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The rotating black holes in the quintessential dark energy correspond tothree horizons: inner, outer, and quintessential horizon. The domain of outercommunication is the region between outer and quintessential horizon. Here, inthis work we study the photon region and shadows of the quintessential darkenergy black holes when the observer stays statically in the domain of outercommunication. The quintessential dark energy black holes shadow characterizesby 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 theequation of state $\omega_q$=pressure$(p)$/energy density($\rho_q)$. This stateparameter significantly affects the shape and size of the black hole shadow. Wegeneralize all the geodesic equations of motion for $\omega_q$ and obtainrelation to visualize the black hole shadow by a static observer at anyarbitrary distance in the domain of outer communication. We analyticallyestimate 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 increaseswith the quintessence parameter $\omega_q$ and takes values $\theta_d \approx20 \pm 3{^o}$ with the parameter $-0.66 \leq \omega_q \leq -0.62$ for thestatic observer at $r_o=5M$ in the domain of outer communication.

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