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A WFI survey in the Chamaeleon II dark cloud

We present the results of an optical multi-band survey for low-mass Pre-Main Sequence (PMS) stars and young Brown Dwarfs (BDs) in the Chamaeleon II (Cha II) dark cloud. This survey constitutes the complementary optical data to the c2d Spitzer Legacy survey in Cha II. Using the Wide-Field Imager (WFI) at the ESO 2.2m telescope, we surveyed a sky area of about 1.75 square degrees in Cha II. The region was observed in the Rc, Ic and z broad-bands, in H-alpha and in two medium-band filters centered at 856 and 914 nm. We select PMS star and young BD candidates using colour-magnitude diagrams (CMDs) and theoretical isochrones reproduced ad-hoc for the WFI at the ESO2.2m telescope system. The selection criteria are also reinforced by using the previously known PMS stars in Cha II to define the PMS locus on the CMDs and by investigating the infrared (IR) colours of the candidates. By exploiting the WFI intermediate-band photometry we also estimate the effective temperature and the level of H-alpha emission of the candidates. Our survey, which is one of the largest and deepest optical surveys conducted so far in Cha II, recovered the majority of the PMS stars and 10 member candidates of the cloud from previous IR surveys. In addition, the survey revealed 10 new potential members. From our photometric characterisation, we estimate that some 50% of the 20 candidates will result in true Cha II members. Based on our temperature estimates, we conclude that several of these objects are expected to be sub-stellar and give a first estimate of the fraction of sub-stellar objects.


Introduction
Recent investigations in star-forming regions (SFRs) have pointed out that the fraction of young Brown Dwarfs (BDs) relative to low-mass and more massive Pre-Main Sequence (PMS) stars may vary significantly among different SFRs (Kroupa 2002). In particular, the fraction is different in T and in OB associations (Briceño et al. 2002;Hillenbrand & Carpenter 2000;Luhman et al. 2000;Muench et al. 2003;Preibisch et al. 2003). Different environments may give rise to different initial conditions for star and planet formation and, hence, to differences in the observed spectrum of masses (Kroupa 2001(Kroupa , 2002. This may have strong consequences on the Initial Mass Function (IMF), in particular in the sub-stellar domain. It has also been proposed that BDs may form as members of small groups of objects, that may be ejected by dynamical interactions before they can grow to stellar masses (Reipurth & Clarck 2001); hence, many low-mass and sub-stellar objects might have es-caped detection in surveys that concentrate sharply in the cores of SFRs. Thus, one possible reason for the differences in the fraction of young sub-stellar objects in T and OB associations can in principle be ascribed to the photometric and spatial incompleteness of the imaging surveys. Spatially complete deep imaging surveys are thus crucial in order to single out low-mass star and BD candidates to be investigated by follow-up spectroscopy. Only then, problems like mass segregation in SFRs and the low-mass end of the IMF can be addressed.
In this paper, optical wide-field imaging observations in the Chamaeleon II dark cloud (hereafter Cha II), complemented with JHK photometry from 2MASS (Cutri et al. 2003), are used to search for low-mass PMS stars and young BDs. Our survey covers almost 2 square degrees in the Cha II cloud.
Because of its proximity to the Sun (d≈178 pc, Whittet et al. 1997), young age (0.1-10 Myr, Hughes & Hartigan 1992) and relatively high galactic latitude (b≈−15 deg, Schwartz 1991), which decreases the effects of contamination by background stars, the Cha II dark cloud is particularly well-suited for studies of low-mass PMS stars and young BDs. It is indeed characterised by the presence of objects with Hα emission (Hartigan 1993;Hughes & Hartigan 1992), as well as of embedded Class-I and Class-II IR sources Prusti et al. 1992;Whittet et al. 1991) and X-rays sources (Alcalá et al. 2000).
Investigations in the near-IR by the DENIS survey revealed several candidate young BDs in Cha II (Vuong et al. 2001); however, a spectroscopic follow-up by Barrado y Navascuès & Jayawardhana (2004), though revealing the least massive classical T Tauri star in the cloud, failed in confirming the young BD candidates. Persi et al. (2003) performed ISOCAM observations and IR spectroscopy of several objects in the core of Cha II and found a number of sources with IR excess. Their most promising candidate, ISO-CHA II 13, was confirmed recently as the first BD in the region known to be surrounded by a disk (Alcalá et al. 2006). An optical widefield imaging survey by López Martí et al. (2005) proposed two young BD candidates. However, that survey covered only about 10% of the cloud area.
The Cha II cloud has also been included in the Spitzer Legacy survey "From Molecular Cores to Planet Forming Disks" or c2d (Evans et al. 2003) as a test case of a cloud with moderate star formation activity. Results of the c2d survey in Cha II have been published recently by Young et al. (2005), Allers et al. (2006) and Porras et al. (2006) . The data presented in this paper constitute the optical ancillary data for the c2d survey in Cha II. As such, they are part of a multi-wavelength study of the Cha II cloud which will be presented in a forthcoming paper (Alcalá et al., in preparation).
The outline of the paper is as follows. In Sec. 2 the observations, data reduction and calibration procedures are described. In Sec. 3 we present specific tools for the analysis of the photometric data. Sec. 4 describes the criteria for the selection of PMS star and BD candidates in Cha II, using the tools developed in Sec. 3. The results of the survey and, in particular, the fraction of sub-stellar objects estimated in Cha II are discussed in Sec. 5. Our conclusions are presented in Sec. 6 and, finally, a few notes on some individual objects are presented in Appendix C.

Observations
The observations were carried out in two observing runs (27-30 April 2001 and20-23 March 2002) using the Wide Field Imaging (WFI) mosaic camera attached to the ESO 2.2m telescope at La Silla (Chile). The mosaic consists of eight 2k×4k CCDs forming a 8k×8k array with a pixel scale of 0.238 ′′ /pix; hence, a single WFI pointing covers a sky area of about 30 ′ ×30 ′ . The Cha II dark cloud has an extention of about 2 square degrees (Hughes & Hartigan 1992). Thus, seven adjacent WFI pointings allowed us to cover about 70% of the cloud area. The distribution on the sky of the WFI pointings is shown in Fig. 1. The overlap of about 2 ′ between adjacent pointings allowed us to check the consistency in the photometry as well as in the astrometry.
The observations were performed in the R C , I C and z broad-bands, in two Hα filters, narrow (Hα 7 , λ c =658 nm and FWHM=7.4 nm) and wide (Hα 12 , λ c =665 nm and

Pre-reduction and Astrometry
The pre-reduction of the raw images, passing through bias subtraction, flat-fielding and correction for fringing, was performed on a nightly basis, using the mscred package under IRAF 1 , following the guidelines described in Alcalá et al. (2002). The resulting pre-reduced images are uniform to about 1 IRAF is distributed by the National Optical Astronomy Observatories (NOAO).
1%. In order to correct for large-scale illumination variations a super-flat was used.
The astrometric calibration and relative flux scaling between ditherings were done using the ASTROMETRIX tool 2 . ASTROMETRIX performs a global astrometric solution which takes into account overlapping sources falling on adjacent CCDs in different ditherings. For each pointing, the astrometric solution was first computed for the R-band dithering-set using the USNO-A2.0 catalogue (Monet et al. 1998) as a reference. A catalogue of sources was then extracted from the re-sampled R-band image and used as reference catalogue for all the other bands. Within the global astrometry process, the astrometric solution was constrained for each CCD by both the positions from the R-band catalogue and those from overlapping sources in all the other CCDs. The co-addition of the different dithered images for a given filter and pointing was performed using the SWARP tool 3 . The resulting 8k×8k stacked images were normalised by the exposure time. The absolute astrometric precision of our images is about 0.35 arcsec, corresponding to the RMS accuracy of the USNO-A2.0 catalogue, while the internal RMS, computed from overlapping sources in different exposures, is within 0.05 arcsec, indicating the good performance of ASTROMETRIX.

The photometric calibration
In order to transform the R and I instrumental magnitudes to the standard Cousins system, the Landolt standard fields SA 98, SA 101 and SA 107 (Landolt 1992) were observed nightly. The standard R C and I C magnitudes were determined using the transformation equations: (1) where r 0 and i 0 are the instrumental magnitudes corrected for atmospheric extinction and c R and ZP R and c I and ZP I the colour terms and zero points for the R and I bands respectively. The standard magnitudes from Stetson (2000) were used in order to determine the zero points and colour terms.
The intermediate-band instrumental photometry was transformed to the standard AB photometric system following the prescriptions by Jacoby et al. (1987) and Alcalá et al. (2002) by using the equation: where m 0 is the instrumental magnitude in a given intermediate-band filter corrected for atmospheric extinction and ZP λ the zero point derived by using the spectrophotometric standard stars Hiltner 600, LTT 4364 and Eg 274 (Hamuy et al. 1992), observed by us in the same run. The resulting magnitudes in the intermediate band filters are in the AB system.
The nightly calibration coefficients are reported in Tab. 2.

The z-band photometric calibration
The calibration of the z magnitudes required more effort as there are no data for standard stars available in the literature.
Since we aimed at determining the colour-magnitude diagrams (CMDs) of the sources in Cha II (Sec. 4) and their spectral energy distributions (SEDs, Sec. 5), we needed both to tie the z magnitudes with some "reference" photometric system and to determine the flux at Earth of a star with magnitude z = 0. To this aim, we observed the same Landolt standard fields in the z filter. In the Landolt SA 98 field we selected the A0-type star SA 98 653, whose visual magnitude and colours are reported in Tab. 3. This star is very well characterised and its absolute spectrophotometry is well determined (Gutièrrez Moreno et al. 1988). For this A0-type star we can assume (I C − z) = 0, thus defining the "standard" z-magnitude system as that for which the colour (I C − z) is zero for A0 type stars. The zero point of this calibration is then determined as follows: where I C = 9.522 is the standard magnitude of SA 98 653 in the Cousins system and z 0 its z-band instrumental magnitude corrected for atmospheric extinction. We then applied this zero point correction to the z 0 instrumental magnitude of all the stars in the Landolt fields. In this way we obtained a catalogue of Landolt stars with z magnitudes and (I − z) colours in our internal WFI-Cousins system. We then used this catalogue to find the least squares solution to the equation: where z 0 and i 0 are the standard stars instrumental magnitudes corrected for atmospheric extinction and ZP z and c z the z calibration coefficients for the newly defined WFI-Cousins photometric system. The nightly mean values obtained for ZP z and c z are reported in Tab. 2.
Since the absolute spectrophotometry of SA 98 653 is available from Gutièrrez Moreno et al. (1988), we can use this star  Stetson (2000).
.539 −0.004 −0.097 0.007 0.008 to obtain the absolute flux calibration in the z filter, i.e. to obtain the flux at Earth of a star with z=0. Following the procedure outlined in Appendix A we derive: This value can be used to derive the flux in the z-band of the sources in our catalogue using their corresponding z-band magnitudes.
2.4. The catalogue extraction 2.4.1. PSF fitting procedure PSF fitting photometry has been performed by using the IRAF/daophot package (Stetson 1987). Since we are interested in the faintest stellar objects, the threshold level was defined in order to select all the sources having a signal-to-noise ratio (σ) greater than 3. This choice may lead to the extraction of many spurious detections, however daophot allows us to discriminate between stars, extended sources (galaxies), saturated objects and other spurious detections. The PSF fitting procedure was re-iterated twice for each Cha II field; given the moderate crowding of these fields, this choice allowed us to detect the faintest neighbours to bright stars while keeping the number of spurious detections relatively small. The typical residual of the PSF fitting is less than 2% of the peak brightness. A single catalogue comprising all the stellar sources detected in all the available photometric bands was finally produced. In Fig. 2 the internal photometric errors of all the detected point-like sources are plotted against the magnitude for all the available filters; the relative exponential fits are over-plotted. Tab. 4 summarises the number of point-like sources detected in the surveyed area in each filter and the limiting magnitudes achieved at the 10σ, 5σ and 3σ levels, respectively.

Completeness
The completeness of our catalogues was estimated in the standard way by inserting artificial stars into the images and recovering them using the same extraction parameters as for the real objects; the fraction of the recovered artificial objects provides a measure of the completeness. We used the IRAF/addstar package to perform the exercise. We inserted 3000 artificial sources; this number should not alter significantly the crowding statistics in the images. The profile for the artificial sources was Photometric errors versus magnitudes and relative exponential fits for all the point-like sources detected in Cha II and for all the available filters. The "double sequence", clearly visible in R and Hα 12 bands, is due to different seeing conditions in the individual exposures. generated by using the same PSF model used for the source extraction; the position of the artificial objects are randomly distributed over the entire area of the mosaic and their magnitudes range uniformly between the detection and the saturation limits in each band. As an example we show the results for the ChaII 2 field (see Tab. 1). Fig. 3 shows the fraction of recovered artificial objects as a function of magnitude for each filter. The corresponding magnitude limits at 95% completeness level (C=95%) are reported in Tab. 4.

Tools for candidates selection
Our primary criterion for the selection of low-mass PMS star and BD candidates from the extracted catalogue was based on the comparison of the object location in CMDs with theoretical isochrones. In addition, our WFI data in the 865-nm and 914-

Theoretical Isochrones
Theoretical isochrones for low-mass stars and BDs down to 0.001 M ⊙ are provided by Baraffe et al. (1998) and Chabrier et al. (2000) in the Cousins photometric system (Bessel 1990). Since the WFI filters transmission curves are somewhat different from the original Cousins ones, in particular for the I-band, it is crucial to transform the colours and magnitudes into the appropriate photometric system. We thus transformed the isochrones by Baraffe et al. (1998) and Chabrier et al. (2000) into the WFI-Cousins system as described in Appendix B. In this way, we can use the isochrones to define the PMS locus in the CMDs (e.g. Fig. 9) in a photometrically consistent way. In Fig. 4 the theoretical R C vs. (R-I) C colour-magnitude diagram is shown. The 95% completeness limit was determined from the values reported in Tab. 4. For A V =0 we are complete down to 0.02 M ⊙ at the 95% level for objects younger The isochrones (continuous curves) and PMS tracks (dashed curves), shifted to the distance modulus of Cha II (6.25 mag, Whittet et al. (1997)) are in the WFI-Cousins photometric system. The dashed straight line represents the 95% completeness limit. The A V =2 mag reddening vector is shown. than 10 Myr. For an average extinction A V ≈2 mag for Cha II (Cambrésy 1999) a 95% completeness limit corresponds to 0.03 M ⊙ .

The (m 856 − m 914 ) index vs. temperature relation
Late-type dwarfs are characterised by strong molecular absorption bands essentially due to metallic oxides (TiO and VO). The ESO-WFI medium-band filter centered at 856 nm covers important TiO absorption features that deepen with decreasing temperature, while the medium-band filter centered at 914 nm lies in a wavelength range which is relatively featureless in latetype objects (see Fig. B.1 lower panel in Appendix B). Thus, the (m 856 − m 914 ) colour index is sensitive to the effective temperature for very cool objects (2000 K T eff 3800 K), where TiO dominates the opacity (Allard 1990;Burrows & Liebert 1993;O'Neal et al. 1998). In the absence of interstellar extinction, this index can provide a first reliable guess of the temperature of the cool candidates.
Using the filter transmission curves for the corresponding intermediate-band filters and the synthetic low-resolution StarDusty spectra for low-mass stars and BDs by Allard et al. (2000) we derived the relationship between the (m 856 − m 914 ) index and the effective temperature, applying the methods described in Appendix B. The synthetic (m 856 − m 914 ) index, derived by integrating the StarDusty spectra under the filter transmissions and CCD quantum efficiency curves, is in the instrumental WFI system. As such, it was transformed into the standard AB photometric system by applying the zero points derived from the spectrophotometric standard stars Hiltner 600, LTT 4364 and Eg 274, observed with WFI in the 856-nm and 914-nm bands (see Sec. 2.3). From the standard fluxes (Hamuy et al. 1992) integrated under the WFI passbands like-  Allard et al. (2000). The two solid curves show the relation for log g=5.0 (lower boundary) and log g=3.5 (upper boundary); the dashed curve represents the T eff -colour relation for log g=4.0. The straight line is the empirical relationship derived by López Martí et al. (2004).
wise the StarDusty spectra, we found an average zero-point correction for the (m 856 − m 914 ) colour of −0.13 mag, which allowed us to obtain the calibrated synthetic (m 856 − m 914 ) index as: In Fig. 5 we show the resulting (m 856 − m 914 ) index versus temperature relation. This relation depends on the stellar gravity, as indicated by the shaded area in Fig. 5, which encompasses all the calibrations for models in the range 3.5≤ log g ≤5. We also derived this relationship using other stellar atmosphere models (e.g. NextGen, COND, etc.); the StarDusty models were chosen because they better match the empirical relationship between the (m 856 − m 914 ) index and the effective temperature by López Martí et al. (2004) (straight line in Fig. 5). Furthermore, Allard et al. (2001) found that silicate dust grains can form abundantly in the outer atmospheric layers of the latest M dwarfs and BDs.
In the case of high interstellar extinction (A V 4 mag), the temperature derived from this relation may be underestimated because the (m 856 − m 914 ) index becomes larger than in the absence of extinction. Thus, without any reliable evaluation of A V , we can use these temperature estimates only for candidate selection purposes (see Sec. 4).

Hα Equivalent Width calibration
The WFI Hα 7 filter covers the Hα line, while the Hα 12 filter lies in a wavelength range which is affected by neither the Hα wings nor strong photospheric lines (see Fig. B.1 mid panel in Appendix B). The (Ha 12 − Ha 7 ) index is thus sensitive to the intensity of the Hα line. We used the StarDusty spectra by Allard et al. (2000) to define a calibration relation between this index and the Hα equivalent width (EW Hα ). In order to simulate stellar spectra with different values of EW Hα , we added to the synthetic spectra a Gaussian emission profile centered at Hα (656.2 nm) and having a FWHM of 3 Å. The latter value was fixed by considering the Hα line profiles of a sample of 75 PMS stars presented by Fernàndez et al. (1995); we found that the typical FWHM of the Hα emission lines of these objects is around 3 Å, though it can be higher for classical T Tauri stars (5-6 Å). However, from tests made by using profiles with different FWHM, we have verified that the FWHM value has no significant effect on the (Hα 12 − Hα 7 ) vs. EW Hα calibration.
By applying the method described in Appendix B and correcting the synthetic (Hα 12 − Hα 7 ) colour by the mean (Hα 12 − Hα 7 ) colour of the spectrophotometric standard stars used to transform the intermediate-band photometry into the AB system (see Sec. 2.3), we obtained the calibration relation (Hα 12 − Hα 7 ) vs. EW Hα displayed in Fig. 6. This relation does not depend on the FWHM of the Gaussian emission core but is strongly dependent on the effective temperature for objects cooler than about 4500 K. As expected from the contribution of the Hα absorption wings (see Fig. B.1, mid panel), for a fixed EW Hα the (Hα 12 − Hα 7 ) index is higher for cooler objects; between 3000 and 2000 K this trend is inverted because the Hα 12 filter covers strong molecular absoption bands that heavily affect the continuum of very cool stars.
The relationship between the Hα index and EW Hα derived above was checked by using unpublished WFI Hα photometry and spectroscopy of already confirmed PMS stars in the L1616 cometary cloud obtained with HYDRA@WIYN3.5m (Alcalá et al. 2004) and FORS@VLT (Alcalá et al., in preparation). The spectra of the PMS stars in L1616 were integrated under the transmission curves of the WFI Hα filters to derive their "synthetic" (Hα 12 − Hα 7 ) index. Such index was then transformed into the AB system by using the mean Hα colour   8. Comparison between the Hα equivalent width estimated in this work from the (Hα 12 − Hα 7 ) photometric index and that measured by Hughes & Hartigan (1992) and Barrado y Navascuès & Jayawardhana (2004) for confirmed PMS stars in Cha II (open circles). The smaller black dots mark the objects recovered by our selection criteria (see Sec. 4).
index of the corresponding spectrophotometric standard stars observed in the L1616 run. The WFI Hα photometry of these PMS stars was then used to compare the observed (Hα 12 −Hα 7 ) index with the one derived from the spectra. Fig. 7 shows the results. The best fitting line (continuous line in Fig. 7) has a slope close to 1 and an offset close to zero; this implies that no significant correction must be applied to the (Hα 12 − Hα 7 ) vs. EW Hα relation deduced from the synthetic spectra. Based on the errors of the observed (Hα 12 − Hα 7 ) index we conclude that bona-fide emission line objects will have an Hα index greater than 0.1, corresponding to EW Hα ≈ 10 Å for an object with T eff ≈ 4000 K.
The Hα index versus EW Hα relation was also checked using data from the literature for the Cha II PMS stars. In Fig. 8 the Hα equivalent width derived from spectroscopic data (Hughes & Hartigan 1992), EW Hα (spec), is compared with the one derived from the Hα photometric index, EW Hα (phot). In order to estimate the latter, the effective temperatures reported by Hughes & Hartigan (1992) were used, while for the PMS star C 41 the temperature reported by Barrado y Navascuès & Jayawardhana (2004) was used. From  Fig. 8, the EW Hα values derived from the Hα photometric index are in good agreement with those derived from spectroscopic data. The computed RMS suggests that the relationship shown in Fig. 6 can be used to estimate the EW Hα from the WFI Hα photometry for objects with EW Hα 10 Å and EW Hα 30 Å, at the 1σ and 3σ levels respectively, provided we have an estimate of the stellar temperature.

Selection of the candidates
For the selection of low-mass PMS star and young BD candidates we exploited both the optical data from our survey and the JHK photometry available from the 2MASS catalogue (Cutri et al. 2003), using the tools described in the previous sections. A matching radius of 0.5 ′′ was used to merge the WFI and the 2MASS catalogues; this value was set by taking into account the astrometric accuracy of both catalogues.
Low-mass PMS star and BD candidates in SFRs can be identified in optical CMDs. In such diagrams the colour increases rapidly for late spectral types and hence, the contamination from foreground stars is expected to decrease.
A first sample of candidates was then selected based on the I C vs. (I C − z) and I C vs. (R − I) C CMDs. All the pointlike sources detected in Cha II above the 3σ level were placed in these CMDs ( Fig. 9) and their position was compared with the theoretical isochrones. The isochrones transformed into the WFI-Cousins system, as described in Sec. 3.1, were scaled to the Cha II distance of 178 pc (Whittet et al. 1997) in both CMDs. We then selected all the objects falling above the 10 Myr isochrone in both CMDs (Fig. 9). This criterion takes into account the age spread of the previously known PMS stars in Cha II (0.1-10 Myr, Hughes & Hartigan 1992) and the PMS locus that they define on the CMDs, as well as the uncertainties in interstellar extinction. In this way we selected 114 objects of which 17 were previously known Cha II members.
However, the 97 new candidates from the selection above may still be contaminated by background giants and highlyreddened objects. We therefore investigated the properties of the selected sample in the JHK bands using their 2MASS magnitudes. It has been found by different authors that the intrinsic (J − H) and (H − K) colours of young late-M objects are dwarf-like with, in some cases, an (H − K) excess, mainly arising from a circumstellar disk or an in-falling envelope (Lee et al. 2005;Luhman & Rieke 1999;Meyer et al. 1997). Furthermore, Meyer et al. (1997) found that classical T Tauri stars, with prominent IR excesses due to circumstellar accretion disks, exhibit a narrow range of colours in the Fig. 9. I C vs. (I C − z) and I C vs. (R − I) C diagrams for the point-like objects in our survey (small gray dots). The lines represent the theoretical isochrones derived as explained in Sec. 3.1, shifted to the distance modulus of Cha II (6.25 mag, Whittet et al. (1997)). The continuous line in each diagram represents the saturation limit. The big black dots represent the 37 sources selected from our criteria, while the open circles and squares represent the known PMS stars and candidates selected from previous surveys respectively. The magnitudes reported by Hughes & Hartigan (1992) were used to plot the objects above and/or close to our saturation limits in any of the three broad-bands. Note that basically all the known PMS stars and candidates are recovered in our selection. The A V =2 mag reddening vector is shown in both diagrams. Fig. 10). By using the (J − H) vs. (H − K) diagram we then performed a secondary selection on the sample coming from the optical CMDs, following similar criteria as in Lee et al. (2005). The sub-sample of all the objects falling below the dividing line between giants and dwarfs (c.f. Fig. 10) should be less contaminated by background giant stars. In this way we end up with a sub-sample of  Meyer et al. (1997). The continuous line is dividing line between giants and dwarfs. The shaded area indicates the locus presumably uncontaminated by giants. The previously known PMS stars and candidates are indicated with open circles and squares respectively. The big black dots represent the objects selected in this work. The A V =2 mag reddening vector is shown. The two PMS stars which fall outside the selection area are the heavily veiled star Sz 47 (below the shaded area) and the binary Sz 60E (above the shaded area). 84 objects, which still include the 17 previously known members.
The sub-sample passing the secondary selection may still contain foreground and highly-reddened background objects. We thus performed a third-level selection as follows. We assumed that the objects passing the primary and secondary selections above are all at the distance of Cha II and estimated their temperature and luminosity as described in Sec. 5. Although these are first guesses of the actual stellar temperatures and luminosities, these values already provide good estimates for candidate selection purposes. We then constructed the HR diagram of our candidates sample and selected all the objects falling between the birth-line and the 20 Myr isochrone, using the models by Baraffe et al. (1998) and Chabrier et al. (2000). Although the age distribution of the confirmed members of Cha II ranges between 0.1 and 10 Myr (Hughes & Hartigan 1992), the more relaxed criterion of a 20 Myr cut-off for the candidates with a high membership probability was set by taking into account the uncertainties on the distance to the Cha II cloud (∆d=18 pc, Whittet et al. 1997) and the interstellar extinction. The evolutionary tracks of low-mass PMS stars run almost parallel to the luminosity axis of the H-R diagram. Thus, though mass estimates are not greatly affected by interstellar extinction, the age dispersion may be considerably increased if the adopted extinction for each candidate is not well determined. The mean uncertainty on our visual extinction determinations is ∼1.5 mag (see Sec. 5.3.1); this would correspond to a luminosity uncertainty of ∼16% and, hence, and age uncertainty of ∼2 Myr for an object with mass ∼0.5M ⊙ and age 2-3 Myr, i.e. the typical values in Cha II (Alcalá et al., in preparation). Thus, the criterion of the 20 Myr isochrone ensures that the selected objects are, to a first approximation, consistent with Cha II membership.
The theoretical isochrones depend on the physics involved in the models. As such they may be rather uncertain, in particular in the very low-mass domain. We have thus tested the reliability of our selection criteria using as test-bench the publicly available samples of confirmed PMS stars and BDs in Taurus and IC348 reported by Briceño et al. (2002) and Luhman et al. (2003), respectively. As can be seen in Fig. 14 (available only in electronic form), the selection criteria recover the vast majority of the previously known PMS stars and BDs in these regions, providing a good check that they work well on selecting these type of objects.
The screening of our data lead, on the other hand, to the selection of 37 interesting objects. Of these, 17 were already known (16 PMS stars plus the BD) and 10 are candidates with high probability of membership based on their selection in previous surveys (Allers et al. 2006;Persi et al. 2003;Vuong et al. 2001;Young et al. 2005). The remaining 10 selected objects are completely new candidates. The other 13 previously known PMS stars are saturated and/or close to the saturation limit in at least one of our broad-band RIz images and hence, we could not apply our selection criteria. However, using their magnitudes and colours from the literature (Alcalá et al. 1995;Hughes & Hartigan 1992), these objects would fall within our selection; this means that, adding these to the 17 previously known non-saturated objects, our criteria recover 30 of the 36 previously known Cha II members.
There are a few exceptions in which the above selection criteria fail: the heavily veiled T Tauri stars Sz 47 (Hughes & Hartigan 1992) and C 41 (Barrado y Navascuès & Jayawardhana 2004), which exhibit strong UV excess that affects their colours, and the Class-I source IRAS 12500-7658 , which is a deeply embedded object. These three sources are subluminous in both CMDs. In addition, the other Class-I source, ISO-CHA II 28, is not detected in any of our images. Although this type of objects would escape our selection, they are expected to be rare in Cha II ; Alcalá et al., in preparation). The two planetary-mass candidates reported by Allers et al. (2006) also escaped selection because they were barely detected only in our I-band images. The Herbig-Haro object HH 54 (Giannini et al. 2006) and the Class-0 source BHR 86 (Garay et al. 2002) are also associated with Cha II.
HH 54 was detected only in our R-band and Hα images, while BHR 86 was not detected in any of the optical bands. These objects will be discussed in detail in a forthcoming paper (Alcalá et al., in preparation).
In conclusion, our selection criteria recover the majority (about 80%) of the confirmed and candidate members of Cha II reported in previous surveys. For the sake of clarity, in all the diagrams we use dots to represent the 37 objects selected with our criteria, open circles to represent the already confirmed members and open squares to represent the 10 candidates selected in previous surveys. The 10 new candidates appear simply as dots in all the diagrams.
In Tab. 7 we report all the objects with at least one photometric measurement in the optical bands 4 . The table contains the confirmed members of Cha II, the candidates selected by previous surveys and the new candidates selected in this work, as well as other sources identified as possible candidates in previous studies, but which were rejected by our selection criteria. The latter sample includes objects like the candidates reported by López Martí et al. (2005) 5 and some of the sources identified by Persi et al. (2003). Comments on some individual objects are given in Appendix C.
In the following we concentrate on the sample of 20 candidates, namely the 10 candidates selected from previous surveys, but also recovered from our selection criteria, and the 10 new candidates; they are reported in Tab. 6 and their spatial distribution is shown in Fig. 1. The 10 previously known candidates we recovered in our selection have also been proposed as young members of Cha II by recent studies (Allers et al. 2006;Vuong et al. 2001;Young et al. 2005); this supports their membership to the cloud and, at the same time, the reliability of our selection method. Moreover, several of them possess Hα emission (see Sec. 5.2). We remark that these are the candidates with the highest membership likelihood but we do not exclude that a few true Cha II members could have escaped some of our selection criteria. In particular, if they are heavily veiled, deeply embedded or components of unresolved binaries. If all the 20 candidates will be confirmed by spectroscopy, the population of Cha II will increase to some 56 members. Two of the 10 new candidates in our sample (WFI J12585611-7630105 and WFI J13005531-7708295) have been spectroscopically confirmed to be PMS stars (Alcalá et al., in preparation).

Possible contaminants
One possible source of contamination of our candidates is represented by field dwarfs. In order to estimate the number of possible foreground dwarfs in the field of ChaII we followed the prescriptions by Burgasser et al. (2004). We used the lowmass luminosity function simulations from Burgasser (2004) and the absolute magnitudes for late M and L field dwarfs from Dahn et al. (2002). Assuming a limiting magnitude of I=20, i.e. the I magnitude of our faintest candidates, and a mass function dN/dM ∝ M α with 0.5< α <1.5, we expect 8-10 foreground dwarfs with 2000<T eff <3000 K in the ∼2 square degrees area observed in Cha II. Therefore, up to about 50% of the candidates might be foreground dwarfs unrelated to the SFR.
Another possible source of contamination is represented by faint galaxies which may have colours similar to those of PMS objects, in particular of BD candidates. From the K-band galaxy number counts toward the celestial south pole, the expected number of background galaxies with K 13 mag, i.e. the K magnitude of our faintest candidates, in a ∼2 square degrees area is ∼20 (Minezaki & Kobayashi 1998). For this estimate only diffuse interstellar extinction, which is negligible (∼0.02 mag) at the K-band (Jones et al. 1981), is considered. In Cha II, the extinction may be as high as A V ≈6-8 mag, i.e. A K ≈1 mag. Thus, in order to contaminate our sample, the background galaxies should have K 12 mag; the predicted galaxy number count at this magnitude is less than 2 in the surveyed area. In addition, our PSF extraction methods remove the extended objects quite efficiently; thus, the only contaminants may be eventually the point-like extra-galactic objects, mainly QSO's. According to Prescott et al. (2006) only a handful of QSO's are expected to be present in 2 square degrees for magnitudes brighter than R =20 mag. The number increases for fainter magnitudes, but the vast majority of our candidates are brighter. Thus, we do not expect that extra-galactic objects represent a major problem of contamination.

Hα emission of the candidates
The calibration relation between the (Hα 12 − Hα 7 ) index and the EW Hα (see Sec. 3.3) allows us to investigate a possible Hα emission of the candidates. Based on this calibration, a threshold of (Hα 12 − Hα 7 )=0.1 mag would translate into an equivalenth width EW Hα ≈ 10 Å at the 1σ level of detection (c.f. Sec. 3.3). Most of the previously known PMS stars and candidates have an Hα index larger than this value (c.f. Fig. 11). 40% of the 20 candidates show Hα emission at the 1σ level, but only 2 of the 20 show it at the 3σ level. Considering that the Hα line can be strongly variable in young objects, we cannot use the index as a major diagnostic for the selection of the candidates, but only as a consistency check on their possible PMS nature. However, the 1σ level detections are yet consistent with recent spectroscopic evidence of Hα emission (Alcalá et al., in preparation). Moreover, the EW Hα range covered by our candidates (10-35 Å) is in line with that found by White & Basri (2003) for the slowly rotating, non-accreting stars and BDs in Taurus-Auriga. For the remaining candidates the (Hα 12 − Hα 7 ) index does not indicate clear evidence for Hα emission. For three objects (WFI J12533662-7706393, WFI J12583675-7704065, and WFI J13005297-7709478) the level of Hα emission could not be estimated because they are not detected in our Hα images (the magnitude limit is ∼20.5 mag at the 3σ level). These very faint candidates are indeed of relevant importance because their optical colours resemble those of ISO-CHA II-13 (Alcalá et al. 2006). Note that also ISO-Cha II-13 was not de- tected on our Hα images. The Hα information drawn from our data for the selected candidates is reported in Tab. 6.

Towards the fraction of sub-stellar objects in ChaII
An interesting and important quantity in this investigation is the number of sub-stellar objects relative to the PMS stars in Cha II. In order to determine this quantity, we must single out the sub-stellar objects. According to Chabrier et al. (2000), the sub-stellar limit for 3-4 Myr objects, the approximate age of Cha II (Alcalá et al. 2000;Cieza et al. 2005;Hughes & Hartigan 1992), falls at a temperature of about 2900 K. Using the tools described in Sec. 3 and exploiting the potential of our photometric data, we attempted a first estimate of the temperature of the candidate members of Cha II and hence, a guess on the fraction of sub-stellar candidates relative to the PMS stars. We derived first the dereddened SEDs of the candidates and then provided a first estimate of their temperature.

Dereddened SEDs
The SEDs were derived by merging the RIz WFI-Cousins photometry with the 2MASS JHK magnitudes. The standard fluxes at each of the optical and near-IR pass-bands have been derived from the observed magnitudes using the expression is the observed magnitude corrected for interstellar reddening and F 0 λ is the Earth flux of an A0-type star of magnitude V = 0 (Tab. 5). In order to derive the visual extinction, A V , a SED minimization procedure was used as follows. We assume that the observed magnitude at   Cutri et al. (2003) each wavelength (m λ obs ) can be derived by the following equation: where m λ re f is a distance-scaled reference magnitude at a given wavelength (λ) and temperature (T eff ). In Eq. 7 A V is the visual extinction, A λ the wavelength-dependent extinction and S a scaling factor depending only on the stellar radius. Using a grid of reference magnitudes and temperatures, we perform a linear fit to the previous expression were dA λ dA V and m λ obs − m λ re f are the independent and dependent variables, respectively, and A V and S the two free parameters of the fit. The dA λ dA V term was derived using the extinction law by Cardelli et al. (1989), assuming the standard value R V =3.1. The grid of reference SEDs was constructed by combining the tabulations of colours as function of spectral types by , Luhman et al. (2003) and Ducati et al. (2001). The A V value of the reference SED minimizing the χ 2 of the fit corresponds to the best approximation of the actual visual extinction. As a check, we have compared the results from our fitting procedure with the extinction derived from the spectral types and the observed colours of previously known PMS stars in Cha II. The RMS difference in A V is less than 1.5 mag, with only one object having a residual of about 4 mag.
In Fig. 12 the SEDs of the 10 new candidates selected in this work are shown. For six of these, we found a match in the c2d Spitzer catalogues and their IRAC and/or MIPS fluxes are also included. As appears from their SEDs, no significant IR excess is detected in these six objects. If they will be spectroscopically confirmed as Cha II members, they will most likely correspond to weak-line T Tauri stars (WTTS) or to BDs with thin disks. For the four remaining objects lacking Spitzer data we cannot assess the presence of strong IR excess. However, for three of the latter we estimate an Hα equivalenth width greater than about 20Å.
It is interesting to note that the number of WTTS relative to CTTS in Cha II is very small. Even assuming that all the candidates in our sample (see Tab. 6) would result in WTTS, which is not likely because several of them show evidence for strong Hα emission, the CTTS would outnumber the WTTS by a factor ∼2. This would be in contrast with what it is found Fig. 13. Upper panel: comparison between the effective temperature resulting from the SED fitting procedure described in Sec. 5.3.2 and that derived from the spectral classification for the confirmed T Tauri stars in Cha II reported by Hughes & Hartigan (1992) and, for C 41, by Barrado y Navascuès & Jayawardhana (2004) (open circles). The black dots mark the objects recovered by our selection criteria. The point at T spec ≈2900 K represents ISO-CHA II 13 as reported by Alcalá et al. (2006). Lower Panel: comparison between the effective temperature resulting from the SED fitting procedure described in Sec. 5.3.2 and that derived from the T eff vs. (m 856 − m 914 ) calibration. The open circles and squares represent previously known PMS stars and candidates respectively. The black dots mark the objects recovered by our selection criteria in other clouds, like Cha I and Taurus, where WTTS dominate the PMS population (Feigelson & Montmerle 1999). Our selection based on the (J − H) vs. (H − K) diagram, picks up objects later than about K5. This might lead to the conclusion that some earlier type WTTS could have escaped our selection. However, such objects would have been detected in the previous ROSAT X-ray surveys by Alcalá et al. (1995Alcalá et al. ( , 2000. Only two WTTS in the cloud, namely RXJ1301.0-7654a and RXJ1303.1-7706 were discovered in such surveys. Thus, the low fraction of WTTS in Cha II seems to be real. More details on this will be discussed in a future c2d paper (Alcalá et al., in preparation), with a more complete set of SEDs for the Cha II members.

Temperature
The temperature of the candidates was estimated using the T eff vs. (m 856 − m 914 ) calibration relation reported in Sec. 3.2. This calibration is valid for cool objects with temperature in the range 2000-3800 K, corresponding to a dereddened (m 856 − m 914 ) index in the range 1.16-0.16 mag. Thus, we ap-plied the calibration to objects with dereddened index (m 856 − m 914 )>0.16 mag. The A V values determined as explained in Section 5.3.1 and the extinction law by Cardelli et al. (1989) were used to deredden the (m 856 − m 914 ) index. For objects with (m 856 − m 914 )<0.16 mag, i.e. hotter than about 3800 K, a temperature estimate was done by fitting a grid of reference SEDs to the dereddened SEDs. The grid of reference SEDs was constructed by combining the tabulations of colours as a function of spectral type by , Luhman et al. (2003) and Ducati et al. (2001); the best approximation to the dereddened SED was then obtained by χ 2minimization of the flux differences between the dereddened SED and the reference SED. The minimization procedure was applied to the short-wavelength portion (λ ≤ λ J ) of the SED, which is less affected by an eventual IR excess (Fig. 12). The method results to be accurate within 250 K relative to the spectroscopic temperature estimates for most of the previously known PMS stars. This is shown in the upper panel of Fig. 13, where the residuals between the temperature derived from the dereddened SED fitting, T fit , and that obtained from spectroscopy by Hughes & Hartigan (1992), T spec , are shown. For ISO-CHA II 13 we adopt the temperature value determined spectroscopically by Alcalá et al. (2006).
For the cool candidates, we also performed a consistency check between the temperature derived from SED fitting and that coming from the T eff vs. (m 856 − m 914 ) calibration. We find that the two methods yield consistent results within ∼200 K, as can be seen from the lower panel of Fig. 13. We can then use the T eff vs. (m 856 − m 914 ) calibration confidently for those objects with dereddened (m 856 − m 914 )>0.16 mag.
The resulting temperature for each of the candidates is reported in Tab. 6. Using these estimates, we attempted to determine their radius and luminosity as follows: 1. First the reference SED of the same effective temperature as the object was selected and scaled to the Cha II distance (d= 178 pc, Whittet et al. 1997): where R ⋆ is the stellar radius; since R ⋆ is an unknown quantity, we let it vary between 0.1, i.e. the value expected for a BD at the Deuterium burning limit (Baraffe et al. 2003), and 10 R ⊙ ; for the objects whose effective temperature could not be estimated from the (m 856 − m 914 ) index, both T eff and R ⋆ were set as free parameters in the assumption that the short-wavelength side of the dereddened SED (λ ≤ λ J ) is mainly influenced by T eff ; 2. the best estimate of R ⋆ was then obtained by minimizing the flux differences between the observed dereddened SED and the reference one. The minimization procedure was performed, as above, to the short-wavelength portion (λ ≤ λ J ) of the SED; 3. Finally, we calculated the bolometric luminosities by applying bolometric corrections to both the dereddened Iband and J-band data. Bolometric corrections were taken from  for objects earlier than M6 (i.e. T eff 3000 K), while for cooler objects we followed the prescriptions by Luhman (1999) and combined the compilations of bolometric corrections as a function of temperature by Bessel (1991), Monet et al. (1992), Tinney et al. (1993) and Leggett et al. (1996).
Having an estimate of the temperature and luminosity of the candidates, we determined their masses and ages by comparison with the set of evolutionary tracks by Baraffe et al. (1998) and Chabrier et al. (2000) on the HR diagram.

The fraction of sub-stellar objects
Previous investigations (Alcalá et al. 2000;Hughes & Hartigan 1992) showed some evidences that the mass spectrum in Cha II might be biased towards very-low mass objects. It is thus interesting to investigate what our data suggest on this matter.
Assuming that all the 20 candidates are true cloud members, we end up with 6 candidates with T eff ≤2900 K, i.e. below the substellar limit for 5 Myr old objects. The remaining 14 objects result to be PMS star candidates (see Tab. 6). Taking into account the BD ISO-CHA II 13 and the 33 confirmed PMS stars, the resulting fraction of sub-stellar objects (0.02M ⊙ < M < 0.08M ⊙ ) relative to the PMS stars (0.08M ⊙ < M < 10M ⊙ ), R ss = N(0.02−0.08) N(0.08−10) , in Cha II would be ∼15% (19% if we consider the two planetary-mass objects reported by Jayawardhana & Ivanov 2006). This last value would imply a peculiar mass-spectrum for the population of Cha II relative to other T associations (where R ss =12-14%, Briceño et al. 2002;López Martí et al. 2004), in particular in the sub-stellar domain. If we assume that only the candidates having Hα emission are true cloud members, the R ss value would drop to ∼10% (15% if we consider the two planetary-mass objects reported by Jayawardhana & Ivanov 2006), i.e. more similar to that measured in other T associations and lower than that measured in OB associations (∼26%, Barrado y Navascuès et al. 2001;Boulanger et al. 1998;Briceño et al. 2002;Hillenbrand & Carpenter 2000;Muench et al. 2002). If R ss in Cha II is similar as in other T associations, we expect that at least 50% of the candidates reported in Tab. 6 will be genuine Cha II members.
Assuming that the 7 IRAS sources with Hα emission discussed in Appendix C are PMS stars, the fraction of substellar objects would drop to about 8% or 13% depending on whether the two planetary-mass objects are counted among the substellar ones.
By comparing the position of the candidates in the HR diagram with the Baraffe et al. (1998) andChabrier et al. (2000) evolutionary tracks, their age distribution would peak between 2 and 3 Myr, if they were genuine Cha II members. This would be fairly consistent with the average age of 3.6 Myr determined by Cieza et al. (2005) for a sample of T Tauri stars in Cha II. Taking into account the candidates, the mean mass in Cha II would be ∼0.5M ⊙ , i.e. slightly lower than the mean mass of the confirmed members alone (0.6 M ⊙ ) and comparable to the mean mass for the Cha I population (∼0.45 M ⊙ 6 ). References: a) Larson et al. (1998); b) Vuong et al. (2001); c) Allers et al. (2006); d) Young et al. (2005).

Conclusions
The optical survey presented here is one of the deepest and more extensive conducted so far in Cha II and constitutes the optical ancillary data for the c2d Spitzer Legacy survey in this cloud.
The photometric selection based on our optical imaging data, combined with data in the near-IR from the 2MASS, allowed us to recover basically all the previously known members of the cloud, including 10 candidates from previous IR surveys, with a high membership probability. Furthermore, we provided 10 new likely member candidates that were not detected by previous surveys, thereby increasing the total number of candidates to 20. Should all these objects be spectroscopically confirmed as PMS stars and young BDs, the population of Cha II will increase to 56 members. Up to 50% of the sample may be contaminated by field dwarfs. According to our characterisation criteria of the candidates, we estimate that at ages for these objects using the evolutionary tracks by Baraffe et al. (1998) and Chabrier et al. (2000) in a homogeneous way. least some 50% of them will result in true Cha II members and, based on our temperature estimates, several of these objects are expected to be sub-stellar. Under these assumptions, we conclude that the fraction of substellar objects relative to the PMS stars in Cha II is on the order of ∼19%, i.e. larger than that reported for other T associations like Taurus. In the most conservative hypothesis in which only the candidates showing Hα emission would result in true member of the cloud, this fraction would drop to ∼15%, i.e. comparable with that measured in other T associations.
From the completeness of our survey, both in space and flux, we conclude that the optical population of Cha II members discovered so far is nearly complete. We do not expect to find many more PMS stars based on optical observations. More clues to these issues will be addressed in a forthcoming paper by combining the optical data presented here with those from the MIPS@Spitzer and IRAC@Spitzer observations in Cha II (Alcalá et al., in preparation).
dell'Istruzione, Universitá e Ricerca (MIUR). We thank the anonymous referee for his/her constructive comments and suggestions. We also thank M. Radovich for many explanations on the use of ASTROMETRIX. We thank N. Evans, PI of the c2d Spitzer Legacy Program, and L. Cieza for many useful comments and suggestions on an earlier version of the paper. We also thank F. Coméron and E. Marilli for discussions. L. Spezzi acknowledges financial support from COFIN-MIUR-2004 (The X-Shooter spectrograph for the VLT) and PRIN-INAF-2005 (Stellar clusters: a benchmark for star formation and stellar evolution) and a grant by the Europen Southern Observatory (ESO) for a two-months stay at Garching. Support for this work, part of the Spitzer Legacy Science Program, was provided by NASA through contract 1224608 issued by the Jet Propulsion Laboratory, California Institute of Technology, under NASA contract 1407. We also thank the Lorentz Center in Leiden for hosting several meetings that contributed to this paper. This research made use of the SIMBAD database, operated at CDS (Strasbourg, France) and the data products from the Two-Micron All-Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center at California Institute of Technology, funded by NASA and the National Science Foundation. Gutièrrez Moreno et al. (1988) in the form of monochromatic instrumental magnitudes, covering a wavelength range from 3200 to 8000 Å, in steps of 40 Å for λ ≤ 5400 Å and 80 Å for λ > 5400Å. Since the z band is centered at 9648 Å (FWHM=616 Å), we need the spectrophotometry in a wider wavelength range. We have thus extrapolated the SED of SA 98 653, up to 16000 Å, by using the Kurucz grid of stellar atmosphere models (Kurucz 1979) in the following way. We first dereddened the SED of SA 98 653 using the canonical absorption-to-reddening ratio R V =3.2, as suggested by Chen et al. (2001) for the SA 98 field. Assuming that SA 98 653 is a main sequence star, as indicated by its spectrophotometry and broad-band photometric indexes, we derived its distance by comparing its observed V magnitude with the expected absolute visual magnitude (M V = 0.7, Gray 1992) for an A0-type main sequence star. Assuming an error of two spectral sub-classes on SA 98 653 spectral type, we constrained its distance between 300 and 450 pc, i.e. 0.30 mag< A V <0.45 mag. Note that the extinction of the nearby star SA 98-667 (spectral type B9V) is A V =0.33 calculated from its Hipparcos parallax (Chen et al. 2001), which is consistent with the range of values allowed for SA 98 653. The interstellar extinction coefficients at each wavelength were derived by using the extinction curve by Cardelli et al. (1989). We then performed a two-parameters least-square fit to the observed spectrophotometry of SA 98 653 by taking as free parameters the extinction (in the range 0.30 mag< A V <0.45 mag in steps of 0.01 mag) and the effective temperature of the model spectrum. Both the Kurucz models and the dereddened SED of SA 98 653 were normalised to the flux at 5556 Å. A minimum χ 2 for a model with T eff = 11000 K, log g=4 and A V =0.33 was derived (Fig. A.1). We then used this synthetic spectrum reddened with A V =0.33 to extrapolate the spectrophotometry of SA 98 653 in the near-IR. 2. The absolute Earth flux at 5556 Å of a star with magnitude V * calibrated with Vega, the primary photometric standard, is given by (Gray 1992): in units of erg · cm −2 · s −1 · Å −1 . When this expression is used for stars whose effective temperature is different from Vega (T eff = 9790 K), as in the case of SA 98 653, a small systematic error is introduced because the effective wavelength of the V band is 5480 Å, i.e. 76 Å shorter than the reference wavelength (5556 Å). An adequate correction for this is given by the following colour term (Gray 1992 where mag synt S A 98 653 is the synthetic magnitude of SA 98 653 at each wavelength normalised to the magnitude at 5556 Å, determined in the previous step. 3. We finally determined the synthetic flux of SA 98 653 in the z band by integrating its synthetic spectrum F synt S A 98 653 (λ) in the z filter transmission curve T λ , i.e. the product of the detector quantum efficiency and the filter transmission curve: where: We obtained: F z S A 98 653 = 1.62 · 10 −13 erg · cm −2 · s −1 · Å −1 F z S A 98 653 is the flux in the z filter of an A0 type star with visual magnitude V = 9.539 and z = I C = 9.522. What we need, in order to obtain an absolute flux calibration for the z band, is the flux of an A0-type star with V = 0 and z = 0 (F z A0V ). Since SA 98 653 is an A0-type star and we have defined its intrinsic colour as (I C − z) = 0, we have: By considering the uncertainties on magnitude and interstellar extinction measurements, we obtained: F z A0V = (8.4 ± 0.1) · 10 −10 erg cm −2 s −1 Å −1 = (2608 ± 31) Jy A slightly smaller absolute flux calibration constant for the WFI z band has been estimated by F. Coméron (private communication) using the absolute flux calibration of Vega obtained by Bohlin & Gilliland (2004) with the Space Telescope Imaging Spectrograph (STIS). Using these data we derive a value of 7.2 · 10 −10 erg · cm −2 · s −1 · Å −1 . However, for the sake of homogeneity, we prefer to use the value we derive above.

Appendix B: Isochrones
In order to transform the colours and magnitudes of the isochrones reported by Baraffe et al. (1998) and Chabrier et al. (2000) into the WFI-Cousins system we determined first the WFI synthetic magnitudes, m ∆λ : m ∆λ = −2.5 · log 10 ( f ∆λ ) + C ∆λ (B.1) where C ∆λ is the absolute calibration constant of the photometric system, tied to the Earth flux of an A0-type star with magnitude V = 0 (see Tab. 5), and f ∆λ is the observed flux.
In order to compute the expected flux of a PMS star or a young BD in the pass-band ∆λ of a given filter we proceeded as follows. We first determined the transmission curve, T λ , i.e. the product of the detector quantum efficiency and the given filter transmission curve 7 . We then computed: and F λ is the absolute flux of a given PMS star or BD. For this purpose we used the synthetic low-resolution spectra for low-mass stars by Hauschildt et al. (1999) calculated with their NextGen model-atmosphere code. For simulating very cool objects (i.e. T eff <3000 K) we used the StarDusty and BD-Dusty atmosphere models by Allard et al. (2000), which include dust opacity. 7 Available at: http://www.ls.eso.org/lasilla/sciops/2p2/E2p2M/WFI/ filters.  (Hauschildt et al. 1999) with T eff =2500 K and T eff =6000 K are over-plotted .   Fig. B.2. The Cousins colours as a function of the WFI instrumental colours for the standard stars in the Landolt's field SA 98. The continuous lines display the best fit of the data while the dashed lines have slope equal to 1 (i.e. no correction).
As an example of our procedure we show in Fig. B.1 (upper panel) two model spectra and the R, I and z WFI+ESO2.2m transmission curves over-plotted. However, the flux f ∆λ that we obtained in this way is the one at the surface of the star. The observed flux at any distance (d) is given by: where R ⋆ is the object radius. The values for R ⋆ can be computed from theoretical PMS evolutionary tracks, which in our case are those by Baraffe et al. (1998) for low-mass stars and those by Chabrier et al. (2000) for sub-stellar objects (i.e. M 0.1M ⊙ ). Finally, setting d=10 pc and using Eq. B.1, one can derive the absolute magnitudes for a given T eff , age and R ⋆ and hence, determine the isochrones in the CMDs.
Note that, consistently with the RIz photometric calibration of the sources in Cha II, the absolute calibration constants used in Eq. B.1 are those of the WFI-Cousins photometric system (see Tab. 5). However, a non-negligible difference between the I-WFI and the I-Cousins pass-bands arises from the fact that the red cut-off of the I-WFI filter is defined by the CCD response and it is centered at a redder wavelength (0.85µm) with respect to the standard Cousins I filter (0.79µm). In order to take into account this difference in the determination of the theoretical isochrones, we have exploited the relations between the WFI-Cousins (R − I) C and (I C − z) standard colours and the WFI instrumental colours for the standard stars in the Landolt's fields. By a least-square linear fitting (Fig. B.2), we derive the coefficients which allow us to correct the colours of the computed isochrones: