2024ApJ...976..138B

We investigate the observable characteristics of the extended atmospheres of asymptotic giant branch (AGB) stars across a wide range of radio and (sub-)millimeter wavelengths using state-of-the-art 1D dynamical atmosphere and wind models over one pulsation period. We also study the relationships between the observable features and model properties. We further study practical distance ranges for observable sources assuming the capabilities of current and upcoming observatories. We present time-variable, frequency-dependent profiles of pulsating AGB stars' atmospheres, illustrating observable features in resolved and unresolved observations, including disk brightness temperature, photosphere radius, and resolved and unresolved spectral indices. Notably, temporal variations in disk brightness temperature closely mirror the temperature variability of the stellar atmosphere. We find that while the photospheric radius decreases due to gas dilution in the layers between consecutive shocks, the increase in the observed stellar radius reflects shock propagation through the atmosphere during the expansion phase, providing a direct measurement method for the shock velocity. Furthermore, our models indicate that enhanced gas temperatures after the passage of a strong shock might be observable in the high-frequency Atacama Large Millimeter/submillimeter Array (ALMA) bands as a decrease in the brightness temperature with increasing frequency. We demonstrate that synthetic observations based on state-of-the-art dynamical atmosphere and wind models are necessary for proper interpretations of current (ALMA and Very Large Array (VLA)) and future (Square Kilometre Array and next-generation VLA) observations and that multiwavelength observations of AGB stars are crucial for empirical studies of their extended atmospheres.