Abstract. The intensities of submillimeter and millimeter continua, which are formed in LTE and depend linearly on temperature, may be able to provide a test of models of the Solar chromosphere. We have taken a collection of submillimeter and millimeter wave observed brightness temperatures T b of the quiet Sun from the literature and compared it with brightness temperatures computed from the standard static models of Fontenla, Avrett and Loeser (FAL) and the dynamic simulations of Carlsson & Stein (CS). The analysis of the dynamic simulations of Carlsson & Stein reveals that radio emission at millimeter wavelengths is extremely sensitive to dynamic processes in the chromosphere, if these are spatially and temporally resolved. The most striking result is that the dynamic picture of the solar internetwork chromosphere is consistent with currently available millimeter and submillimeter brightness observations. The spectrum obtained by averaging over the spectra from all time-steps of CS simulations provides a good fit to observed temporally and spatially averaged millimeter data in spite of the absence of a permanent temperature rise at low chromospheric heights in the simulations. This does not by itself rule out the presence of a chromospheric temperature rise as present in the FAL models, since a combination of such models also reproduces the (low resolution) data relatively well. Millimeter observations indicate that using radio techniques it is possible to extend observations of the solar oscillatory component to the heights above those previously observed in the photospheric and low chromospheric spectral lines and submillimeter continuum. For more precise diagnostics of chromospheric dynamics, high temporal and spatial resolution interferometric observations in the millimeter-wavelength region would be particularly useful.

The Atacama Large Millimeter/submillimeter Array (ALMA) is a new powerful tool for observing the Sun at high spatial, temporal, and spectral resolution. These capabilities can address a broad range of fundamental scientific questions in solar physics. The radiation observed by ALMA originates mostly from the chromosphere -a complex and dynamic region between the photosphere and corona, which plays a crucial role in the transport of energy and matter and, ultimately, the heating of the outer layers of the solar atmosphere. Based on first solar test observations, strategies for regular solar campaigns are currently being developed. State-of-the-art numerical simulations of the solar atmosphere and modeling of instrumental effects can help constrain and optimize future observing modes for ALMA. Here we present a short technical description of ALMA and an overview of past efforts and future possibilities for solar observations at submillimeter and millimeter wavelengths. In addition, selected numerical simulations and observations at other wavelengths demonstrate ALMA's scientific potential for studying the Sun for a large range of science cases.