The Chromospheric Solar Limb Brightening at Radio, Millimeter, Sub-Millimeter, and Infrared Wavelengths

Abstract

Observations of the emission at radio, millimeter, sub-millimeter, and infrared wavelengths in the center of the solar disk validate the autoconsistence of semi-empirical models of the chromosphere. Theoretically, these models must reproduce the emission at the solar limb. In this work, we tested both the VALC and C7 semi-empirical models by computing their emission spectrum in the frequency range from 2 GHz to 10 THz at solar limb altitudes. We calculate the Sunʼs theoretical radii as well as their limb brightening. Non-local thermodynamic equilibrium was computed for hydrogen, electron density, and H − . In order to solve the radiative transfer equation, a threedimensional (3D) geometry was employed to determine the ray paths, and Bremsstrahlung, H − , and inverse Bremsstrahlung opacity sources were integrated in the optical depth. We compared the computed solar radii with high-resolution observations at the limb obtained by Clark. We found that there are differences between the observed and computed solar radii of 12,000 km at 20 GHz, 5000 km at 100 GHz, and 1000 km at 3 THz for both semi-empirical models. A difference of 8000 km in the solar radii was found when comparing our results against the heights obtained from Hα observations of spicules-off at the solar limb. We conclude that the solar radii cannot be reproduced by VALC and C7 semi-empirical models at radio-infrared wavelengths. Therefore, the structures in the high chromosphere provide a better measurement of the solar radii and their limb brightening as shown in previous investigations.

H−photodetachment and radiative attachment for astrophysical applications

“…The photodetachment of H − is well-known to be an important opacity source in a variety of cool stellar atmospheres including the Sun, hydrogen-rich white dwarfs, and M dwarfs [92][93][94]. Its peak over the ∼1-2 eV (1.2 μm to ∼620 nm) photon energy range is in a region relatively devoid of other continuum opacity sources, such as atoms, positive atomic ions, and molecules.…”

Exoplanet transits with next-generation radio telescopes

“…Timing this effect precisely gives a direct measure of the extent of the stellar chromosphere or corona (probing different regions depending on wavelength); depending on the duration of transit and achievable time sampling, this may be a challenging but worthwhile observation. Likewise, the baseline transit shape will differ significantly from the optical because where in the optical regime the Sun and sun-like stars are limb-darkened, they are actually limb-brightened at radio and millimetre wavelengths (Kundu et al 1979;Horne et al 1981;De la Luz 2016), so that instead of having a "u" shape as in the optical, the transit will actually have a "w" shape in the radio. Exoplanetary transits are the only way of detecting this effect in single stars more distant than the Sun without resolving them on extremely long baselines, a key observation for models of stellar chromospheres (Selhorst et al 2011).…”

Preliminary studies of solar limb brightening at 8mm

“…Many of these previous studies have made at 17 GHz. 1,4 Theoretical models 8 predict the solar brightening is caused by the temperature gradient of the solar atmosphere. We only want to study the limb brightening at the intermediate regions of the Sun.…”