Astron. Astrophys. 360, 539-548 (2000)

Appendix A: stellar calibrations

The analysis presented in this work makes use of calibrations between intrinsic K magnitudes and colours on the one side, and spectral types and initial masses on the other side. The employed calibrations, valid for luminosity class V, are summarised in Table A.1. The use of luminosity class V calibrations for all stars is justified by the young age of Cyg OB2 (Massey & Thompson 1991).

Table A1. Stellar calibrations employed in this work (all data are for luminosity class V). was calculated using the relation (see Appendix B).

The relation between spectral type and absolute visual magnitudes has been compiled from data published by Vacca et al. (1996) for O3V - B0.5V stars, Humphreys & McElroy (1984) for B1V - B3V stars, and Schmidt-Kaler (1982) for B5V - G0V stars. The intrinsic colour calibrations and were taken from Wegner (1994) for spectral types O6V - B9V and from Koornneef (1983) for later spectral types. The calibration of Wegner (1994) was extrapolated in the , plane to spectral type O3V using the relation

which has been obtained form a fit to the data for spectral types B2V and earlier. The same relation was also used to interpolate the calibration for some O subtypes that were not covered by the analysis of Wegner (1994).

Based on the and calibrations, the intrinsic K magnitudes were derived using

To derive the mass-luminosity relation, the initial stellar mass to spectral type relation has been taken from Schaerer & de Koter (1997) for O and Schmidt-Kaler (1982) for later type stars. Using a fit in the , plane, the following relation has been established

Appendix B: photometric sample selection

For the photometric sample selection two constraints have been applied in the K, plane. First, all association stars with identical intrinsic magnitude are collected along the reddening line. To understand the selection, recall that the apparent K magnitude of a Cyg OB2 member star is related to the intrinsic magnitude , the extinction , and the distance modulus DM via

The extinction of a star can be estimated from the colour excess

using

(Rieke & Lebofsky 1985). Thus all member stars of identical intrinsic magnitude but different extinction lie in the K, CMD on a line of constant slope, given by

Hence, selecting stars within a band

results in a reddening independent selection of stars, where

The values of are listed in Column 6 of Table A.1. Fitting a linear relation to these data results in

Second, the K band extinction of an association star can be estimated by calculating its displacement along the reddening line. To understand this, notice that for main sequence stars, is a function of intrinsic colour , which for massive stars can be roughly approximated by a linear function. From the calibration table (cf. Table A.1) the relation

has been determined for . Using Eqs. (B.2) and (B.3) the relation can be rewritten as

Replacing this approximation in Eq. (B.1) and solving for result in an approximative relation between apparent magnitude and colour and extinction in the K band:

© European Southern Observatory (ESO) 2000

Online publication: August 17, 2000
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