Using the slope of the brightness temperature continuum as a diagnostic tool for solar ALMA observations

¹ Rosseland Centre for Solar Physics, University of Oslo, Postboks 1029, Blindern, 0315 Oslo, Norway
² Institute of Theoretical Astrophysics, University of Oslo, Postboks 1029, Blindern, 0315 Oslo, Norway
³ Institute for Solar Physics, Department of Astronomy, Stockholm University AlbaNova University Centre, 106 91 Stockholm, Sweden
e-mail: henrik.eklund@astro.su.se

Received: 1 July 2022
Accepted: 9 November 2022

Abstract

Context. The intensity of radiation from the solar atmosphere at millimetre wavelengths is closely related to the plasma temperature, and the formation height of the radiation is wavelength dependent. It follows from this that the slope of the intensity continuum, or the brightness temperature continuum, samples the local gradient of the gas temperature of the sampled layers in the solar atmosphere.

Aims. We aim to show the added information and diagnostics potential of the solar atmosphere that comes with measuring the slope of the brightness temperature continuum.

Methods. We used solar observations from the Atacama Large Millimeter/sub-millimeter Array (ALMA) and estimated and predicted the slope using a numerical three-dimensional radiation-magnetohydrodynamic simulation. The slope was estimated by the differences between observables at wavelengths corresponding to different sub-bands at opposite sides of the ALMA receiver band 3 (2.8–3.2 mm) and band 6 (1.20–1.31 mm).

Results. The sign of the brightness temperature slope indicates temperature changes with increasing height at the sampled layers. A positive sign implies an increase in temperature, while a negative sign implies a temperature decrease. The differences in brightness temperature between the sub-bands across the field of view of the simulation typically span from −0.4 kK to 0.75 kK for band 3 and −0.2 kK to 0.3 kK at band 6. The network patches are dominated by large positive slopes, while the quiet-Sun region shows a mixture of positive and negative slopes. As the slope of the continuum is coupled to the small-scale dynamics, a negative slope is seen typically under quiet-Sun conditions as a result of propagating shock waves and the corresponding post-shock regions. The temporal evolution of the slopes can therefore be used to identify shocks. The observability of the slope of the brightness temperatures is estimated at bands 3 and 6 for different angular resolutions corresponding to ALMA observations. The simulations also show that the intensity of the radiation at bands 3 and 6 can simultaneously originate from several major components at different heights, which is strongly dependent on the small-scale dynamics and is seen in both quiet-Sun and network patches. Our in-depth analysis of selected shock waves that propagating upward in the atmosphere shows that the delay of shock signatures between two wavelengths (e.g., bands 6 and 3) does not necessarily reflect the propagation speed of the shock front, but might be cause by the rate of change in opacity of higher layers at these wavelengths.

Conclusions. The slope of the brightness temperature continuum sampled at different ALMA receiver sub-bands serves as an indicator of the slope of the local plasma temperature at the sampled heights in the atmosphere. This offers new diagnostic possibilities for measuring the underlying physical properties of small-scale dynamic features and thus contributes to the understanding of these features and the related transport of energy and heat in the chromosphere.