Constructing computationally tractable models of SiI for the 1082.7 nm transition

The Si I 1082.7 nm line is often observed together with the He I 1083.0 nm. The silicon line is assumed to give a measure of the photospheric driver of the chromospheric dynamics observed in the He I 1083.0 nm line. To exploit the diagnostic potential of the silicon line it is of interest to study its line formation. We here analyze physical processes in the formation of the Si I 1082.7 nm line and find that it is formed in non-LTE (NLTE). Its line core intensity is lower than the corresponding LTE value because the source function is below the Planck function due to photon losses in the line itself. In order to make possible full NLTE dynamic calculations of this line we develop a general method for reducing the size of atomic models used in NLTE calculations by representing several physically similar energy levels as one mean level. Our procedure preserves all the important physical properties of the atom that have a bearing on the observable spectrographic properties of the line under study. We apply our procedure to the Si I atom for the 1082.7 nm transition under solar conditions, and we are able to reduce the size of the atomic model from 238 levels and 3152 transitions to 23 levels and 171 transitions with no significant change in the calculated emergent intensity of the 1082.7 nm line. We calculate the response functions for the Si I 1082.7 nm line both in the quiet Sun and above sun-spot umbrae. We find that the line-center Doppler shift has a mean response height to velocity perturbations of 541 km in a quiet-Sun atmosphere and 308 km in a sunspot atmosphere. These numbers depend on the model atmosphere employed.