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tokens: including SNe II). We have found a good agreement between the L X – M ⋆ relation of the models and that of observed ETGs, over the whole M ⋆ range. In particular, the largely different observed L X values at the same M ⋆ are reproduced by the sensitivity of the gas flow to many properties characterizing ETGs, as galaxy shape, presence of rotation, presence of star formation, and AGN feedback. The models also show an overall agreement with the observed L X – relation, though of the models is slightly larger than that derived by F17 , for ETGs of the same M ⋆ . The agreement between models and observations holds with and without radiative and mechanical (from AGN winds) AGN feedback. These results imply that the mass input from the stellar population is able to account for a large part of the observed L X , and that—under the assumptions of this work—AGN feedback does not have a significant role in determining the present epoch L X . This is an important conclusion about the fate of recycled stellar material in the presence of AGN feedback, since an outcome of the simulations could have been, for example, a major degassing of the galaxies. Such a different outcome would have implied the necessity to assume other sources of mass (as gas accretion from outside). F17 noticed a good agreement between their results and the predictions of cosmological SPH simulations, where the hot gas mostly originates from a cosmological reservoir from which gas falls into the dark matter halos, is shock-heated, and is then further significantly heated by mechanical feedback due to AGN winds (Choi et al. 2015 ). If this mechanical feedback is not included, the simulations predict an L X far larger than that observed; thus, it is concluded that the AGN plays an important role in determining L X (in addition to M t ). This conclusion is not in contradiction with the results of the present work, which starts after z ≃ 2, and indicates that the AGN has not shaped dramatically the value of L X observed today. In fact the cosmological simulations of Choi et al. ( 2015 ) as of many others (see, e.g., Section 1 ), start from the galaxy formation epoch, and obtain at early times AGN-driven powerful outflows that remove nearly all the gas, and stop star formation. In this sense, the role of the AGN is certainly very important. Our simulations ( N14 , N15 , C17 ) start from these “initial conditions” created at the epoch of quenching, and find that at later epochs the energy injected by the AGN is not crucial in determining L X of the recycled material (while fundamental to stop the recurrent cooling flow and keep the MBH mass low). The conclusions of the two approaches, one including and the other excluding the epoch of galaxy formation and the presence of cosmological gas, then agree, provided that AGN feedback in the first approach is stronger than that found here. In fact, if AGN-driven outflows are to clear the gas out of massive ETGs at early epochs and/or prevent a