Calibrating non-parametric morphological indicators from {\it JWST} images for galaxies over $0.5<z<3$

The measurements of morphological indicators of galaxies are often influenced by a series of observational effects. In this study, we utilize a sample of over 800 TNG50 simulated galaxies with log($M_*$/M$_\odot$)$>9$ at $0.5<z<3$ to investigate the differences in non-parametric morphological indicators ($C$, $S$, $Gini$, $M_{\rm 20}$, $A_{\rm O}$, and $D_{\rm O}$) derived from noise-free and high-resolution TNG50 images and mock images simulated to have the same observational conditions as {\it JWST}/NIRCam. We quantify the relationship between intrinsic and observed values of the morphological indicators and accordingly apply this calibration to over 4600 galaxies in the same stellar mass and redshift ranges observed in {\it JWST} CEERS and JADES surveys. We find a significant evolution of morphological indicators with rest-frame wavelength ($\lambda_{\rm rf}$) at $\lambda_{\rm rf}<1$\,$\mu$m, while essentially no obvious variations occur at $\lambda_{\rm rf}>1$\,$\mu$m. The morphological indicators of star-forming galaxies (SFGs) and quiescent galaxies (QGs) are significantly different. The morphologies of QGs exhibit a higher sensitivity to rest-frame wavelength than SFGs. After analyzing the evolution of morphological indicators in the rest-frame V-band (0.5-0.7\,$\mu$m) and rest-frame J-band (1.1-1.4\,$\mu$m), we find that the morphologies of QGs evolve substantially with both redshift and stellar mass. For SFGs, the $C$, $Gini$ and $M_{\rm 20}$ show a rapid evolution with stellar mass at log($M_*$/M$_\odot$)$\geq10.5$, while the $A_{\rm O}$, $D_{\rm O}$ and $A$ evolve with both redshift and stellar mass. Our comparison shows that TNG50 simulations effectively reproduce the morphological indicators we measured from {\it JWST} observations when the impact of dust attenuation is considered.