Shadow and photon ring of black hole in asymptotically safe gravity

In this paper, we focus on discussing the influence of thin disk accretion and asymptotically safe (AS) gravity correction parameter on the shadow and photon ring of black holes. For the thin disk accretion, the dark region is the shadow of the black hole, and the bright photon ring is composed of Direct image, lensing ring and Photon ring. For the specific intensity of the radiation source of the accretion disk, we consider three different emission profile models. For the second-order attenuation function model in which emission starts from the innermost circular orbit, Direct image, lensing ring and Photon ring can be clearly distinguished. The Direct image contributes most of the brightness, and the lensing ring contributes a small portion, while the contribution of the Photon ring can almost be ignored. And the peak value of the corresponding observed intensity decreases with the increase of the AS gravity parameter, that is, the corresponding brightness of the photon ring darkens as correction parameter increases. For the third-order attenuation function model in which the emission begins at the radius of the photon sphere, lensing ring and Photon ring are superimposed on the direct radiation. Thus a new extreme value of the observed intensity emerges, and the extreme value increases with the increase of the AS gravity parameter, which leads to observed photon ring brighter. For the anti-trigonometric attenuation function model in which the radiation starts from the event horizon, the superposition range of lensing ring and Photon ring on the direct radiation becomes larger, which makes photon ring wider. The smaller the AS gravity parameter is, the more difficult it is to distinguish the lensing ring and Photon ring, and the photon ring gets brighter. In short, the results show that the shadow radius decreases with the increase of the AS correction parameter. For different AS gravity correction parameters, the light intensity of emission source, especially emission profiles of the observed intensity are significantly different, resulting in obvious differences for the shadow and bright photon ring of the black hole.