Formation of solar calcium H and K bright grains

We have simulated the generation of Ca II H-2V bright grains by acoustic shocks. We employ a one-dimensional, non-LTE radiation-hydrodynamic code, with six-level model atoms for hydrogen and singly ionized calcium. We drive acoustic waves through a stratified radiative equilibrium atmosphere by a piston, whose velocity is chosen to match the Doppler shift observed in the Fe I 396.68 nm line in the H line wing, formed at about 260 km above tau(500) = 1. The simulations closely match the observed behavior of Ca II H-2V bright grains down to the level of individual grains. The bright grains are produced by shocks near 1 Mm above tau(500) = 1. Shocks in the mid-chromosphere produce a large source function (and therefore high emissivity) because the density is high enough for collisions to couple the Ca II populations to the local conditions. The asymmetry of the line profile is due to velocity gradients near 1 Mm. Material motion Doppler-shifts the frequency at which atoms emit and absorb photons, so the maximum opacity is located at-and the absorption profile is symmetric about-the local fluid velocity, which is shifted to the blue behind shocks. The optical depth depends upon the velocity structure higher up. Shocks propagate generally into downflowing material, so there is little matter above to absorb the Doppler-shifted radiation. The corresponding red peak is absent because of small opacity at the source function maximum and large optical depth due to overlying material. The bright grains are produced primarily by waves from the photosphere that are slightly above the acoustic cutoff frequency. The precise time and strength of a grain depend upon the interference between these waves near the acoustic cutoff frequency and higher frequency waves. When waves near the acoustic cutoff frequency are weak, then higher frequency waves may produce grains. The ''5 minute'' trapped p-mode oscillations are not the source of the grains, although they can slightly modify the behavior of higher frequency waves.