Chemical evolution of ultra-faint dwarf galaxies in the self-consistently calculated IGIMF theory

The galaxy-wide stellar initial mass function (gwIMF) of a galaxy in dependence of its metallicity and star formation rate (SFR) can be calculated by the integrated galactic IMF (IGIMF) theory. Lacchin et al. (2019) apply the IGIMF theory for the first time to study the chemical evolution of the ultra-faint dwarf (UFD) satellite galaxies and failed to reproduce the data. Here, we find that the IGIMF theory is naturally consistent with the data. We apply the time-evolving gwIMF calculated at each timestep. The number of type Ia supernova explosions per unit stellar mass formed is renormalised according to the gwIMF. The chemical evolution of Bo\"otes I, one of the best observed UFD, is calculated. Our calculation suggests a mildly bottom-light and top-light gwIMF for Bo\"otes I, and that this UFD has the same gas-consumption timescale as other dwarfs but was quenched about 0.1 Gyr after formation, being consistent with independent estimations and similar to Dragonfly 44. The recovered best fitting input parameters in this work are not covered in the work of Lacchin et al. (2019), creating the discrepancy between our conclusions. In addition, a detailed discussion of uncertainties is presented addressing how the results of chemical evolution models depend on applied assumptions. This study demonstrates the power of the IGIMF theory in understanding the star-formation in extreme environments and shows that UDFs are a promising pathway to constrain the variation of the low-mass stellar IMF.Comment: 17 pages, 16 figures, accepted for publication in A&

The optimally-sampled galaxy-wide stellar initial mass function - Observational tests and the publicly available GalIMF code

Here we present a full description of the integrated galaxy-wide initial mass function (IGIMF) theory in terms of the optimal sampling and compare it with available observations. Optimal sampling is the method we use to discretize the IMF into stellar masses deterministically. Evidence has been indicating that nature may be closer to deterministic sampling as observations suggest a smaller scatter of various relevant observables than random sampling would give, which may result from a high level of self-regulation during the star formation process. The variation of the IGIMFs under various assumptions are documented. The results of the IGIMF theory are consistent with the empirical relation between the total mass of a star cluster and the mass of its most massive star, and the empirical relation between a galaxy's star formation rate (SFR) and the mass of its most massive cluster. Particularly, we note a natural agreement with the empirical relation between the IMF's power-law index and a galaxy's SFR. The IGIMF also results in a relation between the galaxy's SFR and the mass of its most massive star such that, if there were no binaries, galaxies with SFR $<10^{-4}$ M$_\odot$/yr should host no Type II supernova events. In addition, a specific list of initial stellar masses can be useful in numerical simulations of stellar systems. For the first time, we show optimally-sampled galaxy-wide IMFs (OSGIMF) which mimics the IGIMF with an additional serrated feature. Finally, A Python module, GalIMF, is provided allowing the calculation of the IGIMF and OSGIMF in dependence on the galaxy-wide SFR and metallicity.Comment: 15 pages, 15 figures, A&A, in press; paper remains unchanged (version1 equals version2); the GalIMF module is downloadable at githu

The possible role of stellar mergers for the formation of multiple stellar populations in globular clusters

Many possible scenarios for the formation of multiple stellar populations (MSP) in globular clusters (GCs) have been discussed so far, including the involvement of asymptotic giant branch stars, fast rotating main sequence stars, very massive main sequence stars and mass-transferring massive binaries based on stellar evolution modelling. But self-consistent, dynamical simulations of very young GCs are usually not considered. In this work, we perform direct $N$-body modelling such systems with total masses up to $3.2\times10^5$ M$_\odot$, taking into account the observationally constrained primordial binary properties, and discuss the stellar-mergers driven both by binary stellar evolution and dynamical evolution of GCs. The occurrence of stellar mergers is enhanced significantly in binary-rich clusters such that stars forming from the gas polluted by mergers-driven ejection/winds would appears as MSPs. We thus emphasize that stellar mergers can be an important process that connects MSP formation with star cluster dynamics, and that multiple MSP formation channels can naturally work together. The scenario studied here, also in view of a possible top-heavy IMF, may be particularly relevant for explaining the high mass fraction of MSPs (the mass budget problem) and the absence of MSPs in young and low-mass star clusters

The formation of UCDs and massive GCs: Quasar-like objects for testing for a variable stellar initial mass function (IMF)

The stellar initial mas function (IMF) has been described as being invariant, bottom heavy or top-heavy in extremely dense star burst conditions. To provide usable observable diagnostic we calculate redshift dependent spectral energy distributions of stellar populations in extreme star burst clusters which are likely to have been the precursors of present day massive globular clusters (GCs) and of ultra compact dwarf galaxies (UCDs). The retention fraction of stellar remnants is taken into account to asses the mass to light ratios of the ageing star-burst. Their redshift dependent photometric properties are calculated as predictions for James Webb Space Telescope (JWST) observations. While the present day GCs and UCDs are largely degenerate concerning bottom-heavy or top-heavy IMFs, a metallicity- and density-dependent top-heavy IMF implies the most massive UCDs, at ages <100 Myr, to appear as objects with quasar-like luminosities with a 0.1-10% variability on a monthly time scale due to core collapse supernovae.Comment: Accepted for publication in A&A, 12 pages, 10 figures + appendix, version 2: language corrections adde

The star formation timescale of elliptical galaxies -- Fitting [Mg/Fe] and total metallicity simultaneously

The alpha element to iron peak element ratio, for example [Mg/Fe], is a commonly applied indicator of the galaxy star formation timescale (SFT) since the two groups of elements are mainly produced by different types of supernovae that explode over different timescales. However, it is insufficient to consider only [Mg/Fe] when estimating the SFT. The [Mg/Fe] yield of a stellar population depends on its metallicity. Therefore, it is possible for galaxies with different SFTs and at the same time different total metallicity to have the same [Mg/Fe]. This effect has not been properly taken into consideration in previous studies. In this study, we assume the galaxy-wide stellar initial mass function (gwIMF) to be canonical and invariant. We demonstrate that our computation code reproduces the SFT estimations of previous studies where only the [Mg/Fe] observational constraint is applied. We then demonstrate that once both metallicity and [Mg/Fe] observations are considered, a more severe "downsizing relation" is required. This means that either low-mass ellipticals have longer SFTs (> 4 Gyr for galaxies with mass below $10^{10}$ M$_\odot$) or massive ellipticals have shorter SFTs ($\approx 200$ Myr for galaxies more massive than $10^{11}$ M$_\odot$) than previously thought. This modification increases the difficulty in reconciling such SFTs with other observational constraints. We show that applying different stellar yield modifications does not relieve this formation timescale problem. The quite unrealistically short SFT required by [Mg/Fe] and total metallicity would be prolonged if a variable stellar gwIMF were assumed. Since a systematically varying gwIMF has been suggested by various observations this could present a natural solution to this problem.Comment: 9 pages, 7 figures, A&A, in press. Version 2 added reference

The most massive stars in very young star clusters with a limited mass: Evidence favours significant self-regulation in the star formation processes

The stellar initial mass function (IMF) is commonly interpreted to be a scale-invariant probability density distribution function (PDF) such that many small clusters yield the same IMF as one massive cluster of the same combined number of stars. Observations of the galaxy-wide IMF challenge this as dwarf galaxies do not form as many massive stars as expected. This indicates a highly self-regulated star formation process in which stellar masses are not stochastically sampled from the IMF and are instead related to the environment of star formation. Here, the nature of star formation is studied using the relation between the most massive star born in a star cluster and its parental stellar cluster mass (the $m_{\rm max}$--$M_{\rm ecl}$ relation). This relation has been argued to be a statistical effect if stars are sampled randomly from the IMF. By comparing the tightness of the observed $m_{\rm max}$--$M_{\rm ecl}$ distribution with synthetic star clusters with stochastically sampled stellar masses, we find that the expected dispersion of the mock observations is much larger than the observed dispersion. Assuming that $m_{\rm max}$ and $M_{\rm ecl}$ uncertainties from the literature are correct, our test rejects the hypothesis that the IMF is a PDF at a more than $4.5\sigma$ confidence level. Alternatively, we provide a deterministic stellar mass sampling tool which reproduces the observed $m_{\rm max}$--$M_{\rm ecl}$ distribution and compares well with the luminosities of star-forming molecular clumps. In addition, we find that there is a significant flattening of the $m_{\rm max}$--$M_{\rm ecl}$ relation near $m_{\rm max}=13~M_\odot$. This may suggest strong feedback of stars more massive than about $13~M_\odot$ and/or the ejections of the most massive stars from young clusters in the mass range 63 to $400~M_\odot$ to be likely important physical processes in forming clusters.Comment: 16 pages, 10 figures. Accepted for publication in A&

The cosmological star formation history from the Local Volume of galaxies and constraints on the matter homogeneity

The Lilly-Madau plot is commonly interpreted as the history of the cosmic star formation of the Universe by showing the co-moving star formation rate density (SFRD) over cosmic time. Therefore, the Lilly-Madau plot is not only sensitive to the star formation history (SFH) but also to the number density of galaxies. Assessing the Catalogue of Neighbouring Galaxies, we reconstruct the SFHs of galaxies located in the Local Volume (LV) based on delayed-$\tau$ and power-law SFH models. Galaxies with stellar masses of $M_{*} \gtrsim 10^{10}\,\rm{M_{\odot}}$ typically evolve according to the delayed-$\tau$ model by having first increasing followed by exponentially declining SFRs, while the majority of less massive star-forming galaxies has an almost constant or increasing SFH. Deducing the cosmic SFRD evolution of the LV reveals that the SFHs of local galaxies are inconsistent with the Lilly-Madau plot. The SFRDs of the LV are significantly lower at redshifts of $z \lesssim 3$ underestimating the Lilly-Madau peak at $z = 1.86$ by a factor of $2.16\pm0.32$ (delayed-$\tau$) and $5.90\pm0.88$ (power-law model). Assuming the delayed-$\tau$ model for galaxies with $M_{*} \geq 10^{10}\,\rm{M_{\odot}}$ and a power-law model for less massive galaxies, the SFRD is $2.22\pm0.33$ lower than measured at $z = 1.86$. This inconsistency between the evolution of the local and global SFRD has cosmological implications. Since the Lilly-Madau plot also constrains the cosmological matter field, the near-constancy of SFHs of LV galaxies could imply that the peak of the Lilly-Madau plot at $z = 1.86$ is the imprint of a $\approx~5$ Gpc-scale inhomogeneity.Comment: Accepted for publication in the Monthly Notices of the Royal Astronomical Society (MNRAS), 12 pages, 5 figure