single line curve of growth m: molecules cm -2 cm – atm g cm -2 as we increase amount of gas from m 1 to m 3 we see more absorption. Note: No multiple scattering is attempted here. Define Equivalent width

The way Wan is defined, it is a measure of the area Optically thin case Note: W is linear in amount of gas a, and “integrated cross-section” set Then

Optically thick case

Note W is square root in the amount of gas a, the line width α L and integrated crossection S. The quantities a and S are clear to understand. Square root means things are no longer very efficient. Why α L 1/2 ? Reason: We are eating into the far wings, and α L tells us where to stop.

Band Models A band consists of a large number of lines each with intensity S, width α, and spacing δ e.g. Since there are a large number of lines, it is convenient to define some sort of statistical mean transmission over the entire band.

There are two types of band models * (1) Elsasser type models (a) v i equally spaced (b) s i all equal α i (2) Goody type models ; Godson (a) v i random (b) S has a distribution P(s, σ ) such that s = σ (Malkmus) ( * ) Analytic Computer age “band models” k – distributions spectral mapping technique

Godson Goody Malkmus Godson Elssasser : Regular

Elsasser Model Infinite band Note that is a measure of the packing of lines One line (4.66) (4.67) Langest contribution to (4.66) is n≡0 term

Goody’s random band Lorentz Define probability distribution Given m, the system has a chance to Sample range of weak and string lines exponential