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Sebastián F. Sánchez

Publications and source records attributed to Sebastián F. Sánchez.

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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The host galaxies of 2003fg-like type Ia supernovae

SN~2003fg-like events are a peculiar type Ia supernova (SN~Ia) subtype characterized by broader light curves, higher near-infrared luminosities, and stronger carbon absorptions at early times. Here we present observations of the largest compilation of 2003fg-like SN Ia host galaxies to date, obtained with Integral Field Spectroscopy (IFS). For 20 objects, we study both the global host-galaxy properties and, for the first time for a sizeable sample, the local environment at the SN position. Globally, 2003fg-like SNe~Ia occur in galaxies with lower stellar mass, lower oxygen abundance, and marginally higher specific star-formation rate (sSFR) than those of normal SNe~Ia, although their hosts are not as extreme in such properties as superluminous SNe, nor representative of metal-poor dwarf-galaxy samples. Locally, the SN positions show lower star-formation-rate, stellar-mass surface densities, and lower sSFR, than normal SN~Ia environments, consistent with a significant preference for the outskirts of their hosts, while their stellar age indicators are typical. The most distinctive local property is metallicity, with 2003fg-like SNe~Ia occupying the most metal-poor environments among SNe~Ia. We also find a tentative positive correlation between the light-curve width and the oxygen abundance for 2003fg-like events. Our results imply that 2003fg-like SNe~Ia arise from the merger of two white dwarfs (WDs) or the core-degenerate scenario, but disfavor the single, rapidly rotating super-M$_{ch}$ C-O WD progenitor, as this channel requires a young stellar population that we do not observe at the SN positions. The preference of 2003fg-like SNe~Ia for low-metallicity environments suggests that they may have been more common in the early Universe. (abridged)

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SDSS-V Local Volume Mapper (LVM): Dithered Data Cube Reconstruction with 3dcubegen

The Sloan Digital Sky Survey V (SDSS-V) Local Volume Mapper (LVM) is conducting an unprecedented wide-field integral field spectroscopic survey of the Milky Way, the Magellanic Clouds, and nearby galaxies using a strategy based on multiple dithered observations to achieve full spatial coverage, improved spatial sampling, and enhanced spectral depth. However, the scientific exploitation of these observations requires a robust methodology to combine the individual row-stacked spectra (RSS) into homogeneous three-dimensional data cubes. In this work, we present 3DCubeGen, a flexible and scalable reconstruction tool designed to combine multiple LVM dithers while preserving flux and propagating uncertainties. The method enables the coaddition of large datasets, improving the signal-to-noise ratio, enhancing spatial resolution, and increasing sensitivity to faint emission features, following and extending approaches previously implemented in integral field surveys such as CALIFA. We apply 3DCubeGen to a large set of LVM observations, including the Large and Small Magellanic Clouds and nearby galaxies, combining thousands of dithers corresponding to millions of spectra. The resulting data products demonstrate significant improvements in spatial sampling and spectral depth, enabling detailed studies of the ionised gas, stellar populations, and kinematics across extended regions. 3DCubeGen provides a robust and scalable solution for LVM data cube reconstruction and represents a key tool for exploiting the scientific potential of the SDSS-V Local Volume Mapper.

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There is no single density: star-forming regions and galaxies hold more dense ionized gas than long assumed

Ionized gas fills star-forming regions and galaxies, and nearly everything we know about its temperature, pressure, mass, and composition is inferred from its emission lines [1-3]. The electron density is needed for all of these, yet a longstanding puzzle has resisted explanation: different density-sensitive lines, applied to the same gas, return values that disagree by up to two orders of magnitude. This is usually attributed either to each line tracing a physically distinct ionization zone or to imperfect atomic data [4-7]. Here we show that the disagreement is neither a flaw in the atomic data nor an ionization-stratification effect, but something more fundamental. Each diagnostic is tuned to a particular density, and when a nebula contains gas across a wide range of densities, as real nebulae do, each line reports the part of that range it is most sensitive to. The diagnostics do not measure a representative average density; they respond to different parts of a broad density distribution. This resolves the discrepancy with a simple relation between the density each line returns and the density it is most sensitive to, a relation that holds from individual H II regions to whole galaxies, near and far, and reveals that ionized nebulae contain far more dense gas than any one diagnostic implies. A nebula has no single electron density to measure, but a broad density distribution, and the masses, pressures, abundances and energetics built on the single-density assumption must be reconsidered, from nearby star-forming regions to galaxies across cosmic time.

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The Gas-Phase Mass-Metallicity Relation of Dwarf Galaxies Across Large-Scale Environments Using the CAVITY Parent Sample

The gas-phase mass-metallicity relation (MZR) of galaxies shows a noticeable break in slope and increased scatter at low stellar masses, suggesting that the physical processes governing chemical enrichment differ between dwarf and high-mass systems. Dwarf galaxies are highly susceptible to internal and environmental mechanisms due to shallow potential wells. We assess whether a single MZR describes dwarf galaxies across diverse large-scale environments using the CAVITY parent sample. We examine the MZR and star formation rate (SFR) of dwarfs with stellar masses 8.9 < log(M_star/M_sun) < 9.5. Using SDSS optical spectra, we measured emission line fluxes via the pyPipe3D pipeline to derive the MZR and SFR for 353, 311, and 22 dwarf galaxies in voids, filaments, and clusters, respectively. We find a systematic variation in the MZR slope, which is steeper in voids (0.28 +/- 0.03) and progressively flatter in clusters (0.17 +/- 0.08), indicating an environmental dependence in this mass regime. When separated by local environment, isolated and non-isolated dwarfs in voids show no significant differences. Isolated dwarfs in filaments exhibit properties similar to void counterparts. However, non-isolated filament galaxies display flatter MZR slopes, comparable to cluster dwarfs. We report both large- and local-scale environmental dependencies in the gas-phase metallicity and MZR slope. Consistent with the pre-processing framework, our results indicate that the local environment becomes significant within cosmic web filaments, affecting the chemical enrichment and star formation of low-mass systems. This suggests that part of the MZR scatter in dwarf galaxies arises from environmental effects.

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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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SDSS-V LVM: A spatially resolved study of the physical conditions and the chemical abundance discrepancy in the Lagoon Nebula (M 8)

The abundance discrepancy problem refers to the systematic differences observed between chemical abundances derived from collisionally excited lines (CELs) and recombination lines (RLs) of heavy ions. It remains a major unsolved problem in the study of ionized nebulae and is quantified by the abundance discrepancy factor (ADF). In this work, we present a deep integral field spectroscopic dataset covering the entire Lagoon Nebula (M 8), obtained by the SDSS-V Local Volume Mapper project, at a spatial resolution of 0.21 pc per spaxel. This unique dataset allows us, for the first time, to investigate spatially resolved maps of oxygen RL intensities (O II V1), together with maps of H I RLs, heavy-ion CELs, and dust attenuation across a whole H II region. We map the electron temperature using CELs and RLs of $O^{2+}$, CELs of $N^{+}$, and the electron density using CELs of $S^{+}$. We derive CEL-based ionic and elemental oxygen abundances and, for the first time, a spatially resolved map of the RL-based $O^{2+}$ abundance in an H II region. These measurements enable the construction of the first spatially resolved ADF($O^{2+}$) map of an H II region and yield a global mean ADF of ~0.47 +/- 0.02 dex. Focusing on the central region of M 8, where ionization is dominated by the O-type star Her 36, we find radial variations in the ADF ranging between ~0.35-0.50 dex. Our findings provide novel constraints on the spatial behavior and origin of the abundance discrepancy in H II regions.

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The ALMaQUEST Survey XVII: Unveiling Multiple Quenching Pathways in Green Valley Galaxies via Molecular Gas and Quenching Timescale Analyses

Statistically, green valley (GV) galaxies exhibit lower molecular gas fractions ($f_{gas}$) and reduced star formation efficiency (SFE) compared to star-forming galaxies. However, it remains unclear whether quenching is primarily driven by one factor or results from a combination of mechanisms in individual GV galaxies. In this study, we address this question by examining the spatial distributions of star formation and molecular gas in 28 GVs selected from the ALMaQUEST survey and additional literature samples. For each galaxy, we identify regions with suppressed specific star formation rate (sSFR) and measure $Δf_{gas}$ and $Δ$SFE-offsets from the resolved scaling relations of the star-forming main sequence galaxies. By comparing the fraction of regions with negative $Δf_{gas}$ and $Δ$SFE, we classify 35.7$\pm$13.2\% (57.1$\pm$17.9\%) of GV galaxies as $f_{gas}$-driven, 39.3$\pm$14.0\% (39.3$\pm$14.0\%) as SFE-driven, and 25.0$\pm$10.6\% (3.6$\pm$3.6\%) as mixed mode when adopting a fixed (variable) CO-to-$\rm H_{2}$ conversion factor ($α_{CO}$). These results indicate that GVs undergo quenching through multiple pathways. As sSFR decreases from the main sequence to the green valley, we observe a transition toward predominantly SFE-driven quenching, possibly linked to internal processes such as morphological quenching or AGN activity. We further estimate the quenching timescale ($τ_{decay}$), defined as the time from the peak SFR to 1/e (approximately 37\%) of its value, using integrated MaNGA spectra. SFE-driven quenching is typically associated with short $τ_{decay}$ , while $f_{gas}$-driven quenching shows a broader range. Overall, 75\% of GVs exhibit $τ_{decay}$ shorter than 1 Gyr, suggesting that quenching in most GVs proceeds rapidly, challenging purely slow-quenching scenarios like starvation.

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SDSS-V LVM: Resolving Physical Conditions in the Trifid Nebula

The chemical abundance of the interstellar medium sets the initial conditions for star formation and provides a probe of chemical galaxy evolution models. However, unresolved inhomogeneities in the electron temperature can lead to a systematic underestimation of the abundances. We aim to directly test this effect. We use the SDSS-V Local Volume Mapper to spatially map the physical conditions of the Trifid Nebula (M 20), a Galactic H II region ionized by a single mid-type O star, at 0.24 pc resolution. We exploit various emission lines (e.g., Hydrogen recombination lines and collisionally excited lines, including also faint auroral lines) and compute spatially resolved maps of [O II] and [S II] electron densities; [N II], [O II], [S II], [S III] electron temperatures; and the ionic oxygen abundances. We find internal variations of electron density that result from the ionization front, along with a negative radial gradient. However, we do not find strong gradients or structures in the electron temperature and the total oxygen abundance, making the Trifid Nebula a relatively homogeneous H II region at the observed spatial scale. We compare these spatially resolved properties with equivalent integrated measurements of the Trifid Nebula and find no significant variations between integrated and spatially resolved conditions. This isolated H II region, ionized by a single O-star, represents a test case of an ideal Strömgren sphere. The physical conditions in the Trifid Nebula behave as expected, with no significant differences between integrated and resolved measurements.

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Unified Spectrospatial Forward Models: Spatially Continuous Maps of Weak Emission Lines in the Rosette Nebula with SDSS-V LVM

Analyses of IFU data are typically performed on a per-spaxel basis, with each spectrum modelled independently. For low signal-to-noise (S/N) features such as weak emission lines, estimating properties is difficult and imprecise. Arbitrary binning schemes boost S/N at the cost of resolution, and risk introducing biases. We present a general forward-modelling approach that assumes spectra close on the sky are more similar than distant ones, and so can be modelled jointly. These "spectrospatial" models exploit spatial correlation to provide robust inferences, while simultaneously providing continuous predictions of line properties like strength and kinematics across the sky. Instrumental and calibration systematics are straightforward to include and infer. The model provides a natural trade-off between spatial resolution and S/N in a data-driven way. We apply this to Sloan Digital Sky Survey V (SDSS-V) Local Volume Mapper (LVM) data of the Rosette Nebula, producing continuous maps of fluxes and kinematics for Balmer, nebular, and auroral lines, as well as weak C II and N II recombination lines, demonstrating the approach across three orders of magnitude in S/N, including in the very low-S/N regime. The method recovers identical morphologies across different lines tracing similar ionisation volumes, at varying resolutions set by the S/N. We additionally provide a general framework for building and fitting such models in JAX, suitable for many applications. The implementation is fast and memory efficient, scales to large data volumes as in LVM, and can be deployed on hardware accelerators.

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Physical properties of gas departing from circular rotation at 50 pc scales using the PHANGS-MUSE galaxies

Noncircular motions have been observed across various spatial scales in disk galaxies, yet the physical properties of the gas involved in these motions remain poorly constrained. Using data from 19 galaxies from the PHANGS-MUSE sample, we investigated the prevalence of noncircular flows at spatial resolutions of tens of parsecs. We developed a new tool for 3D kinematic modelling of data cubes and applied it to the PHANGS-MUSE H$α$ spectral lines to recover the underlying circular, noncircular motions, as well as the intrinsic velocity dispersion in these objects. The PHANGS-MUSE galaxies exhibit rotation supported disks with $V_\mathrm{rot}/σ_\mathrm{intrin}$ ratios $\gtrsim$ 5. Our analysis revealed ionized gas exhibiting noncircular motions at different amplitudes, with low velocity amplitudes of about $5\mathrm{km\,s^{-1}}$ associated with the axisymmetric rotation component, deviations of $\sim10\mathrm{km\,s^{-1}}$ primarily linked to interarm and spiral arms, and larger deviations ($>20 \mathrm{km\,s^{-1}}$), found in the central and bar regions. We found that the velocity dispersion and the strength of ionization correlate with the amplitude of noncircular motions, suggesting that the underlying dynamics of the warm gas are closely tied to its physical properties.

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The vertical structure of the stellar disk in NGC 551

We self-consistently determine the 3D density distribution of NGC 551's stellar disk and study observational signatures of two-component stellar disks. Assuming baryonic disks are in hydrostatic equilibrium, we solved the Poisson-Boltzmann equation to estimate 3D density distribution. We used integral-field spectroscopic observations to estimate stellar velocity dispersion and built a 3D dynamical model using these density solutions and the observed rotation curve. We generated simulated surface brightness maps and compared them with observations to verify modeling consistency. The dynamical model was inclined to 90° to produce an edge-on surface density map, which we investigated by fitting different 2D functions and plotting vertical cuts in logarithmic scale. We estimated vertical stellar velocity dispersion using an iterative method, obtaining results consistent with the Disk Mass Survey formalism. Through dynamical modeling, we produced moment maps that reasonably matched observations. We examined the simulated edge-on model by taking vertical cuts and decomposing them into multiple Gaussian components. We find that artificial double Gaussian components arise due to line-of-sight integration effects, even for single-component disks. This indicates that decomposing vertical intensity cuts into multiple Gaussian components is unreliable for multicomponent disks. Instead, an up-bending break visible in logarithmic-scale vertical cuts serves as a more reliable indicator for two-component disks. We performed 2D fitting on the edge-on surface density map using the product of a scaled modified Bessel function and $sech^2$ function to estimate structural parameters. These traditional methods systematically underestimate the scale length and flattening ratio. Therefore, we suggest using detailed modeling to accurately deduce stellar disk structural parameters.

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Nebular emission from composite star-forming galaxies -- I. A novel modelling approach

We introduce a novel approach to modelling the nebular emission from star-forming galaxies by combining the contributions from many HII regions incorporating loose trends in physical properties, random dust attenuation, a predefined Halpha luminosity function and a diffuse ionized-gas component. Using a machine-learning-based regression artificial neural network trained on a grid of models generated by the photoionization code Cloudy, we efficiently predict emission-line properties of individual HII regions over a wide range of physical conditions. We generate 250,000 synthetic star-forming galaxies composed of up to 3000 HII regions and explore how variations in parameters affect their integrated emission-line properties. Our results highlight systematic biases in oxygen-abundance estimates derived using traditional methods, emphasizing the importance of accounting for the composite nature of star-forming galaxies when interpreting integrated nebular emission. Future work will leverage this approach to explore in detail its impact on parameter estimates of star-forming galaxies.

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Comparing metallicity correlations in nearby non-AGN and AGN-host galaxies

The gas-phase metallicity distribution within galaxies records critical information about galactic evolution. In this work we investigate how active galactic nuclei (AGN) influence this distribution by measuring the two-point correlation functions of gas-phase metallicity in 95 non-AGN and 37 AGN-host galaxies from the Calar Alto Legacy Integral Field spectroscopy Area integral field spectrographic survey. We measure metallicity using a novel Bayesian method that properly includes both stellar and AGN contributions to emission line fluxes and allows us to measure metallicities in both AGN-host and non-AGN galaxies in a single, consistent framework. We find that the two-point correlation functions of both AGN-host and non-AGN galaxies are well-fit by a simple injection-diffusion model, and that the correlation lengths $l_\mathrm{corr}$ we derive for the non-AGN galaxies are reasonably consistent with those obtained in earlier work. The AGN-host galaxies generally have smaller $l_\mathrm{corr}$ than non-AGN galaxies at fixed stellar mass, but similar $l_\mathrm{corr}$ at fixed star formation rate (SFR), suggesting that the primary effect of hosting an AGN in this sample is a reduction in SFR at fixed stellar mass, and that this in turn suppresses the correlation length. Our findings further indicate that, while both SFR and stellar mass are positively correlated with metallicity correlation length $l_\mathrm{corr}$, the former is more fundamental, implying that fluctuations in the metallicity distribution within galaxies are driven more by short-term responses to physical processes such as star formation that can change much faster than a Hubble time.

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CAVITY: Calar Alto Void Integral-field Treasury surveY. I. First public data release

The Calar Alto Void Integral-field Treasury surveY (CAVITY) is a legacy project aimed at characterising the population of galaxies inhabiting voids, which are the most under-dense regions of the cosmic web, located in the Local Universe. This paper describes the first public data release (DR1) of CAVITY, comprising science-grade optical data cubes for the initial 100 out of a total of $\sim$300 galaxies in the Local Universe ($0.005 < z < 0.050$). These data were acquired using the integral-field spectrograph PMAS/PPak mounted on the 3.5m telescope at the Calar Alto observatory. The DR1 galaxy sample encompasses diverse characteristics in the color-magnitude space, morphological type, stellar mass, and gas ionisation conditions, providing a rich resource for addressing key questions in galaxy evolution through spatially resolved spectroscopy. The galaxies in this study were observed with the low-resolution V500 set-up, spanning the wavelength range 3745-7500 Å, with a spectral resolution of 6.0 Å (FWHM). Here, we describe the data reduction and characteristics and data structure of the CAVITY datasets essential for their scientific utilisation, highlighting such concerns as vignetting effects, as well as the identification of bad pixels and management of spatially correlated noise. We also provide instructions for accessing the CAVITY datasets and associated ancillary data through the project's dedicated database.

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The CAVITY project. The spatially resolved stellar population properties of galaxies in voids

The Universe is shaped as a web-like structure, formed by clusters, filaments, and walls that leave large volumes in between named voids. Galaxies in voids have been found to be of a later type, bluer, less massive, and to have a slower evolution than galaxies in denser environments (filaments and walls). However, the effect of the void environment on their stellar population properties is still unclear. We aim to address this question using 118 optical integral field unit datacubes from the Calar Alto Void Integral-field Treasury surveY (CAVITY), observed with the PMAS/PPaK spectrograph at the 3.5m telescope at the Calar Alto Observatory (Almería, Spain). We used the non-parametric full spectral fitting code STARLIGHT to estimate their stellar population properties: stellar mass, stellar mass surface density, age, star formation rate (SFR), and specific star formation rate (sSFR). We analysed the results through the global and spatially resolved properties. Then, we compared them with a control sample of galaxies in filaments and walls from the CALIFA survey, matched in stellar mass and morphological type. Key findings include void galaxies having a slightly higher half-light radius (HLR), lower stellar mass surface density, and younger ages across all morphological types, and slightly elevated SFR and sSFR (only significant enough for Sas). Many of these differences appear in the outer parts of spiral galaxies in voids (HLR > 1), which are younger and exhibit a higher sSFR, indicative of less evolved discs. This trend is also found for early-type spirals, suggesting a slower transition from star-forming to quiescent states in voids. Our analysis indicates that void galaxies, influenced by their surroundings, undergo a more gradual evolution, especially in their outer regions, with a more pronounced effect for low-mass galaxies.

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More fundamental than the fundamental metallicity relation: The effect of the stellar metallicity on the gas-phase mass-metallicity and gravitational potential-metallicity relations

Context. One of the most fundamental scaling relations in galaxies is observed between metallicity and stellar mass -- the mass-metallicity relation (MZR) -- although recently a stronger dependence of the gas-phase metallicity with the galactic gravitational potential ($Φ\rm ZR$) has been reported. Further dependences of metallicity on other galaxy properties have been revealed, with the star formation rate (SFR) being one of the most studied and debated secondary parameters in the relation (the so-called fundamental metallicity relation). Aims. In this work we explore the dependence of the gas-phase metallicity residuals from the MZR and $Φ\rm ZR$ on different galaxy properties in the search for the most fundamental scaling relation in galaxies. Methods. We applied a random forest regressor algorithm on a sample of 3430 nearby star-forming galaxies from the SDSS-IV MaNGA survey. Using this technique, we explored the effect of 147 additional parameters on the global oxygen abundance residuals obtained after subtracting the MZR. Alternatively, we followed a similar approach with the metallicity residuals from the $Φ\rm ZR$. Results. The stellar metallicity of the galaxy is revealed as the secondary parameter in both the MZR and the $Φ\rm ZR$, ahead of the SFR. This parameter reduces the scatter in the relations $\sim 10-15\%$. We find the 3D relation between gravitational potential, gas metallicity, and stellar metallicity to be the most fundamental metallicity relation observed in galaxies.

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