5 Placing the components into the HRD

In this section we will place the components of young binary systems into the HRD and compare their positions in this diagram with theoretical PMS evolutionary models to derive masses and mass ratios. For this purpose one has to know their luminosities and spectral types. Since these quantities are not known as directly measured values we have to make some assumptions to estimate them from our resolved NIR photometry and the system properties that are given in the literature.

5.1 Luminosities

As described in Sect. 4.1 for the colour-magnitude diagrams, we transform the theoretical atmosphere models that give $T_{{\rm eff}}$and L as functions of mass and age into a diagram in which the luminosity is represented by a NIR magnitude.

Circumstellar excess emission is minimal around $\lambda\approx 1~\mu{\rm m}$(e.g. Kenyon & Hartmann 1995). For this reason we prefer the J-band magnitudes of the components to H and K as luminosity indicator. It is however not clear if this excess emission is negligible in the J-band. Hartigan et al. (1995) have measured the veiling in optical spectra of T Tauri stars. Assuming that the excess emission in the J-band is $r_{{J}} = 0.1\times r_{{V}}$, where $r_{\lambda} = F_{\lambda, {\rm excess}}/F_{\lambda, \ast}$, they come to the conclusion that for a sample of 19 CTTS and 10 WTTS the mean value is consistent with $<r_{{J}}>\, = 0.0$. Folha & Emerson (1999) determined the NIR excess emission directly using infrared spectra of 50 T Tauri stars. Their result is that $<r_{{J}}>\, = 0.57$ for the CTTS in their sample and thus much larger than expected. To take this into account, we apply an excess correction of $0.49~{\rm mag}$ corresponding to this <r_J>, if we use J magnitudes as an indicator for CTTS stellar luminosities. For the WTTS in their sample Folha & Emerson (1999) find values of r_J that are compatible with zero, so for the components of WTTS systems no excess correction is necessary.

   
5.2 Spectral types

Figure 5: The components of the young binary system IKLup placed into the HRD as an example for the method described in Sect. 5. The cross gives the position of the primary, the horizontal dashed lines the locus for the secondary and the respective error. The theoretical model is by Baraffe et al. (1998). The evolutionary tracks are given for masses of 0.04, 0.06, 0.08, 0.10, 0.15, 0.20, 0.25, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, 1.00 and 1.20$M_{\odot }$, the isochrones denote ages of 1, 2, 5, 10, 20, 50 and 90 Myr. If the components are coeval their masses will be $0.9\pm 0.2~M_{\odot}$ and $0.3\pm 0.1~M_{\odot}$.

For nearly all of the systems discussed here we know the combined optical spectral type from the literature (see Sect. 2.1 and Table A.2). We assume that these combined spectra represent to a good approximation those of the optical primary components, and we assign the optical spectral type of the system to the brightest component in the J-band. The spectral type and effective temperature of the companion is estimated using the assumption that all components within a system are coeval. We are now ready to place the components into the HRD. The procedure is shown in Fig. 5 using the T Tauri binary system IKLup as an example. For 48 more systems the placement of the components into the HRD is shown in Fig. C.1, available in electronic form. The theoretical PMS evolutionary model used is by Baraffe et al. (1998). The position of the primary is determined by its J-band magnitude and the system's spectral type. For the latter quantity we assume an error of one spectral subclass as given by Kenyon & Hartmann (1995) for the systems in Taurus-Auriga. The companion's J-band magnitude and the respective error define a locus for the companion in the HRD. If we assume that both components are coeval the companion is situated at the point of intersection between this locus and the isochrone of the primary. In the same way we also defined the loci of the components in the HRD for the evolutionary tracks of Swenson et al. (1994) and D'Antona & Mazzitelli (1998).