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

4. Search in parameter space and the role of

A first broad search for the parameters and requires specifying . It could be thought firsthand that any value of high enough to simulate infinity would do, but we tried and did not obtain any fit, over the range , . We distinguished three cases, fixing the maximum number of stars per MSFR, , to 500, 1000 and 2000. Fig. 3 shows the 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 . The number of degrees of freedom is thus 3, which corresponds to the five bins in comparison less two free parameters ( and ). The fit to is a lot more noisy, a consequence of the reduced number of IRAS/CS sources used to compute the LF.

Fig. 3. Search in () parameter space for the best fit model, with three guesses for . Plotted is the 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 , the middle two with , and the bottom two with

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

As the distribution of 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 to synthesise more complex processes. Observational constraints to fix 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.

© European Southern Observatory (ESO) 2000

Online publication: June 8, 2000
helpdesk.link@springer.de