Plot distance projected to the ecliptic plane instead of radial distance (optionally)

[jgieseler]

At the moment, Solar-MACH shows the configuration plot only with respect to longitude and radius. For high latitude orbits (e.g., Solar Orbiter), it might be worthwhile to (optionally) plot the distance projected to the ecliptic plane instead of the radial distance (in spherical coordinates). So in the following picture (where x, y span the ecliptic), using r instead of ρ:

(Figure source. Note that this picture plots the colatitude ф, and not the latitude, which would be 90-ф)

Thanks to @AthKouloumvakos for the idea

[jgieseler]

Maybe rather plot the distance projected to the heliographic equatorial plane (instead of ecliptic plane)? 🤔

[jgieseler]

SolarMACH.plot() now has a new option, plot_distance. It is by default 'heliographic-equator', i.e., for plotting, the spherical radius is projected to the heliographic equatorial plane. For backwards-compatibility (and testing), plot_distance='heliographic-radius' provides the previous behavior, i.e., as distance in the polar plot the value of the actual spherical radius is used.

In the following example, Ulysses coordinates are:

>>> sm.body_dict['Ulysses'][3]
<SkyCoord (HeliographicStonyhurst: obstime=2021-10-20T00:00:00.000, rsun=695700.0 km): 
    (lon, lat, radius) in (deg, deg, AU)
    (124.84379058, 25.40222722, 4.42381195)>

To obtain the projected distance in the heliographic equatorial plane, the SkyCoord object is given in cylindrical coordinates:

>>> sm.body_dict['Ulysses'][3].cylindrical
<CylindricalRepresentation (rho, phi, z) in (AU, deg, AU)
    (3.9961117, 124.84379058, 1.89768371)>

Here, rho is equal to radius * cos(lat) = 3.9961117 AU

• Plot spherical radius projected to the heliographic equatorial plane as distance in polar plot (plot_distance='heliographic-radius'):
  

• Plot value of spherical radius as distance in polar plot (plot_distance='heliographic-equator'):
  

[jgieseler]

Note that for calculating the Parker spiral, the distance projected to the heliographic equatorial plane is used together with the solar rotation according to the actual heliographic latitude! Thus, we get the latitude-dependent Parker spiral (blue and red curve in the following plot) projected to the heliographic equatorial plane (black curve):

(From Sternal, O., 2010. Transport of galactic cosmic rays in different heliospheric magnetic field configurations, https://macau.uni-kiel.de/receive/diss_mods_00005136)

[jgieseler]

Update: With 5196c78, all calculations are carried out in spherical coordinates. Only for the two-dimensional visualization, the coordinates are projected to the heliographic equatorial plane. In the course of this last commit, the plot_distance option has been removed!

[AthKouloumvakos]

So, by default the plot will be made in the 'heliographic-equator' mode?

[jgieseler]

Yes! Before it was actually a mix of two coordinate systems, so it doesn't make sense to continue that.

Of course, one could think of providing another (optional) coordinate system...