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Matthias Steinmetz

Publications and source records attributed to Matthias Steinmetz.

At least 19 recordsLinked to original sources
arXiv2026

Effects of resolution and local stability on galactic disks: Halo resolution and softening on bar formation

Using N-body simulations, we examine the impact of dark matter (DM) halo resolution and gravitational softening on bar formation. We generate isolated disk-halo systems with fixed stellar disk parameters, varying the number of halo particles, softening lengths, and halo concentration to modulate disk stability via the central DM fraction. The effects of DM resolution ($\mratio=1$, 10, and 100) on bar formation are less pronounced in more unstable disks, in which the overall evolutionary path is similar except that the lowest DM resolution model suffers gradual bar weakening. Irrespective of the halo resolution, large softening, $\epsdm$, flattens the central halo density profile within the softening scale, impeding angular momentum transfer to the nascent bar and preventing bar formation in more stable models. In unstable models with $\epsdm=0.96 \, \kpc$, a small bar still emerges due to enhanced initial instability and a larger seed perturbation, yet its strength remains capped at $F_2 \approx 0.3$ owing to unresolved central dynamical friction. Despite the destabilizing effect of reduced central DM fractions, our results indicate that deficient central angular momentum exchange can still suppress bar growth. Furthermore, halo softening influences buckling instability, as larger values ($\epsdm=0.30$ and $0.60 \, \kpc$) inhibit central vertical heating, exacerbating radial-vertical velocity dispersion anisotropies and triggering stronger buckling. We recommend adopting $ \mratio \le 10 $, $ \mstar \leq 10^4 \, \Msun $, and $ \epsdm < 0.30\,\mathrm{kpc}$ when investigating the formation and evolution of non-axisymmetric structures in Milky Way-mass galaxies.

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arXiv2026

SMUGGLE-Ring: Evolutionary link between nuclear star cluster and nuclear disk

We present a high-resolution hydrodynamical simulation of the formation and evolution of nuclear structures in a Milky Way-mass galaxy using the SMUGGLE model. The system naturally develops a bar in isolation of $\approx5$ kpc in length, driving sustained gas inflows toward the center that lead to the formation of a nuclear stellar disk (NSD) and a nuclear star cluster (NSC). By only considering stars born after bar formation, we can cleanly isolate the nuclear structures and recover a clear inside-out growth of the NSD. In line with observations, we find that stellar feedback induces repeated shocks that regulate the size of the nuclear gas disk and drive gas from its outer edge toward the NSC region. Over time, the NSD and NSC share similar mass growth and star formation histories, except during the accretion of a massive star cluster. Our results suggest that both the evolutionary timescale of the bar (and thus of the NSD) and the accretion history of star clusters are essential for obtaining tighter scaling relations for nuclear structures and their host galaxies. Finally, our results favor a lower bulge mass for the Milky Way than that of our model ($B/D\approx 0.045$) to explain the compact size of its nuclear disk.

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arXiv2026

The Milky Way as a distant galaxy: an IFU and panchromatic view

Understanding the structure and evolution of galaxies increasingly benefits from placing the Milky Way (MW), the best-studied stellar system, in an external-galaxy context. To analyse the MW as an extragalactic system, we construct an integrated-light view of it using two complementary approaches: composite stellar populations built from a selection-function-free orbit-superposition solution constrained by APOGEE DR17, and full SKIRT radiative-transfer modelling of a hydrodynamical MW simulation initialised from the same solution. In both cases, the MW data are assembled into mock IFU datacubes and analysed with with full spectral fitting (pPXF). We find, however, that the underlying LOSVD is more complex than can be captured by a Gauss-Hermite parametrisation, as is likely the case in MW-like late-type barred galaxies. For the composite-population mocks, we recover the main large-scale kinematic structures, including the rotation and velocity-dispersion patterns associated with the thin and thick discs and the bar/bulge, together with the mean stellar-population maps. The known disc chemical bimodality in [α/M]-[M/H] cannot be recovered directly from the IFU, regardless of the α-resolution of the SSP templates, but its MW-like spatially varying double-sequence behaviour is recovered across the disc. The broad global star-formation history is reproduced, although artificial bursts, likely driven by the age-metallicity degeneracy, remain even after regularisation. For the radiative-transfer mocks, the main kinematic maps are recovered with moderate accuracy, whereas higher-order moments and stellar-population properties remain difficult to constrain, primarily because of the lower spectral resolution and lower statistical SNR of the datacubes. These results indicate that forward panchromatic modelling remains challenging for high-resolution IFU-like observations.

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arXiv2026

The SMUGGLE-Ring project: Bar and bulge effects on nuclear disk and ring formation

We present the first results from the SMUGGLE-Ring project, a suite of simulations employing the SMUGGLE ISM and stellar feedback model to explore nuclear structures in Milky Way-mass galaxies. We discuss results from three simulations evolved for 5 Gyr in isolation, in which we vary the classical bulge mass, while keeping the disk and halo structures identical. Nuclear stellar disks and rings emerge exclusively in our bulge models, with more massive bulges associated with earlier formation and more extended initial gas reservoirs shortly after bar formation. After gas depletion via active star formation, the nuclear stellar disks bifurcate into pressure-supported nuclear star clusters (NSCs, $v_ϕ/σ_R < 0.7$) and rotationally supported nuclear stellar rings (NSRs, $v_ϕ/σ_R = 1.2$--1.7, radii 0.64--0.76 kpc). The bulgeless model fails to build up and sustain stable nuclear gas disks against feedback disruptions. The enclosed stellar mass of NSCs ($\sim10^{9}\Msun$) dominates over that of NSRs ($\sim10^{8}\Msun$). The star formation rates decline over time due to gas depletion (NSCs 0.1--1 $\Msun$/yr, NSRs 0.01--$0.1 \Msun$/yr). Kinematics reveal outward-shifting rotation peaks with $σ$-drops in NSRs, while a fraction of stars in NSCs exhibits radial shift after 3 Gyr. These findings support inside-out NSD formation via secular bar evolution, with NSRs tracing the star-forming outer edge of the nuclear gas disk and NSCs forming the kinematically hotter inner component. The range of nuclear stellar disk sizes (0.25--0.76 kpc) falls within the observationally inferred ranges, but the existence of larger rings would require external gas flow and/or a longer period of evolution. Future SMUGGLE-Ring extensions will incorporate varying gas fractions, tidal/merger effects, and the circumgalactic medium to further elucidate nuclear diversity and outliers.

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arXiv2026

Effects of Resolution and Local Stability on Galactic Disks: I. Multiple Spiral Mode Formation via Swing Amplification

We investigate the formation of multiple spiral modes in Milky Way-like disk-halo systems without explicitly exciting perturbations. We explore how numerical resolution, the level of local disk stability, and the presence of a live halo influence both the initial appearance and the subsequent evolution of these modes. To characterize spiral structure, we compute Fourier amplitudes for modes $m=1$-$6$. In marginally unstable, lower-resolution disks ($N_\star=5\times10^6$, $N_{\rm DM}=1.14\times10^7$), faint features appear within the first $0.5$ Gyr due to numerical noise, in contrast to high-resolution models where perturbations emerge later. Across all sufficiently resolved, live-halo models with $m_{\rm DM}/m_\star \le 10$, the spirals exhibit a cascading sequence in both mode number and radius: higher-$m$ modes form and decay first, followed by the delayed emergence of lower-$m$ modes, with an inward drift of the activity's epicenter. This behavior reflects a combination of local swing amplification, which explains the initial growth of short-wavelength modes, and interference between coexisting long-lived spiral modes, which accounts for the recurrent short-timescale amplitude modulations. In contrast, models with a fixed halo potential or coarse halo resolution ($N_{\rm DM}=1.14\times10^6$ and $m_{\rm DM}/m_\star=100$) show strong early spirals but lack this coherent cascading behavior, owing to excessive shot noise and insufficient halo responsiveness. The $m=3$ mode plays a transitional role, marking the onset of angular-momentum transport in the inner disk that precedes bar formation, a process absent in fixed-potential models. Our results show that a live halo with appropriate mass resolution provides the gravitational response needed to sustain and regenerate multi-mode spiral structure, even though the total angular-momentum exchange remains small.

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arXiv2025

The Spheroidal Bulge of the Milky Way: Chemodynamically Distinct from the Inner-Thick Disc and Bar

Studying the composition and origin of the inner region of our Galaxy -- the "Galactic bulge" -- is crucial for understanding the formation and evolution of the Milky Way and other galaxies. We present new observational constraints based on a sample of around 18,000 stars in the inner Galaxy, combining Gaia DR3 RVS and APOGEE DR17 spectroscopy. Gaia-RVS complements APOGEE by improving sampling of the metallicity, [Fe/H] in the -2.0 to -0.5 dex range. This work marks the first application of Gaia-RVS spectroscopy to the bulge region, enabled by a novel machine learning approach (hybrid-CNN) that derives stellar parameters from intermediate-resolution spectra with precision comparable to APOGEE's infrared data. We performed full orbit integrations using a barred Galactic potential and applied orbital frequency analysis to disentangle the stellar populations in the inner Milky Way. For the first time, traced by the field stars, we are able to robustly identify the long-sought pressure supported bulge. We show this stellar population to be chemically and kinematically distinct from the other main components co-existing in the same region. The spheroidal bulge has a metallicity distribution function (MDF) peak at around -0.70 dex extending to solar value, is dominated by a high-[alpha/Fe] population with almost no dependency on metallicity, consistent with very rapid early formation, predating the thick disc and the bar. We find evidence that the bar has influenced the dynamics of the spheroidal bulge, introducing a mild triaxiality and radial extension. We identify a group of stars on X4 orbits, likely native to the early spheroid, as this population mimics the chemistry of the spheroidal bulge, with a minor contamination from the more metal-poor ([Fe/H] < -1.0) halo. We find the inner-thick disc to be kinematically hotter (mean Vphi ~125 km/s) than the local-thick disc. ...

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arXiv2025

A Pre-Infall Magellanic Analog-Corona and Stream formation in the \textsc{HESTIA} cosmological simulations

We identify and investigate a pre-infall analog of the Large and Small Magellanic Clouds (LMC, SMC) in the HESTIA suite of constrained cosmological simulations. The system, dynamically isolated from the Local Group, evolves over ~6 Gyr and forms a multiphase warm coronal halo and a neutral gas stream via repeated tidal interactions, ~150 kpc in length. The LMC-analog's corona forms self-consistently through virial accretion and inhibits the survival of clumpy neutral structures beyond ~600 Myr. The SMC analog remains bound through to z=0, and the pair also exhibits bridge-like and leading-arm features. These results suggest that while most of the ionized Stream is formed by the LMC coronal gas, the neutral gas stream, bridge, and leading arm components of the Magellanic System can arise from dwarf-dwarf interactions prior to infall, while the survival and ionization of these features likely require additional environmental processing. Furthermore, we identify a stellar component out of phase to the neutral component of the stream, implying that if the Magellanic stellar stream exists, it may not be spatially coexistent to the dominant H I stream. This system offers a valuable pre-infall reference point for interpreting the Magellanic System and identifying analogs beyond the Local Group.

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arXiv2025

Rediscovering the Milky Way with an orbit superposition approach and APOGEE data V. The disc growth and history of star formation

The Milky Way's (MW's) star formation history (SFH) offers insight into the chronology of its assembly and the mechanisms driving its structural development. In this study, we present an inference and analysis of the spatially resolved SFH and the MW disc growth. Our approach leverages both stellar birth radii estimates and the complete reconstruction of the MW stellar disc using a novel orbit superposition method from APOGEE data, allowing us to trace the orbit-mass weighted SFH based on formation sites while taking into account stellar mass loss. We find that the MW is a typical disc galaxy exhibiting inside-out formation: it was compact at $z > 2$ ($\rm R_{\rm eff} \approx 2$ kpc), had a peak in its star formation rate (SFR) 9--10 Gyr ago, and grew to a present-day size of $\rm R_{\rm eff} \approx 4.3$ kpc. A secondary peak in SFR $\sim 4$ Gyr ago is responsible for the onset of the outer disc, which comprises the metal-poor, low-$α$ population. We find that in-situ star formation in the solar neighbourhood started 8--9 Gyr ago. The MW disc is characterised by a negative mean age gradient, as the result of the inside-out growth, with additional flattening induced by stellar radial migration. Our work showcases the importance of accounting for radial migration and stellar sample selection function when inferring the SFH and build-up of the MW disc.

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arXiv2025

Bar-spiral interaction produces radial migration and star formation bursts

Central bars and spirals are known to strongly impact the evolution of their host galaxies, both in terms of dynamics and star formation. Their typically different pattern speeds cause them to regularly overlap, which induces fluctuations in bar parameters. In this paper, we analyze both numerical simulations of disk galaxies and observational data to study the effect of bar-spiral physical overlap on stellar radial migration and star formation in the bar vicinity, as a function of time and galactic azimuth. We study three different numerical models, two of which are in a cosmological context, as well as APOGEE DR17 data and the WISE catalog of Galactic HII regions. We find that periodic boosts in stellar radial migration occur when the bar and spiral structure overlap. This mechanism causes net inward migration along the bar leading side, while stars along the bar trailling side and minor axis are shifted outward. The signature of bar-spiral induced migration is seen between the bar's inner Lindbald resonance and well outside its corotation, beyond which other drivers take over. We also find that, in agreement with simulations, APOGEE DR17 stars born at the bar vicinity (mostly metal-rich) can migrate out to the solar radius while remaining on cold orbits. For the Milky Way, 13% of stars in the solar vicinity were born inside the bar, compared to 5-20% in the simulations. Bar-spiral reconnections also result in periodic starbursts at the bar ends with an enhancement of up to a factor of 4, depending on the strength of the spiral structure. Similarly to the migration bursts, these do not always happen simultaneously at the two sides of the bar, hinting at the importance of odd spiral modes. Data from the WISE catalog suggest this phhenomenon is also relevant in our own Galaxy.

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arXiv2024

Rediscovering the Milky Way with orbit superposition approach and APOGEE data III. Panoramic view of the bulge

The innermost parts of the Milky Way (MW) are very difficult to observe due to the high extinction along the line of sight, especially close to the disc mid-plane. However, this region contains the most massive complex stellar component of the MW, the bulge, primarily composed of disc stars whose structure is (re-)shaped by the evolution of the bar. In this work, we extend the application of the orbit superposition method to explore the present-day 3D structure, orbital composition, chemical abundance trends and kinematics of the MW bulge. Thanks to our approach, we are able to transfer astrometry from Gaia and stellar parameters from APOGEE DR 17 to map the inner MW without obscuration by the survey footprint and selection function. We demonstrate that the MW bulge is made of two main populations originating from a metal-poor, high-α thick disc and a metal-rich, low-α thin disc, with a mass ratio of 4:3, seen as two major components in the MDF. Finer MDF structures hint at multiple sub-populations associated with different orbital families of the bulge, which, however, have broad MDFs themselves. Decomposition using 2D GMMs in [Fe/H] -[Mg/Fe] identifies five components including a population with ex-situ origin. Two dominant ones correspond to the thin and thick discs and two in between trace the transition between them. We show that no universal metallicity gradient value can characterise the MW bulge. The radial gradients closely trace the X-shaped bulge density structure, while the vertical gradient variations follow the boxy component. While having, on average, subsolar metallicity, the MW bulge populations are more metal-rich compared to the surrounding disc, in agreement with extragalactic observations and state-of-the-art simulations reinforcing its secular origin.

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arXiv2024

Rediscovering the Milky Way with orbit superposition approach and APOGEE data II. Chrono-chemo-kinematics of the disc

The stellar disc is the dominant luminous component of the Milky Way (MW). Although our understanding of its structure is rapidly expanding due to advances in large-scale stellar surveys, our picture of the MW disc remains substantially obscured by selection functions and incomplete spatial coverage of observational data. In this work, we present the comprehensive chrono-chemo-kinematic structure of the MW disc, recovered using a novel orbit superposition approach combined with data from APOGEE DR 17. We detect periodic azimuthal metallicity variations within 6-8 kpc with an amplitude of 0.05-0.1 dex peaking along the bar major axis. The radial metallicity profile of the MW also varies with azimuth, displaying a pattern typical among other disc galaxies: a decline outside the solar radius and an almost flat profile in the inner region, attributed to the presence of old, metal-poor high-α populations, which comprise about 40% of the total stellar mass. The geometrically defined thick disc and the high-α populations have comparable masses, with differences in their stellar population content, which we quantify using the reconstructed 3D MW structure. The well-known [α/Fe]-bimodality in the MW disc, once weighted by stellar mass, is less pronounced at a given metallicity for the whole galaxy but distinctly visible in a narrow range of galactic radii (5-9 kpc), explaining its relative lack of prominence in external galaxies and galaxy formation simulations. Analysing a more evident double age-abundance sequence, we construct a scenario for the MW disc formation, advocating for an inner/outer disc dichotomy genetically linked to the MW's evolutionary stages. In this picture, the extended solar vicinity is a transition zone that shares chemical properties of both the inner (old age-metallicity sequence) and outer discs (young age-metallicity sequence).

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arXiv2024

Evolution of the radial ISM metallicity gradient in the Milky Way disk since redshift $\approx 3$

Recent works identified a way to recover the time evolution of a galaxy's disk metallicity gradient from the shape of its age--metallicity relation. However, the success of the method is dependent on how the width of the star-forming region evolves over time, which in turn is dependent on a galaxy's present-day bar strength. In this paper, we account for the time variation in the width of the star-forming region when deriving the interstellar medium (ISM) metallicity gradient evolution over time ($\rm \nabla [Fe/H](τ)$), which provides more realistic birth radii estimates of Milky Way (MW) disk stars. Using MW/Andromeda analogues from the TNG50 simulation, we quantified the disk growth of newly born stars as a function of present-day bar strength to provide a correction that improves recovery of $\rm \nabla [Fe/H](τ)$. In TNG50, we find that our correction reduces the median absolute error in recovering $\rm \nabla [Fe/H] (τ)$ by over 30%. To confirm its universality, we test our correction on two galaxies from NIHAO-UHD and find the median absolute error is over 3 times smaller even in the presence of observational uncertainties for the barred, MW-like galaxy. Applying our correction to APOGEE DR17 red giant MW disk stars suggests the effects of merger events on $\rm \nabla [Fe/H](τ)$ are less significant than originally found, and the corresponding estimated birth radii expose epochs when different migration mechanisms dominated. Our correction to account for the growth of the star-forming region in the disk allows for better recovery of the evolution of the MW disk's ISM metallicity gradient and, thus, more meaningful stellar birth radii estimates. With our results, we are able to suggest the evolution of not only the ISM gradient, but also the total stellar disk radial metallicity gradient, providing key constraints to select MW analogues across redshift.

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arXiv2024

The Blue Multi Unit Spectroscopic Explorer (BlueMUSE) on the VLT: science drivers and overview of instrument design

BlueMUSE is a blue-optimised, medium spectral resolution, panoramic integral field spectrograph under development for the Very Large Telescope (VLT). With an optimised transmission down to 350 nm, spectral resolution of R$\sim$3500 on average across the wavelength range, and a large FoV (1 arcmin$^2$), BlueMUSE will open up a new range of galactic and extragalactic science cases facilitated by its specific capabilities. The BlueMUSE consortium includes 9 institutes located in 7 countries and is led by the Centre de Recherche Astrophysique de Lyon (CRAL). The BlueMUSE project development is currently in Phase A, with an expected first light at the VLT in 2031. We introduce here the Top Level Requirements (TLRs) derived from the main science cases, and then present an overview of the BlueMUSE system and its subsystems fulfilling these TLRs. We specifically emphasize the tradeoffs that are made and the key distinctions compared to the MUSE instrument, upon which the system architecture is built.

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arXiv2024

Why does the Milky Way have a bar?

There is no doubt that the Milky Way is a barred galaxy; however, factors that establish its prominent morphology remain largely elusive and poorly comprehended. In this work, we attempt to constrain the history of the MW by tracing the present-day parameters and evolution of a set of MW and M31 analogues from the TNG50 cosmological simulations. We find that the strength of bars at $z=0$ correlates well not only with the total mass build-up of galaxies but, more crucially, with the time of rapid onset of stellar discs. Discs of strongly barred galaxies form early ($ z \gtrsim 2-3$), compared to weakly barred and non-barred galaxies ($z \approx 1-1.5$). Although we are cautious to draw ultimate conclusions about the governing factor of discs formation due to the complexity and correlations between different physical phenomena~(dark matter mass growth, gas accretion rate, mergers and others) affecting galaxy growth, the observed morphological diversity of galaxies can be tentatively explained by a substantial variation in the gas angular momentum around proto-galaxies already at $z\approx 3-5$; in such a way, early discs with the strongest bars at $z=0$ formed from gas with the largest angular momentum. By comparing the formation time scales of discs of barred galaxies in the TNG50 sample, we suggest that the MW has a strong bar ($0.35<A_2<0.6$) and that its stellar disc started to dominate over the spheroidal component already at $z \approx 2$, with a mass of $\approx 1 \pm 0.5 \times 10^{10} M_\odot$. We, therefore, conclude that the presence of a strong bar in the MW is a natural manifestation of the early formation of the stellar disc, which made possible bursty but highly efficient star formation at high redshift.

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arXiv2024

WST -- Widefield Spectroscopic Telescope: Motivation, science drivers and top-level requirements for a new dedicated facility

In this paper, we describe the wide-field spectroscopic survey telescope (WST) project. WST is a 12-metre wide-field spectroscopic survey telescope with simultaneous operation of a large field-of-view (3 sq. degree), high-multiplex (20,000) multi-object spectrograph (MOS), with both a low and high-resolution modes, and a giant 3x3 arcmin2 integral field spectrograph (IFS). In scientific capability, these specifications place WST far ahead of existing and planned facilities. In only 5 years of operation, the MOS would target 250 million galaxies and 25 million stars at low spectral resolution, plus 2 million stars at high resolution. Without need for pre-imaged targets, the IFS would deliver 4 billion spectra offering many serendipitous discoveries. Given the current investment in deep imaging surveys and noting the diagnostic power of spectroscopy, WST will fill a crucial gap in astronomical capability and work in synergy with future ground and space-based facilities. We show how it can address outstanding scientific questions in the areas of cosmology; galaxy assembly, evolution, and enrichment, including our own Milky Way; the origin of stars and planets; and time domain and multi-messenger astrophysics. WST's uniquely rich dataset may yield unforeseen discoveries in many of these areas. The telescope and instruments are designed as an integrated system and will mostly use existing technology, with the aim to minimise the carbon footprint and environmental impact. We will propose WST as the next European Southern Observatory (ESO) project after completion of the 39-metre ELT.

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arXiv2024

Discovery of the local counterpart of disc galaxies at z > 4: The oldest thin disc of the Milky Way using Gaia-RVS

JWST has recently detected numerous disc galaxies at high-redshifts and there have been observations of cold disc galaxies at z > 4 with ALMA. In the Milky Way, recent studies find metal-poor stars in cold disc orbits, suggesting an ancient disc. We investigated a sample of 565,606 stars from the hybrid-CNN analysis of the Gaia-DR3 RVS stars. The sample contains 8,500 stars with [Fe/H]<-1. For a subset of ~200,000 MSTO and subgiant stars we computed distances and ages using the StarHorse code with a mean precision of 1% and 12%, respectively. First, we confirm the existence of metal-poor stars in thin disc orbits - over 50% are older than 13 Gyr. Second, we report the discovery of the oldest thin disc of the Milky Way(MW), which extends across a wide range of metallicities, from metal-poor to super-solar stars. The metal-poor stars in disc orbits manifest as a readily visible tail of the metallicity distribution. The high-[α/Fe] thick disc exhibits a vertical velocity dispersion of 35 km/s, while the thin disc shows 10 to 15 km/s lower at similar ages. Our old thin disc $σ_{V_z}$ appears similar to those estimated for the high-z disc galaxies. Third, we extend the [Y/Mg] chemical clock to the oldest ages and estimate a slope of -0.038 dex/Gyr. Finally, we confirm our discovery by showing that the splash includes high- and low-[α/Fe] populations that are both old and extends to super-solar [Fe/H]. We find about 6 to 10% of the old thin disc was heated to thick disc orbits with the youngest splashed stars being 9 to 10 Gyrs. We conclude the MW thin disc forms <1 billion years from Big Bang, building up inside-out, preceding earlier estimates by about 4-5 billion years. Considering a massive merger event such as the GSE, a Splash is expected - we find a portion of the old thin disc is heated to thick disc velocities and the Splash extends to super-solar [Fe/H] regimes.

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arXiv2024

There is No Place Like Home -- Finding Birth Radii of Stars in the Milky Way

Stars move away from their birthplaces over time via a process known as radial migration, which blurs chemo-kinematic relations used for reconstructing the Milky Way (MW) formation history. To understand the true time evolution of the MW, one needs to take into account the effects of this process. We show that stellar birth radii can be derived directly from the data with minimum prior assumptions on the Galactic enrichment history. This is done by first recovering the time evolution of the stellar birth metallicity gradient, $d\mathrm{[Fe/H]}(R, τ)/dR$, through its inverse relation to the metallicity range as a function of age today, allowing us to place any star with age and metallicity measurements back to its birthplace, $R_b$. Applying our method to a large, high-precision data set of MW disk subgiant stars, we find a steepening of the birth metallicity gradient from 11 to 8 Gyr ago, which coincides with the time of the last massive merger, Gaia-Sausage-Enceladus (GSE). This transition appears to play a major role in shaping both the age-metallicity relation and the bimodality in the [$α$/Fe]-[Fe/H] plane. By dissecting the disk into mono-$R_b$ populations, clumps in the low-[$α$/Fe] sequence appear, which are not seen in the total sample and coincide in time with known star-formation bursts, possibly associated with the Sagittarius Dwarf Galaxy. We estimated that the Sun was born at $4.5\pm 0.4$~kpc from the Galactic center. Our $R_b$ estimates provide the missing piece needed to recover the Milky Way formation history.

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