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Astron. Astrophys. 358, 514-520 (2000)

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5. The IMF index and possible large scale variations

After finding reasonable values for [FORMULA], we extend the search to include all three parameters, and obtain


Thus the best fitting sets of parameters have [FORMULA]. Values for the significance of the fits are [FORMULA], with two degrees of freedom (5 bins in comparison less 3 free parameters). Fig. 4 shows the models that best fit the LFs. Due to the Monte Carlo approach, secondary [FORMULA] minima are found about the true minimum. Multiple minimization runs with various initial guesses fluctuate about the above values: from [FORMULA] to [FORMULA] for [FORMULA].

[FIGURE] Fig. 4. Best fit models (dotted lines) to the inner and outer Galaxy IRAS/CS LFs (solid lines), above the completeness limit [FORMULA]. In ordinates is the LF normalised over [FORMULA], as a function of [FORMULA]

Keeping [FORMULA] fixed at the best fit value, with the [FORMULA] uncertainties quoted in the previous section (i.e. above a 50% confidence level in a 2-D slice), our best values for [FORMULA] are [FORMULA] in the inner Galaxy, and [FORMULA] in the outer Galaxy.

As an indication of the uncertainty level related to the use of Eq. 1, increasing the bolometric fluxes to [FORMULA] results in [FORMULA] for [FORMULA]. Only very low significance fits were found using either [FORMULA], or [FORMULA]. A factor of 2 in the mass-luminosity relation [FORMULA] gives [FORMULA], i.e. no significant change. A steep IMF index seems to be a robust result of our analysis.

The IMF index [FORMULA] for the inner and outer Galaxy seems to be the same, although [FORMULA] changes significantly. In other words, although the average mass of newly formed stars is the same inside and outside the solar circle, the average number of stars per star forming region and in a finite mass range is lower in the outer Galaxy. The best fits of the parameter [FORMULA] imply that the expectation value for the number of stars per MSFR with [FORMULA], [FORMULA], decreases from 225 for [FORMULA] to 120 for [FORMULA]. The decrease in [FORMULA] is not an effect related to the area covered by the 100[FORMULA]m IRAS beam: due to the lower FIR background towards the outer Galaxy, the IRAS point sources are detected to greater distances than in the inner Galaxy (the average distance to IRAS/CS sources is 6.92 kpc for the outer Galaxy, and 5.32 kpc in terms of the effective distances for the inner Galaxy).

Is there a gradient in the IMF index with galactocentric radius? How does our value for the IMF index compare with other estimates? The gradient proposed by Garmany et al. (1982) has been re-interpreted as a result of contamination from field O stars (Massey et al. 1995a), which seem to derive from a very steep IMF. The values Massey et al. (1995b) and Massey (1998) quote for [FORMULA] in the Milky Way and the Magellanic Clouds OB associations are [FORMULA] and [FORMULA], which argues against a metallicity dependence of [FORMULA], at least over 10 -120 [FORMULA]. But constraining the analysis to nearby OB associations gives steeper values, Claudius & Grosbol (1980) give [FORMULA] over 2.2 -10 [FORMULA], and Brown (1998) gives [FORMULA]=1.9 for the Upper Scorpius subgroup of Sco OB2, over 3 -16 [FORMULA]. Brown (1998) used Hipparcos data to ascertain membership (see de Zeeuw et al. 1999), which is crucial in the coeval approximation; the very large OB associations in Massey et al. probably have a complex star formation history. Although Massey et al. establish a good case for a universal massive star IMF, the exact value of the IMF index is still an open issue. Our contribution to this debate is that there certainly are differences in the physical processes governing star formation in the outer spiral arms and the molecular ring. In our simple approach, and understanding that we restricted our study to regions of massive star formation embedded in dense molecular cores and with at least one UCH II region, it seems that although the IMF index is constant, the average number of stars born per region is lower outside the solar circle. We favour a rather steep IMF index, close to the values from Brown (1998).

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© European Southern Observatory (ESO) 2000

Online publication: June 8, 2000