Relativistic compact stars coupled with dark energy in Heintzmann spacetime

The literature suggests that dark energy is responsible for the accelerating expansion of the universe due to its negative pressure, therefore, dark energy can be used as a possible option to prevent the gravitational collapse of compact objects into singularities. In this regard, there is a great possibility that dark energy can interact with the compact stellar matter configuration [Phys. Rev. D 103, 084042 (2021)]. In this article, we introduce a physically viable model for celestial compact stars made of isotropic baryonic matter and isotropic dark energy with Heintzmann's ansatz [Zeitschrift f\"ur Physik 228, 489-493 (1969)] in the context of Einstein's gravity. Here, the density of dark energy is assumed to be proportional to the density of baryonic matter. The main focus of the present article is to see the effects of dark energy on the physical properties of the stars. We perform an in-depth analysis of the physical attributes of the model, such as metric function, density, pressure, mass-radius relation, compactness parameter, gravitational and surface redshifts, along with the energy conditions for three well-known compact stars. We analyse the equilibrium of the present model via the generalised Tolman-Oppenheimer-Volkoff equation and the stability with the help of the adiabatic index and Harrison-Zeldovich-Novikov's static stability condition. Moreover, we estimate the solutions representing the maximum masses and the predicted surface radii from the M-R graph for different values of the coupling parameter {\alpha}. All the analyses ensure that the present model is non-singular and physically viable by satisfying all the essential conditions.