[Paper Review] Downsizing revised: Star formation timescales for elliptical galaxies with an environment-dependent IMF and number of SNIa

Zhiqiang Yan, Tereza Jeřabková+1 more|arXiv (Cornell University)|Jul 7, 2021

Galaxies: Formation, Evolution, Phenomena167 references45 citations

TL;DR

This paper resolves the downsizing paradox in massive elliptical galaxies by applying an environment-dependent initial mass function (IMF) via the IGIMF theory, showing that star formation timescales (SFTs) become consistent with stellar population synthesis (SPS) models when the number of SNIa per unit stellar mass increases in more massive galaxies. The key result is that SFTs peak at ~2 Gyr for galaxies of ~10⁹.⁵M⊙, with faster formation in more massive systems due to enhanced SNIa production from dense star clusters.

ABSTRACT

Previous studies of the stellar mean metallicity and [Mg/Fe] values of massive elliptical (E)~galaxies suggest that their stars were formed in a very short timescale which cannot be reconciled with estimates from stellar population synthesis (SPS) studies and with hierarchical-assembly. Applying the previously developed chemical evolution code, GalIMF, which allows an environment-dependent stellar initial mass function (IMF) to be applied in the integrated galaxy initial mass function (IGIMF) theory instead of an invariant canonical IMF, the star formation timescales (SFT) of E galaxies are re-evaluated. The code's uniqueness lies in it allowing the galaxy-wide IMF and associated chemical enrichment to evolve as the physical conditions in the galaxy change. The calculated SFTs become consistent with the independent SPS results if the number of type Ia supernovae (SNIa) per unit stellar mass increases for more massive E~galaxies. This is a natural outcome of galaxies with higher star-formation rates producing more massive star clusters, spawning a larger number of SNIa progenitors per star. The calculations show E~galaxies with a stellar mass $\approx 10^{9.5} M_\odot$ to have had the longest mean SFTs of $\approx2\,$Gyr. The bulk of more massive E~galaxies were formed faster (SFT$\,\approx 1\,$Gyr) leading to domination by M~dwarf stars and larger dynamical mass-to-light ratios as observed, while lower-mass galaxies tend to lose their gas supply more easily due to their shallower potential and therefore also have similarly-short mean SFTs. This work achieves, for the first time, consistency of the SFTs for early-type galaxies between chemical-enrichment and SPS modelling and leads to an improved understanding of how the star formation environment may affect the total number of SNIa per unit stellar mass formed.

Motivation & Objective

• To resolve the longstanding downsizing problem in massive elliptical galaxies, where chemical evolution models suggest shorter star formation timescales (SFTs) than those inferred from stellar population synthesis (SPS) studies.
• To investigate whether an environment-dependent integrated galaxy-wide IMF (IGIMF) can reconcile SFT estimates from chemical enrichment with those from SPS models.
• To determine how the number of type Ia supernovae (SNIa) per unit stellar mass varies with galaxy mass and whether this variation can explain observed SFT discrepancies.
• To test whether the IGIMF theory, which allows the IMF to evolve with star formation rate and metallicity, naturally accounts for observed stellar metallicities, [Mg/Fe] ratios, and dynamical mass-to-light ratios in early-type galaxies.

Proposed method

• The study employs the GalIMF chemical evolution code, which incorporates an environment-dependent IMF through the IGIMF theory, allowing the galaxy-wide IMF to evolve with changing physical conditions such as star formation rate (SFR) and metallicity.
• The IMF is modeled as a function of SFR and metallicity, with top-heavy IMFs at high SFRs and bottom-light IMFs in metal-poor environments, consistent with observational constraints.
• The total number of SNIa per unit stellar mass formed is calculated using a modified SNIa realisation parameter that varies with IMF shape, as formalized in Eq. 15, 20, and 21.
• The model computes SFTs using both stellar mean metallicity and [Mg/Fe] as constraints, comparing results with SPS-derived SFTs.
• The SNIa delay-time distribution (DTD) and stellar yields are calibrated to match observed abundance patterns.
• The model is tested across a range of galaxy masses, with special attention to the transition mass at ~10⁹.⁵M⊙ where SFTs peak.

Experimental results

Research questions

• RQ1 Can an environment-dependent IMF, as described by the IGIMF theory, reconcile the discrepancy between star formation timescales derived from chemical evolution models and those from stellar population synthesis (SPS) studies in massive elliptical galaxies?
• RQ2 How does the number of type Ia supernovae (SNIa) per unit stellar mass vary with galaxy mass, and is this variation consistent with theoretical expectations?
• RQ3 What is the role of star cluster mass and density in enhancing SNIa production in high-SFR environments, and how does this affect the inferred SFT?
• RQ4 Why do massive elliptical galaxies exhibit higher dynamical mass-to-light ratios and bottom-heavy stellar mass functions, and can this be explained by IMF evolution?
• RQ5 Does the IGIMF theory naturally account for the observed [Mg/Fe] enhancement and metallicity in massive early-type galaxies without requiring fine-tuning?

Key findings

• The star formation timescale (SFT) for massive elliptical galaxies reaches a maximum of approximately 2 Gyr for galaxies with a stellar mass of ~10⁹.⁵M⊙, resolving the downsizing paradox.
• For more massive elliptical galaxies (M⋆ > 10⁹.⁵M⊙), the SFT decreases to around 1 Gyr, consistent with SPS estimates, due to enhanced SNIa production from dense, massive star clusters formed in high-SFR environments.
• The number of SNIa per unit stellar mass increases with galaxy mass, with a required 2.5-fold increase in the SNIa realisation parameter for the most massive galaxies to match SPS-derived SFTs.
• The environment-dependent IMF naturally explains the observed [Mg/Fe] enhancement and high metallicity in massive ellipticals, as top-heavy IMFs at high SFRs produce more alpha elements early.
• Low-mass elliptical galaxies have similarly short SFTs (~1 Gyr) due to their shallow potential wells, which lead to rapid gas loss and quenching, consistent with the model’s predictions.
• The model successfully accounts for the high dynamical mass-to-light ratios observed in massive ellipticals through the combined effects of bottom-heavy IMFs and enhanced SNIa production.