1997A&A...321..343A

The observed trend of mass-to-light ratio M/L_B versus elliptical galaxy mass M has been interpreted in various ways by different authors in recent years. We explore in greater detail than previously done the hypothesis that the mentioned trend can be ascribed to a systematic change of the initial mass function (IMF) with M. We use a three-segment power-law IMF with mass exponents x₁, x₂, and x₃ for stellar masses m (in M_☉) in the ranges 0.1<m<0.3, 0.3<m<2, and 2<m<100, respectively. The exponent x₁ is considered as a free parameter in the range 0/3.5, while x₂ and x₃ are determined using relations M/L_B versus M and [Fe/H] versus M as constraints. We find that x₂+3.4x₃≃-0.72logM+const., irrespectively of whether the bottom IMF exponent x₁ varies from a flat to a very steep behaviour. We single out a number of realistic solutions; for all of them dx₃/dlogM=-0.16/-0.35. On the other hand, solutions with x₂=const., x₃=const., and x₁ variable with M are to be excluded, being at variance with the observed [Fe/H]-M relationship. We confirm that a variable single-slope IMF is not a very appealing solution since it requires a minimum stellar mass m_l>0.24.