Open/closed field map

Creating an open/closed field map on the solar surface.

First, import required modules

import os

import astropy.units as u
import astropy.constants as const
from astropy.coordinates import SkyCoord
import matplotlib.pyplot as plt
import matplotlib.colors as mcolor

import numpy as np
import sunpy.map

import pfsspy
from pfsspy import coords
from pfsspy import tracing
from gong_helpers import get_gong_map

Load a GONG magnetic field map. If ‘gong.fits’ is present in the current directory, just use that, otherwise download a sample GONG map.

gong_fname = get_gong_map()

We can now use SunPy to load the GONG fits file, and extract the magnetic field data.

The mean is subtracted to enforce div(B) = 0 on the solar surface: n.b. it is not obvious this is the correct way to do this, so use the following lines at your own risk!

gong_map = sunpy.map.Map(gong_fname)
# Remove the mean
gong_map = sunpy.map.Map(gong_map.data - np.mean(gong_map.data), gong_map.meta)

Set the model parameters

nrho = 60
rss = 2.5

Construct the input, and calculate the output solution

input = pfsspy.Input(gong_map, nrho, rss)
output = pfsspy.pfss(input)

Finally, using the 3D magnetic field solution we can trace some field lines. In this case a grid of 90 x 180 points equally gridded in theta and phi are chosen and traced from the source surface outwards.

First, set up the tracing seeds

r = const.R_sun
# Number of steps in cos(latitude)
nsteps = 30
lon_1d = np.linspace(0, 2 * np.pi, nsteps * 2 + 1)
lat_1d = np.arcsin(np.linspace(-1, 1, nsteps + 1))
lon, lat = np.meshgrid(lon_1d, lat_1d, indexing='ij')
lon, lat = lon*u.rad, lat*u.rad
seeds = SkyCoord(lon.ravel(), lat.ravel(), r, frame=output.coordinate_frame)

Trace the field lines

print('Tracing field lines...')
tracer = tracing.FortranTracer(max_steps=2000)
field_lines = tracer.trace(seeds, output)
print('Finished tracing field lines')

Plot the result. The to plot is the input magnetogram, and the bottom plot shows a contour map of the the footpoint polarities, which are +/- 1 for open field regions and 0 for closed field regions.

fig = plt.figure()
m = input.map
ax = fig.add_subplot(2, 1, 1, projection=m)
m.plot()
ax.set_title('Input GONG magnetogram')

ax = fig.add_subplot(2, 1, 2)
cmap = mcolor.ListedColormap(['tab:red', 'black', 'tab:blue'])
norm = mcolor.BoundaryNorm([-1.5, -0.5, 0.5, 1.5], ncolors=3)
pols = field_lines.polarities.reshape(2 * nsteps + 1, nsteps + 1).T
ax.contourf(np.rad2deg(lon_1d), np.sin(lat_1d), pols, norm=norm, cmap=cmap)
ax.set_ylabel('sin(latitude)')

ax.set_title('Open (blue/red) and closed (black) field')
ax.set_aspect(0.5 * 360 / 2)

plt.show()