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

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4. Search in parameter space and the role of [FORMULA]

A first broad search for the parameters [FORMULA] and [FORMULA] requires specifying [FORMULA]. It could be thought firsthand that any value of [FORMULA] high enough to simulate infinity would do, but we tried [FORMULA] and did not obtain any fit, over the range [FORMULA], [FORMULA]. We distinguished three cases, fixing the maximum number of stars per MSFR, [FORMULA], to 500, 1000 and 2000. Fig. 3 shows the [FORMULA] cumulative probability for the goodness of fit as a function of parameter space. In the observed IRAS/CS LF, we have five bins with non-zero counts above the completeness limit of [FORMULA]. The number of degrees of freedom is thus 3, which corresponds to the five bins in comparison less two free parameters ([FORMULA] and [FORMULA]). The fit to [FORMULA] is a lot more noisy, a consequence of the reduced number of IRAS/CS sources used to compute the LF.

[FIGURE] Fig. 3. Search in ([FORMULA]) parameter space for the best fit model, with three guesses for [FORMULA]. Plotted is the [FORMULA] cumulative probability for the goodness of fit (with 2 free parameters), with contours at 10%, 30%, 50% and 70%. The upper two plots were computed with [FORMULA], the middle two with [FORMULA], and the bottom two with [FORMULA]

It is apparent that for any value of [FORMULA], [FORMULA] is similar inside and outside the solar circle, while the acceptable values for [FORMULA] are markedly different. It can also be noticed from Fig. 3 that the best fit [FORMULA] are rather independent of [FORMULA], in contrast with the behaviour of the best fit IMF index [FORMULA]. For [FORMULA], the IMF index in the inner Galaxy, at 50% confidence level for the goodness of fit (with two free parameters), corresponds to [FORMULA]. This is very close to the result for the outer Galaxy, [FORMULA]. The case where [FORMULA] seems to give better results for [FORMULA], and constrains [FORMULA] at 50% confidence. This range of values, [FORMULA] for [FORMULA] and [FORMULA] for [FORMULA], will be used as an indication of the uncertainty level in the best fit [FORMULA].

As the distribution of [FORMULA] seems to be a bounded power law, there exists a maximum for the number of stars born in a MSFR within a finite mass range. It should be kept in mind that the total number of stars could in fact depend on the stellar masses and the star formation history of a MSFR; we expect the parameter [FORMULA] to synthesise more complex processes. Observational constraints to fix [FORMULA] are difficult to find, because stellar censuses are available only for much larger regions like OB associations, open clusters, or longer lived H II regions.

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© European Southern Observatory (ESO) 2000

Online publication: June 8, 2000