The Simultaneous Multiple Constraints of the IMF and SFR History in Star Formation Complexes

Abstract

The multiple constraints method of the IMF and SFR history in star formation complexes (SFCs) attempts to match simultaneously the observed UBVR colours, Lyman continuum fluxes and chemical abundances by finding a best set of the IMF parameters (α, Mmax), age t and SFR history. The method of using simultaneous multiple constraints of the IMF and SFR history in SFCs (SMC method) is based on the evolutionary synthesis models of stellar clusters, in which the SFR was either an instantaneous burst of age t (simultaneous star formation — SSF model) or a constant with duration t (constant star formation — CSF model) and, parameterized the IMF as a power law of index α with upper and lower mass limits Mmax, Mmin. This procedure results in large uncertainties for individual star forming regions \( \left( {{\sigma _\alpha } = 0.35,\;{\sigma _{{M_{\max }}}} = 30{M_ \odot },\;{\sigma _{\log (t)}} = 0.20} \right) \), but may be adequate for a study of the average properties of a large sample. The simultaneous multiple constraints of the IMF and SFR history in star formation complexes resolved the IMF-SFR ambiguity in 100 SFCs in 20 galaxies. Star formation episodes proceed either instantaneously or at continuous rate in individual regions. There are correlations between the parameters that define the star formation process (IMF, SFR), and the local properties of the parent galaxy (density, metallicity). The dependence of ages on linear sizes (S in parsec) of star forming regions derived from independent observations of star clusters in LMC (Efremov and Elmegreen: 1998, MNRAS 299, 588) is confirmed. SFR history depends on the star density of SFC. Low density regions demonstrate instantaneous starburst, while in high density SFCs one can see a continuous star formation process. A trend towards greater ages at high stellar densities in the case of constant SFR history indicates that the lifetimes of SFCs are longer than corresponding dynamical time scales of clouds, and that star formation seems to be no fast process on every scale The mechanisms that triggered the burst of star formation depend on the star density and metallicity of SFC. There is a trend toward flatter IMFs at low densities in both cases of SFR history. The density dependence of IMF indicates the role of interactions in protostellar clouds. Dust plays an important role in the transport and redistribution of the Lyc photons emitted by the OB stars; a fraction (l-f) of the Lyc photons escapes, not absorbed by gas in individual SFCs varies from 0 to 90% with a mean = (50 ± 30)%. Different star formation episodes (SSF or CSF) show different correlations between the observed parameters (L, S, Z, f). Estimated empirical relations between IMF, ages and observed luminosities, sizes, and colour indices, allow to constrain integrated (cumulative) IMF in a parent galaxy between two extreme versions of star formation regimes SSF and CSF. It is shown that the integrated IMF in the parent galaxy depends not only on the distribution of IMF slopes in individual SFCs but also on the luminosity (size) distribution of SFCs.