Variation of the low-mass end of the stellar initial mass function with redshift and metallicity (2501.06082v2)

Abstract: We report the stellar mass functions obtained from 20 radiation hydrodynamical simulations of star cluster formation in 500 M$_\odot$ molecular clouds with metallicities of 3, 1, 1/10 and 1/100 of the solar value, with the clouds subjected to levels of the cosmic microwave background radiation that are appropriate for star formation at redshifts z=0, 3, 5, 7, and 10. The calculations include a thermochemical model of the diffuse interstellar medium and treat dust and gas temperatures separately. We find that the stellar mass distributions obtained become increasingly bottom light as the redshift and/or metallicity are increased. Mass functions that are similar to a typical Galactic initial mass function are obtained for present-day star formation (z=0) independent of metallicity, and also for the lowest-metallicity (1/100 solar) at all redshifts up to z=10, but for higher metallicities there is a larger deficit of brown dwarfs and low-mass stars as the metallicity and redshift are increased. These effects are a result of metal-rich gas being unable to cool to as lower temperatures at higher redshift due to the warmer cosmic microwave background radiation. Based on the numerical results we provide a parameterisation that may be used to vary the stellar initial mass function with redshift and metallicity; this could be used in simulations of galaxy formation. For example, a bottom-light mass function reduces the mass-to-light ratio compared to a typical Galactic stellar initial mass function, which may reduce the estimated masses of high-redshift galaxies.

• The paper presents high-resolution radiation hydrodynamical simulations to analyze how the low-mass IMF changes with redshift and metallicity.
• Results show that higher metallicity leads to a bottom-light IMF at increased redshifts due to warmer gas temperatures imposed by the CMBR.
• An empirical formula is provided to adjust the IMF in galaxy formation models, refining mass-to-light ratio estimates and improving cosmic star formation studies.

Variation of the Low-Mass End of the Stellar Initial Mass Function with Redshift and Metallicity

This paper presents an in-depth analysis of how the low-mass end of the stellar initial mass function (IMF) varies with redshift and metallicity. Using high-resolution radiation hydrodynamical simulations, this research explores changes in the IMF over five redshifts ($z=0, 3, 5, 7, \text{and } 10$) and four metallicities (1/100, 1/10, 1, and 3 times solar). The simulations incorporate radiation transport and a thermochemical model, allowing for the independent treatment of gas and dust temperatures, which is crucial for accurately modeling the star formation process under varying cosmic conditions.

Key Findings

1. IMF Variability with Redshift and Metallicity: The simulations reveal that at low metallicities, the stellar mass distribution remains consistent with a typical Galactic IMF across all redshifts. However, at higher metallicities, the IMF becomes increasingly bottom-light (deficient in low-mass stars and brown dwarfs) as redshift increases. This is attributed to the warmer cosmic microwave background radiation (CMBR) at higher redshifts, which inhibits fragmentation by maintaining warmer gas temperatures, especially in metal-rich environments.
2. Effects of the Cosmic Microwave Background Radiation: Metal-rich gas remains warmer due to less effective cooling in the presence of the CMBR, especially at high redshifts. This results in a reduced number of low-mass stars across different redshifts, demonstrating the significant impact of CMBR as a temperature floor in early star-forming galaxies.
3. Parameterization of the IMF: An empirical formula was developed to parameterize the observed variations in the IMF with redshift and metallicity. The formulation provides a practical means to adjust the IMF in simulations of galaxy formation, potentially improving our understanding of stellar populations in different cosmic epochs and environments.
4. Mass-to-Light Ratio Implications: The paper also explores the consequences of a bottom-light IMF on the mass-to-light ratio of stellar populations. It predicts that at high redshifts and higher metallicities, the zero-age mass-to-light ratio decreases compared to a typical Galactic IMF—suggesting earlier and massive high-redshift galaxies observed by JWST might be overestimated in mass if a standard IMF is assumed.

Implications and Future Directions

The findings of this paper have significant implications for understanding star formation across cosmic time. The results propose that the IMF is not universal but varies with environmental conditions set by the redshift and the chemical makeup of the star-forming regions. This variability must be considered in models of galaxy formation and evolution, particularly when interpreting data from high-redshift observations such as those from the James Webb Space Telescope. The parameterization provided can be integrated into galaxy formation simulations, potentially leading to revised interpretations of galaxy mass estimates and star formation rates in the early universe.

Further research is needed to explore the high-mass end of the IMF under varying conditions and to refine the empirical relationships derived, perhaps by extending simulations over a broader range of parameters or utilizing different initial conditions to assess robustness. Observational validation, particularly in the context of metal-rich environments and high stellar mass-to-light ratios in early-type galaxies, will also be crucial for verifying these theoretical predictions.