Galactic backtracking
[1]:
from crpropa import *
# magnetic field setup
B = JF12Field()
#seed = 691342
#B.randomStriated(seed)
#B.randomTurbulent(seed)
# simulation setup
sim = ModuleList()
sim.add(PropagationCK(B, 1e-4, 0.1 * parsec, 100 * parsec))
obs = Observer()
obs.add(ObserverSurface( Sphere(Vector3d(0), 20 * kpc) ))
# obs.onDetection(TextOutput('galactic_backtracking.txt', Output.Event3D))
sim.add(obs)
print(sim)
ModuleList
Propagation in magnetic fields using the Cash-Karp method. Target error: 0.0001, Minimum Step: 0.0001 kpc, Maximum Step: 0.1 kpc
Observer
ObserverSurface: << Sphere:
Center: 0 0 0
Radius: 6.17136e+20
Flag: '' -> ''
MakeInactive: yes
Backtracking a single cosmic ray
Let’s assume we observed a 10 EeV cosmic ray coming from the direction given by longitude and colatitude (1.95, 0.96) radian and want to investigate its direction before having traversed the Galaxy.
Backtracking corresponds to forward-tracking a particle of the opposite charge, thus we select an anti-proton, which in the HEP ID numbering scheme is denoted by a negative sign. Assuming the cosmic ray was a proton the backtracking turns out as follows.
[2]:
pid = - nucleusId(1,1) # (anti-)proton
energy = 10 * EeV
position = Vector3d(-8.5, 0, 0) * kpc
lat = 0.96
lon = 1.95
direction = Vector3d()
direction.setRThetaPhi(1, lat, lon)
p = ParticleState(pid, energy, position, direction)
c = Candidate(p)
sim.run(c)
print(c)
d1 = c.current.getDirection() # direction at Galactic border
print('Galactic deflection %.2f radian' % direction.getAngleTo(d1))
CosmicRay at z = 0
source: Particle -1000010010, E = 10 EeV, x = -0.0085 0 0 Mpc, p = -0.303249 0.760996 0.57352
current: Particle -1000010010, E = 10 EeV, x = -0.0144674 0.011531 0.00759822 Mpc, p = -0.434112 0.764527 0.476493
Galactic deflection 0.16 radian
Backtracking including uncertainties
The impact of the cosmic ray uncertainties on backtracked directions can be investigated with a MC approach. In the following, the cosmic ray energy and direction are varied within the statistical uncertainties before backtracking.
[3]:
R = Random() # CRPropa random number generator
pid = - nucleusId(1,1)
meanEnergy = 10 * EeV
sigmaEnergy = 0.1 * meanEnergy # 10% energy uncertainty
position = Vector3d(-8.5, 0, 0) * kpc
lat0 = 0.96
lon0 = 1.95
meanDir = Vector3d()
meanDir.setRThetaPhi(1, lat0, lon0)
sigmaDir = 0.002 # 1 degree directional uncertainty
lons, lats = [], []
for i in range(100):
energy = R.randNorm(meanEnergy, sigmaEnergy)
direction = R.randVectorAroundMean(meanDir, sigmaDir)
c = Candidate(ParticleState(pid, energy, position, direction))
sim.run(c)
d1 = c.current.getDirection()
lons.append(d1.getPhi())
lats.append(d1.getTheta())
(Optional) Plotting
Finally we are plotting a skymap of the observed direction along with the distribution of directions at the galactic border.
[4]:
%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
# Angle definitions:
# CRPropa uses
# longitude (phi) [-pi, pi] with 0 pointing in x-direction
# colatitude (theta) [0, pi] with 0 pointing in z-direction
# matplotlib expects
# longitude [-pi, pi] with 0 = 0 degrees
# latitude [pi/2, -pi/2] with pi/2 = 90 degrees (north)
lat0 = np.pi/2 - lat0
lats = np.pi/2 - np.array(lats)
plt.figure(figsize=(12,7))
plt.subplot(111, projection = 'hammer')
plt.scatter(lon0, lat0, marker='+', c='black', s=100)
plt.scatter(lons, lats, marker='o', c='blue', linewidths=0, alpha=0.2)
plt.grid(True)
Backtracking to Generate a Lens
The following is an example for a backtracking simulation with a uniform isotropic coverage suitable to generate a magnetic lens. Here, anti-particles are emitted following the healpic scheme to achieve an uniform coverage of the starting direction. Please note that for production use, nside = 1024 should be used and as well a fine binning of rigidities extendig down to ~0.1 EeV is required, e.g. \(10^{16.99}\) eV; \(10^{17.01}\) eV; \(10^{17.03}\) eV … ;. The backtracking data can be post processed with the create-lens.py program.
[9]:
from crpropa import *
import healpy
def backtrackingRun(logE=18., nside=16):
"""Galactic Lens: Backtracking run
Runs the backtracking simulation for a given rigidity and
healpy pixel configuration. Creates a file with detected
candidate properties at r_gal=20*kpc.
Input
-----
logE=18. : float
log10(R/V), rigidity of the backtracked particles
nside=16 : int
healpix parameter, should be increased to ~1024 for production
of real lenses
Returns
-------
"""
# magnetic field setup
B = JF12Field()
seed = 1703202123
B.randomStriated(seed)
B.randomTurbulent(seed)
# simulation setup
sim = ModuleList()
sim.add(PropagationCK(B, 1e-4, 0.1 * parsec, 100 * parsec))
obs = Observer()
obs.add(ObserverSurface( Sphere(Vector3d(0.), 20 * kpc) ))
ofname = 'galactic_backtracking_{:.2f}.h5'.format(logE)
print("Writing output to {}".format(ofname))
out = HDF5Output(ofname, Output.Event3D)
obs.onDetection(out)
sim.add(obs)
pid = - nucleusId(1,1) # (anti-)proton
energy = 10**logE * electronvolt
print("Running at 10**{} eV = {} EeV".format(logE, energy / EeV))
position = Vector3d(-8.5, 0, 0) * kpc
# submit a particle in every direction of a healpix map, 256 per pixel of the
# lens
nparts = healpy.nside2npix(nside)
print('simulating {} particles'.format(nparts))
# Use candidate vector to enable multi core processing
cv = CandidateVector()
print("Preparing Particles ...")
for i in range(nparts):
v = healpy.pix2vec(nside, i)
direction = Vector3d(v[0], v[1], v[2])
p = ParticleState(pid, energy, position, direction)
c = CandidateRefPtr(Candidate(p))
cv.push_back(c)
sim.setShowProgress()
sim.run(cv)
out.close()
print ("Finished!")
[10]:
backtrackingRun()
Writing output to galactic_backtracking_18.00.h5
Running at 10**18.0 eV = 1.0 EeV
simulating 3072 particles
Preparing Particles ...
crpropa::ModuleList: Number of Threads: 8
Run ModuleList
Started Thu Feb 2 12:43:59 2023 : [ Finished ] 100% Needed: 00:00:20 - Finished at Thu Feb 2 12:44:19 2023
Finished!