Mechanism of Outflows in Accretion System: Advective Cooling Cannot Balance Viscous Heating?

TL;DR

This paper investigates the energy balance in accretion flows, showing advective cooling alone cannot offset viscous heating, implying outflows are necessary to carry away excess thermal energy in various accretion regimes.

Contribution

It demonstrates that advective cooling is insufficient to balance viscous heating in steady accretion flows, highlighting the need for outflows in low and high accretion rate regimes.

Findings

Advective cooling accounts for less than 30% of viscous heating.

Outflows are necessary to remove excess thermal energy in low and high accretion rate flows.

Thermal equilibrium cannot be maintained without outflows under the no-outflow assumption.

Abstract

Based on no-outflow assumption, we investigate steady state, axisymmetric, optically thin accretion flows in spherical coordinates. By comparing the vertically integrated advective cooling rate with the viscous heating rate, we find that the former is generally less than 30% of the latter, which indicates that the advective cooling itself cannot balance the viscous heating. As a consequence, for radiatively inefficient flows with low accretion rates such as $\dot M \la 10^{-3} \dot M_{Edd}$, where $\dot M_{Edd}$ is the Eddington accretion rate, the viscous heating rate will be larger than the sum of the advective cooling rate and the radiative cooling one. Thus, no thermal equilibrium can be established under the no-outflow assumption. We therefore argue that in such case outflows ought to occur and take away more than 70% of the thermal energy generated by viscous dissipation. Similarly, for optically thick flows with extremely large accretion rates such as $\dot M \ga 10 \dot M_{Edd}$, outflows should also occur due to the limited advection and the low efficiency of radiative cooling. Our results may help to understand the mechanism of outflows found in observations and numerical simulations.