Shadow and deflection angle of rotating black hole in asymptotically safe gravity

We analytically investigate the shadows cast by rotating black holes in the asymptotically safe gravity (ASG) by deriving complete null geodesics and observables using the Hamilton-Jacobi equation and Carter separable method. It turns out that the apparent shape and size of the shadow depend on the ASG parameters ($\zeta, \gamma$) in addition to other black hole parameters ($M, a$). The size of black hole shadows monotonically decreases and shadows get more distorted with increasing values of ASG parameters when compared with the Kerr black hole shadows. In turn, we use shadow observables to estimate black hole spin and ASG parameters. Noteworthy, we find that the deflection angle of the light has been modified by ASG parameters to generalize the Kerr deflection angle, and the corrections in the deflection angle are of $\mathcal{O}(\mu$as). In the vanishing limits of ASG parameters, our results smoothly reduced to the Kerr black holes. The inferred circularity deviation $\Delta C\leq 0.10$ for the M87* black hole shadow merely constrains the ASG parameter $\zeta$, however, shadow angular diameter $\theta_d=42\pm 3\, \mu$as, within the $1\sigma$ region, places bounds $\zeta\leq 0.1324$ for $\gamma=0.10$.