= Solution
<galactic feedback> couples <star formation> and <black-hole accretion> back to the <gas> supply. Stellar radiation, winds, <supernovae> and <cosmic rays> inject <energy> and <momentum>; <active-galactic-nucleus feedback> adds radiation, jets and winds powered by <accretion>. Heating, <turbulence> or <gas> ejection can suppress later <star formation>, while compression can sometimes promote it. Negative feedback permits self-regulation rather than unrestricted <gas> consumption.
Define the <mass-loading factor> $\eta=\dot M_{\rm out}/\dot M_*$. If the launch speed scales with the <escape speed> and the injected <energy> per stellar <mass> is fixed, <conservation of energy> suggests $\eta\propto v_{\rm esc}^{-2}$; fixed injected <momentum> instead suggests $\eta\propto v_{\rm esc}^{-1}$. Coupling efficiencies, radiative losses and recycling change these ideal scalings. Thermal <energy> injected into dense <gas> can radiate away before driving an outflow, so an <energy> budget alone does not demonstrate effective feedback.
Radio-filled <X-ray> cavities provide a mechanical diagnostic. For a cavity containing a relativistic fluid with $\gamma=4/3$, its <enthalpy> is $\gamma PV/(\gamma-1)\simeq4PV$; dividing by an estimated age gives a mechanical-power estimate. <Chandra X-ray Observatory> observations of the <Perseus cluster> revealed fronts and ripples associated with radio bubbles, interpreted as weak <shocks> and <pressure> waves that can transport jet <energy> into the cooling atmosphere.<A deep Chandra observation of the Perseus cluster: shocks and ripples by A. C. Fabian and others>[2003, abstract: radio bubbles, weak-shock fronts, ripples and the proposed heating/cooling balance]{ref}
The test requires ambient <density> and <temperature> estimates, radio/<X-ray> spatial comparison, projected cavity volumes and an age model. Brightness edges must be distinguished from <absorption> and cool rims; wave <energy> is not automatically thermalized locally. These controls determine whether inferred mechanical heating can actually offset <radiative cooling>.
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