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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.06281 |
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Table of Contents:
- 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 $γ_1=2.40\pm0.09$, $γ_2=2.00\pm0.14$, and $γ_3=1.85\pm0.11$ in the regimes 0.08-0.5 Msun, 0.5-1 Msun, and >1 Msun respectively. The IMF parameter $α$, the mass excess compared to a Milky Way IMF, ranges from $\log(α)\approx+0.3$ for present-day galaxies to $\log(α)\approx-0.1$ for their star forming progenitors. The concordance IMF applies only to the central regions of the most massive galaxies, with velocity dispersions ~300 km/s, 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 $σ\gtrsim 160$ km/s: $γ_1\approx1.3+4.3\logσ_{160}$; $γ_2\approx2.3-1.2\logσ_{160}$; and $γ_3\approx2.3-1.7\logσ_{160}$, with $σ_{160}=σ/160$ km/s. If galaxies grow primarily inside-out, so that velocity dispersions are relatively stable, these relations should also hold at high redshift.