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Astron. Astrophys. 335, 522-532 (1998)

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3. Analysis

3.1. Outline of the procedure

A detailed description of our analysis method applied to ground-based observations of embedded clusters has been published elsewhere (CRBR; Comerón et al. 1996), so we will only give an overview. Our goal is to determine the intrinsic properties of a young stellar object, possibly surrounded by a circumstellar disk or envelope, and embedded in a heavily obscuring molecular cloud. Foreground extinction decreases and reddens the observed fluxes. The circumstellar material tends to add primarily to the longer wavelength output, either by thermally reprocessing the shorter wavelength luminosity of the object, or through emission of the viscously heated material accreted onto the di sk.

In color-magnitude and color-color diagrams, therefore, the reddening vectors due to extinction and circumstellar excess are well separated. In the commonly used [FORMULA], [FORMULA] diagram, the T Tauri star locus can be explained by models of emission and reprocessing of radiation in circumstellar disks and envelopes (Adams et al. 1987; Lada & Adams 1992; Meyer et al. 1997; Calvet et al. 1997) and is easily distinguished from the effects of reddening (Strom et al. 1989). It is therefore possible in principle to derive the intrinsic properties of embedded objects by moving the observational data points in a multidimensional magnitude-color-color... diagram along the reddening and circumstellar excess vectors, until they fall on the locus defined by models of pre-main sequence evolution. The behavior of an embedded object is basically controlled by four parameters: luminosity, temperature, infrared excess, and foreground extinction (the distance can be usually considered as known and we have taken it to be 160 pc for [FORMULA] Oph). Therefore, to achieve a well constrained fit it is necessary to have measures in at least four bands, although three bands can suffice if one uses the theoretical isochrones and an assumed age to give a relation between luminosity and temperature. In practice, however, uncertainties in photometric measurements and possible deviations of real objects from the models used for the fits make it desirable to have a wide wavelength coverage in as many bands as possible to constrain the fits reliably. Our ISOCAM measurements provide an important advance in this regard.

3.2. Theoretical isochrones

The choice of the set of pre-main sequence evolutionary tracks is clearly an important aspect of the fit. In studies of emerged clusters, it is usually possible to place the object on a temperature-luminosity diagram, and then to estimate the mass and the age by overlaying the evolutionary tracks on the same diagram. However, mass estimates for embedded cluster members rely more strongly on the adopted evolutionary tracks, since in the procedure outlined above it is not possible to derive the temperature and luminosity independently of them.

Several recent sets of isochrones exist in the literature covering the mass range expected for our objects (Burrows et al. 1993, 1997; D'Antona & Mazzitelli 1994; Baraffe et al. 1997). A critical discussion of the different sets of isochrones from an observational point of view has been presented by Luhman 1998 and Luhman & Rieke 1998, who have examined the ability of existing models to reproduce the coevality of open cluster members, to provide well-behaved mass functions, and to fit well determined physical parameters of components of eclipsing binaries. For the lower masses of interest in this paper, the use of detailed model atmospheres and an explicit treatment of radiative transfer at the surface are major factors in producing realistic results. At the present time, Burrows et al. 1997 and Baraffe et al. 1997 provide the most adequate treatment of the atmosphere boundary condition, using the new, still unpublished Allard NextGen models. The differences between these two sets in this range are minor; we have used the tracks of Burrows et al. 1997 in the analysis presented here.

3.3. Modeling the infrared excess

The spectral energy distributions of sources with infrared excesses are approximated as described by CRBR, based on the circumstellar envelope models of Adams et al. 1987. The amount of infrared excess required is parametrized by the spectral index [FORMULA]: a stellar photosphere radiating like a blackbody would have [FORMULA], and [FORMULA] implies infrared excess. The results of this approximation reproduce well both the observed T Tauri locus and the model predictions of Lada & Adams 1992 (which are also based on the work of Adams et al. 1987). They also agree over the wavelengths sampled by our observations with the model spectral energy distributions of stars surrounded by disks or infalling envelopes calculated by Calvet et al. 1997 and Meyer et al. 1997. Temperature-dependent photospheric features have been computed using the synthetic spectra of cool photospheres of Allard & Hauschildt 1995.

3.4. Foreground extinction

The adopted extinction law is that of Rieke & Lebofsky 1985 for wavelengths below 4.5 µm. Deviations from a universal extinction law in star forming regions such as [FORMULA] Ophiuchi are well known (Mathis 1990), but they seem to affect mostly wavelengths shorter than those used in our analysis. In the JHK bands, the detailed analysis of the extinction in [FORMULA] Ophiuchi of Kenyon et al. 1998 confirms the applicability of the results of Rieke & Lebofsky 1985. For longer wavelengths, the analysis of line ratios in the direction of the galactic center carried out by Lutz et al. 1996 using ISO SWS data give an extinction at 4.5 µm similar to the one derived by Rieke & Lebofsky, but the values found around 6 µm by Lutz et al. are larger than those that one gets by interpolating the results of Rieke & Lebofsky at that wavelength. We have adopted Lutz et al.'s extinction law for the ISOCAM passbands. However, for the levels of obscuration of our targets (see Sect. 4), the relative transparency of the dust near 6 µm makes the uncertainties due to the choice of the extinction law of the same order as the uncertainties in the photometry.

3.5. Effects of binarity

Some of the objects in our sample may be unresolved binaries, as can be expected given the large fraction of binaries detected among T Tauri stars (Brandner et al. 1996). Undetected binarity in this mass range can affect our fits in different ways, depending on the mass ratio of the system. If one of the components is cooler than the other, the combined spectral energy distribution of the system is dominated by the brighter member in the near infrared, with the fainter and cooler companion contributing at longer wavelengths. The effect of the companion would then be similar to that of a circumstellar excess, and the parameters of the primary will be well estimated by our method. If the system has two components of similar brightness and temperature, the isochrone fitting will yield a single object with higher temperature, extinction, luminosity, and mass than those of each component. Binarity can thus lead us to classify a brown dwarf erroneously as a star, but not the opposite.

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© European Southern Observatory (ESO) 1998

Online publication: June 18, 1998
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