Context. Due to their wide wavelength coverage across the millimeter to centimeter (mm–cm) range and their increased sensitivity, modern interferometric arrays facilitate observations of the thermal and non-thermal radiation that is emitted from different layers in the outer atmospheres of stars. Aims. We study the spectral energy distribution (Sobs(ν)) of main-sequence stars based on archival observations in the mm–cm range with the aim to study their atmospheric stratification as a function of stellar type. Methods. The main-sequence stars with significant detection in mm bands were identified in the ALMA Science Archive. These data were then complemented with spectral flux data in the extreme ultraviolet to cm range as compiled from various catalogues and observatory archives. We compared the resultant Sobs(ν) of each star with a photospheric emission model (Smod(ν)) calculated with the PHOENIX code. The departures of Sobs(ν) from Smod(ν) were quantified in terms of a spectral flux excess parameter (ΔS∕Smod) and studied as a function of stellar type. Results. The initial sample consists of 12 main-sequence stars across a broad range of spectral types from A1 to M3.5 and the Sun-as-a-star as reference. The stars with Teff = 3000–7000 K (F–M type) showed a systematically higher Sobs(ν) than Smod(ν) in the mm–cm range. Their ΔS∕Smod exhibits a monotonic rise with decreasing frequency. The steepness of this rise is higher for cooler stars in the Teff = 3000–7000 K range, although the single fully convective star (Teff ~ 3000 K) in the sample deviates from this trend. Meanwhile, Sobs(ν) of the A-type stars agrees with Smod(ν) within errors. Conclusions. The systematically high ΔS∕Smod in F–M stars indicates hotter upper atmospheric layers, that is, a chromosphere and corona in these stars, like for the Sun. The mm–cm ΔS∕Smod spectrum offers a way to estimate the efficiency of the heating mechanisms across various outer atmospheric layers in main-sequence stars, and thereby to understand their structure and activity. We emphasise the need for dedicated surveys of main-sequence stars in the mm–cm range.

Context. An activity indicator, which can provide a robust quantitative mapping between the stellar activity and the physical properties of its atmosphere, is important in exploring the evolution of the observed active phenomena across main-sequence stars of different spectral types. Common activity indicators do provide qualitative correlations with physical properties such as Teff and the rotation period, among others. However, due to the large variability in their values, even for a single star, defining robust quantitative mappings between activity and physical properties is difficult. Millimetre (mm) wavelengths probe the different atmospheric layers within the stellar chromosphere, providing a tomographic view of the atmospheric dynamics. Aims. The project aims to define a robust activity indicator by characterising mm brightness temperature spectra (TB(ν)) of the cool main-sequence stars (Teff ∼ 5000–7000 K) compiled by Paper I in this series. The sample contains 13 stars, including the Sun. Methods. We derived the mm TB(ν) spectral indices (αmm) for cool stars, including the Sun, based on observations in the 30–1000 GHz range. The derived values for αmm are explored as a function of various physical parameters and empirical power-law functions were derived. We also compared αmm estimates with other activity indicators. Results. Despite the estimation errors, αmm values could distinguish the cool stars well, unlike common activity indicators. The low estimation errors on the derived trends of αmm vs. physical parameters suggest that αmm could be a robust activity indicator. Conclusions. We note that αmm, which is linked to chromospheric thermal stratification and activity in cool stars, can well distinguish and physically characterise the stars more robustly than common activity indicators. We emphasise the need for multi-frequency data across the mm band for stars, with a range of physical parameters and gathered at multiple epochs during their activity cycles. This will help to explore αmm in a statistically robust manner and to study the emergence of chromospheric heating on the main sequence.