differential_rotation#

sunpy.sun.models.differential_rotation(duration: Unit('s'), latitude: Unit('deg'), *, model='howard', frame_time='sidereal')[source]#

Computes the change in longitude over a duration for a given latitude.

Since the Sun is not a rigid body, different heliographic latitudes rotate with different periods. This is known as solar differential rotation.

Parameters:

duration (Quantity) – Amount of time to rotate over.
latitude (Quantity) – Heliographic latitude.
model (str) – The differential-rotation model to use.

One of:

howard : Use values from Howard et al. (1990)

snodgrass : Use values from Snodgrass et. al. (1983)

allen : Use values from Allen’s Astrophysical Quantities, and simpler equation.

rigid : Use values from sidereal_rotation_rate.
frame_time (str) – If 'sidereal', returns the change in longitude as referenced to distant stars. If 'synodic', returns the apparent change in longitude as observed by the average orbital motion of Earth, which results in a slower rotation rate. Defaults to 'sidereal'.

Returns:

Quantity – The change in longitude

Notes

The rotation rate at a heliographic latitude \(\theta\) is given by

\[A + B \sin^{2} \left (\theta \right ) + C \sin^{4} \left ( \theta \right )\]

where \(A, B, C\) are constants that depend on the model:

Model	A	B	C	Unit
howard	2.894	-0.428	-0.370	microrad/s
snodgrass	2.851	-0.343	-0.474	microrad/s
allen	14.44	-3.0	0	deg/day
rigid	14.1844	0	0	deg/day

1 microrad/s is approximately 4.95 deg/day.

References

Examples

Simple Differential Rotation

Default rotation calculation over two days at 30 degrees latitude:

>>> import numpy as np
>>> import astropy.units as u
>>> from sunpy.sun.models import differential_rotation
>>> differential_rotation(2 * u.day, 30 * u.deg)
<Longitude 27.36432679 deg>

Default rotation over two days for a number of latitudes:

>>> differential_rotation(2 * u.day, np.linspace(-70, 70, 20) * u.deg)
<Longitude [22.05449682, 23.03214991, 24.12033958, 25.210281  ,
            26.21032832, 27.05716463, 27.71932645, 28.19299667,
            28.49196765, 28.63509765, 28.63509765, 28.49196765,
            28.19299667, 27.71932645, 27.05716463, 26.21032832,
            25.210281  , 24.12033958, 23.03214991, 22.05449682] deg>

With rotation model ‘allen’:

>>> differential_rotation(2 * u.day, np.linspace(-70, 70, 20) * u.deg, model='allen')
<Longitude [23.58186667, 24.14800185, 24.82808733, 25.57737945,
        26.34658134, 27.08508627, 27.74430709, 28.28087284,
        28.6594822 , 28.85522599, 28.85522599, 28.6594822 ,
        28.28087284, 27.74430709, 27.08508627, 26.34658134,
        25.57737945, 24.82808733, 24.14800185, 23.58186667] deg>