Authors: Jessica Hamilton (Georgia State University), Viacheslav Sadykov (Georgia State Univesity), Irina Kitiashvili (NASA Ames Research Center), Alan Wray (NASA Ames Research Center)

Investigating the propagation and dissipation of magnetohydrodynamic (MHD) 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 atmosphere in combination with radiative transfer for spectral line synthesis. In this work, we consider the realistic 3-D radiative hydrodynamic simulations of a 6.4 Mm X 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 Å , 6301 Å, and 6302 Å (formed at 0-300 km) and Na I Doublet, 5890 Å and 5896 Å (500-1000 km), with high-resolution for about one hour of solar time. We compute Doppler shifts of the spectral lines and explore their cross-spectrum and oscillation phase differences as a function of wave frequency and spatial resolution. Our analysis shows the presence of upward-propagating acoustic waves in the frequency range of 5 mHz – 9 mHz, as well as atmospheric gravity waves. Signatures of these waves in the oscillation phase-frequency plot are most evident at the spatial scales of ~700 km to ~2 Mm and weaken for the resolutions that are both higher and lower than these scales. We discuss the characteristic spatial scales of the waves from the cross-spectrum and phase-frequency relations. With the use of the power spectrum and computed formation height differences between two spectral lines, we can approximate kinetic energy ratios. In addition, we investigate the limitations of the slit-based spectrometer observations for recovering the properties of upward-propagating acoustic waves.