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The initial mass function is presently approximated by a segmented power-law distribution. The principal goal of this study is to show that the real shape of the initial mass function for low- and intermediate-mass stars differs from the observed one.
In particular, comparison of radii of eclipsing binary components and single stars shows a noticeable difference for B0V-G0V components of eclipsing binaries and single stars of the corresponding spectral type. This difference is confirmed by a re-analysis of results of other published investigations. In ts shown that the mass-luminosity relation based on empirical data of eclipsing binary components cannot be used to derive the stellar initial mass function. The initial mass function for masses more than 1.5 solar masses should be revised.
The initial mass function is normally not corrected for the effect that many if not most stars occur in (unresolved) binary systems. Under assumptions that star formation rate is constant, a random pairing of objects drawn from a pre-assumed single star power-law IMF is generated. Stellar evolution and selection effects are taken into account. Orbital parameters are assumed to be spread according to common distributions. Each pair, depending on brightness difference of components and separation falls in one of the following categories: i) only primary is observed; ii) only secondary is observed; iii) pair observed as a photometrically unresolved binary; iv) both components are observed correctly. It is shown that under given assumptions power-law IMF does lead to quasi-lognormal turnovers for the resulting observational mass function.