A 2.5-dimensional viscous, resistive, advective magnetized accretion-outflow coupling in black hole systems: A higher order polynomial approximation. I

The correlated and coupled dynamics of accretion and outflow around black holes (BHs) are essentially governed by the fundamental laws of conservation as outflow extracts matter, momentum and energy from the accretion region. Here we analyzed a robust form of 2.5-dimensional viscous, resistive, advective magnetized accretion-outflow coupling in BH systems, in the mean field magnetohydrodynamical (MHD) regime. We solve the complete set of coupled MHD conservation equations self-consistently, through invoking a generalized polynomial expansion in two dimensions. We perform a critical analysis of accretion-outflow region and provide a complete quasi-analytical family of solutions for advective flows. We obtain the physical plausible outflow solutions at high turbulent viscosity parameter $\alpha \, (\ge 0.3)$, and at a reduced scale-height, as magnetic stresses compress or squeeze the flow region. We found that the value of the large-scale poloidal magnetic field $\bar B_P$ is enhanced with increasing geometrical thickness of the accretion flow. On the other hand differential magnetic torque ($-r^2 \bar B_{\varphi} \bar B_z$) increases with the increase in $\dot M$. $\bar B_P$, $-r^2 \bar B_{\varphi} \bar B_z$ as well as the plasma beta $\beta_P$ get strongly augmented with the increase in the value of $\alpha$, enhancing the transport of vertical flux outwards. Our solutions indicate that magnetocentrifugal acceleration plausibly plays a dominant role in effusing out plasma from the radial accretion flow in moderately advective paradigm which are more centrifugally dominated, however in strongly advective paradigm it is likely that the thermal pressure gradient would play a more contributory role in the vertical transport of the plasma.