Velocity law (velocity vs. distance from the star) in two of our AGB wind models. Both models are based on the MARCS hydrostatic model with T_eff = 3500 K, log  g = −0.5, and solar chemical composition. The red model is computed with velocity at infinite of 12 km s^-1, mass-loss rate of 10^-8  M_⊙ yr^-1, and β exponent of 0.2. The blue model has a velocity at infinite of 6 km s^-1, mass-loss rate of 10^-7  M_⊙ yr^-1, and β exponent of 1.0. We note that a smaller step is taken where the velocity gradient is steepest.

Rb I (left panel) and K I (right panel) line profiles obtained using dynamical models given by the (,Ṁ β) = (1 × 10^-7, 0.2) pair (see Sect. 3.2) for the star IRAS 06300+6058. The hydrostatic model (blue line) is also shown for comparison. The colours have similar meaning in the two panels but in the case of K I, all models were computed with a sligthly higher terminal velocity of 15 kms^-1, as suggested by the blue-shift of the K I line. We note that the red wing of the K I profile is not fully reproduced because of the presence of at least one interstellar component that is not seen in Rb I.

High-resolution optical spectra (in black) and dynamical models that provide the best fits (in red) in the ZrO 6474 Å region for our sample stars. Synthetic spectra obtained for Zr abundances shifted +0.25 dex (in blue) and +0.50 dex (in green) from the adopted values are also shown.

Illustrative example of nine Monte Carlo simulations carried out with the envelope parameters T = 1000 K and v_exp = 10 km s^-1. The density (n, in cm^-3) and the envelope size (R_max, in cm) increase from left to right and from top to bottom, respectively. We show the displacement (in Angstroms) from the rest wavelength (Delta = λ − λ₀, where λ₀ is indicated by a vertical line) to the emergent wavelength distribution.