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Ignacio Martín-Navarro

Publications and source records attributed to Ignacio Martín-Navarro.

At least 19 recordsLinked to original sources

Semiresolved Stellar Populations as Distance Indicators

Galaxy distances are central to our understanding of the Universe. Despite the success of existing approaches, independent and complementary methods remain valuable for testing systematic effects and extending the applicability range of different distance metrics. Here we demonstrate that the spectrum of an individual semi-resolved stellar population encodes direct information about its distance and that valuable distance constraints can, in principle, be obtained by combining multiple independent measurements. When applied to optical spectra of bulge of the Andromeda galaxy (M\,31), we derive a stellar population-based distance of 756$\pm$57 kpc ($μ_0 = 24.39 \pm 0.15$), in agreement with state-of-the-art measurements. Crucially, semi-resolved stellar population distances does not require secondary calibrations, although its absolute scale remains conditional on the adopted stellar population models. Our findings provide a first assessment of the feasibility of deriving stellar population-based distance estimates from simple stellar population models, motivating further tests of the broader applicability and precision of the method.

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Hidden mass in early galaxies revealed by bottom-heavy initial mass functions

James Webb Space Telescope (JWST) observations have revealed that massive galaxies formed and evolved faster than predicted by galaxy formation models, with many having already assembled a large mass in stars approximately 12 billion years ago. However, masses of distant galaxies are uncertain, as they assume a distribution of stellar birth masses (the initial mass function (IMF)) similar to that in the Milky Way. Specifically, the contribution from low-mass stars, which make up the bulk of stellar mass, is not directly observed, but inferred based on an extrapolation of the Milky Way IMF. Here, we provide robust constraints on the low-mass IMF beyond the local Universe from full-spectrum models. Using ultra-deep spectra of nine massive quiescent galaxies at redshift $z$ $\approx0.7$ from the JWST Initial Mass Function of Early Red NIRSpec Objects program, extended to bluer wavelengths with deep Very Large Telescope Large Early Galaxy Astrophysics Census spectra, we find that the most massive galaxies have excess low-mass stars. Remarkably, our oldest galaxy (formation redshift $z_{\rm form} > 5$) has the most bottom-heavy IMF. This galaxy may be a descendant of JWST's 'impossibly early' galaxies, implying that the latter may have had similarly bottom-heavy IMFs increasing their masses by a factor of approximately $4\pm1$. Our findings may thus amplify the tension with galaxy formation models.

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Hector Galaxy Survey: Linking the low- and high-mass ends of the initial mass function in star-forming galaxies

The stellar initial mass function (IMF) is a fundamental ingredient in galaxy evolution, linking observed integrated light to galaxy properties. Constraining the full IMF shape beyond the Milky Way remains challenging, as most studies focus either on the low-mass end of quiescent galaxies or the high-mass end of star-forming galaxies. Here we present the first simultaneous analysis of both ends of the IMF in 214 star-forming galaxies from the Hector survey. We estimate the low-mass end slope using a stellar population approach that fits IMF-sensitive absorption features with extended star formation histories, while the high-mass end slope is derived via the Kennicutt diagnostic, which compares the observed H-alpha equivalent width and g-r colour with stellar population synthesis model predictions. We find substantial diversity in IMF shapes and a weak but statistically robust correlation between the low- and high-mass IMF slopes. Both IMF slopes show significant correlations with stellar mass, star formation activity, and stellar metallicity ([M/H]). In general, higher stellar mass, stronger star formation activity, and higher metallicity are associated with both bottom-heavy and top-heavy IMFs. Partial correlation analysis reveals that the low-mass end slope is primarily driven by [M/H], whereas the high-mass end is mainly linked to stellar mass and recent star formation. Because the low-mass end slope traces the IMF over long-term averages and the high-mass end slope captures only recent star formation, the processes shaping each end likely occur over different and possibly decoupled timescales. Our findings challenge the universality of the IMF and emphasise the need for galaxy evolution and stellar population models to incorporate a flexible IMF prescription. Accounting for these variations is essential to build an IMF-consistent picture of galaxy evolution across cosmic time.

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Clues to inside-out quenching in quiescent galaxies at $1.2\lesssim z\lesssim2.2$: Age, Fe-, and Mg-abundance gradients from JWST-SUSPENSE

[Abridged] Spatially resolved stellar populations of massive quiescent galaxies at cosmic noon provide powerful insights into quenching and assembly mechanisms. Previous photometric studies have revealed that the cores of these galaxies are redder than their outskirts. However, spectroscopy is needed to break the age-metallicity degeneracy and uncover the driver of colour gradients. We derive age and elemental abundance gradients for eight distant ($1.2 \lesssim z \lesssim 2.2$), massive ($10.3\lesssim\log({\rm M}_*/{\rm M}_\odot)\lesssim 11.1$) quiescent galaxies by fitting full-spectrum models to ultra-deep NIRSpec-MSA spectroscopy from the JWST-SUSPENSE survey. We find that these galaxies have negative age and flat [Fe/H] gradients, and tentative indications of positive [Mg/H] and [Mg/Fe] gradients. These results suggest that galaxy cores are older and perhaps also Mg deficient compared to galaxy outskirts. The age gradients may indicate inside-out quenching, while Mg-deficient cores could suggest rapid gas expulsion as the central quenching mechanism. Thus, galaxy cores may have formed faster and quenched more efficiently than their outskirts. However, our [Fe/H] and [Mg/Fe] gradients are still puzzling, and further investigation is required to understand the nature of [Mg/H] gradients in massive galaxies at these redshifts. Our results contrast with those of lower-$z$ studies, which find flat age and [Mg/Fe] gradients and negative metallicity gradients. Additionally, we find a positive trend between age gradients and rotational support and marginal trends between [Fe/H] gradients and velocity dispersions and ages. We discuss our findings in the context of galaxy growth scenarios, including minor mergers and progenitor bias. With this work, we present the first stellar population gradients from NIRSpec-MSA spectroscopy in the current largest sample of distant quiescent galaxies.

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FASTAR -- II. Semi-resolved evolutionary stellar population models

Standard evolutionary synthesis models rely on the assumption of a fully sampled stellar initial mass function (IMF). Under this assumption, the age, chemical composition, and IMF uniquely define the predicted absorption spectra. However, with current instrumentation pushing observations towards higher spatial resolutions and lower surface brightnesses, the assumption of a fully sampled IMF does not always hold true. Here we present the semi-resolved version of the FASTAR models, a comprehensive set of evolutionary synthesis predictions able to reproduce the stochastic behavior of discretely-sampled IMFs. Semi-resolved FASTAR predictions share the same evolutionary principles, ingredients, and features of the integral (fully sampled IMF) version of the FASTAR models, expanding a range of ages from 20 Myr to 14 Gyr, metallicities between -2.5 < [M/H] < +0.3, and several IMF functional forms. Detailed spectroscopic measurements can be carried out within the 3,540-7,400 A wavelength range, and low-resolution spectral energy distributions can also be synthesized over a wider 2,000-to-12,000 A coverage. Semi-resolved FASTAR models also depend on the number of stars contributing to the observed spectra, which determines the effective sampling of the different stellar evolutionary phases along the isochrones. This incomplete sampling implies that semi-resolved FASTAR models are inevitably stochastic. On top of the inherent stochasticity of the models, derived quantities such as equivalent widths, colors, or mass-to-light ratios might present strong deviations compared to standard fully sampled simple stellar population models. This stochasticity dilutes the boundary between model predictions and data, promoting new sampling-based inference approaches. FASTAR semi-resolved models allow for the effective exploration of the parameter space thanks to their optimized, JAX-based computation.

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FASTAR -- I. Continuous and differentiable evolutionary stellar population models

The development of evolutionary stellar population models is central to interpreting observations of galaxies in terms of astrophysical quantities. Stellar population models must therefore be both accurate and compatible with inversion algorithms in order to extract meaningful information from the observed data. Here we present FASTAR, a fully differentiable stellar population synthesis code. Contrary to traditional, grid-based single stellar population models, FASTAR can be continuously evaluated at any age (between 20 Myr and 14 Gyr), metallicity (-2.5 < [M/H] < +0.3), and initial mass function (IMF). Changes in the IMF parameterization are straightforward, allowing for consistent conversions of colors, magnitudes, and mass-to-light ratios, as well as the synthesis of models under the assumption of arbitrary IMF functional forms. FASTAR provides detailed spectroscopic predictions over the MILES wavelength range (3,540-7,400 A) as well as more coarsely sampled spectral energy distributions across a wider 2,000-to-12,000 A, which can be directly convolved with any arbitrary set of photometric filters. FASTAR performs at the same level of state-of-the-art simple stellar population models benchmarked against observations of globular clusters and high signal-to-noise spectra of early-type galaxies, but it is faster, lighter, and more flexible. Moreover, its differentiable nature allows for a quantitative understanding of model behavior and uncertainties, as well as a natural framework for gradient descent inference algorithms.

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Disc growth and vertical heating of lenticular galaxies in the Fornax cluster

We present a detailed analysis of the vertical and radial structure of mono-age stellar populations in three edge-on lenticular galaxies (FCC 153, FCC 170, and FCC 177) in the Fornax cluster, using deep MUSE observations. By measuring the half-mass radius (R$_{50}$) and half-mass height (z$_{50}$) across 1 Gyr-wide age bins, we trace the spatial evolution of stellar populations over cosmic time. All galaxies exhibit a remarkably constant disc thickness for all stars younger than ~6 Gyr, suggesting minimal secular heating and limited impact from environmental processes such as tidal shocking or harassment. Evidence of past mergers (8-10 Gyr ago) is found in the increase of z$_{50}$ for older populations. We find that accreted (metal-poor) stars have been deposited in quite thick configurations, but that the interactions only moderately thickened pre-existing stars in the galaxies, and only caused mild flaring in the outer regions of the discs. The radial structure of the discs varies across galaxies, but in all cases we find that the radial extent of mono-age populations remains constant or grows over the past 8 Gyr. This leads us to argue that within the radial range we consider, strangulation, rather than ram-pressure stripping, is the dominant quenching mechanism in those galaxies. Our results highlight the usefulness of analysing the structure of mono-age population to uncover the mechanisms driving galaxy evolution, and we anticipate broader insights from the GECKOS survey, studying 36 nearby edge-on disc galaxies.

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Accelerated quenching and chemical enhancement of massive galaxies in a $z\sim4$ gas-rich halo

Stars in galaxies form when baryons radiatively cool down and fall into gravitational wells whose mass is dominated by dark matter. Eventually, star formation quenches as gas is depleted and/or perturbed by feedback processes, no longer being able to collapse and condense. We report the first spatially resolved spectroscopic observations, using the JWST/NIRSpec IFU, of a massive, completely quiescent galaxy (Jekyll) and its neighborhood at $z=3.714$, when the Universe age was 10% of today's. Jekyll resides in a massive dark matter halo (with mass M$_\mathrm{DM}>10^{12}$ M$_\odot$) and forms a galaxy pair with Hyde, which shows very intense dust-enshrouded star formation (star formation rate $\sim300$ M$_\odot$yr$^{-1}$). We find large amounts of kinematically perturbed ionized and neutral gas in the circumgalactic medium around the pair. Despite this large gas reservoir, Jekyll, which formed $10^{11}$ M$_\odot$ in stars and chemically enriched early (first billion years of the Universe) and quickly (200-300 Myr), has remained quiescent for over 500 Myr. The properties of the gas found around the two galaxies are consistent with intense, AGN-induced photoionization, or intense shocks. However, with the current data no obscured or unobscured AGN is detected in the central galaxy (Jekyll) nor in the very active and dust rich star-forming galaxy (Hyde).

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Relatively young thick disks in star-forming late-type galaxies

We trace the evolution of eight edge-on star-forming disk galaxies by analyzing stellar population properties of their thin and thick disks. These galaxies have relatively low stellar masses (4~$\times$~10$^9$ to 6~$\times$~10$^{10}$~$M_{\odot}$). We used Multi-Unit Spectroscopic Explorer (MUSE) observations and a full-spectrum fitting to produce spatially resolved maps of the ages, metallicities, and [Mg/Fe] abundances, and we extracted the star formation histories of the stellar disks. Our maps show thick disks that are older, more metal-poor, and more [Mg/Fe]-enhanced than thin disks on average. The age differences between thin and thick disks are small (about 2~Gyr), however, and the thick disks are younger than previously observed in more massive and more quiescent galaxies. The thin and thick disks both show mostly sub-solar metallicities, and the vertical metallicity gradient is milder than previously observed in similar studies. The [Mg/Fe] differences between thick and thin disks are not sharp. The star formation histories of thick disks extend to recent times, although most of the mass in young stars was formed in thin disks. Our findings show thick disks that are different from the old quiescent thick disks that were previously observed in galaxies with different morphologies and/or masses. We propose that the thick disks in these galaxies did not form quickly at high redshift, but formed slowly over an extended time. The thin disks also formed slowly, but a larger mass fraction was created at very recent times.

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ZF-UDS-7329: A relic galaxy in the early Universe

The formation time scales of quiescent galaxies can be estimated in two different ways: by their star formation history and by their chemistry. Previously, the methods yielded conflicting results, especially when considering $α$-enhanced objects. This is primarily due to the time resolution limitations of very old stellar populations, which prevent accurately constraining their star formation histories. We analysed the JWST observations of the extremely massive galaxy ZF-UDS-7329 at z$\sim$3.2 and show that the higher time resolution necessary to match the chemical formation time scales using stellar population synthesis can be achieved by studying galaxies at high redshift. We compare the massive galaxy to the well-known relic galaxy NGC~1277, arguing that ZF-UDS-7329 is an early Universe example of the cores of present-day massive elliptical galaxies or, if left untouched, a relic galaxy.

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INSPIRE: INvestigating Stellar Population In RElics -- VII. The local environment of ultra-compact massive galaxies

Relic galaxies, the oldest ultra-compact massive galaxies (UCMGs), contain almost exclusively "pristine" stars formed during an intense star formation (SF) burst at high redshift. As such, they allow us to study in detail the early mechanism of galaxy assembly in the Universe. Using the largest catalogue of spectroscopically confirmed UCMGs for which a degree of relicness (DoR) had been estimated, the INSPIRE catalogue, we investigate whether or not relics prefer dense environments. The objective of this study is to determine if the DoR, which measures how extreme the SF history was, and the surrounding environment are correlated. In order to achieve this goal, we employ the AMICO galaxy cluster catalogue to compute the probability for a galaxy to be a member of a cluster, and measure the local density around each UCMG using machine learning-based photometric redshifts. We find that UCMGs can reside both in clusters and in the field, but objects with very low DoR (< 0.3, i.e., a relatively extended SF history) prefer under-dense environments. We additionally report a correlation between the DoR and the distance from the cluster centre: more extreme relics, when located in clusters, tend to occupy the more central regions of them. We finally outline potential evolution scenarios for UCMGs at different DoR to reconcile their presence in both clusters and field environments

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Deriving the star formation histories of galaxies from spectra with simulation-based inference

High-resolution galaxy spectra encode information about the stellar populations within galaxies. The properties of the stars, such as their ages, masses, and metallicities, provide insights into the underlying physical processes that drive the growth and transformation of galaxies over cosmic time. We explore a simulation-based inference (SBI) workflow to infer from optical absorption spectra the posterior distributions of metallicities and the star formation histories (SFHs) of galaxies (i.e. the star formation rate as a function of time). We generated a dataset of synthetic spectra to train and test our model using the spectroscopic predictions of the MILES stellar population library and non-parametric SFHs. We reliably estimate the mass assembly of an integrated stellar population with well-calibrated uncertainties. Specifically, we reach a score of $0.97\,R^2$ for the time at which a given galaxy from the test set formed $50\%$ of its stellar mass, obtaining samples of the posteriors in only $10^{-4}$\,s. We then applied the pipeline to real observations of massive elliptical galaxies, recovering the well-known relationship between the age and the velocity dispersion, and show that the most massive galaxies ($σ\sim300$ km/s) built up to 90\% of their total stellar masses within $1$\,Gyr of the Big Bang. The inferred properties also agree with the state-of-the-art inversion codes, but the inference is performed up to five orders of magnitude faster. This SBI approach coupled with machine learning and applied to full spectral fitting makes it possible to address large numbers of galaxies while performing a thick sampling of the posteriors. It will allow both the deterministic trends and the inherent uncertainties of the highly degenerated inversion problem to be estimated for large and complex upcoming spectroscopic surveys, such as DESI, WEAVE, or 4MOST.

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Unveiling the (in)consistencies among the galaxy stellar mass function, star formation histories, satellite abundances and intracluster light from a semi-empirical perspective

In a hierarchical, dark matter-dominated Universe, stellar mass functions (SMFs), galaxy merger rates, star formation histories (SFHs), satellite abundances, and intracluster light, should all be intimately connected observables. However, the systematics affecting observations still prevent universal and uniform measurements of, for example, the SMF and the SFHs, inevitably preventing theoretical models to compare with multiple data sets robustly and simultaneously. We here present our holistic semi-empirical model DECODE (Discrete statistical sEmi-empiriCal mODEl) that converts via abundance matching dark matter merger trees into galaxy assembly histories, using different SMFs in input and predicting all other observables in output in a fully data-driven and self-consistent fashion with minimal assumptions. We find that: 1) weakly evolving or nearly constant SMFs below the knee ($M_\star \lesssim 10^{11} \, M_\odot$) are the best suited to generate star formation histories aligned with those inferred from MaNGA, SDSS, GAMA, and, more recently, JWST; 2) the evolution of satellites after infall only affects the satellite abundances and star formation histories of massive central galaxies but not their merger histories; 3) the resulting SFR-$M_\star$ relation is lower in normalization by a factor of $\sim 2$ with respect to observations, with a flattening at high masses more pronounced in the presence of mergers; 4) the latest data on intracluster light can be reproduced if mass loss from mergers is included in the models. Our findings are pivotal in acting as pathfinder to test the self-consistency of the high-quality data from, e.g., JWST and Euclid.

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[Mg/Fe] and variable initial mass function: Revision of [$α$/Fe] for massive galaxies

Observations of nearby massive galaxies have revealed that they are older and richer in metals and magnesium than their low-mass counterparts. In particular, the overabundance of magnesium compared to iron, [Mg/Fe], is interpreted to reflect the short star formation history that the current massive galaxies underwent early in the Universe. We present a systematic revision of the [Mg/Fe] - velocity dispersion ($σ$) relation based on stacked spectra of early-type galaxies with a high signal-to-noise ratio from the Sloan Digital Sky Survey (SDSS). Using the penalized pixel-fitting (pPXF) method of Cappellari & Emsellem 2004 and the Vazdekis et al. 2015 MILES single stellar population (SSP) models, we fit a wide optical wavelength range to measure the net $α$-abundance. The combination of pPXF and $α$-enhanced MILES models incorrectly leads to an apparently decreasing trend of [$α$/Fe] with velocity dispersion. We interpret this result as a consequence of variations in the individual abundances of the different $α$-elements. This warrants caution for a naïve use of full spectral fitting algorithms paired with stellar population models that do not take individual elemental abundance variations into account, especially when deriving averaged quantities such as the mean [$α$/Fe] of a stellar population. In addition, and based on line-strength measurements, we quantify the impact of a non-universal initial mass function on the recovered abundance pattern of galaxies. In particular, we find that a simultaneous fit of the slope of the initial mass function and the [Mg/Fe] results in a shallower [Mg/Fe]-$σ$ relation. Therefore, our results suggest that star formation in massive galaxies lasted longer than what has been reported previously, although it still occurred significantly faster than in the solar neighbourhood.

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INSPIRE: INvestigating Stellar Population In RElics VI -- The low-mass end slope of the stellar Initial Mass Function and chemical composition

The INSPIRE project has built the largest sample of ultra-compact massive galaxies (UCMGs) at 0.1 2, and the other stellar population parameters.We use the Full-Index-Fitting method to fit the INSPIRE spectra to single stellar population (SSP) models. This allows us to measure, for the first time, the low-mass end slope of the IMF, as well as stellar metallicity [M/H], [Mg/Fe], [Ti/Fe] and [Na/Fe] ratios, and study correlations between them and the DoR. Similarly to normal-sized galaxies, UCMGs with larger stellar masses have overall higher metallicities. We found a correlation between the low-mass end of the IMF slope and the DoR, that, however, breaks down for systems with a more extended SFH. An even stronger dependency is found between the IMF and the fraction of mass formed at high-z. At equal velocity dispersion and metallicity, galaxies with a higher DoR have a dwarf-richer IMF than that of low-DoR counterparts. This might indicate that the cosmic epoch and formation mechanisms influence the fragmentation of the star formation cloud and hence might be the explanation for IMF variations detected in massive ETGs.

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The universal variability of the stellar initial mass function probed by the TIMER survey

The debate about the universality of the stellar initial mass function (IMF) revolves around two competing lines of evidence. While measurements in the Milky Way, an archetypal spiral galaxy, seem to support an invariant IMF, the observed properties of massive early-type galaxies (ETGs) favor an IMF somehow sensitive to the local star formation conditions. The fundamental methodological and physical differences between both approaches have hampered, however, a comprehensive understanding of IMF variations. We describe here an improved modelling scheme that allows for the first time consistent IMF measurements across stellar populations with different ages and complex star formation histories. Making use of the exquisite MUSE optical data from the TIMER survey and powered by the MILES stellar population models, we show the age, metallicity, [Mg/Fe], and IMF slope maps of the inner regions of NGC 3351, a spiral galaxy with a mass similar to that of the Milky Way. The measured IMF values in NGC3351 follow the expectations from a Milky Way-like IMF, although they simultaneously show systematic and spatially coherent variations, particularly for low-mass stars. In addition, our stellar population analysis reveals the presence of metal-poor and Mg-enhanced star-forming regions that appear to be predominantly enriched by the stellar ejecta of core-collapse supernovae. Our findings showcase therefore the potential of detailed studies of young stellar populations to better understand the early stages of galaxy evolution and, in particular, the origin of the observed IMF variations beyond and within the Milky Way.

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Initial mass function variability from the integrated light of diverse stellar systems

We present a uniform analysis of the stellar initial mass function (IMF) from integrated light spectroscopy of 15 compact stellar systems (11 globular clusters in M31 and 4 ultra compact dwarfs in the Virgo cluster, UCDs) and two brightest Coma cluster galaxies (BCGs), covering a wide range of metallicities ($-$1.7 $<$ [Fe/H] $<$ 0.01) and velocity dispersions (7.4 km~s$^{-1}$ $< σ<$ 275 km~s$^{-1}$). The S/N $\sim 100$ Å$^{-1}$ Keck LRIS spectra are fitted over the range $4000<λ/\mboxÅ<10,000$ with flexible, full-spectrum stellar population synthesis models. We use the models to fit simultaneously for ages, metallicities, and individual elemental abundances of the population, allowing us to decouple abundance variations from variations in IMF slope. We show that compact stellar systems do not follow the same trends with physical parameters that have been found for early-type galaxies. Most globular clusters in our sample have an IMF consistent with that of the Milky Way, over a wide range of [Fe/H] and [Mg/Fe]. There is more diversity among the UCDs, with some showing evidence for a bottom-heavy IMF, but with no clear correlation with metallicity, abundance, or velocity dispersion. The two Coma BCGs have similar velocity dispersion and metallicity, but we find the IMF of NGC~4874 is consistent with that of the Milky Way while NGC~4889 presents evidence for a significantly bottom-heavy IMF. For this sample, the IMF appears to vary between objects in a way that is not explained by a single metallicity-dependent prescription.

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Disc galaxies are still settling: The discovery of the smallest nuclear discs and their young stellar bars

When galactic discs settle and become massive enough, they are able to form stellar bars. These non-axisymmetric structures induce shocks in the gas, causing it to flow to the centre where nuclear structures, such as nuclear discs and rings, are formed. Previous theoretical and observational studies have hinted at the co-evolution of bars and nuclear discs, suggesting that nuclear discs grow "inside-out", thereby proposing that smaller discs live in younger bars. Nevertheless, it remains unclear how the bar and the nuclear structures form and evolve with time. The smallest nuclear discs discovered to date tend to be larger than $\sim200~\rm{pc}$, even though some theoretical studies find that when nuclear discs form they can be much smaller. Using MUSE archival data, we report for the first time two extragalactic nuclear discs with radius sizes below $100~\rm{pc}$. Additionally, our estimations reveal the youngest bars found to date. We estimate that the bars in these galaxies formed $4.50^{+1.60}_{-1.10}\rm{(sys)}^{+1.00}_{-0.75}\rm{(stat)}$ and $0.7^{+2.60}\rm{(sys)}^{+0.05}_{-0.05}\rm{(stat)}~\rm{Gyr}$ ago, for NGC\,289 and NGC\,1566, respectively. This suggests that at least some disc galaxies in the Local Universe may still be dynamically settling. By adding these results to previous findings in the literature, we retrieve a stronger correlation between nuclear disc size and bar length and we derive a tentative exponential growth scenario for nuclear discs.

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