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The continuum intensity at wavelengths around 1 mm provides an excellent wayto probe the solar chromosphere. Future high-resolution millimetre arrays, suchas the Atacama Large Millimeter Array (ALMA), will thus produce valuable inputfor the ongoing controversy on the thermal structure and the dynamics of thislayer. Synthetic brightness temperature maps are calculated on basis ofthree-dimensional radiation (magneto-)hydrodynamic (MHD) simulations. While themillimetre continuum at 0.3mm originates mainly from the upper photosphere, thelonger wavelengths considered here map the low and middle chromosphere. Theeffective formation height increases generally with wavelength and also fromdisk-centre towards the solar limb. The average intensity contributionfunctions are usually rather broad and in some cases they are evendouble-peaked as there are contributions from hot shock waves and coolpost-shock regions in the model chromosphere. Taking into account thedeviations from ionisation equilibrium for hydrogen gives a less strongvariation of the electron density and with it of the optical depth. The resultis a narrower formation height range. The average brightness temperatureincreases with wavelength and towards the limb. The relative contrast dependson wavelength in the same way as the average intensity but decreases towardsthe limb. The dependence of the brightness temperature distribution onwavelength and disk-position can be explained with the differences in formationheight and the variation of temperature fluctuations with height in the modelatmospheres.

Inter-network regions of the Sun at millimetre wavelengths