Fornax 3D project: a two-dimensional view of the stellar initial mass function in the massive lenticular galaxy FCC 167

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Table 1.

Conversion coefficients between commonly used IMF shapes and ξ mass ratios.

Single power law (Γ) ^(a)
c₀	c₁	c₂	c₃

0.3751	0.1813	0.0223	−0.0095

Broken power law (Γ_B)

c₀	c₁	c₂	c₃

0.3739	0.1269	0.0000	−0.0014

Notes. For a given IMF slope γ, the corresponding ξ can be accurately approximated by a polynomial ξ(γ) = c₀ + c₁γ + c₂γ² + c₃γ³. For a Chabrier (2003) IMF, ξ = 0.4607; for Kroupa (2002), ξ = 0.5194; and for Salpeter (1955), ξ = 0.6370.

^(a)

Γ is in log units. In linear mass units, the IMF slope is α = Γ + 1.

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