Open/closed field map

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

First, import required modules

import os
import astropy.constants as const
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

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

if not os.path.exists('190310t0014gong.fits') and not os.path.exists('190310t0014gong.fits.gz'):
    import urllib.request
    urllib.request.urlretrieve(
        'https://gong2.nso.edu/oQR/zqs/201903/mrzqs190310/mrzqs190310t0014c2215_333.fits.gz',
        '190310t0014gong.fits.gz')

if not os.path.exists('190310t0014gong.fits'):
    import gzip
    with gzip.open('190310t0014gong.fits.gz', 'rb') as f:
        with open('190310t0014gong.fits', 'wb') as g:
            g.write(f.read())

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!

[[br, header]] = sunpy.io.fits.read('190310t0014gong.fits')
br = br - np.mean(br)

GONG maps have their LH edge at -180deg in Carrington Longitude, so roll to get it at 0deg. This way the input magnetic field is in a Carrington frame of reference, which matters later when lining the field lines up with the AIA image.

br = np.roll(br, header['CRVAL1'] + 180, axis=1)

Set the model parameters

nrho = 60
rss = 2.5

Construct the input, and calculate the output solution

input = pfsspy.Input(br, 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 = 1
# Number of steps in cos(latitude)
nsteps = 90
phi_1d = np.linspace(0, 2 * np.pi, nsteps * 2 + 1)
theta_1d = np.arccos(np.linspace(-1, 1, nsteps + 1))
phi, theta = np.meshgrid(phi_1d, theta_1d, indexing='ij')
seeds = np.array(coords.sph2cart(r, theta.ravel(), phi.ravel())).T

Trace the field lines

print('Tracing field lines...')
tracer = tracing.FortranTracer()
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, axs = plt.subplots(nrows=2, sharex=True, sharey=True)
ax = axs[0]
input.plot_input(ax)
ax.set_title('Input GONG magnetogram')

ax = axs[1]
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(phi_1d), np.cos(theta_1d), pols, norm=norm, cmap=cmap)

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

plt.tight_layout()
plt.show()