Active-galactic-nucleus wind bubble (AGN wind bubble)

An active-galactic-nucleus wind bubble forms when a fast nuclear wind shocks against galactic gas. From inside outward it contains free wind, a reverse shock, shocked wind, a contact discontinuity, a swept-up shocked shell, a forward shock, and undisturbed interstellar gas.

An outflow is momentum driven when shocked driving material cools rapidly, so it cannot retain enough thermal energy to inflate a pressure-supported bubble. The swept shell then receives approximately the direct wind momentum flux, often of order $L/c$.

A swept gas shell of fraction $f$ at radius $R$ in a galaxy of one-dimensional dispersion $\sigma$ has mass $2f{\sigma }^{2}R/G$. Interior non-gas gravity supplies weight $4f(1-f){\sigma }^4/G$. Fully intercepted single-scattering Eddington momentum overcomes it when $M_{\mathrm{BH}}>f(1-f){\sigma }^4{\sigma }_T/(\pi m_p{G}^2)$. This neglects shell self-gravity, central-hole gravity and stored outward kinetic energy; weaker coupling raises the required luminosity.

An outflow is energy driven when cooling of the shocked wind is slow. Its hot bubble stores mechanical energy and expands by pressure work on the swept-up shell.

A quantitative momentum boost needs an energy-transfer convention as well as a momentum input. For one-speed outflow diagnostics, ${\dot{p}}_s={\dot{M}}_s{v}_s$ and ${\dot{E}}_s={\dot{M}}_s{v}_s^2/2$. A driving wind similarly has ${\dot{E}}_w={\dot{p}}_w{v}_w/2$. If a fraction $f_E={\dot{E}}_s/{\dot{E}}_w$ appears in the shell's inferred kinetic energy flux, thenThus the estimate below assumes a wind momentum input of order $L/c$ and an order-one shell energy fraction, with $f_E\sim 1/2$ giving its stated factor. Large momentum transfer is compatible with energy conservation because the swept shell moves much more slowly than the driving wind. Cooling, thermal energy retained inside the bubble and the observational definition of the shell rates change the coefficient.

A momentum boost is a shell momentum flux exceeding the direct input momentum flux. An energy-conserving wind of speed $v_w$ driving a shell of speed $v_s\ll v_w$ can give ${\dot{p}}_s/(L/c)$ of order $v_w/(2v_s)$.