3. Synthetic fits to the IRAS/CS luminosity function
One immediate consequence of the shape of the IRAS/CS luminosity function is that these sources are better understood as clusters of stars rather than in the framework of one dominant star per source. A single exciting star would result in a power law LF: an IMF index (see below), and mass-luminosity relation , give a probability distribution in luminosity .
We used a simple model to examine whether the variations in the LFs of IRAS/CS sources from inside to outside the solar circle can be traced to the underlying young stellar population. We proceed to describe a Monte Carlo analysis for the ensemble of massive star forming regions in the galactic disk. The luminosity of a MSFR is the sum of the luminosities of each star, given by the mass-luminosity relationship. We used a polynomial fit to the mass-luminosity relation of the tracks presented in Schaller et al. (1992) for Z=0.02, at the first time step they list,
The metallicity dependence of the mass-luminosity relation was neglected, as the Z=0.001 tracks in Schaller et al. (1992) have luminosities within 10% of Eq. 3 for .
The synthetic population of MSFRs was generated in the following way. The number of stars in a given MSFR, , is generated randomly within the range , and subject to a power law probability distribution with exponent , . A discussion of the model sensitivity on will be found in Sect. 4. Given , the total luminosity of a MSFR is calculated by summing the individual luminosities of each star, using the mass-luminosity relationship. The mass of each star is generated randomly, within the range and satisfying the IMF distribution,
in this notation the Salpeter (1955) IMF corresponds to . Thus the luminosity of each MSFR is randomly generated with , and an ensemble of 5000 MSFRs provides a population large enough to compute the synthetic luminosity function (that this is one order of magnitude larger than the number considered in the observed LF does not affect the results, only helps to reduce the random fluctuations).
An important simplification in this approach is that the ensemble of MSFRs is assumed to be homogeneous in age (see Sect. 6). Furthermore, it should be mentioned before discussing the results of the model that the mass-luminosity relation remains mainly theoretical for massive stars. Although Burkholder et al. (1997) give observational evidence that support the massive star models up to , the upper mass limit we used is , where to our knowledge no direct observational information exists to back the theoretical models.
© European Southern Observatory (ESO) 2000
Online publication: June 8, 2000