Temperature gradient in the solar photosphere. Test of a new spectroscopic method and study of its feasibility for ground-based telescopes

Context. The contribution of quiet-Sun regions to the solar irradiance variability is currently unclear. Some solar-cycle variations of the quiet-Sun physical structure, such as the temperature gradient, might affect the irradiance. The synoptic measurement of this quantity along the activity cycle would improve our understanding of long-term irradiance variations. Aims. We intend to test a method previously introduced for measuring the photospheric temperature gradient from high-resolution spectroscopic observation and to study its feasibility with ground-based instruments with and without adaptative optics. Methods. We used synthetic profiles of the FeI 630.15 nm obtained from realistic three-dimensional hydrodynamical simulations of the photospheric granulation and line radiative transfer computations under local thermodynamical equilibrium conditions. Synthetic granulation images at different levels in the line are obtained by convolution with the instrumental point spread function (PSF) under various conditions of atmospheric turbulence, with and without correction by an adaptative optics (AO) system. The PSF are obtained with the PAOLA software, and the AO performances are inspired by the system that will be operating on the Daniel K. Inouye Solar Telescope. Results. We consider two different conditions of atmospheric turbulence, with Fried parameters of 7 cm and 5 cm, respectively. We show that the degraded images lead to both a bias and a loss of precision in the temperature-gradient measurement, and that the correction with the AO system allows us to drastically improve the measurement quality. Conclusions. Long-term synoptic observations of the temperature gradient in the solar photosphere can be undertaken by implement- ing this method on ground-based solar telescopes that are equipped with an AO correction system.