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Context. The contribution of quiet-Sun regions to the solar irradiancevariability is currently unclear. Some solar-cycle variations of the quiet-Sunphysical structure, such as the temperature gradient, might affect theirradiance. The synoptic measurement of this quantity along the activity cyclewould improve our understanding of long-term irradiance variations. Aims. Weintend to test a method previously introduced for measuring the photospherictemperature gradient from high-resolution spectroscopic observation and tostudy its feasibility with ground-based instruments with and without adaptativeoptics. Methods. We used synthetic profiles of the FeI 630.15 nm obtained fromrealistic three-dimensional hydrodynamical simulations of the photosphericgranulation and line radiative transfer computations under localthermodynamical equilibrium conditions. Synthetic granulation images atdifferent levels in the line are obtained by convolution with the instrumentalpoint spread function (PSF) under various conditions of atmospheric turbulence,with and without correction by an adaptative optics (AO) system. The PSF areobtained with the PAOLA software, and the AO performances are inspired by thesystem that will be operating on the Daniel K. Inouye Solar Telescope. Results.We consider two different conditions of atmospheric turbulence, with Friedparameters of 7 cm and 5 cm, respectively. We show that the degraded imageslead to both a bias and a loss of precision in the temperature-gradientmeasurement, and that the correction with the AO system allows us todrastically improve the measurement quality. Conclusions. Long-term synopticobservations of the temperature gradient in the solar photosphere can beundertaken by implement- ing this method on ground-based solar telescopes thatare equipped with an AO correction system.

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