Solar-MACH¶

Multi-spacecraft longitudinal configuration plotter

The Solar MAgnetic Connection Haus tool (Solar-MACH) is an open-source tool completely written in Python that derives and visualizes the spatial configuration and solar magnetic connection of different observers (i.e., spacecraft or planets) in the heliosphere at different times. For this, the magnetic connection in the interplanetary space is obtained by the classic Parker Heliospheric Magnetic Field (HMF), while in close vicinity of the Sun a Potential Field Source Surface (PFSS) model can be applied to connect the HMF to the solar corona.

GitHub: https://github.com/jgieseler/solarmach
PyPI: https://pypi.org/project/solarmach
conda: https://anaconda.org/conda-forge/solarmach
web app: https://solar-mach.github.io

Please refer to the following paper for more information and cite it if you use this tool in your publication:

Gieseler, J., Dresing, N., Palmroos, C., von Forstner, J. L. F., Price, D. J., Vainio, R., Kouloumvakos A., Rodríguez-García L., Trotta D., Génot V., Masson A., Roth M., Veronig A. (2023). Solar-MACH: An open-source tool to analyze solar magnetic connection configurations. Front. Astronomy Space Sci. 9. doi:10.3389/fspas.2022.1058810

Table of Contents¶

1. Minimal example
2. Example with all the details
3. Example using Stonyhurst coordinates for reference
4. Only obtain data as Pandas DataFrame
5. Advanced plotting options
6. Advanced: edit the figure
7. Ideas for further usage
- 7.1 Loop over multiple datetimes (plots)
- 7.2 Loop over multiple datetimes (only data)
8. Further backmapping with PFSS

Importing¶

In [ ]:

from solarmach import SolarMACH, print_body_list, get_sw_speed, get_gong_map, calculate_pfss_solution

1. Minimal example ¶

Necessary options are a list of wanted spacecraft/bodies and the date of interest.

Note that since version 0.2.3, you don't need to provide a list with solar wind speeds (in km/s) corresponding to the spacecraft/bodies, but you can. If vsw_list is not provided (or as an empty list, vsw_list=[]), it is automatically tried to obtain measured solar wind speeds per spacecraft. If this does not succeed for a spacecraft, a default solar wind speed of 400 km/s is assumed (this can be adjusted with default_vsw, e.g., default_vsw=300).

In [ ]:

body_list = ['Earth', 'Solar Orbiter', 'PSP']
date = '2022-3-1 12:00:00'

Initialize the SolarMACH object for these options:

In [ ]:

sm1 = SolarMACH(date=date, body_list=body_list)

No solar wind speeds defined, trying to obtain measurements...
Using 'ACE' measurements for 'Earth'.

And produce the final plot:

In [ ]:

sm1.plot(plot_sun_body_line=True)

This plot shows a view from the top on the ecliptic plane with the Sun in the center and the Earth (indicated by green symbol) at "6 o'clock". The solid lines give estimations of single field lines of an ideal Parker heliospheric magnetic field connecting the corresponding observers to the Sun, while the dashed lines just indicate the line of sight from each of them to the Sun.

If you do not want or need that the solar wind speeds are obtained from online sources, you can manually define them with vsw_list. Note that each speed corresponds position-wise with the corresponding spacecraft/bodies list:

In [ ]:

vsw_list = [400, 400, 400]    # position-sensitive solar wind speed per body in body_list
body_list = ['Earth', 'Solar Orbiter', 'PSP']
date = '2022-3-1 12:00:00'

sm1a = SolarMACH(date=date, body_list=body_list, vsw_list=vsw_list)
sm1a.plot(plot_sun_body_line=True)

2. Example with all the details ¶

First, get a list of available bodies/spacecraft:

In [ ]:

print(print_body_list().index)

Index(['Mercury', 'Venus', 'Earth', 'Mars', 'Jupiter', 'L1', 'ACE', 'STEREO B',
       'STEREO A', 'SOHO', 'Solar Orbiter', 'PSP', 'BepiColombo', 'MAVEN',
       'Mars Express', 'MESSENGER', 'JUICE', 'Juno', 'Cassini', 'Rosetta',
       'Pioneer10', 'Pioneer11', 'Ulysses', 'Voyager1', 'Voyager2'],
      dtype='object', name='Key')

Provide the necessary options, this time for more spacecraft:

In [ ]:

body_list = ['Mercury', 'Venus', 'Earth', 'Mars', 'STEREO A', 'STEREO B', 'Solar Orbiter', 'PSP', 'BepiColombo']
vsw_list = len(body_list) * [350]  # position-sensitive solar wind speed per body in body_list
date = '2021-6-1 12:00:00'

The default coordinate system is Carrington coordinates, alternatively one could select the Earth-centered Stonyhurst coordinate system:

In [ ]:

coord_sys = 'Carrington'     # 'Carrington' (default) or 'Stoneyhurst'

Now we also want to indicate the position and direction of a flare, and the (assumed) solar wind speed at its location:

In [ ]:

reference_long = 0            # Carrington longitude of reference (None to omit)
reference_lat = 0             # Carrington latitude of reference (None to omit)
reference_vsw = 400           # define solar wind speed at reference

In addition, we explicitly provide all availabe plotting options:

In [ ]:

plot_spirals = True           # plot Parker spirals for each body
plot_sun_body_line = False    # plot straight line between Sun and body
long_offset = 0               # longitudinal offset for polar plot; defines where Earth's longitude is (by default 270, i.e., at "6 o'clock")
transparent = False           # make output figure background transparent
markers = 'numbers'           # use 'numbers' or 'letters' for the body markers (use False for colored squares)
filename = f'Solar-MACH_{date.replace(" ", "_")}.png'  # define filename of output figure

Finally, initializing and plotting with these options. If outfile is provided, the plot will be saved next to the Notebook with the provided filename.

In [ ]:

sm2 = SolarMACH(date=date, body_list=body_list, vsw_list=vsw_list,
                reference_long=reference_long, reference_lat=reference_lat,
                coord_sys=coord_sys)

sm2.plot(plot_spirals=plot_spirals,
         plot_sun_body_line=plot_sun_body_line,
         long_offset=long_offset,
         reference_vsw=reference_vsw,
         transparent=transparent,
         markers=markers,
         outfile=filename
         )

All the data can also be obtained as a Pandas DataFrame for further use:

In [ ]:

df = sm2.coord_table
display(df)

	Spacecraft/Body	Carrington longitude (°)	Carrington latitude (°)	Heliocentric distance (AU)	Longitudinal separation to Earth's longitude	Latitudinal separation to Earth's latitude	Vsw	Magnetic footpoint longitude (Carrington)	Longitudinal separation between body and reference_long	Longitudinal separation between body's mangetic footpoint and reference_long	Latitudinal separation between body and reference_lat
0	Mercury	64.572366	-3.374752	0.456577	-17.161028	-2.767176	350	96.911462	64.572366	96.911462	-3.374752
1	Venus	304.308841	-2.405230	0.718663	-137.424553	-1.797654	350	355.463238	-55.691159	-4.536762	-2.405230
2	Earth	81.733394	-0.607576	1.014084	0.000000	0.000000	350	154.136171	81.733394	154.136171	-0.607576
3	Mars	328.690673	-4.569037	1.657439	-113.042721	-3.961461	350	86.722920	-31.309327	86.722920	-4.569037
4	STEREO A	31.671472	-5.969301	0.963303	-50.061921	-5.361726	350	99.918030	31.671472	99.918030	-5.969301
5	STEREO B	126.320990	4.463536	1.085839	44.587597	5.071112	350	203.548635	126.320990	-156.451365	4.463536
6	Solar Orbiter	342.893742	-1.038420	0.952075	-98.839652	-0.430845	350	50.838628	-17.106258	50.838628	-1.038420
7	PSP	142.038810	3.210198	0.715577	60.305417	3.817774	350	192.923248	142.038810	-167.076752	3.210198
8	BepiColombo	331.970837	-3.538780	0.807266	-109.762557	-2.931204	350	29.390736	-28.029163	29.390736	-3.538780

In [ ]:

df['Heliocentric distance (AU)'].values

Out[ ]:

array([0.45657717, 0.71866253, 1.0140839 , 1.65743876, 0.9633026 ,
       1.08583866, 0.95207518, 0.7155775 , 0.80726552])

3. Example using Stonyhurst coordinates for reference ¶

Let's take a look at the situation at the first ground-level enhancement (GLE) of solar cycle 25 on 28 October 2021

First, we just provide some options as before:

In [ ]:

body_list = ['STEREO-A', 'Earth', 'BepiColombo', 'PSP', 'Solar Orbiter', 'Mars']
vsw_list = [340, 300, 350, 350, 320, 350]        # position-sensitive solar wind speed per body in body_list
date = '2021-10-28 15:20:00'
coord_sys = 'Stoneyhurst'

# optional parameters
plot_spirals = True           # plot Parker spirals for each body
plot_sun_body_line = True     # plot straight line between Sun and body
transparent = False           # make output figure background transparent
markers = 'letters'           # use 'numbers' or 'letters' for the body markers (use False for colored squares)
filename = f'Solar-MACH_{date.replace(" ", "_")}.png'  # define filename of output figure

But now we want to provide the coordinates of the flare in Stonyhurst coordinates (instead of Carrington).

In [ ]:

reference_long = 2            # Stonyhurst longitude of reference (None to omit)
reference_lat = 26            # Stonyhurst latitude of reference (None to omit)
reference_vsw = 300           # define solar wind speed at reference

Finally, initializing and plotting with these options:

In [ ]:

sm3 = SolarMACH(date=date, body_list=body_list, vsw_list=vsw_list,
                reference_long=reference_long, reference_lat=reference_lat,
                coord_sys=coord_sys)
sm3.plot(plot_spirals=plot_spirals,
         plot_sun_body_line=plot_sun_body_line,
         reference_vsw=reference_vsw,
         transparent=transparent,
         markers=markers,
         outfile=filename
         )

4. Only obtain data as Pandas DataFrame ¶

We can also just obtain a table with the spatial data, without producing a plot at all.

First provide necessary options:

In [ ]:

body_list = ['STEREO-A', 'Earth', 'BepiColombo', 'PSP', 'Solar Orbiter', 'Mars']
vsw_list = [400, 400, 400, 400, 400, 400]        # position-sensitive solar wind speed per body in body_list
date = '2022-6-1 12:00:00'

Then initialize SolarMACH and obtain data as Pandas DataFrame:

In [ ]:

sm4 = SolarMACH(date=date, body_list=body_list, vsw_list=vsw_list)
df = sm4.coord_table
display(df)

	Spacecraft/Body	Carrington longitude (°)	Carrington latitude (°)	Heliocentric distance (AU)	Longitudinal separation to Earth's longitude	Latitudinal separation to Earth's latitude	Vsw	Magnetic footpoint longitude (Carrington)
0	STEREO-A	275.723483	-3.999131	0.961351	-28.467807	-3.361541	400	335.567204
1	Earth	304.191289	-0.637590	1.014043	0.000000	0.000000	400	7.540620
2	BepiColombo	330.303801	-1.980711	0.570648	26.112511	-1.343121	400	5.799167
3	PSP	162.146839	-2.129984	0.068020	-142.044450	-1.492394	400	166.120423
4	Solar Orbiter	108.356580	2.066323	0.933521	-195.834709	2.703913	400	166.604495
5	Mars	16.893904	4.867268	1.384205	-287.297385	5.504858	400	103.046865

If we also provide the reference information, it will be available in the table, too:

In [ ]:

sm4 = SolarMACH(date=date, body_list=body_list, vsw_list=vsw_list,
                reference_long=273, reference_lat=7)
df = sm4.coord_table
display(df)

	Spacecraft/Body	Carrington longitude (°)	Carrington latitude (°)	Heliocentric distance (AU)	Longitudinal separation to Earth's longitude	Latitudinal separation to Earth's latitude	Vsw	Magnetic footpoint longitude (Carrington)	Longitudinal separation between body and reference_long	Longitudinal separation between body's mangetic footpoint and reference_long	Latitudinal separation between body and reference_lat
0	STEREO-A	275.723483	-3.999131	0.961351	-28.467807	-3.361541	400	335.567204	2.723483	62.567204	-10.999131
1	Earth	304.191289	-0.637590	1.014043	0.000000	0.000000	400	7.540620	31.191289	94.540620	-7.637590
2	BepiColombo	330.303801	-1.980711	0.570648	26.112511	-1.343121	400	5.799167	57.303801	92.799167	-8.980711
3	PSP	162.146839	-2.129984	0.068020	-142.044450	-1.492394	400	166.120423	-110.853161	-106.879577	-9.129984
4	Solar Orbiter	108.356580	2.066323	0.933521	-195.834709	2.703913	400	166.604495	-164.643420	-106.395505	-4.933677
5	Mars	16.893904	4.867268	1.384205	-287.297385	5.504858	400	103.046865	-256.106096	-169.953135	-2.132732

Note again that by default all coordinates are given in Carrington coordinates (as indicated in the column titles). To have this data in Stoneyhurst coordinates, define the coord_sys when initilizing SolarMACH:

In [ ]:

sm4a = SolarMACH(date=date, body_list=body_list, vsw_list=vsw_list, coord_sys='Stoneyhurst')
df = sm4a.coord_table
display(df)

	Spacecraft/Body	Stonyhurst longitude (°)	Stonyhurst latitude (°)	Heliocentric distance (AU)	Longitudinal separation to Earth's longitude	Latitudinal separation to Earth's latitude	Vsw	Magnetic footpoint longitude (Stonyhurst)
0	STEREO-A	-28.467809	-3.999131	0.961351	-28.467807	-3.361541	400	31.375912
1	Earth	-0.000002	-0.637590	1.014043	0.000000	0.000000	400	63.349329
2	BepiColombo	26.112509	-1.980711	0.570648	26.112511	-1.343121	400	61.607876
3	PSP	-142.044452	-2.129984	0.068020	-142.044450	-1.492394	400	-138.070868
4	Solar Orbiter	164.165289	2.066323	0.933521	164.165291	2.703913	400	222.413203
5	Mars	72.702613	4.867268	1.384205	72.702615	5.504858	400	158.855574

5. Advanced plotting options ¶

Since version 0.1.6, solarmach provides the option to color a cone-shaped area or an area between two Parker spirals in the heliographic plane. For this, SolarMACH.plot() has three new options:

long_sector: list of 2 numbers: start and stop longitude of a shaded area; e.g. [350, 20] to get a cone from 350 to 20 degree longitude (for long_sector_vsw=None`).
long_sector_vsw: list of 2 numbers: Solar wind speed used to calculate Parker spirals (at start and stop longitude provided by long_sector) between which a reference cone should be drawn; e.g. [400, 400] to assume for both edges of the fill area a Parker spiral produced by solar wind speeds of 400 km/s. If None, instead of Parker spirals, straight lines are used, i.e. a simple cone will be plotted. By default, None.
long_sector_color: String defining the matplotlib color used for the shading defined by long_sector. By default, 'red'.

In addition, it is now possible to plot a set of evenly distributed Parker spirals in the background, see 5.3 Example 3: plot background Parker spirals.

5.1 Example 1: plot cone-shaped area¶

In [ ]:

body_list = ['STEREO-A', 'Earth', 'BepiColombo', 'PSP', 'Solar Orbiter']
vsw_list = [400, 400, 400, 400, 400]
date = '2022-3-11 12:00:00'

sm5a = SolarMACH(date=date, body_list=body_list, vsw_list=vsw_list)
sm5a.plot(long_sector=[290, 328], long_sector_vsw=None, long_sector_color='red')

5.2 Example 2: shade area between two Parker spirals¶

In [ ]:

body_list = ['STEREO-A', 'Earth', 'BepiColombo', 'PSP', 'Solar Orbiter']
vsw_list = [400, 400, 400, 400, 400]
date = '2022-3-11 12:00:00'

sm5b = SolarMACH(date=date, body_list=body_list, vsw_list=vsw_list)
sm5b.plot(long_sector=[290, 328], long_sector_vsw=[400,600], long_sector_color='cyan')

Note that there still is a bug if the speeds in long_sector_vsw differ to some extent; then the plotting might not work as intended.

5.3 Example 3: plot background Parker spirals¶

Since version 0.1.6, solarmach provides the option to plot a set of evenly distributed Parker spirals in the background, using the option background_spirals in SolarMACH.plot():

background_spirals: list of 2 numbers (and 3 optional strings). If defined, plot evenly distributed Parker spirals over 360°. background_spirals[0] defines the number of spirals, background_spirals[1] the solar wind speed in km/s used for their calculation.

Optionally, background_spirals[2], background_spirals[3], and background_spirals[4] change the plotting line style, color, and alpha setting, respectively (default values ':', 'grey', and 0.1).

In [ ]:

body_list = ['STEREO-A', 'Earth', 'BepiColombo', 'PSP', 'Solar Orbiter']
vsw_list = [400, 400, 400, 400, 400]
date = '2022-3-11 12:00:00'

sm = SolarMACH(date=date, body_list=body_list, vsw_list=vsw_list)
sm.plot(background_spirals=[6, 600])

In [ ]:

body_list = ['STEREO-A', 'Earth', 'BepiColombo', 'PSP', 'Solar Orbiter']
vsw_list = [400, 400, 400, 400, 400]
date = '2022-3-11 12:00:00'

sm = SolarMACH(date=date, body_list=body_list, vsw_list=vsw_list)
sm.plot(background_spirals=[6, 600, '-', 'red', 0.5])

6. Advanced: edit the figure ¶

Let's produce again the figure for the Oct 2021 GLE event.

In [ ]:

body_list = ['STEREO-A', 'Earth', 'BepiColombo', 'PSP', 'Solar Orbiter', 'Mars']
vsw_list = [340, 300, 350, 350, 320, 350]  # position-sensitive solar wind speed per body in body_list
date = '2021-10-28 15:20:00'
reference_long = 130           # Carrington longitude of reference (None to omit)
reference_lat = 0             # Carrington latitude of reference (None to omit)
reference_vsw = 400           # define solar wind speed at reference
sm6 = SolarMACH(date=date, body_list=body_list, vsw_list=vsw_list,
                reference_long=reference_long, reference_lat=reference_lat)

But now we prodive the option return_plot_object=True to the plot() call, so that the matplotlib figure and axis object will be returned:

In [ ]:

fig, ax = sm6.plot(plot_spirals=True,
                   plot_sun_body_line=True,
                   transparent=False,
                   markers='numbers',
                   return_plot_object=True
                  )

Now we can make some post-adjustments to the figure (requires of course some Python knowledge):

In [ ]:

ax.set_title("What's that?! A new title!", pad=60)

Out[ ]:

Text(0.5, 1.0, "What's that?! A new title!")

In [ ]:

fig

Out[ ]:

We can also add another red reference arrow to the figure, e.g., to indicate another flare:

In [ ]:

import numpy as np

new_reference_long = 60

arrow_dist = min([sm6.max_dist/3.2, 2.])  # arrow length
ax.arrow(np.deg2rad(new_reference_long), 0.01, 0, arrow_dist, head_width=0.2, head_length=0.07, edgecolor='red', facecolor='red', lw=1.8, zorder=5, overhang=0.2)
ax.set_rmax(sm6.max_dist + 0.3)  # re-set max. radial dist. of plot

In [ ]:

fig

Out[ ]:

7. Ideas for further usage ¶

7.1 Loop over multiple datetimes (plots) ¶

This might be useful to either:

read-in an event catalog, and loop over those datetimes to quickly get the constellations of all these events,
create a series of daily constellation plots, and combine them into one animation:

In [ ]:

body_list = ['Mercury', 'Venus', 'Earth', 'Mars', 'STEREO A', 'STEREO B', 'Solar Orbiter', 'PSP', 'BepiColombo']
vsw_list = len(body_list) * [350]   # position-sensitive solar wind speed per body in body_list
plot_spirals = True                 # plot Parker spirals for each body
plot_sun_body_line = False          # plot straight line between Sun and body
transparent = False                 # make output figure background transparent
markers = 'numbers'                 # use 'numbers' or 'letters' for the body markers (use False for colored squares)

for i in range(2,19,1):    
    j = str(i).rjust(2, '0')
    date = f'2022-6-{j} 12:00:00'
    filename = f'animate_{date[:-9]}.png'        # define filename of output figure

    sm7 = SolarMACH(date=date, body_list=body_list, vsw_list=vsw_list, coord_sys='Stoneyhurst')
    sm7.plot(plot_spirals=plot_spirals,
             plot_sun_body_line=plot_sun_body_line,
             transparent=transparent,
             markers=markers,
             outfile=filename
             )

Get a sorted list of the files just created using glob:

In [ ]:

import glob
files = sorted(glob.glob(filename.replace(f'{i}', '*')))

Build an animated GIF out of these files using imageio:

In [ ]:

import imageio
images_data = []
for filename in files:
    data = imageio.v2.imread(filename)
    images_data.append(data)

# write to animated gif; duration (in ms) defines how fast the animation is.
imageio.mimwrite('solarmach.gif', images_data, format= '.gif', duration=100, loop=0)

When completed, this will have created an animated GIF file solarmach.gif in the same directory as this notebook (as well as a series of files animate_DATE.png that can be deleted).

7.2 Loop over multiple datetimes (only data) ¶

For example, to look for spacecraft alignments, like "When are PSP and Solar Orbiter at the same magnetic footpoint?"

In [ ]:

body_list = ['Mercury', 'Venus', 'Earth', 'Mars', 'STEREO A', 'Solar Orbiter', 'PSP', 'BepiColombo']
vsw_list = len(body_list) * [350]  # position-sensitive solar wind speed per body in body_list

df = []
dates = []
for i in range(1,31,1):
    date = f'2022-6-{i} 12:00:00'

    sm8 = SolarMACH(date=date, body_list=body_list, vsw_list=vsw_list)
    df = df + [sm8.coord_table]
    dates = dates + [date]

In [ ]:

display(df[0])
display(df[1])
display(df[2])

	Spacecraft/Body	Carrington longitude (°)	Carrington latitude (°)	Heliocentric distance (AU)	Longitudinal separation to Earth's longitude	Latitudinal separation to Earth's latitude	Vsw	Magnetic footpoint longitude (Carrington)
0	STEREO-A	233.080604	7.169518	0.958294	-37.595981	2.455532	340	302.733100
1	Earth	270.676585	4.713986	0.993489	0.000000	0.000000	300	353.039432
2	BepiColombo	0.634907	0.905419	0.411322	-270.041678	-3.808567	350	29.801105
3	PSP	217.026554	3.853925	0.623148	-53.650031	-0.860061	350	261.252554
4	Solar Orbiter	267.858104	2.189101	0.803886	-2.818480	-2.524885	320	330.499586
5	Mars	79.738619	-4.884758	1.610970	-190.937966	-9.598744	350	194.379501

	Spacecraft/Body	Carrington longitude (°)	Carrington latitude (°)	Heliocentric distance (AU)	Longitudinal separation to Earth's longitude	Latitudinal separation to Earth's latitude	Vsw	Magnetic footpoint longitude (Carrington)
0	STEREO-A	233.080604	7.169518	0.958294	-37.595981	2.455532	340	302.733100
1	Earth	270.676585	4.713986	0.993489	0.000000	0.000000	300	353.039432
2	BepiColombo	0.634907	0.905419	0.411322	-270.041678	-3.808567	350	29.801105
3	PSP	217.026554	3.853925	0.623148	-53.650031	-0.860061	350	261.252554
4	Solar Orbiter	267.858104	2.189101	0.803886	-2.818480	-2.524885	320	330.499586
5	Mars	79.738619	-4.884758	1.610970	-190.937966	-9.598744	350	194.379501

	Spacecraft/Body	Carrington longitude (°)	Carrington latitude (°)	Heliocentric distance (AU)	Longitudinal separation to Earth's longitude	Latitudinal separation to Earth's latitude	Vsw	Magnetic footpoint longitude (Carrington)
0	STEREO-A	233.080604	7.169518	0.958294	-37.595981	2.455532	340	302.733100
1	Earth	270.676585	4.713986	0.993489	0.000000	0.000000	300	353.039432
2	BepiColombo	0.634907	0.905419	0.411322	-270.041678	-3.808567	350	29.801105
3	PSP	217.026554	3.853925	0.623148	-53.650031	-0.860061	350	261.252554
4	Solar Orbiter	267.858104	2.189101	0.803886	-2.818480	-2.524885	320	330.499586
5	Mars	79.738619	-4.884758	1.610970	-190.937966	-9.598744	350	194.379501

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display(dates)

['2022-6-1 12:00:00',
 '2022-6-2 12:00:00',
 '2022-6-3 12:00:00',
 '2022-6-4 12:00:00',
 '2022-6-5 12:00:00',
 '2022-6-6 12:00:00',
 '2022-6-7 12:00:00',
 '2022-6-8 12:00:00',
 '2022-6-9 12:00:00',
 '2022-6-10 12:00:00',
 '2022-6-11 12:00:00',
 '2022-6-12 12:00:00',
 '2022-6-13 12:00:00',
 '2022-6-14 12:00:00',
 '2022-6-15 12:00:00',
 '2022-6-16 12:00:00',
 '2022-6-17 12:00:00',
 '2022-6-18 12:00:00',
 '2022-6-19 12:00:00',
 '2022-6-20 12:00:00',
 '2022-6-21 12:00:00',
 '2022-6-22 12:00:00',
 '2022-6-23 12:00:00',
 '2022-6-24 12:00:00',
 '2022-6-25 12:00:00',
 '2022-6-26 12:00:00',
 '2022-6-27 12:00:00',
 '2022-6-28 12:00:00',
 '2022-6-29 12:00:00',
 '2022-6-30 12:00:00']

8. Further backmapping with PFSS ¶

A recent extension to Solar-MACH is the ability to further extend the magnetic connection of an observer to the close vicinity of the Sun using a Potential Field Source Surface (PFSS) model that connects the heliospheric magnetic field (HMF) to the solar corona.

Let's first load again Solar-MACH for the April 17, 2021 event. We will use the outputs of it as inputs for the PFSS model.

Note that we do not pre-define the solar wind speeds per spacecraft with vsw_list, but use the interal function to try to obtain the actual measured values.

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date = '2021-4-17 13:00:00'
body_list = ['STEREO-A', 'PSP', 'Earth', 'BepiColombo', 'Solar Orbiter']
coord_sys = 'Carrington'  # 'Stonyhurst' or 'Carrington'

sm9 = SolarMACH(date=date, body_list=body_list, coord_sys=coord_sys)

No solar wind speeds defined, trying to obtain measurements...
Using 'ACE' measurements for 'Earth'.
Body 'BepiColombo' not supported, assuming default Vsw value of 400.0 km/s.

First acquire a GONG (Global Oscillation Network Group) map of the Sun's surface¶

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gong_map = get_gong_map(time=date, filepath=None)

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display(gong_map)

INFO: Missing metadata for solar radius: assuming the standard radius of the photosphere. [sunpy.map.mapbase]
INFO: Missing metadata for solar radius: assuming the standard radius of the photosphere. [sunpy.map.mapbase]

<pfsspy.map.GongSynopticMap object at 0x7f60ee151480>

Observatory	NSO-GONG
Instrument
Detector
Measurement	676.8
Wavelength	676.8
Observation Date	2021-04-17 13:04:00
Exposure Time	Unknown
Dimension	[360. 180.] pix
Coordinate System	heliographic_carrington
Scale	[1. 0.63661914] deg / pix
Reference Pixel	[179.5 89.5] pix
Reference Coord	[76. 0.] deg

Image colormap uses histogram equalization
Click on the image to toggle between units

Based on the map and a boundary condition, calculate a pfss solution¶

Note that depending on the computer used, this process can take up to a few minutes.

In [ ]:

# Set the height of the source surface as a boundary condition for pfss extrapolation
rss = 2.5

Note that you have to define the coordinate system to be used. This has to be the same one as for initializing SolarMACH(date=date, body_list=body_list, coord_sys=coord_sys); the default for that is coord_sys='Carrington'. The system will complain while plotting if the coordinate systems do not agree.

In [ ]:

# Calculate the potential field source surface solution. 
pfss_solution = calculate_pfss_solution(gong_map=gong_map, rss=rss, coord_sys=coord_sys)

Generate a semi-logarithmic PFSS plot (can take a minute)¶

Note that the output figure combines linear and logarithmic scaling for the radial axis: Up to the PFSS at (usually) 2.5 solar radii the figure uses a linear scaling, whereas the main part of the heliosphere is shown with a logarithmic scale in radial distance. This allows to highlight the magnetic connections close to the Sun, while maintaining the connection further out in interplanetary space. The color coding below the PFSS indicates the corresponding latitudes.

Note: 'vary' is a boolean variable that controls if a flux rope should also be calculated around the point at which ballistic backmapping intersects with the source surface. Enabling this option increases computation time.

In [ ]:

sm9.plot_pfss(rss=rss, pfss_solution=pfss_solution, markers='numbers', vary=True)

  0%|          | 0/5 [00:00<?, ?it/s]

And obtain the data as a Pandas DataFrame:

In [ ]:

display(sm9.coord_table)

	Spacecraft/Body	Carrington longitude (°)	Carrington latitude (°)	Heliocentric distance (AU)	Longitudinal separation to Earth's longitude	Latitudinal separation to Earth's latitude	Vsw	Magnetic footpoint longitude (Carrington)
0	STEREO-A	262.418507	-7.208736	0.966691	-53.737948	-1.800815	382.050000	324.943066
1	PSP	106.076768	3.762509	0.421693	-210.079687	9.170431	327.621688	137.939240
2	Earth	316.156455	-5.407921	1.003933	0.000000	0.000000	604.140015	357.425921
3	BepiColombo	182.049262	0.097123	0.629558	-134.107193	5.505044	400.000000	221.271689
4	Solar Orbiter	217.705609	0.400377	0.842629	-98.450846	5.808298	365.543969	275.257324

Look into the sub-pfss field lines with 3D view¶

In [ ]:

sm9.pfss_3d(color_code="object")

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