Three-dimensional simulations of solar magneto-convection including effects of partial ionization

Astronomy & Astrophysics Volume 618 (October 2018) is just out with a figure from our paper on the cover!

The paper (Khomenko, Vitas, Collados & de Vicente 2018: A&A, ADS) describes the effects of the partial ionization on the structure, dynamics and energy balance of the low chromosphere.

How to display magnetic field lines in IDL?

It is a common problem in visualization of magnetic fields. If we assume that the potential $A$ of the magnetic field is knows, the field lines are, by definition, iso-$A$ curves. The quickest way to display them is by using the CONTOUR procedure. If the potential field is given as a 2D variable potential, then:

IDL> CONTOUR, potential, levels = levels, /xs, /ys

gives:




However, the information here is not complete without showing the actual direction of the field along the lines. It is easy to do it in IDL:

IDL> CONTOUR, potential, levels = levels, /xs, /ys
IDL> CONTOUR, potential, levels = levels, /xs, /ys, path_xy = c
IDL> FOR i = 1, N_ELEMENTS(c)/2-1, 50 DO $     ARROW, c[0, i-1], c[1, i-1], c[0, i], c[1, i], /norm, /solid, hsize = 5         


produces:

It is much better now, but the arrow heads from different field lines make it crowded. If we are interested in individual field lines, we can add color to this:

Effective Lande g-factor (in IDL)

The effective Lande g-factor (Shenstone and Blaire, 1929) is defined for a spectral line. It shows how much the $\sigma$ components of the normal Zeeman triplet are separated from the line center.  The higher the Lande factor is, the line is more sensitive to the magnetic field. It is computed as a combination of g-factors for each of the involved atomic levels. Derivation of the equation can be found, for example, in Landi Degl'Innocenti (1982SoPh...77..285L, see it for more details and for an alternative expression useful in the polarized radiative transfer).

For each of the levels (u for upper, l for lower) in LS coupling holds:
$$g_\mathrm{LS} =\frac{3}{2}+\frac{S (S+1) - L (L+1)}{2J(J+1)}, $$ 
where $L$, $S$ and $J$ are the orbitatl, spin and total angular momentum quantum numbers of the atomic level (note that it is undefined for $J=0$). The effective Lande g-factor is then defined as:
$$\bar{g} = \frac{1}{2}(g_\mathrm{l} +g_\mathrm{u}) + \frac{1}{4}(g_\mathrm{l} - g_\mathrm{u})(J_\mathrm{l}(J_\mathrm{l}+1) - J_\mathrm{u}(J_\mathrm{u}+1)).$$

Here is my IDL code for computing the effective Lande g-factor of a spectral line in LS coupling. At the input the code takes the quantum number of the lower and the upper level of a transition. The numbers may be specified either as an array [L, S, J] or in spectroscopic notation.

Example:

IDL> PRINT, LANDE_FACTOR(lower  = [3., 1, 2.], upper = '3p1.0')
  Upper term: 3p1.0 => l = 1.00000s = 1.00000j = 1.00000
          0.250000

IDL> PRINT, LANDE_FACTOR(lower  = '5F1.0', upper = '5d0.0')
  Lower term: 5f1.0 => l = 3.00000s = 2.00000j = 1.00000
  Upper term: 5d0.0 => l = 2.00000s = 2.00000j = 0.00000
          0.00000

Download: lande_factor.pro