In the past few years, the ALMA radio telescope has become available for solar observations. ALMA diagnostics of the solar atmosphere are of high interest because of the theoretically expected linear relationship between the brightness temperature at millimeter wavelengths and the local gas temperature in the solar atmosphere. Key for the interpretation of solar ALMA observations is understanding where in the solar atmosphere the ALMA emission originates. Recent theoretical studies have suggested that ALMA bands at 1.2 (band 6) and 3 mm (band 3) form in the middle and upper chromosphere at significantly different heights. We study the formation of ALMA diagnostics using a 2.5D radiative MHD model that includes the effects of ion-neutral interactions (ambipolar diffusion) and nonequilibrium ionization of hydrogen and helium. Our results suggest that in active regions and network regions, observations at both wavelengths most often originate from similar heights in the upper chromosphere, contrary to previous results. Nonequilibrium ionization increases the opacity in the chromosphere so that ALMA mostly observes spicules and fibrils along the canopy fields. We combine these modeling results with observations from IRIS, SDO, and ALMA to suggest a new interpretation for the recently reported dark chromospheric holes, regions of very low temperatures in the chromosphere.

Context. Numerical simulations of the solar chromosphere predict a diverse thermal structure with both hot and cool regions. Observations of plage regions in particular typically feature broader and brighter chromospheric lines, which suggests that they are formed in hotter and denser conditions than in the quiet Sun, but also implies a nonthermal component whose source is unclear. Aims. We revisit the problem of the stratification of temperature and microturbulence in plage and the quiet Sun, now adding millimeter (mm) continuum observations provided by the Atacama Large Millimiter Array (ALMA) to inversions of near-ultraviolet Interface Region Imaging Spectrograph (IRIS) spectra as a powerful new diagnostic to disentangle the two parameters. We fit cool chromospheric holes and track the fast evolution of compact mm brightenings in the plage region. Methods. We use the STiC nonlocal thermodynamic equilibrium (NLTE) inversion code to simultaneously fit real ultraviolet and mm spectra in order to infer the thermodynamic parameters of the plasma. Results. We confirm the anticipated constraining potential of ALMA in NLTE inversions of the solar chromosphere. We find significant differences between the inversion results of IRIS data alone compared to the results of a combination with the mm data: the IRIS+ALMA inversions have increased contrast and temperature range, and tend to favor lower values of microturbulence (similar to 3-6 km s(-1) in plage compared to similar to 4-7 km s(-1) from IRIS alone) in the chromosphere. The average brightness temperature of the plage region at 1.25 mm is 8500 K, but the ALMA maps also show much cooler (similar to 3000 K) and hotter (similar to 11000 K) evolving features partially seen in other diagnostics. To explain the former, the inversions require the existence of localized low-temperature regions in the chromosphere where molecules such as CO could form. The hot features could sustain such high temperatures due to non-equilibrium hydrogen ionization effects in a shocked chromosphere - a scenario that is supported by low-frequency shock wave patterns found in the MgII lines probed by IRIS.