The effects of irradiation of the low mass companion in a low-mass X-ray binary or a cataclysmic variable have received much attention in the recent years. In cataclysmic variables, the external illumination flux due to accretion onto the primary compact object is comparable to the intrinsic stellar flux produced by nuclear reactions, whereas this external flux exceeds by orders of magnitude that of the secondary in low-mass X-ray binaries. A fraction of the illumination flux is absorbed in optically thin regions of the secondary photosphere, and this may result in the formation of a wind (see e.g. London et al. 1981; Ruderman et al. 1989; Tavani & London 1993), which can in turn affect the long term evolution of the system. We shall not discuss this effect here, but instead consider energy deposition below the photosphere of the secondary.
Early calculations in the case of low-mass X-ray binaries (Podsiadlowski 1991; Harpaz & Rappaport 1991) in which it was assumed that the secondary is illuminated in a spherically symmetric manner showed a quite dramatic effect. The intrinsic luminosity of the secondary star is very efficiently blocked by the impinging radiation in the outer convective layers, so that the secondary must expand until it becomes almost fully radiative. The secular evolution is then quite different from the standard case, namely the systems rapidly evolve towards longer periods, with mass transfer rates close to or above the Eddington limit. This would have accounted for the fact that the period distribution of LMXBs seems to be significantly different from that of cataclysmic variables, showing a lack of systems at short periods. This would have also increased by a large factor the number of LMXBs, making it compatible with what is required to account for the observed density of millisecond pulsars which are believed to be the descendants of LMXBs (Frank et al. 1992). However, the spherically symmetric assumption is obviously incorrect, and it was later shown by Hameury et al. (1993) and confirmed by Harpaz & Rappaport (1995) that the unilluminated side can efficiently cool the secondary. The secular evolution of LMXBs is not drastically different from the unilluminated case, although the short term behaviour is very significantly affected by illumination, and exhibits on and off states, with relatively high mass transfer rates.
In the simpler context of cataclysmic variables, Ritter et al. (1995, 1996a)
showed that irradiation-induced mass transfer cycles could also be present in
these systems; King (1995) and King et al. (1995, 1996) discussed from a very
general point of view the occurrence of such mass transfer cycles in CVs. The
existence of these cycles could be responsible for the observed spreading of
mass transfer rates 
for a given orbital period P, whereas models
would predict a fair correlation between 
and P. Ritter et al.
(1996b) showed that, in the bi-polytrope approximation (Kolb & Ritter 1992),
the stability criterion depends critically upon the variation of the
effective temperature of the illuminated star as a function of the
irradiating flux. For modeling the response of the stellar surface to
illumination, they used a very simple one zone model for the
superadiabatic layers of the low-mass secondary. Here, we use detailed
stellar models to calculate the response of the secondary, namely the
secondary luminosity as a function of irradiation, for a range of values of
the surface gravity and unperturbed effective temperature. We give our
results in a tabular form that can be used to calculate the evolution of a
compact system in the presence of illumination. The advantage of this
formulation is that it can be used in bi-polytropic codes, which are much
faster that full stellar codes, and thus allow the exploration of a wide
range of parameters, but have to be calibrated.