# Formation of Ca II lines¶

In this exercise we will explore the formation of Ca II lines. First, we will work with different model atoms, and adjust the atoms.input file accordingly.

## Working with different atom files¶

We've seen before that atoms can be either PASSIVE or ACTIVE. ACTIVE means they will be treated in full non-LTE, while PASSIVE are only included in background opacity calculations if their transitions are covered by a wavelength used in the calculations (determined by the ACTIVE atoms).

For completeness, we will include a few large atoms as PASSIVE. Create a new atoms.input file with the following atom files:

• MgII-IRIS.atom
• CaII_PRD.atom
• Si.atom
• Al.atom
• Fe.atom
• He.atom
• N.atom
• Na.atom
• S.atom

These are available in the ../../Atoms directory, so adjust the paths. Use LTE_POPULATIONS for all but the H, Ca II and Mg II atoms (use ZERO_RADIATION for these). The population file column can be left empty, but adjust the Nmetal value at the start of atoms.input. Set only CaII_PRD.atom as ACTIVE and run RH.

## Selecting wavelengths for detailed output¶

Look at the output from the previous run. Chose a line of Ca II to work with (e.g. Ca II H or Ca II 854.2 nm). To examine the output in detail not all wavelengths are written to disk (to save space), so we must decide which ones to include. You will need to create a file ray.input that contains the indices of wavelengths to be saved.

The indices of wavelengths are dependent on the model atoms and other input options, so it is handy to examine the previous run so you can identify the indices. For example, after loading the output into data, you can find the indices of 392.8 $< \lambda <$ 394.0 by doing:

data = rh15d.Rh15dout()
wave = data.ray.wavelength
indices = np.arange(len(wave))[(wave > 392.8) & (wave < 394.0)]

We want to save also the wavelength of 500 nm. To make sure it is actually calculated, you can do:

wave.sel(wavelength=500, method='nearest')

and get its index with:

index500 = np.argmin(np.abs(wave.data - 500))

To save this into a file ray.input we do:

f = open('ray.input', 'w')  # this will overwrite any existing file!
f.write('1.00\n')
output = str(len(indices) + 1)
for ind in indices:
output += ' %i' % ind
output += ' %i\n' % index500
f.write(output)
f.close()

And now we run RH again! If you examine the output_ray.hdf5 with ncdump -h or h5dump -H you'll see that it contains several other arrays, such as chi and source function. We will work with these next.

## Calculating optical depths¶

For the detailed output wavelengths, RH saves the monochromatic linear extinction coefficient (per length unit, variable chi) but not the optical depth. We can obtain the optical depths by integrating chi over height. After you have run RH with detailed output and loaded the arrays, you can do:

height = data.atmos.height_scale[0, 0].dropna('height')  # first column
index500 = np.argmin(np.abs(data.ray.wavelength_selected - 500))  # index of 500 nm
tau500 = cumtrapz(data.ray.chi[0, 0, :, index500].dropna('height'), x=-height)
tau500 = np.concatenate([[1e-20], tau500])  # ensure tau500 and height have same size

Info

In the above we make use of .dropna('height'), a method in xarray. This is only needed when you ran RH with the option 15D_DEPTH_ZCUT = TRUE. When TRUE, RH 1.5D will not include the top of the atmosphere, defined as where the temperature first reaches a temperature equal to 15D_TMAX_CUT, another option in keyword.input. The reasoning for this is to save computer time by removing depth points from the calculation, and prevent any numerical instabilities from large gradients when calculating lines formed in the photosphere or chromosphere. When 15D_DEPTH_ZCUT = TRUE, the output files will still have arrays that have all the depth points of the input atmosphere. RH 1.5D will write the missing points with a special fill value (typically 9.96921e+36), which xarray will interpret as NaN. Using .dropna('height') will cause xarray to exclude points with NaN from the calculations.

Now you can plot $\tau_{500}$ vs height:

fig, ax = plt.subplots()
ax.plot(height / 1e6, tau500)  # height in Mm

Now you can answer the following:

• At what height does $\tau$ reach unity at 500 nm? What about in the core of your Ca II line?
• Plot the departure coefficients for the ground Ca II level on a height scale and on a $\tau_{500}$ scale
• Plot the $\tau$=1 height as function of wavelength for the Ca II line

## Source function widget¶

Now that your output files have the detailed output, you can use the SourceFunction widget from rh15d_vis:

rh15d_vis.SourceFunction(data);

And you can answer the following:

• At what height does the source function depart from the Planck function for the wings of the Ca II line? And at the line core?