Search for Missing Links Between Two Extreme Wind Speed Profiles : Dark Energy Accretion and Adiabatic Fluid Accretion

In recent past, the progresses in accretion studies onto relativistically gravitating central objects like a Schwarzschild singularity reveal that the accretion flow must be transonic. For such cases, the radial inward speed gradient can be written as a numerator by denominator form among which the later vanishes somewhere in between infinite distance from the attracter to the event horizon of the same. For sustainability of a physical solutions, the numerator should vanish at the same radial distance where denominator does vanish. From this point, we obtain a second degree first order differential equation of radial inward speed and hence we obtain two branches of flow, namely accretion and wind. For adiabatic accretion case, the wind curve 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, this curve is parallel to the radial velocity axis. Here we face a question. Why there is no fluid speed profiles in between these two extremities. While searching the reasons, we follow that dark energy, if treated as an accreting object, should stay around the central \emph{compact star} and hence will contaminate the metric which propertises 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 parameters of the black hole are 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.

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