4. Size, mass, and stellar content
In order to determine the size, centre, and stellar content of Cyg OB2, radial star density profiles have been extracted from the 2MASS data by counting the number of stars intrinsically brighter than in concentric radial annuli around an assumed centre, divided by the annuli surface. Geometrical corrections have been applied for the outer annuli that partially fall outside the rectangular survey region. The profiles were fitted by a King law (King 1962)
on top of a constant to determine the core radius , the tidal radius , and the field star density. By searching the central position that minimises the radial extent of the profile the centre of Cyg OB2 has been determined to and . The corresponding density profile is shown in Fig. 6. The central stellar density reaches 4.5 stars arcmin-2 above the field star density, and drops to at a radius of , resulting in a half light radius of pc at a distance of 1.7 kpc.
Best fitting King parameters for the profile are and , leading to a concentration parameter of 0.5. The reduced of the fit is only 10.9, indicating that the King law is not a very accurate description of the radial density profile. Indeed, there is no physical reason to believe that Cyg OB2 should follow a King profile. The basic aim of using King profiles was the estimation of the field star density, and comparison with Fig. 6 convinces that at least this goal was reached.
By integrating the radial profile after subtraction of the fitted field star density, the total number of association stars with (corresponding to spectral types of F3V and earlier) amounts to . The error (as all following error quotations) includes a possible systematic uncertainty from the field star subtraction. This systematic uncertainty was estimated by applying different methods for the extraction of the association stars, such as analysing star density profiles along constant Right Ascension or declination, estimating the field star density from a circular region around the association, or by performing the analysis without removing the gradient in the field star density distribution.
Selecting only K magnitudes brighter than limits the sample to stars intrinsically brighter than , corresponding roughly to spectral type B9V and earlier. Repeating the radial density profile analysis for this limited sample allows the determination of the total number of OB stars in Cyg OB2 to . This number is at the upper end of the range quoted by RLP (300 - 3000), confirming their suggestion that many of the highly reddened stars in the DSS survey are indeed OB stars. Further, restricting , by requiring , selects only O stars from the PSC, resulting in a total number of objects. In their survey, Massey & Thompson (1991)find 40 O stars within a central field of 0.35 degrees squared of the Cyg OB2 association. Integrating over the same region in the 2MASS data gives O stars, demonstrating that the present analysis is in excellent agreement with the Massey & Thompson observations. Hence, the large number of O stars found in this analysis is mainly due to the large extent of the association, which previously was missed due to the high extinction in the area.
Taking an initial mass of 1.5 for a F3V star (Schmidt-Kaler 1982), and assuming the slope of the initial mass function (IMF) 2 to be comprised between -1.1 and -1.7, the number of association stars converts into a total stellar mass of above 1.5 . Extrapolation of the IMF to lower masses using the prescription of Kroupa et al. (1993)results in a total association mass of , where the boundaries correspond to a lower mass cut-off of 1.0 and 0.08 , respectively. Since the actual value of the mass cut-off in Cyg OB2 is unknown, the total association mass is uncertain to within the quoted limits. However, even at the lower mass limit, Cyg OB2 would be the most massive OB association known in the Galaxy, being comparable in mass to a small globular cluster.
From the radial density profile and the total mass estimates, the central mass density of Cyg OB2 can be estimated. Assuming a total mass of results in a mass density of pc-3, where the lower value comes from the extrapolation of the best fitting King profile into the centre, and the upper value comes from the observed central stellar density. Correspondingly, the central mass density estimate for a total mass of amounts to pc-3. As before, the distance to Cyg OB2 has been assumed to 1.7 kpc.
© European Southern Observatory (ESO) 2000
Online publication: August 17, 2000