The dynamics of the solar chromosphere: comparison of model predictions with millimeter-interferometer observations

We analyze the millimeter intensity spectrum expected from the dynamic model of Carlsson & Stein together with the interferometric observations of the quiet Sun obtained at a wavelength of 3.5 mm with the Berkeley-Illinois-Maryland Array. The observational data products (Fourier and wavelet spectra, brightness histograms) are compared with the corresponding products obtained for the Carlsson & Stein (CS) models. We estimate how the limited spatial resolution of the observations influences the comparison with the predictions of chromospheric dynamic models and discuss the limitations of a one-dimensional non-magnetic modeling approach. In addition, we test the effect of the integration time of the BIMA observations on the dynamic signatures. The dependence of the observed brightness variations on spatial resolution is studied by employing artificial image degradation and approximating the obtained dependence by power laws. We are able to establish a correspondence between the CS model predictions and the observational data under assumptions on the horizontal coherence length of the oscillations. The reconstructed brightness rms values indicate that, assuming the coherence length of oscillating elements to be of order of 1, the oscillation power in the observations recorded with 10 resolution agrees within a factor of 2 with the power predicted by the CS model. We argue that millimeter continuum observations promise to be an important diagnostic of chromospheric structure and dynamics. Based on the analysis carried out in this work, the appropriate wavelengths to look for dynamic signatures are in the range 0.8-5.0 mm. Further millimeter interferometric observations with longer sequences and higher spatial resolution are highly desirable along with the development of realistic three-dimensional radiation magnetohydrodynamic simulations.