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We present a new chemical evolution model meant to be a first step in theself-consistent study of both optical and X-ray properties of ellipticalgalaxies. Detailed cooling and heating processes in the interstellar medium aretaken into account using a mono-phase one-zone treatment which allows a morereliable modelling of the galactic wind regime with respect to previous work.The model successfully reproduces simultaneously the mass-metallicity,colour-magnitude, the L_X - L_B and the L_X - T relations, as well as theobserved trend of the [Mg/Fe] ratio as a function of sigma, by adopting theprescriptions of Pipino & Matteucci (2004) for the gas infall and starformation timescales. We found that a late secondary accretion of gas from theenvironment plays a fundamental role in driving the L_X - L_B and L_X - Trelations and can explain their large observational scatter. The irondiscrepancy, namely the too high predicted iron abundance in X-ray haloes ofellipticals compared to observations, still persists. On the other hand, wepredict [O/Fe] in the ISM which is in good agreement with the most recentobservations. We suggest possible mechanisms acting on a galactic scale whichmay solve the iron discrepancy. In particular, mixing of gas driven by AGNs maypreserve the gas mass (and thus the X-ray luminosity) while diluting the ironabundance. New predictions for the amounts of iron, oxygen and energy ejectedinto the intracluster medium (ICM) are presented and we conclude that Type Iasupernovae (SNe Ia) play a fundamental role in the ICM enrichment. SNe Iaactivity, in fact, may power a galactic wind lasting for a considerable amountof the galactic lifetime, even in the case for which the efficiency of energytransfer into the ISM per SN Ia event is less than unity.Comment: 16 pages, 9 figures, A&A accepte

Massive elliptical galaxies in X-rays: The role of late gas accretion