Comparison of chromospheric diagnostics in a 3D model atmosphere

Abstract

Context. The Hα line, one of the most studied chromospheric diagnostics, is a tracer of magnetic field structures, while the intensity of its line core provides an estimate of the mass density. The interpretation of Hα observations is complicated by deviations from local thermodynamic equilibrium (LTE) or instantaneous statistical equilibrium conditions. Meanwhile, millimetre (mm) continuum radiation is formed in LTE, and therefore the brightness temperatures from Atacama Large Millimetre-submillimetre Array (ALMA) observations provide a complementary view of the activity and the thermal structure of stellar atmospheres. These two diagnostics together can provide insights into the physical properties of stellar atmospheres, such as their temperature stratification, magnetic structures, and mass density distribution. Aims. In this paper, we present a comparative study between synthetic continuum brightness temperature maps at mm wavelengths (0.3 mm to 8.5 mm) and the width of the Hα 6565 Å line. Methods. We used the 3D radiative-transfer codes Multi3D and Advanced Radiative Transfer (ART) to calculate synthetic spectra for the Hα line and the mm continua, respectively, from an enhanced network atmosphere model with non-equilibrium hydrogen ionisation generated with the state-of-the-art 3D radiation magnetohydrodynamics (rMHD) code Bifrost. We use a Gaussian point spread function (PSF) to simulate the effect of ALMA’s limited spatial resolution and calculate the Hα versus mm continuum correlations and slopes of scatter plots for the original and degraded resolution of the whole box, quiet sun, and enhanced network patches separately. Results. The Hα linewidth and mm brightness temperatures are highly correlated and the correlation is highest at a wavelength of 0.8 mm, that is, in ALMA Band 7. The correlation systematically increases with decreasing resolution. On the other hand, the slopes decrease with increasing wavelength. The degradation of resolution does not have a significant impact on the calculated slopes. Conclusions. With decreasing spatial resolution, the standard deviations of the observables, Hα linewidth, and brightness temperatures decrease and the correlations between them increase, but the slopes do not change significantly. These relations may therefore prove useful in calibrating the mm continuum maps observed with ALMA.