2 The basic information and hypotheses

2.1 The filters

All simulations presented hereafter were established on the basis of synthetic photometry. The filter passbands that we used for the XMM-OM photometric system are extracted from the XMM Users' Handbook (Dahlem & Schartel 1999). Their transmission curves result from the product of the transmission curves and/or sensitivity curves of all physical devices in the XMM-OM light path. Namely, we have the filters themselves, three aluminized mirrors, one window at the entry of the detector and the detector response curve. All these curves originate from the same reference as above. The resulting passbands are plotted in Fig. 1a and their physical characteristics are summarized in Table 1. Throughout the rest of this paper, small characters refer to the XMM-OM filters and capital letters refer to the standard ones (i.e. the U, B and V taken from Bessel 1990).

The XMM-OM filter set consists of 3 UV and 3 optical filters, further denoted by uvw2, uvm2, uvw1 and u, b, v respectively, in order of increasing central wavelength. The u, b and v filters are intended to match the Johnson U, B and V (Bessel 1990) filters respectively, but they possess more or less rectangularly shaped passbands, which greatly affects the quality of the match and of the subsequent colour transformations between the two systems. This is especially true for what concerns the (mis)match between the Johnson U and XMM-OM u filters and thus the (U-u) and (U-B) related colour transformations. The XMM-OM u band is characterized by:

• a strong sensitivity in the 3100-3300 Å region, where the ground-based Johnson's U is essentially blind;
• a reduced sensitivity in the critical Balmer decrement region (3850-4100 Å), leading to untransformability between both bands for stars showing Balmer jump (see Sects. 3.1.1, 3.1.6, 3.1.7). As we show later, (U-u) can be evaluated thanks to uvw1.

Figure 1b allows comparison between XMM-OM and standard U, B and V filters.

The UV XMM-OM filters do not correspond to any pre-existing standard system. No transmission measurements below 1800 Å are given in the XMM flight simulator software files, so we added a point with $\sim0\%$ transmission at 1700 Å in the UV filters.

2.2 The stellar spectra

The spectra we used for the synthetic photometry are those of the Kurucz' ATLAS 9 atmosphere models (Kurucz 1992), reddened by the Cardelli interstellar extinction model (Cardelli et al. 1989) with an average reddening law ( R_V=A_V/E(B-V)=3.1) when necessary. Except when otherwise stated, the set of spectra we chose mimics an unreddened solar composition main sequence (MS) since these 55 spectra possess the following characteristics: A_V=0.;  $[\rm Fe/H]=0.$; $\log~g=4.$;   $3500\,{\rm K}\leq T_{\rm eff} \leq 35000\,{\rm K}$. Stars we refer to as giants have $\log~g=3.5$ (Allen 1976), those we refer to as metal poor stars have $[\rm Fe/H]=-1.5$, typical for the halo of our Galaxy. The temperature interval between two adjacent Kurucz models varies along the tracks: it is 250 K below 10000 K, 500 K between 10000 K and 13000 K, 1000 K between 13000 K and 35000 K, and 2500 K between 35000 K and 50000 K.

Throughout the rest of this paper, the MS spectrum with $T_{\rm eff}=9500\,$K was attributed a magnitude of zero in all filters.

All colour transformations established on the basis of the Kurucz spectra were compared with their equivalent obtained with the stellar spectral atlas prepared by Fioc & Rocca-Volmerange (1997, hereafter FRV). This atlas comprises 65 spectra of stars of various luminosity classes (3 supergiants, 30 giants and 32 dwarfs) and spectral types ( $T_{\rm eff}\in[2500,180000]$ K). It was constructed from observed spectra whenever possible (Gunn & Strycker 1983; Heck et al. 1984), from synthetic spectra otherwise (Kurucz 1992; Clegg & Middlemass 1987).

2.3 The stellar locus for the quasar fields

In Sect. 6, we analyse the ability of the XMM-OM photometric system to discriminate between quasars and stars. Therefore, we have to delimit both the quasar (see Sect. 2.4) and the stellar loci in the multidimensional colour space defined by the XMM-OM system. The stellar locus is defined by all the stars that are potential contaminants of the quasar candidate population. When looking at high galactic latitudes, the field stars are halo main sequence stars. We modelize their colours by integrating the emergent fluxes from Kurucz model atmospheres. We represent halo main sequence stars by the whole range of $T_{\rm eff}$, $\log~g=4$ and $[\rm Fe/H]=-1.5$. Due to evolution, only the part for which $T_{\rm eff}\leq 7000\,$K (corresponding to an early F spectral type) is still populated. These latter stars are the major constituents of the field stellar population. The reason why we consider the hotter stars as well is that their colours are close to those of other families of stars. We will use that property in Sect. 6, and discuss it further there.

Disk main sequence stars are also a possible contaminant in a list of quasar candidates. However, only the cool end ( $T_{\rm eff}\leq 7000\,$K) could be a problem and is taken into account. We chose to represent them by a $\log~g=4$ and a solar metallicity. Indeed, the disk is rather thin: it has a typical scale height of 1 kpc, which corresponds to a distance modulus of 10 magnitudes. This means that disk OBA stars are too bright in apparent magnitudes to be mistaken for quasars. Another possible contaminant is constituted by halo giants. We represent them by Kurucz models with the following parameters: $T_{\rm eff}\leq 7000\,{\rm K}$, $\log~g=3$ and $[\rm Fe/H]=-1.5$.

Some hotter stars are also present at high galactic latitudes as trace constituents but since they are bluer, a property they share with low-redshift quasars, they could constitute a strong contaminant in a quasar candidate list. We consider three families. The first one is the Horizontal-Branch (HB) BA stars. These stars have $T_{\rm eff}\geq 10000\,~$K (up to $\sim 30000\,$K). On the HB, the gravity is strongly dependent on the effective temperature: we chose the dependency law we derived by averaging the ones quoted by Moehler et al. (1999) and by Conlon et al. (1991). According to Moehler et al. (1999), the best fit of Kurucz models to HB star's spectra is obtained for metal rich chemical compositions. We adopted $[\rm Fe/H]=0.5$. As noticed by Miller & Mitchell (1988), the population of HB stars corresponds to intrinsically bright objects and is observed to tail-off at faint magnitudes due to the finite dimension of the halo.

A second family is constituted of the subdwarfs of spectral type OB (sd OB). Their evolutionary status is still somewhat uncertain but they are usually associated to the Extended Horizontal Branch and to the evolution thereof (see Caloi 1989), although some authors refer to some of them as being post-AGB objects. We represent them by Kurucz models with $T_{\rm eff}$ between $20000\,$K and $50000\,$K (see Conlon et al. 1991 but also Table 1 of Lenz et al. 1998), $\log~g=5$ and solar metallicity.

Finally, the third family is made of degenerate stars, the so-called white dwarfs. Some models of degenerate stars exist but only a few have their emergent flux published. As a first approximation, degenerate stars are known to have $U\!BV$ colours very similar to black bodies. We therefore computed the colours of black bodies. In any case, this characteristic is perhaps not general and does not apply to the UV part of the spectrum. We finally used the emergent fluxes of the pure-hydrogen atmosphere models for degenerate stars of Koester (1999). We restricted ourselves to effective temperatures ranging from 7000 K to 80000 K and to $\log~g=8.5$. We also integrated the spectra of the four white-dwarf primary spectrophotometric standards described by Bohlin et al. (1995) and the models of Wesemael et al. (1980). Both works are in good agreement (although not necessarily independent) with Koester's models.

2.4 The quasar spectrum

The quasar spectra used in Sect. 6 were derived from an average spectrum build from the composite spectra of Zheng et al. (1997) and Francis et al. (1991). The former was used from 310 to 2000 Å and the latter from 2000 to 6000 Å. The match between both spectra is reasonably good, as shown by Zheng et al. (1997, their Fig. 9). It was performed on the continuum windows identified by these authors between 1400 and 2200 Å. The absorption characteristics of the quasar spectra due to the intervening Ly$\alpha$ clouds were established, between Ly$\alpha$ and the Lyman break, on the basis of the concept of Oke & Korycansky (1982) and of the works presented by Irwin et al. (1991), Zuo & Lu (1993) and Warren et al. (1994). For the region below the Lyman break, three absorption models were computed. The first two were adapted from the works of Møller & Jakobsen (1990), Møller & Warren (1991), Warren et al. (1994) and Giallongo & Trevese (1990). The first one only takes into account the hydrogen clouds with column densities inferior or equal to $10^{17}~{\rm cm}^{-2}$ (sometimes called the Ly$\alpha$ forest clouds). It will further be referred to as model A. The second one additionally includes systems with column densities between 10¹⁷and $10^{20}~{\rm cm}^{-2}$ (sometimes called the Lyman limit systems). It will further be referred to as model B. As an extreme case, we also considered a model where a strong (10 magnitudes) absorption occurs in the Lyman continuum at a redshift very close to the one of the quasar, absorption which persists in the whole observable Lyman continuum. This model will further be referred to as model C. These three models are strongly inspired by those described by Royer (1994) where full details can be found. To fix ideas, it is worth noticing that the higher normalization of Madau (1995) puts his model between our models B and C.

It must be clear that the quasar spectrum defined above is only representative of an average quasar and that some individual quasar spectra deviate strongly from it. The true population of quasars will exhibit some dispersion around the characteristics of this quasar. It is well known (see e.g. Francis et al. 1991) that the population of quasars displays a variety of power-law flux distributions and that the emission-line equivalent widths vary from one object to the other both in a systematic way (the Baldwin effect) and in a random way. On the basis of the power-law index dispersion reported, e.g. by Francis et al. (1991), we expect this effect to spread the colours of quasars by $\pm~0.3$ mag around our tracks. In addition, particular realizations of the distribution of high column density clouds along some line of sight could induce strong deviations from the mean behaviour.