Search for missing links between two extreme wind speed profiles. Dark energy accretion and adiabatic fluid accretion

In the recent past, progress in accretion studies onto general relativistically gravitating central objects viz. a Schwarzschild singularity reveals that the accretion flow should be transonic. Regarding such cases, radial inward speed gradient might be written as a numerator over denominator form among which the denominator vanishes somewhere in between infinite distance to the event horizon of the attractor. For sustainability of a physical solution, the numerator should also have to be equal to zero at the same radial distance where the denominator does vanish. From this point, using L'Hospital's rule, we obtain a second degree first order differential equation of radial inward speed. Hence, using the initial conditions at the said radial distance, we obtain two branches of flow by the virtue of two first order differential equations. These branches are named as accretion and wind. For adiabatic accretion case, the slope of the wind curve in speed vs radial distance plane is formed to be more or less parallel to the radial distance axis as we move far from the central object. For dark energy accretion, alignment of this curve is parallel to the radial velocity axis. Here we face a question why there is no fluid speed profile in between these two extremities. While searching for the reasons, we follow that dark energy, if treated as an accreting object, should stay around the central compact star and hence will contaminate the metric which properties the compact star. In this research work, we have proposed a model with a rotating black hole embedded in quintessence where quintessence equation of state and spin parameter of the black hole are together working as the regulatory factors of the model. The resulting accretion and wind curves are studied. The Effect of negative pressure of dark energy is found to get catalyzed by the entry of the spin of the black hole. We tally our results with observations of accretion or outflow phenomenon near to different quasars.