SIMBAD references

The stellar initial mass function (IMF) is thought to be bottom heavy in the cores of the most massive galaxies, with an excess of low-mass stars compared to the Milky Way. However, studies of the kinematics of quiescent galaxies at 2 < z < 5 find M/L ratios that indicate lighter IMFs. Light IMFs have also been proposed for the unexpected populations of luminous galaxies that JWST has uncovered at z > 7 to reduce tensions with galaxy formation models. Here we explore “ski slope” IMFs that are simultaneously bottom heavy, with a steep slope at low stellar masses, and top heavy, with a shallow slope at high masses. We derive a form of the IMF for massive galaxies that is consistent with measurements in the local universe and yet produces relatively low M/L ratios at high redshift. This concordance IMF has slopes γ₁ = 2.40 ± 0.09, γ₂ = 2.00 ± 0.14, and γ₃ = 1.85 ± 0.11 in the regimes 0.08 M_⊙ - 0.5 M_⊙, 0.5 M_⊙ - 1 M_⊙, and >1 M_⊙, respectively. The IMF parameter α, the mass excess compared to a Milky Way IMF, ranges from $\mathrm{log}(\alpha )\approx +0.3$ for present-day galaxies to $\mathrm{log}(\alpha )\approx -0.1$ for their star-forming progenitors. The concordance IMF applies only to the central regions of the most massive galaxies, with velocity dispersions σ ∼ 300 km s^–1, and their progenitors. However, it can be generalized using a previously measured relation between α and σ. We arrive at the following modification to the Kroupa (2001) IMF for galaxies with σ ≳ 160 km s^–1: ${\gamma }_{1}\approx 1.3+4.3\mathrm{log}{\sigma }_{160}$, ${\gamma }_{2}\approx 2.3-1.2\mathrm{log}{\sigma }_{160}$, and ${\gamma }_{3}\approx 2.3-1.7\mathrm{log}{\sigma }_{160}$, with σ₁₆₀ = σ/160 km s^–1. If galaxies grow primarily inside out, so that velocity dispersions are relatively stable, these relations should also hold at high redshift.