Aims. We investigate the dependence of the low-mass X-ray binary (LMXB) population in early-type galaxies on stellar age. Methods. We selected 20 massive nearby early-type galaxies from the Chandra archive occupying a relatively narrow range of masses and spanning a broad range of ages, from 1.6 Gyr to more than 10 Gyr, with the median value of 6 Gyr. With the ∼2000 X-ray point sources detected in total, we correlated the specific number of LMXBs in each galaxy with its stellar age and globular cluster (GC) content.Results. We found a correlation between the LMXB population and stellar age: older galaxies tend to possess about ≈50% more LMXBs (per unit stellar mass) than the younger ones. The interpretation of this dependence is complicated by large scatter and a rather strong correlation between stellar age and GC content of galaxies in our sample. We present evidence suggesting that the more important factor may be the evolution of the LMXB population with time. Its effect is further amplified by the larger GC content of older galaxies and correspondingly, the larger numbers of dynamically formed binaries in them. We also found clear evolution of the X-ray luminosity function (XLF) with age, i.e., that younger galaxies have more bright sources and fewer faint sources per unit stellar mass. The XLF of LMXBs in younger galaxies appears to extend significantly beyond 10 39 erg/s. Such bright sources seem to be less frequent in older galaxies. We found that 6 out of ≈12 (ultra-) luminous sources are located in GCs.

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The possible importance of the reaction of a low-mass star to external irradiation for the long-term evolution of compact binaries has been noted only rather recently; first in the context of the evolution of low-mass X-ray binaries (e.g. Podsiadlowski 1991; Harpaz & Rappaport 1991; Frank, King & Lasota 1992; Hameury et al. 1993) and subsequently by Ritter, Zhang & Kolb (1995a,b, hereafter RZK) also for the evolution of cataclysmic variables (CVs). Based on a simple model for describing the reaction of a low-mass star to irradiation RZK showed that CVs can be dynamically unstable against irradiation-induced mass transfer and that, as a consequence of this, mass transfer could occur via cycles in which phases of high, irradiation-enhanced mass transfer alternate with phases of little or no mass transfer. The occurrence of such mass transfer cycles in CVs was subsequently discussed from a more general point of view by King (1995) and King et al. (1995). Whereas the possibility of mass transfer cycles in CVs is now fully recognised, the question as to which systems can undergo such cycles and which cannot has not yet been addressed in detail. It is the purpose of this contribution to provide at least a partial answer to this question.