Shadows of quintessential dark energy black holes in the domain of outer communication

The rotating black holes in the quintessential dark energy correspond to three horizons: inner, outer, and quintessential horizon. The domain of outer communication is the region between outer and quintessential horizon. Here, in this work we study the photon region and shadows of the quintessential dark energy black holes when the observer stays statically in the domain of outer communication. The quintessential dark energy black holes shadow characterizes by its mass $(M)$, spin parameter $(a)$, quintessential dark energy parameter $(\omega_q)$, and normalization factor $(\gamma)$. The dark energy parameter $\omega_q$ can take values in between $-1.1<\omega_q<-1/3$ and follows the equation of state $\omega_q$=pressure$(p)$/energy density($\rho_q)$. This state parameter significantly affects the shape and size of the black hole shadow. We generalize all the geodesic equations of motion for $\omega_q$ and obtain relation to visualize the black hole shadow by a static observer at any arbitrary distance in the domain of outer communication. We analytically estimate the black hole shadow observables: radius $R_s$, distortion parameter $\delta_s$ and the shadow area $A$. Using the numerical values of shadow radius $R_s$ and area $A$, we obtain the angular diameter of the black hole shadow. The angular size of the M87 and Sgr A$^*$ black holes are $\ 42 \pm 3 \mu a s$ and $48.7 \pm 7 \mu a s $ respectively as observe by Event Horizon Telescope (EHT). In this case, the angular diameter of the black hole shadow increases with the quintessence parameter $\omega_q$ and takes values $\theta_d \approx 20 \pm 3{^o}$ with the parameter $-0.66 \leq \omega_q \leq -0.62$ for the static observer at $r_o=5M$ in the domain of outer communication.