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We consider a simple gravitational heating mechanism for the long‐term quenching of cooling flows and star formation in massive dark matter haloes hosting elliptical galaxies and clusters. We showed earlier that the virial shock heating in haloes  ≥10 12  M ⊙   triggers natural quenching in  10 12 –10 13  M ⊙   haloes. Our present analytic estimates and simple simulations argue that the long‐term quenching in haloes  ≥ M  min ∼ 7 × 10 12  M ⊙   could be due to the gravitational energy of cosmological accretion delivered to the inner halo hot gas by cold flows via ram‐pressure drag and local shocks.  M  min  is obtained by comparing the gravitational power of infall into the potential well with the overall radiative cooling rate. The heating wins if the gas inner density cusp is not steeper than  r  −0.5  and if the masses in the cold and hot phases are comparable. The effect is stronger at higher redshifts, making the maintenance easier also at later times. Particular energy carriers into the halo core are cold gas clumps of  ∼10 5 –10 8  M ⊙  . Clumps  ≥10 5  M ⊙   penetrate to the inner halo with sufficient kinetic energy before they disintegrate, but they have to be  ≤10 8  M ⊙   for the drag to do enough work in a Hubble time. Pressure‐confined ∼10 4  K clumps are stable against their own gravity and remain gaseous once below the Bonnor–Ebert mass  ∼10 8  M ⊙  . Such clumps are also immune to tidal disruption. Clumps in the desired mass range could emerge by thermal instability in the outer halo or in the filaments that feed it if the conductivity is not too high. Alternatively, such clumps may be embedded in dark matter subhaloes if the ionizing flux is ineffective, but they separate from their subhaloes by ram pressure before entering the inner halo. Heating by dynamical friction becomes dominant for massive satellites, which can contribute up to one‐third of the total gravitational heating. We conclude that gravitational heating by cosmological accretion is a viable alternative to active galactic nucleus feedback as a long‐term quenching mechanism.

Gravitational quenching in massive galaxies and clusters by clumpy accretion