## 1. IntroductionIn the last years much attention has been devoted to the analysis of active galactic nuclei (AGN) ultraviolet variability. In particular the relationship between variability and luminosity in quasars and in Seyfert galaxies has been investigated by many authors (see Paltani & Courvoisier 1997 and references therein). In this framework, Paltani & Courvoisier 1997 were the first to compute variability in the object's rest frame. They found that the variability-versus-luminosity relation is compatible with a power law of slope -0.08. This conclusion does not have a straightforward explanation since a series of discrete, independent (i.e., Poisson distributed) events would produce a slope of which is incompatible with the observed trend. Paltani & Courvoisier 1997 found that to produce the observed slope with a discrete event model it is necessary to suppose that the parameters describing the properties of the events must depend on the average luminosity of the object. From a theoretical point of view, time variability is one of the open problems in understanding the active galactic nuclei physics. As matter of fact not only the above-mentioned relationship between variability and luminosity, but even the observed AGN light curves cannot be easily reproduced by theoretical models. For example the classical accretion disk model (Shakura & Sunyaev 1973) fails, since it is difficult to reconcile to the observed variable emission (Courvoisier & Clavel 1991 ). Even more elaborate models able to produce more realistic spectra by taking into account a hot corona (see e.g. Haardt et al. 1994 and references therein) or comptonization effects (Czerny & Elvis 1987, Ross et al. 1992) have difficulties in explaining the variability features. To explain both the ultraviolet emission and its variability a completely different type of model has been proposed by Terlevich 1992 and by Courvoisier et al. 1996, hereafter Paper I. These models have the common feature of supposing the AGN emission as a superposition of uncorrelated events, supernovae for the former, star collisions for the case of Paper I. In particular the model presented in Paper I has shown that when a very dense cluster of stars surrounds a super massive black hole the energy released in collisions between stars can be comparable to the luminosity observed in galactic nuclei. In addition these energetic star collisions occur at a rate such that the resulting luminosity is highly variable and similar to the observed light curves. For the two above mentioned models reproducing the observed shape of the time evolving emission is not a problem. Hence the relationship between variability and luminosity is an important, non trivial, test. In this framework the analysis presented in this paper has the double purpose of making the stellar collision model of Paper I more realistic and of testing it by comparing its prediction to the variability-luminosity curve. The paper is organized as follows: the model properties, the criteria of the parameter choice and the emission computation procedure are explained in Sects. 2, 3 and 4, respectively. In Sect. 5 the variability is introduced and its dependence on different parameters is illustrated. In Sect. 6 a comparison between our results and those of Paltani & Courvoisier 1997 is discussed. Sect. 7 analyses the influence of an accretion term on our results and Sect. 8 presents the conclusions. © European Southern Observatory (ESO) 2000 Online publication: June 26, 2000 |