3.1. Color-color diagrams
PMS stars are known to present several spectral peculiarities, both in their absorption/emission lines and in their overall spectral energy distribution (SED). While classical T-Tauri stars (CTTS) show strong deviations from the spectral energy distribution of normal stars, as well as strong emission lines, weak-line T-Tauri stars (WTTS), as their name implies, show little or no such peculiarities (Walter et al. 1988).
The SED of classical T-Tauri stars is usually characterized by non-photospheric excesses both in the optical/ultraviolet (the so called `veiling') as well as in the infrared spectral regions. Both types of excess have been successfully related to the emission of accretion disks (e.g. Bertout et al. 1988).
While the infrared excesses due to the presence of accretion disks usually show up at larger wavelengths than those observed here, the blue contribution due to the hot accreting area is known to be extend significantly down to, at least, the V photometric band (see Hartigan et al. 1995).
Such photometric excesses will cause the star to deviate, in a color-color plot, from either the main-sequence or the giant locus. We have thus used the position of our stars in the vs. and vs. planes to select likely PMS stars. Clearly such selection procedure is presumably biased toward CTTS and, in particular, toward the youngest and most actively accreting ones.
The color-color diagram shown in Fig. 3 indeed shows that a large fraction of the redder objects deviate from both the main sequence and the giant loci. These deviations are most likely due to blue excesses in the spectra of these objects and strongly suggest their CTTS nature. This last point is reinforced by the evidence that most of the stars whose line was detected in emission by Herbig (1954), Marcy (1980), Ogura (1984) and Sung et al. (1997) are seen to deviate on average more than the X-ray sources (Flaccomio et al. in prep.): while the former are mostly CTTS, the latter are, more likely, dominated by WTTS having less or no blue excess.
Fig. 4 shows a color-color diagram computed using "redder" colors than the ones used in Fig. 3; such a diagram is thus less affected by the blue excesses that were so evident in Fig. 3. Nevertheless, a numbers of stars still deviate from both the dwarf and the giant sequences.
Considering that field stars are prevalently MS objects (with possibly a few giants) those stars that lie significantly above either the Main Sequence in Fig. 3 or the giant locus in Fig. 4 are, as already suggested, likely to be classical T-Tauri stars and consequently members of NGC 2264.
The position of the few stars below and to the right of the lower of the sequences (i.e. the MS in Fig. 4 and the giant locus in Fig. 3) can be explained assuming a larger than average reddening. As the cloud right behind NGC 2264 can be considered totally opaque, the most plausible possibility is that these object are NGC 2264 members either with a high circumstellar absorption or partially embedded in the cloud. Foreground stars indeed should be even less reddened than the average `interstellar' NGC 2264 value of E(, so that they should remain close enough to the MS not to be mistaken for cluster stars.
Following the previous discussion, we chose to select as NGC 2264 members those stars that, in one or both of the color-color diagrams, are more distant from the region bounded by the MS and the giant locus than the photometric uncertainties would allow. Considering only stars brighter than V=17, whose photometric error can be quite reliably estimated (i.e. 0.1 mag. in both axis, with a confidence) we thus selected 46 likely members, 24 of which were previously unknown.
Although this selection criterium has resulted in a significant number of new members of the population of NGC 2264, the procedure adopted has no claim of completeness (as it is true for the other membership criteria). Inspection of the color-color diagrams shows that known members with earlier spectral types do not show any photometric excesses, and thus that the adopted procedure preferentially selects later spectral types.
3.2. The membership catalog
Our NGC 2264 membership catalog, containing 141 members, is shown in Table 5. The first column refers to the identification number in Table 3. A colon besides this numbers signals an uncertain photometry. We then list the sky position, photometry and derived physical parameters of the selected stars (see Sect. 3.3). The column labeled "Memb" indicates the methods by which each star was selected. The letters indicate: `c', stars selected because of their colors using the method discussed above; `x', the counterparts of the X-ray sources listed by Flaccomio et al. (in prep.); `h', the stars from the catalogs of Herbig (1954), Marcy (1980), Ogura (1984) and Sung et al. (1997); `p', the proper motion stars from Vasilevskis et al. (1965) with membership probabilities greater than 50%. The last column shows the result of the cross identifications.
Table 4. Completeness estimate
Table 5. Catalog of members.
Table 5. (Continued)
Excluding the list by Sung et al. (1997), which include only stars in the northern half of our field of view (), all of the other surveys entirely cover the area of the sky we study in this paper. Anyway, none of these (largely overlapping) samples is complete: Vasilevskis et al. (1965) proper-motion survey has a magnitude limit of , the -selected samples are strongly biased toward the CTTS population, as is our photometrically selected sample. The X-ray sample, which is also the largest, is likely to include both CTTS and WTTS. It also spans a larger range of spectral types than all the other samples but it is biased toward the more active stars.
We will show in the next subsection that, in building the Mass Function for the observed part of NGC 2264, the different biases actually compensate each other to some degree and that the union of these samples reaches near completeness, at least for the most massive stars ().
3.3. The H-R diagram
Fig. 5 shows the H-R diagram for the stars selected as NGC 2264 members, superimposed on the pre-main sequence evolutionary tracks from D'Antona & Mazzitelli (1998). Bolometric luminosities for each star were derived from our photometric data using the Bessel & Stringfellow (1993) vs. relation and assuming a distance of 760 pc; effective temperatures were calculated from the (de-reddened) V-I for stars with , and from for the bluer ones. In the first case we employed the Schmidt-Kaler (1982) color-temperature relation adapted with the aid of the Bessel (1990) color-color relation. In the second we used the Code et al. (1976) relation. A correction for mean reddening (Pérez et al. 1987) was applied to the photometry prior to these calculations.
Although we adopted a distance of 760 pc (Sung et al. 1997), a wide range of distance estimates are available in the literature for NGC 2264. Pérez et al. (1987), for example, observationally derived individual extinction laws for each star, finding evidence of anomalous reddening, and obtaining a distance of 950 pc, higher than most available distance estimate. Our adopted distance however, other than being the most recently obtained value, is also close to the average of all modern estimates.
In the determination of both the bolometric luminosity and the effective temperature of low mass stars we used the color indices and I magnitudes, which better represent the photospheric emission of PMS stars (Kenyon & Hartmann 1990; Sung et al. 1997). Individual differential reddening and residual color excesses may however introduce competing systematic shifts in the effective temperature and bolometric correction for each star. Other sources of uncertainty for the luminosity and/or temperature determination are the possible presence of unresolved companions and, for CTTS, the occultation of part of the photosphere by circumstellar disks (see e.g. Kenyon & Hartmann 1990). The apparent positions of the few stars that lie over the birthline in the H-R diagram may well be explained by these systematics. The mass and age of individual stars were thus estimated by their positions on the D'Antona & Mazzitelli (1998) evolutionary tracks. Five stars in Fig. 5 appear to lie below the main sequence. For the four of these stars closest to the main sequence we assumed the mass of the closest evolutionary track and the age of years, we have discarded the remaining one.
3.4. Dynamical Evolution and Mass Segregation
The area of the sky we study in this work does not cover the entire Star Formation Region (see Fig. 1) but only its southern part around the bright star W178. Our result can thus only be strictly valid for this region.
If the association has undergone significant dynamical evolution the observed mass and age spectra of our sample may differ from the initial distributions that we intend to study. Moreover, as indicated by several studies (see e.g. Sagar et al., 1988; Raboud & Mermilliod, 1998), mass segregation is also present in young clusters with ages smaller than their relaxation time. This fact has been interpreted as a result of inhomogeneous formation conditions within the cloud leading the concentration of massive stars toward its center.
We thus tried to study the spatial distribution of stars in relation to stellar mass. A quantitative study is made rather problematic by the difficulty of defining a cluster center for NGC 2264. Sagar et al. (1988), for example, define two centers, one corresponding to the bright star S Mon, north of our surveyed region, the other close to the star W157 (our star 339 in Table 5).
No clear mass segregation is apparent from the spatial distribution of stars of different masses. Although this failure to detect mass segregation may be due to the small area investigated, it quite possibly reflects the actual situation. First: the relaxation time for NGC 2264, as calculated by Sagar et al. (1988) is , greater than its age. Second: mass segregation in non-relaxed clusters has been usually observed only for more massive stars (, Raboud & Mermilliod, 1998) than those considered; here we are interested only in the low mass () population of NGC 2264 and we only derive masses and ages for these stars.
3.5. The Initial Mass Function in NGC 2264
In order to build a meaningful IMF it is of primary importance to take into account the completeness of the star samples used. Here we assume that, for a given stellar mass, the observational biases of the proper motion sample are not correlated with those affecting the three other samples used (i.e. the ones selected on the basis of X-ray emission, emission, and of strong color excesses). It follows that, although by itself biased toward massive stars, the proper motion sample constitutes, in each mass bin, a random sample of the whole population, free from the biases that affect the other samples. The proper motion members can therefore be used to derive the (mass dependent) selection efficiency of any of the other samples, e.g., for the X-ray sample:
where refers to the total number of NGC 2264 members in the field of view, and refer to members detected in X-rays and proper motion surveys, respectively, and is the number of proper motion members detected in X-rays.
A similar calculation has been performed for all the considered samples (i.e. X-ray, , color excess and proper motion) as well as for their union in the mass range , where the proper motion sample and the other three overlap to some degree. The results are shown in Table 4. For each considered mass bin we report the expected selection efficiency of any of the methods. As expected, each sample is individually incomplete, but the union of all the samples represents reasonably well the actual NGC 2264 population in the considered mass range.
The resulting IMF is shown in Fig. 6; squares with error bars derived from Poisson statistics represent the actual data while the solid-line histogram, where different from zero, is the bias-corrected IMF derived as described above from the composite sample. The dashed line shows the Scalo (1986) local IMF with arbitrary normalization. While we could not estimate the completeness of our sample for , the fall of the IMF in this mass range is most obviously due to the limiting sensitivity of both the existing data and of our survey (and thus to the incompleteness of the resulting sample) at the lower-mass end.
The resulting observational, bias-corrected IMF shows evidence for a bimodal distribution, with a "bump" in the distribution at the higher masses (). We performed the KMM test (Ashman et al. 1994) to detect bimodality in an univariate data set. The test rejects with a high degree of significance (P=0.017 or P=0.015 depending on weather we assume homoscedastic or heteroscedastic populations), the hypothesis of an unimodal distribution, thus giving support to the reality of the high mass excess. A similar result was recently obtained, for the northern part of NGC 2264, by Sung et al. (1997), who performed a study using UBVRI and photometry. The conclusions of Sung et al. (1997) are based on a list of NGC 2264 members which, due to partial spatial overlap of the two studies, has only 18 stars in common with our list, so that the two results are indeed independent.
3.6. Star formation history
While individual stellar ages derived from the position of the stars on evolutionary tracks have a certain (possibly large) degree of uncertainty associated with them, because of the already discussed uncertainties on the position of the stars in the H-R diagram as well as on the tracks themselves, the relative ages (and mass attribution) should be more accurate, thus yielding a useful picture regarding the time-evolution of the star-formation rate in the region.
In Fig. 7a we have plotted the star-formation rate (defined as the number of stars with age in each logarithmic age bin divided by the size - in years - of the bin) as a function of the estimated age for our sample of stars in NGC 2264. The star-formation rate is plotted for the complete sample (square dots, with Poisson-statistics error bars) and for two subsamples segregated by mass: stars with mass greater than 1.0 with the dark continuous curve and those with with the dashed lighter one. For these latter two samples we also plot (Fig. 7b) the distribution of the logarithm of star ages. Note that both of these subsamples are within the mass range whose completeness we have shown in the previous section.
The star-formation rate for NGC 2264 shows (in any mass ranges) a steep rise in formation activity at the early stages of the history of the SFR (i.e. at large stellar ages) and a subsequent flattening. However, the presence of uncertainties in the individual age attribution would introduce such a behavior in the presence of a star-formation activity which started suddenly at some point in the past and then proceeds at constant rate. To verify this, we produced simulated star-forming rate plots under the assumption of a sudden turn-on in star formation which then proceeded at a constant rate, and with characteristic uncertainties equal to the ones we have derived from our sample. Indeed, the observed global star-forming rate for NGC 2264 is compatible with this hypothesis.
The star-formation rate for the whole sample appears to indicate an age of about 1- yr for the beginning of star formation while the two complete subsamples, which, on average, comprise more massive stars, indicate a larger age ( yr). This fact may suggest a scenario of sequential star formation. However the total sample is very likely biased toward younger stars, as can be seen from the HR diagram in Fig. 5. The lack of low mass stars, which can likely be explained by a sensitivity limit, clearly introduces such a bias. Interestingly, however, the curve and the histogram that refer to the lower masses seem to show a somewhat smaller typical age respect to the other one, hinting once again toward a sequential star formation. This difference in age between the two samples can hardly be considered significative, but it will be interesting, for future deeper observations, to test this hypothesis.
In any case it seems clear that star forming activity is continuing to the present day, as shown by the presence of a few stars close (or formally above) the birthline in our sample, as well as the reported presence of several very young objects in the region (e.g. Castelaz & Grasdalen 1988).
To conclude this section, we note that a sequential star formation scenario had already been suggested for NGC 2264 by Adams et al. (1983). However their proposed sequence of star formation was exactly the opposite of what is suggested by our data, starting with low mass stars and proceeding gradually with the onset of formation of more massive ones. Stahler (1985) had later reinterpreted the same data. He concluded that, due to the uncertainty in the dating of those stars that had already reached the main sequence, the observations where instead compatible with a variety of star formation histories and in particular with a contemporaneous onset of formation for all masses. Our results however are not subject to the same criticism for two reasons. First, our sample of stars is comprised of relatively low mass stars and very few of them, if any, seem to have reached the main sequence. Second, the effect described by Stahler (1985) would tend to mask, and not to produce, the kind of mass-age relation we suggest.
© European Southern Observatory (ESO) 1999
Online publication: April 19, 1999