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Astron. Astrophys. 338, 977-987 (1998)

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4. Discussion

4.1. Nature of the sources

In the final sample of 54 candidates, 34 are detected in the 3 channels, 16 only in J and [FORMULA], and 4 only in [FORMULA] band (see Table 2). Fig. 2a and b displays a colour-magnitude and a colour-colour diagram for the known T Tauri Stars (Feigelson & Kriss, 1989; Schwartz, 1991; Prusti et al., 1991; Gauvin & Strom, 1992; Hartigan, 1993; Lawson et al., 1996) and the DENIS candidates. The magnitudes given for the known T Tauri Stars (TTS) come from the DENIS observations.

The known TTS consists of Classical and Weak-line TTS (Feigelson et al., 1993). The weak-line or naked (Feigelson & Kriss, 1989) TTS show only little infrared excess and they are characterised by a [FORMULA] Å. It corresponds to a later stage of evolution when a large fraction of the circumstellar material has been accreted. Hence, our candidates are likely to be classical TTS with strong emission lines and massive circumstellar accretion disks. We stress the point that our estimation of reddening is an upper limit. This explains that already known TTS are represented on the left of the main sequence in the colour-magnitude diagram and in the lower left corner of the colour-colour diagram. These objects probably lie on the front side of the cloud and thus do not suffer the total extinction that we have derived on the line of sight.

The brightest candidates are represented in an area of the diagram where already known TTS are found. Most of the known TTS have a smaller value of [FORMULA], but if we try to extend our sample toward bluer colours, we would enter an area corresponding to the giant and sub-giant stars, where no separation can reliably be made on the basis of near-IR colours.

Moreover, very few known TTS are as red as the DENIS candidates. An explanation could be an underestimation of the dereddening, but the colour-colour diagram indicates that at least 13 objects (detected in the 3 colours) cannot be shifted toward the main sequence simply by removing an additional reddening component. These candidates are among the reddest objects detected by DENIS. They were not previously detected because they are too faint and/or too far away of the cores. The cross-identification of DENIS and ROSAT pointed observations in the Cha I (Feigelson et al., 1993) shows that all X-ray sources detected by ROSAT are brighter than [FORMULA] and they do not exhibit strong infrared excess.

The spatial distribution of the candidates (Fig. 3) is also very remarkable. These sources have a trend to be concentrated near the cores of the cloud which strongly argue in favour of their young nature, since background giant stars would be uniformly spread over the whole field. Another interpretation remains: we could be in presence of small dark clumps that were not resolved in our extinction map. Then, an additional reddening would have to be taken into account, but, again, only a fraction of the candidate locations in colour-colour diagrams can be explained by normal reddening. In such case, the clumps should be smaller than [FORMULA] and would produce a visual extinction greater than 15 magnitudes. Although this interpretation cannot be definitely ruled out, we assume that these objects are more likely to be true young TTS, since the high infrared excess probably reveals the presence of a large amount of circumstellar material.

[FIGURE] Fig. 3. Spatial distribution of YSOs candidates. Extinction isocontour at 2,4 and 7 [FORMULA] are also plotted

Finally, we have examined the interpretation that some of these stars could be brown dwarfs. On the theoretical evolutionary tracks for low-mass stars, young brown dwarfs are actually about 3 magnitudes brighter in K than old ones, hence, they could be detected at the distance of Cha I at our sensitivity limit. Comerón et al. (1998) have, indeed, reported the possible discovery of brown dwarfs in the [FORMULA] Oph molecular cloud at a comparable distance of 160 pc. However, the [FORMULA] excess of young brown dwarfs is generally smaller than 1.5 and the [FORMULA] is greater than 3.5. Since our faintest candidates have all [FORMULA] and [FORMULA], we conclude that they are unlikely to be brown dwarfs.

4.2. Evolutionary status of the new candidates

In order to evaluate the stage of evolution of these new objects, we have attempted to compare their position in a HR diagram with the evolutionary tracks modelled by D'Antona & Mazzitelli (1994). Since this model does not take into account the circumstellar contribution, it is necessary to evaluate the respective contributions of the stellar and circumstellar components to the emergent flux. The TTS, especially the classical ones are surrounded by massive circumstellar accretion disks which produces both extinction and emission. The extinction is caused by the dust grains, but the emission process is more intricate. Rydgren & Zak (1987) have shown that the infrared excess cannot be explained only in terms of thermal emission of grains in the circumstellar disk. An intrinsic disk luminosity contribution is required to account for the observations. They have shown that the intensity of the intrinsic component is directly related to the accretion rate and has the same order of magnitude as the thermal emission. According to Calvet et al. (1997) the near-infrared emission of protostars is largely dominated by an infalling dusty envelope emission. Protostars correspond to Class I objects (Lada, 1987; Andre & Montmerle, 1994) with massive envelopes. TTS are Class II or Class III objects, the essential of their circumstellar matter is in the accretion disk. Meyer et al. (1997) suggest that the infrared excess of TTS is essentially due to the disk emission, without any envelope effect. They found accretion rates in the range from [FORMULA] to [FORMULA]yr-1 and inner disk radii from 2 to 6 [FORMULA].

Fortunately, the contribution of the disk to the emission is likely to be negligible at wavelengths shorter than [FORMULA]. Then, the I, and, with probably less confidence, the J fluxes can be considered as mainly of photospheric origin, although assuming no I excess, Meyer et al. (1997) have estimated the J excess to be only [FORMULA] of the photospheric flux for the classical TTS and to 0 for weak-line TTS. Thus, the colour excess is a good estimator of the extinction suffered by the star. The use of the [FORMULA] colour excess may lead to underestimating the extinction because of the intrinsic luminosity of the accretion disc, but probably not more than 50%.

In order to convert the evolutionary tracks in the HR diagram of D'Antona & Mazzitelli (1994) into similar tracks in colour-magnitude diagram we use the Flower's table (1996) which gives the bolometric correction for the V band versus the effective temperature. Assuming that the star photosphere emits like a black body at the effective temperature, we derive [FORMULA]. The comparison of the main-sequence that we have constructed in this way with main-sequences based upon observations by Bessel & Brett (1988) and Johnson (1966) indicates that the assumption that the photosphere radiates like a black body is basically correct for these colours. We remark that it is not the case for the G4-M6 spectral range in the [FORMULA] band.

Previous studies have shown that the associated members of the Cha I cloud are essentially in the K7-M5 spectral range (Appenzeller et al., 1983; Lawson et al., 1996). Assuming that all stars are of spectral type M0 we can estimate the extinction they suffer. Fig. 4 shows a [FORMULA] versus I diagram where all the TTS (known and candidates) are represented. The representation of the stars is clearly distributed along the reddening vector. Their position is compatible with a M0 spectral type ([FORMULA]) except for a part of the faintest sources for which [FORMULA] seems to be more appropriate. Note that 22 stars are missing because they are not detected in I. The extinction values that we have taken for each individual source are given in Tables 1 and 2. The restriction to the M0 spectral type implies uncertainties smaller than 1 magnitude of visual extinction because the tracks for different masses remain very close to each other.

[FIGURE] Fig. 4. Representation of the associated members of the cloud in a colour-magnitude diagram with pre-main-sequence tracks derived from the model of D'Antona & Mazzitelli (1994). Dashed lines are the isochrones at [FORMULA], [FORMULA], [FORMULA] and [FORMULA] years

Without a circumstellar component, we should have [FORMULA] - the equality standing for a star just located behind the cloud. In Fig. 5 we remark that less than [FORMULA] of the stars are in that case. The dispersion of [FORMULA] increases with [FORMULA]. A first explanation could be simply the fact that the location of each star within the cloud is not known precisely. Moreover, the separation between circumstellar and cloud extinction is not possible. Another explanation could be the evolutionary stage of the star, the closer a star is to its forming area (i.e. the most obscured regions) the younger it is likely to be. So, this dispersion may result from the effect of the circumstellar disk properties : mass, inclination. Fig. 5 shows that visual extinction for stars is smaller than 10 magnitudes which confirms they are likely to be TTS rather than protostars (Lada & Adams, 1992). Protostars have massive envelopes which cause greater extinction of up to tens of magnitudes. Nevertheless, only stars detected in I are represented and, among the 6 stars detected only in [FORMULA], 4 are also detected by ISO (IRS4 and IRS5 in Table 1; nb 23 and 41 in Table 2) in the LW2 and LW3 filters centred at [FORMULA] and [FORMULA], respectively (P. Persi, private communication). These sources are thus likely to be protostars of Class I. According to Prusti et al (1991) Ced110 IRS4 and IRS6 are confirmed Class I objects.

[FIGURE] Fig. 5. Difference between extinction estimated from star count (cloud extinction) and from [FORMULA] colour excess versus cloud extinction. Diamonds represent the DENIS candidates and crosses the known TTS

4.3. The luminosity function

Based on a study of the solar neighbourhood stellar population, Miller & Scalo (1979) have derived the IMF from the V luminosity function of main-sequence stars, and concluded that the IMF can be well approximated by a half-Gaussian distribution. In star-forming regions the population consists of YSOs often too faint in V or too highly reddened to be seen on Schmidt plates. The K band is the most appropriate to investigate the luminosity function in these areas (Lada et al., 1993; Megeath, 1996; Giovannetti et al., 1998). Fig. 6 displays the [FORMULA] luminosity function (KLF) for the TTS of the cloud including known sources and our candidates. The sample of known stars merge various observations that may be neither homogeneous, nor complete, since stars have been selected according to various criteria: [FORMULA] emission, near-infrared excess or X-ray emission. Examination of the KLF (Fig. 7) for all the DENIS selected objects shows 2 turnovers, the first one at [FORMULA] in the KLF is probably real while the second one at [FORMULA] corresponds to the DENIS completeness limit.

[FIGURE] Fig. 6. The [FORMULA] Luminosity Function (KLF) for the associated members of the cloud. The previously known TTS are represented in grey

[FIGURE] Fig. 7. The [FORMULA] Luminosity Function (KLF) for the DENIS selected members of the cloud (new candidates and the 16 reddest known TTS)

The interpretation of the luminosity function requires a model for the star formation. Theoretical evolutionary tracks (D'Antona & Mazzitelli, 1994) are used to derive a mass-luminosity relation. Stellar [FORMULA] magnitudes are computed assuming that they radiate like a black-body at their effective temperature and are calibrated using the standard solar parameters. We compute the mass-luminosity relation for 44 ages ranging from [FORMULA] to [FORMULA] years. We obtain similar results as Zinnecker & McCaughrean (1991) who have derived the relation for the ages [FORMULA], [FORMULA], [FORMULA], [FORMULA] years. To estimate when the star formation occurs in the cloud, we use the half-Gaussian IMF given by Miller & Scalo (1979). A Monte-Carlo simulation gives the 44 luminosity functions [FORMULA] for each age corresponding to a mass-luminosity relation. Since each theoretical KLF, [FORMULA], corresponds to a given age, the observed DENIS KLF can be fitted by a sum of [FORMULA] with different weight coefficients [FORMULA]. The solution consists in the resolution of the linear system of equations :

[EQUATION]

The singular value decomposition is used to invert the matrix and then, derive the [FORMULA] coefficients. When a coefficient is found to be negative, the corresponding luminosity function is removed and the process is iterated with the remaining luminosity functions. Fig. 8 shows the simulated KLF and the DENIS KLF. Because of the small number of stars, the birth rate function cannot be derived accurately. The Poissonian errors do not allow the determination of its shape (increasing, constant or decreasing with time).

[FIGURE] Fig. 8. The DENIS KLF (dashed line) and the simulated KLF (solid line)

Nevertheless, the presence of two peaks in the KLF allows the estimate of the age of the sample. At first glance, one could invoke another period of star formation to explain the second peak at [FORMULA]. This interpretation would, however, require stars older than [FORMULA] years which is in contradiction with our criterion that selects only stars with massive circumstellar accretion disks. Since the accretion rate is known to be about [FORMULA]yr-1 (Meyer et al., 1997) our selected stars cannot be older than a few million years and this interpretation should be ruled out.

To explain this peak, several factors should be taken into account. The intrinsic dispersion of the magnitudes and the completeness limit imply a Malmquist bias which causes an overestimation of the number of faintest stars. This bias is about [FORMULA] magnitude and so, can be ignored. Examination of the position of the 9 stars fainter than [FORMULA] and detected in the three colours (9 objects) in a colour-colour diagram shows that their extreme colour cannot be interpreted in terms of reddening, hence high extinction clumps on their line of sight cannot be invoked.

Among the 11 stars which are not detected in I, 3 (nb 36, 43 and 44) lie in the direction of the molecular outflow observed in CO lines by Mattila et al. (1989) in a [FORMULA] beam size. In this direction, they estimate a visual extinction of 17 magnitudes. Since our estimate of the extinction in this area is only 6 magnitudes with a [FORMULA] resolution map, these stars can be background objects.

The 6 stars detected only in [FORMULA] also contribute to the second peak. Some of them are known protostars (IRS4 and IRS6 in Table 1) and others are likely to be so (see above). Their faintness results from the effect of a massive circumstellar envelope. We remark that the star responsible for the outflow cited above could be the star nb 41, detected only in [FORMULA], rather than the known source T42 = sz32 (Persi P., private communication). Finally, possible unresolved binaries would lead to misleading colours that cannot be corrected. So, this peak is not fully understood and further deeper observations in K are requested to reach a better completeness limit.

The first peak at [FORMULA] requires a period of star formation that would extend from [FORMULA] to [FORMULA] years. Besides, the [FORMULA] excess modifies the luminosity function with a mean of 1.5 magnitude with respect to the spectral energy distribution of a main-sequence star. The mean extinction suffered by stars is about 5 magnitudes of visual extinction (Fig. 5), i.e. 0.5 magnitude of [FORMULA] extinction. The combination of these two effects shifts the KLF of 1 magnitude toward the fainter magnitudes. That led us to change our age estimation from [FORMULA] - [FORMULA] to [FORMULA] - [FORMULA] years. We stress the point that it just means that we do not detect older stars with our infrared excess criterion. Older stars have lost their disk, or, the accretion rate has become smaller and then, they no longer exhibit an infrared excess. The apparent drop of the KLF down to [FORMULA] probably results from a vanishing of the circumstellar disk rather than from a real decrease of the star formation rate. The maximum life time of a circumstellar disk is then estimated to [FORMULA] years for low-mass stars which corresponds to the oldest Classical TTS.

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© European Southern Observatory (ESO) 1998

Online publication: September 17, 1998
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