D MHD models on a uniform grid in CRPropa.

Supplied data

The fields need to be supplied in a raw binary file that contains only single floats, arranged as follows: Starting with the cell values (Bx,By,Bz for magnetic field or rho for density) at the origin of the box, the code continues to read along z, then y and finally x.

On https://crpropa.desy.de/ under “Additional resources” you can find a number of MHD models used with CRPropa in the literature.

In [1]:
from crpropa import *

## settings for MHD model (must be set according to model)
filename_bfield = "clues_primordial.dat" ## filename of the magnetic field
gridOrigin = Vector3d(0,0,0)             ## origin of the 3D data, preferably at boxOrigin
gridSize = 1024                          ## size of uniform grid in data points
size = 249.827*Mpc                       ## physical edgelength of volume in Mpc
b_factor = 1.                            ## global renormalizatino factor for the field

## settings of simulation
boxOrigin = Vector3d( 0, 0, 0,)          ## origin of the full box of the simulation
boxSize = Vector3d( size, size, size )   ## end of the full box of the simulation

## settings for computation
minStep = 10.*kpc                        ## minimum length of single step of calculation
maxStep = 4.*Mpc                         ## maximum length of single step of calculation
tolerance = 1e-2                         ## tolerance for error in iterative calculation of propagation step

spacing = size/(gridSize)                ## resolution, physical size of single cell

m = ModuleList()


## instead of  computing propagation without Lorentz deflection via
# m.add(SimplePropagation(minStep,maxStep))

## initiate grid to hold field values
vgrid = Grid3f( gridOrigin, gridSize, spacing )
## load values to the grid
loadGrid( vgrid, filename_bfield, b_factor )
## use grid as magnetic field
bField = MagneticFieldGrid( vgrid )
## add propagation module to the simulation to activate deflection in supplied field
m.add(PropagationCK( bField, tolerance, minStep, maxStep))
#m.add(DeflectionCK( bField, tolerance, minStep, maxStep))  ## this was used in older versions of CRPropa

to make use of periodicity of the provided data grid, use

In [2]:
m.add( PeriodicBox( boxOrigin, boxSize ) )

to not follow particles forever, use

In [3]:
m.add( MaximumTrajectoryLength( 400*Mpc ) )

Uniform injection

The most simple scenario of UHECR sources is a uniform distribution of their sources. This can be realized via use of

In [4]:
source = Source()
source.add( SourceUniformBox( boxOrigin, boxSize ))

Injection following density field

The distribution of gas density can be used as a probability density function for the injection of particles from random positions.

In [65]:
filename_density = "mass-density_clues.dat" ## filename of the density field

source = Source()
## initialize grid to hold field values
mgrid = ScalarGrid( gridOrigin, gridSize, spacing )
## load values  to grid
loadGrid( mgrid, filename_density )
## add source module to simulation
source.add( SourceDensityGrid( mgrid ) )

Mass Halo injection

Alternatively, for the CLUES models, we also provide a list of mass halo positions. These positions can be used as sources with same properties by use of the following

In [67]:
filename_halos = 'clues_halos.dat'

# read data from file
data = np.loadtxt(filename_halos, unpack=True, skiprows=39)
sX = data[0]
sY = data[1]
sZ = data[2]
mass_halo = data[5]

## find only those mass halos inside the provided volume (see Hackstein et al. 2018 for more details)
Xdown= sX >= 0.25
Xup= sX <= 0.75
Ydown= sY >= 0.25
Yup= sY <= 0.75
Zdown= sZ >= 0.25
Zup= sZ <= 0.75
insider= Xdown*Xup*Ydown*Yup*Zdown*Zup

## transform relative positions to physical positions within given grid
sX = (sX[insider]-0.25)*2*size
sY = (sY[insider]-0.25)*2*size
sZ = (sZ[insider]-0.25)*2*size

## collect all sources in the multiple sources container
smp = SourceMultiplePositions()
for i in range(0,len(sX)):
    pos = Vector3d( sX[i], sY[i], sZ[i] )
    smp.add( pos, 1. )

## add collected sources
source = Source()
source.add( smp )

additional source properties

In [5]:
## use isotropic emission from all sources
source.add( SourceIsotropicEmission() )

## set particle type to be injected
A, Z = 1, 1 # proton
source.add( SourceParticleType( nucleusId(A,Z) ) )

## set injected energy spectrum
Emin, Emax = 1*EeV, 1000*EeV
specIndex = -1
source.add( SourcePowerLawSpectrum( Emin, Emax, specIndex ) )

Observer

To register particles, an observer has to be defined. In the provided constrained simulations the position of the Milky Way is, by definition, in the center of the volume.

In [6]:
filename_output = 'output.txt'

filename_output = 'data/output_MW.txt'

obsPosition = Vector3d(0.5*size,0.5*size,0.5*size) # position of observer, MW is in center of constrained simulations
obsSize = 800*kpc  ## physical size of observer sphere


## initialize observer that registers particles that enter into sphere of given size around its position
obs = Observer()
obs.add( ObserverSmallSphere( obsPosition, obsSize ) )
## write registered particles to output file
obs.onDetection( TextOutput( filename_output ) )
## choose to not further follow particles paths once detected
obs.setDeactivateOnDetection(True)
## add observer to module list
m.add(obs)

finally run the simulation by

In [7]:
N = 1000

m.showModules()         ## optional, see summary of loaded modules
m.setShowProgress(True) ## optional, see progress during runtime
m.run(source, N, True)  ## perform simulation with N particles injected from source