Note

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# Comparing differential-rotation models¶

How to compare differential-rotation models.

The example uses the `RotatedSunFrame`

coordinate
metaframe in `sunpy.coordinates`

to apply differential rotation to a coordinate.
See Differential rotation using coordinate frames for more details on using
`RotatedSunFrame`

.

```
import matplotlib.pyplot as plt
import astropy.units as u
from astropy.coordinates import SkyCoord
import sunpy.map
from sunpy.coordinates import HeliographicStonyhurst, RotatedSunFrame
from sunpy.data.sample import AIA_335_IMAGE
from sunpy.sun.constants import sidereal_rotation_rate
```

First, we use an AIA observation primarily as a pretty background. We also define the meridian using a two-element coordinate array of the south pole and the north pole at zero longitude.

```
aiamap = sunpy.map.Map(AIA_335_IMAGE)
meridian = SkyCoord(0*u.deg, [-90, 90]*u.deg, frame=HeliographicStonyhurst,
obstime=aiamap.date)
```

Next, we calculate the sidereal rotation period of the Sun. This is the time for a full rotation relative to an inertial reference frame (e.g., distant stars), as opposed to the synodic period, which is the apparent rotation period as seen from an Earth-based observer. Since the Earth orbits the Sun in the same direction as the Sun rotates, the Sun appears to rotate slower for an Earth-based observer.

```
sidereal_period = 360*u.deg / sidereal_rotation_rate
print(sidereal_period)
```

```
25.379994924001014 d
```

We use `RotatedSunFrame`

to rotate the
meridian by one sidereal period using each of the available
differential-rotation models. See
`diff_rot()`

for details on each
model.

```
rotated_meridian = {}
for model in ['howard', 'snodgrass', 'allen', 'rigid']:
rotated_meridian[model] = SkyCoord(RotatedSunFrame(base=meridian,
duration=sidereal_period,
rotation_model=model))
```

Finally, we plot the differentially rotated meridians over the map, using
`draw_quadrangle()`

to conveniently draw a line
of constant longitude in the original frame between two endpoints. (One
could instead use `astropy.visualization.wcsaxes.WCSAxes.plot_coord()`

,
but then `meridian`

would need to consist of a sequence of many points
spanning all latitudes between the two poles to render as desired.)
Note that the “rigid” model appears as the meridian again as expected for a
rotation of exactly one sidereal period.

```
plt.figure()
aiamap.plot(clip_interval=(0.5, 99.9)*u.percent)
colors = {
'howard': 'red',
'snodgrass': 'green',
'allen': 'yellow',
'rigid': 'white',
}
for model, coord in rotated_meridian.items():
aiamap.draw_quadrangle(coord, edgecolor=colors[model],
label=model.capitalize())
plt.legend()
plt.title(f'{sidereal_period:.2f} of solar rotation')
plt.show()
```

**Total running time of the script:** ( 0 minutes 1.055 seconds)