A new spectroscopic method for measuring the temperature gradient in the solar photosphere
Authors: Faurobert M. , Criscuoli S. , Carbillet M. , Contursi G. 
Published: August 2020

Context. The contribution of quiet-Sun regions to the solar irradiance variability is currently unclear. Certain solar-cycle variations of the quiet-Sun’s physical structure, such as the temperature gradient, might affect the irradiance. Accurate measurements of this quantity over the course of the activity cycle would improve our understanding of long-term irradiance variations.
Aims. In a previous work, we introduced and successfully tested a new spectroscopic method for measuring the photospheric temperature gradient directly on a geometric scale in the case of non-magnetic regions. In this paper, we generalize this method for moderately magnetized regions that may be encountered in the quiet solar photosphere.
Methods. To simulate spectroscopic observations, we used synthetic Stokes profiles I and V of the magnetic FeI 630.15 nm line and intensity profiles of the non-magnetic FeI 709 nm line computed from realistic three-dimensional magneto-hydrodynamical simulations of the photospheric granulation and line radiative transfer under local thermodynamical equilibrium conditions. We then obtained maps at different levels in the line-wings by convolution with the instrumental point spread function (PSF) under various conditions of atmospheric turbulence – with and without correction by an adaptive optics (AO) system. The PSF were obtained with the PAOLA software and the AO performance is inspired by the system that will be operating on the Daniel K. Inouye Solar Telescope.
Results. We considered different conditions of atmospheric turbulence and photospheric regions with different mean magnetic strengths of 100 G and 200 G. As in non-magnetic cases studied in our previous work, the image correction by the AO system is mandatory for obtaining accurate measurements of the temperature gradient. We show that the non-magnetic line at 709 nm may be safely used in all the cases we have investigated. However, the intensity profile of the magnetic-sensitive line is broadened by the Zeeman effect, which would bias our temperature-gradient measurement. We thus implemented a correction procedure of the line profile for this magnetic broadening in the case of weakly magnetized regions. In doing so, we remarked that in the weak-field regime, the right- and left-hand (I + V and I − V) components have similar shapes, however, they are shifted in opposite directions due to the Zeeman effect. We thus reconstructed the intensity profile by shifting back the I + V and I − V profiles and by adding the re-centered profiles. The measurement then proceeds as in the non-magnetic case. We find that this correction procedure is efficient in regions where the mean magnetic strength is smaller or on the order of 100 G.
Conclusions. The new method we implement here may be used to measure the temperature gradient in the quiet Sun from ground-based telescopes equipped with an efficient AO system. We stress that we derive the gradient on a geometrical scale and not on an optical-depth scale as we would do with other standard methods. This allows us to avoid any confusion due to the effect of temperature variations on the continuum opacity in the solar photosphere.