Authors: Jessica Hamilton (Georgia State University), Viacheslav Sadykov (Georgia State University), Irina Kitiashvili (NASA Ames Research Center, Oana Vesa (Stanford University)

Investigating the propagation and dissipation of acoustic waves in the lower solar atmosphere provides
critical insights into their contribution to chromospheric heating. To diagnose the properties of these waves
via the spectroscopic observations of the quiet Sun, one can use realistic 3-D simulations of the solar atmo-
sphere and combine them with radiative transfer for synthetic spectral line synthesis. We start this work by
considering the realistic 3-D radiative hydrodynamic simulations of a 6.4 Mm×6.4 Mm region of the quiet
Sun by the StellarBox code. Using RH1.5D radiative transfer code, we synthesize five spectral lines formed
in the lower solar atmosphere, Fe I 6713˚A, 6301˚A, and 6302˚A, (formed at 0-300 km) and Na I Doublet,
5890˚A and 5896˚A (500-1000 km), with high 12.5 km resolution for about one hour of the solar time. We
compute Doppler shifts of the spectral lines and explore their cross-spectrum and oscillation phase differ-
ences as a function of wave frequency and spatial resolution. Our analysis shows the most stable presence
of upward-propagating acoustic waves in the frequency range of 5 mHz – 11 mHz and atmospheric gravity
waves for ≤ 3 mHz. Signatures of the high-frequency waves (in terms of stable phase differences and cross-
spectrum behavior) are most evident at the spatial scales of ≥700 km. We discuss the validation of the
synthetic spectrum-based diagnostics with simulation-derived plasma properties. In particular, we note the
agreement of the spectral line formation height differences (based on the strongest correlated heights between
the Doppler and plasma velocities), and the general agreement of the cross-spectra and phase differences up
to ν ∼9 mHz. We discuss the possible reasons for disagreement between the Doppler and plasma velocities
at higher frequencies (ν ≥9 mHz), including non-adiabaticity of acoustic waves and non-locality of the line
formation at those frequencies.