Integrated Galactic Initial Mass Function

The integrated galactic initial mass function (IGIMF) is the galaxy-wide IMF, which describes the distribution of stellar mass in the whole galaxy. Studies on IGIMF can help us to understand the distribution of stellar remnants, the number of supernova, chemical enrichment history and luminosity evolution et al. In this paper, the properties and classifications of the stars, clusters and galaxies are described, and the distributions of stellar mass in clusters are discussed firstly. Then, the IGIMF is restudied systematically by using a simple analytic relationship between M_ecl and m_max, which matches the observations very well, and the special stellar initial mass functions. The results show that the IGIMF differs from the canonical IMF. At the range of large stellar (≥≈1M_⊙), the slope of IGIMF is steeper than that of the canonical IMF. But at the range of low stellar mass (≤≈1M_⊙), their slopes are nearly the same. Moreover, the factors which have impacted on IGIMF are also studied, such as the embedded star cluster mass function (ECMF), the galactic total star formation rate (SFR) and the stellar initial mass function (IMF) in galactic clusters.