Abstract
Aims. Our aim is to investigate the role of acoustic and magneto-acoustic waves in heating the solar chromosphere. Observations in strong chromospheric lines are analyzed by comparing the deposited acoustic-energy flux with the total integrated radiative losses. Methods. Quiet-Sun and weak-plage regions were observed in the Ca II 854.2 nm and Hα lines with the Fast Imaging Solar Spectrograph (FISS) at the 1.6-m Goode Solar Telescope on 2019 October 3 and in the Hα and Hβ lines with the echelle spectrograph attached to the Vacuum Tower Telescope on 2018 December 11 and 2019 June 6. The deposited acoustic energy flux at frequencies up to 20 mHz was derived from Doppler velocities observed in line centers and wings. Radiative losses were computed by means of a set of scaled non-local thermodynamic equilibrium 1D hydrostatic semi-empirical models obtained by fitting synthetic to observed line profiles. Results. In the middle chromosphere (h = 1000–1400 km), the radiative losses can be fully balanced by the deposited acoustic energy flux in a quiet-Sun region. In the upper chromosphere (h > 1400 km), the deposited acoustic flux is small compared to the radiative losses in quiet as well as in plage regions. The crucial parameter determining the amount of deposited acoustic flux is the gas density at a given height. Conclusions. The acoustic energy flux is efficiently deposited in the middle chromosphere, where the density of gas is sufficiently high. About 90% of the available acoustic energy flux in the quiet-Sun region is deposited in these layers, and thus it is a major contributor to the radiative losses of the middle chromosphere. In the upper chromosphere, the deposited acoustic flux is too low, so that other heating mechanisms have to act to balance the radiative cooling.
Highlights
The solar chromosphere is hotter than the photosphere and the increase in temperature in semi-empirical models of the chromosphere cannot be explained by radiative heating
Quiet-Sun and weak-plage regions were observed in the Ca ii 854.2 nm and Hα lines with the Fast Imaging Solar Spectrograph (FISS) at the 1.6-m Goode Solar Telescope on 2019 October 3 and in the Hα and Hβ lines with the echelle spectrograph attached to the Vacuum Tower Telescope on 2018 December 11 and 2019 June 6
Radiative losses were computed by means of a set of scaled non-local thermodynamic equilibrium 1D hydrostatic semi-empirical models obtained by fitting synthetic to observed line profiles
Summary
The solar chromosphere is hotter than the photosphere and the increase in temperature in semi-empirical models of the chromosphere cannot be explained by radiative heating. The strong spectral lines of neutral hydrogen, Ca ii, and Mg ii are the most important lines for studying the released radiative energy from the chromosphere (Carlsson et al 2019). The cores of these spectral lines are formed under non-local thermodynamic equilibrium (non-LTE) conditions, where departures from the LTE are important. In the quiet Sun, Vernazza et al (1981) integrated the radiative losses over the height of the chromosphere, obtaining 4600 W m−2. In active regions, these losses are higher by a factor of two to four (Withbroe & Noyes 1977). They have to be balanced by an energy input supplied by various heating mechanisms
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