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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 "Third" Light
Setup
Let's first make sure we have the latest version of PHOEBE 2.4 installed (uncomment this line if running in an online notebook session such as colab).
Step1:  As always, let's do imports and initialize a logger and a new bundle.
Step2:  Relevant Parameters
An l3_mode parameter exists for each LC dataset, which determines whether third light will be provided in flux units, or as a fraction of the total flux.
Since this is passband dependent and only used for flux measurments - it does not yet exist for a new empty Bundle.
Step3:  So let's add a LC dataset
Step4:  We now see that the LC dataset created an 'l3_mode' parameter, and since l3_mode is set to 'flux' the 'l3' parameter is also visible.
Step5:  l3_mode = 'flux'
When l3_mode is set to 'flux', the l3 parameter defines (in flux units) how much extraneous light is added to the light curve in that particular passband/dataset.
Step6:  To compute the fractional third light from the provided value in flux units, call b.compute_l3s.  This assumes that the flux of the system is the sum of the extrinsic passband luminosities (see the pblum tutorial for more details on intrinsic vs extrinsic passband luminosities) divided by $4\pi$ at t0@system, and according to the compute options.
Note that calling compute_l3s is not necessary, as the backend will handle the conversion automatically.
Step7:  l3_mode = 'fraction'
When l3_mode is set to 'fraction', the l3 parameter is now replaced by an l3_frac parameter.
Step8:  Similarly to above, we can convert to actual flux units (under the same assumptions), by calling b.compute_l3s.
Note that calling compute_l3s is not necessary, as the backend will handle the conversion automatically.
Step9:  Influence on Light Curves (Fluxes)
"Third" light is simply additional flux added to the light curve from some external source - whether it be crowding from a background object, light from the sky, or an extra component in the system that is unaccounted for in the system hierarchy.
To see this we'll compare a light curve with and without "third" light.
Step10:  As expected, adding 5 W/m^3 of third light simply shifts the light curve up by that exact same amount.
Step11:  Influence on Meshes (Intensities)
"Third" light does not affect the intensities stored in the mesh (including those in relative units).  In other words, like distance, "third" light only scales the fluxes.
NOTE
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Python Code:
#!pip install -I "phoebe>=2.4,<2.5"
Explanation: "Third" Light
Setup
Let's first make sure we have the latest version of PHOEBE 2.4 installed (uncomment this line if running in an online notebook session such as colab).
End of explanation
import phoebe
from phoebe import u # units
import numpy as np
import matplotlib.pyplot as plt
logger = phoebe.logger()
b = phoebe.default_binary()
Explanation: As always, let's do imports and initialize a logger and a new bundle.
End of explanation
b.filter(qualifier='l3_mode')
Explanation: Relevant Parameters
An l3_mode parameter exists for each LC dataset, which determines whether third light will be provided in flux units, or as a fraction of the total flux.
Since this is passband dependent and only used for flux measurments - it does not yet exist for a new empty Bundle.
End of explanation
b.add_dataset('lc', times=np.linspace(0,1,101), dataset='lc01')
Explanation: So let's add a LC dataset
End of explanation
print(b.filter(qualifier='l3*'))
Explanation: We now see that the LC dataset created an 'l3_mode' parameter, and since l3_mode is set to 'flux' the 'l3' parameter is also visible.
End of explanation
print(b.filter(qualifier='l3*'))
print(b.get_parameter('l3'))
Explanation: l3_mode = 'flux'
When l3_mode is set to 'flux', the l3 parameter defines (in flux units) how much extraneous light is added to the light curve in that particular passband/dataset.
End of explanation
print(b.compute_l3s())
Explanation: To compute the fractional third light from the provided value in flux units, call b.compute_l3s.  This assumes that the flux of the system is the sum of the extrinsic passband luminosities (see the pblum tutorial for more details on intrinsic vs extrinsic passband luminosities) divided by $4\pi$ at t0@system, and according to the compute options.
Note that calling compute_l3s is not necessary, as the backend will handle the conversion automatically.
End of explanation
b.set_value('l3_mode', 'fraction')
print(b.filter(qualifier='l3*'))
print(b.get_parameter('l3_frac'))
Explanation: l3_mode = 'fraction'
When l3_mode is set to 'fraction', the l3 parameter is now replaced by an l3_frac parameter.
End of explanation
print(b.compute_l3s())
Explanation: Similarly to above, we can convert to actual flux units (under the same assumptions), by calling b.compute_l3s.
Note that calling compute_l3s is not necessary, as the backend will handle the conversion automatically.
End of explanation
b.run_compute(irrad_method='none', model='no_third_light')
b.set_value('l3_mode', 'flux')
b.set_value('l3', 5)
b.run_compute(irrad_method='none', model='with_third_light')
Explanation: Influence on Light Curves (Fluxes)
"Third" light is simply additional flux added to the light curve from some external source - whether it be crowding from a background object, light from the sky, or an extra component in the system that is unaccounted for in the system hierarchy.
To see this we'll compare a light curve with and without "third" light.
End of explanation
afig, mplfig = b['lc01'].plot(model='no_third_light')
afig, mplfig = b['lc01'].plot(model='with_third_light', legend=True, show=True)
Explanation: As expected, adding 5 W/m^3 of third light simply shifts the light curve up by that exact same amount.
End of explanation
b.add_dataset('mesh', times=[0], dataset='mesh01', columns=['intensities@lc01', 'abs_intensities@lc01'])
b.set_value('l3', 0.0)
b.run_compute(irrad_method='none', model='no_third_light', overwrite=True)
b.set_value('l3', 5)
b.run_compute(irrad_method='none', model='with_third_light', overwrite=True)
print("no_third_light abs_intensities: ", np.nanmean(b.get_value(qualifier='abs_intensities', component='primary', dataset='lc01', model='no_third_light')))
print("with_third_light abs_intensities: ", np.nanmean(b.get_value(qualifier='abs_intensities', component='primary', dataset='lc01', model='with_third_light')))
print("no_third_light intensities: ", np.nanmean(b.get_value(qualifier='intensities', component='primary', dataset='lc01', model='no_third_light')))
print("with_third_light intensities: ", np.nanmean(b.get_value(qualifier='intensities', component='primary', dataset='lc01', model='with_third_light')))
Explanation: Influence on Meshes (Intensities)
"Third" light does not affect the intensities stored in the mesh (including those in relative units).  In other words, like distance, "third" light only scales the fluxes.
NOTE: this is different than pblums which DO affect the relative intensities.  Again, see the pblum tutorial for more details.
To see this we can run both of our models again and look at the values of the intensities in the mesh.
End of explanation
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