arXiv subjects

Neige Frankel

Publications and source records attributed to Neige Frankel.

At least 19 recordsLinked to original sources

arXiv2026

Winding, Unwinding, Rewinding the Gaia Phase Spiral

The Gaia Space Satellite has transformed the field of Galactic Dynamics by collecting 6D phase space information for hundreds of millions of stars. In 2018, it enabled the discovery of the Gaia Phase Spiral (Antoja et al., 2018), a clear signal in the vertical motion of the stars that reveals how far from equilibrium the Galactic disk is. Seven years after the discovery of this structure, a workshop dedicated to the Phase Spiral took place at the Lorentz Center. Workshop participants summarized the current state of knowledge about the Phase Spiral and identified open questions and key areas to continue progressing in understanding the origin of the Phase Spiral and the physics governing the response of the disk to perturbations. Here, we aim to summarize the content and discussions of this workshop, share the resources that have been produced at this workshop with the broader community, and invite interested individuals to join on the projects that started.

astro-ph.GA↗

arXiv2026

Dynamical Origins of Azimuthal Metallicity Variations in the Galactic Disk: Insights from Kinematic Ridges with Gaia

Kinematic and spectroscopic studies in the past few years have revealed coherent azimuthal metallicity variations across the Milky Way's disk that may be the result of dynamical processes associated with non-axisymmetric features of the Galaxy. At the same time, stellar kinematics from Gaia have uncovered ridge-like features in the velocity space, raising the question of whether these chemical and dynamical substructures share a common origin. Using a sample of disk stars from Gaia DR3, we find that azimuthal metallicity variations are correlated with kinematic ridges in the V_phi-R plane, suggesting a shared origin. We utilize a suite of Milky Way test-particle simulations to assess the role of transient spiral arms, the bar, and interactions with a Sagittarius-like dwarf galaxy in simultaneously shaping both chemical and kinematic substructures. Among the physical mechanisms explored, bar and spiral arm interactions are the ones that consistently reproduce both the chemo-kinematic features and alignment observed in the Gaia data. While our model of an interaction with a Sagittarius-like dwarf galaxy can also induce kinematic and metallicity substructure, the amplitude of the azimuthal metallicity variations are too weak, suggesting this is likely not the dominant influence. Although additional contributing processes cannot be ruled out, the azimuthal metallicity variations observed in Gaia are best explained by a dynamical origin. Our results support the view that that azimuthal metallicity variations in the Galaxy are driven by similar dynamical mechanisms responsible for generating the kinematic ridges and co-moving groups.

astro-ph.GA↗

arXiv2025

Orbital migration and heating history of the Galactic disc: a transition between the bimodal discs

Stellar orbits in the Galactic disc evolve from their birth to the current shape through both radial migration and dynamical heating. The history of their secular evolution is imprinted in the current kinematics and age-metallicity distribution. We construct a chrono-chemo-dynamical model of the disc, incorporating inside-out growth, metallicity evolution, radial migration, and heating to fit the observed age-metallicity-kinematics distribution of LAMOST subgiant stars in both the low and high-$\alpha$ disc. By modelling all distribution parameters with spline fitting, we present the first non-parametric stellar migration and heating history of the Galaxy. We determine the heating-to-migration ratio, the ratio of the root-mean-square changes in radial/vertical and azimuthal actions, to be $\approx0.075$ for radial to azimuthal actions and $\approx0.015$ for vertical to azimuthal actions, implying a highly anisotropic diffusion in the action space. Furthermore, we identify a transition in radial migration efficiency coinciding with the transition moment of the bimodal disc, for which the radial migration was more efficient for the high-$\alpha$ disc than for the low-$\alpha$ disc. This transition may be attributed to two correlated scenarios: 1) a bar formation epoch accompanied by violent outward migration, and 2) a drop in the gas mass fraction in the disc when the low-$\alpha$ disc began to form. These findings offer further constraints on the formation mechanisms of bimodal discs, favouring the downsizing scenario. We also briefly discuss the connection between our results and recent high-redshift observations. In addition to the secular evolution history, our model maps the Milky Way ISM metallicity gradient at different lookback times, which we find has only varied a little (in the range of $-0.07~\rm to~-0.10~dex/kpc$) since disc formation.

astro-ph.GA↗

arXiv2025

Chemical dissection of merger-induced $m=1$ lopsidedness in Milky Way-like galaxies

The Milky Way harbours a prominent m=1 lopsided distortion in both stellar and neutral gas distributions. On the other hand, chemo-dynamical studies have been proven to be effective in grasping the overall evolution of galaxies. Here, we investigate systematically the excitation and evolution of a merger-driven $m=1$ lopsidedness in a Milky Way (MW)-like host galaxy, as a function of chemical distribution of stars. Using seven dissipationless, high-resolution $N$-body simulations of minor mergers (between a MW-like host and a satellite) under varying orbital configurations (prograde/retrograde and different orientation of the satellite orbital plane), we first show that a tidal interaction excites a prominent $m=1$ lopsidedness in the stellar density and velocity distribution of the MW-like host. Assigning, a posteriori, metallicities to stellar particles of the MW-like host based on the current observational constraints, we sub-divide the stars into metal-rich ([Fe/H] > 0), metal-intermediate (-0.5 < [Fe/H] <0), and metal-poor (- 0.5 < [Fe/H]) populations. We demonstrate that metal-rich population always show a much stronger $m=1$ lopsidedness in both density and velocity distributions when compared to other two populations. This trend holds true for all minor merger model considered here, regardless of their orbital configurations. Furthermore, minor merger also triggers a transient off-centred stellar disc-dark matter halo configuration, with metal-rich population showing the highest degree of disc-halo offset. We show that the metal-rich population which is kinematically colder (i.e. lower velocity dispersion) by construction, is more susceptible to external perturbations. Lastly, using a catalogue of photometry and metalicity for the LMC, we show that the strength of the $m=1$ distortion (predominantly in the form of an one-arm spiral) in stars increases with metallicity as well.

astro-ph.GA↗

arXiv2025

The large-scale kinematics of young stars in the Milky Way disc: first results from SDSS-V

We present a first large-scale kinematic map of $\sim$50,000 young OB stars ($T_{\rm eff} \geq 10,000$ K), based on BOSS spectroscopy from the Milky Way Mapper OB program in the ongoing Sloan Digital Sky Survey V (SDSS-V). Using photogeometric distances, line-of-sight velocities and Gaia DR3 proper motions, we map 3D Galactocentric velocities across the Galactic plane to $\sim$5 kpc from the Sun, with a focus on radial motions ($v_R$). Our results reveal mean radial motion with amplitudes of $\pm 30$ km/s that are coherent on kiloparsec scales, alternating between inward and outward motions. These $\bar{v}_R$ amplitudes are considerably higher than those observed for older, red giant populations. These kinematic patterns show only a weak correlation with spiral arm over-densities. Age estimates, derived from MIST isochrones, indicate that 85% of the sample is younger than $\sim300$ Myr and that the youngest stars ($\le 30$ Myr) align well with density enhancements. The age-dependent $\bar{v}_R$ in Auriga makes it plausible that younger stars exhibits different velocity variations than older giants. The origin of the radial velocity features remains uncertain, and may result from a combination of factors, including spiral arm dynamics, the Galactic bar, resonant interactions, or phase mixing following a perturbation. The present analysis is based on approximately one-third of the full target sample. The completed survey will enable a more comprehensive investigation of these features and a detailed dynamical interpretation.

astro-ph.GA↗

arXiv2025

Origin of the two-armed vertical phase-spiral in the inner Galactic disk

Gaia recently revealed a two-armed spiral pattern in the vertical phase-space distribution of the inner Galactic disk (guiding radius $R_\textrm{g} \sim 6.2$ kpc), indicating that some non-adiabatic perturbation symmetric about the mid-plane is driving the inner disk out of equilibrium. The non-axisymmetric structures in the disk (e.g., the bar or spiral arms) have been suspected to be the major source for such a perturbation. However, both the lifetime and the period of these internal perturbations are typically longer than the period at which stars oscillate vertically, implying that the perturbation is generally adiabatic. This issue is particularly pronounced in the inner Galaxy, where the vertical oscillation period is shorter and therefore adiabatically shielded more than the outer disk. We show that two-armed phase spirals can naturally form in the inner disk if there is a vertical resonance that breaks the adiabaticity; otherwise, their formation requires a perturber with an unrealistically short lifetime. We predict analytically and confirm with simulations that a steadily rotating (non-winding) two-armed phase spiral forms near the resonance when stars are subject to both periodic perturbations (e.g., by spiral arms) and stochastic perturbations (e.g., by giant molecular clouds). Due to the presence of multiple resonances, the vertical phase-space exhibits several local phase spirals that rotate steadily at distinct frequencies, together forming a global phase spiral that evolves over time. Our results demonstrate that, contrary to earlier predictions, the formation of the two-armed phase spiral does not require transient perturbations with lifetimes shorter than the vertical oscillation period.

astro-ph.GA↗

arXiv2024

Dark Galactic subhalos and the Gaia snail

Gaia has revealed a clear signal of disequilibrium in the solar neighborhood in the form of a spiral (or snail) feature in the vertical phase-space distribution. We investigate the possibility that this structure emerges from ongoing perturbations by dark $\left(10^{6} M_{\odot} - 10^8 M_{\odot}\right)$ Galactic subhalos. We develop a probabilistic model for generating subhalo orbits based on a semi-analytic model of structure formation, and combine this framework with an approximate prescription for calculating the response of the disk to external perturbations. We also develop a phenomenological treatment for the diffusion of phase-space spirals caused by gravitational scattering between stars and giant molecular clouds, a process that erases the kinematic signatures of old ($t \gtrsim 0.6$ Gyr) events. Perturbations caused by dark subhalos are, on average, orders of magnitude weaker than those caused by luminous satellite galaxies, but the ubiquity of dark halos predicted by cold dark matter makes them a more probable source of strong perturbation to the dynamics of the solar neighborhood. Dark subhalos alone do not cause enough disturbance to explain the Gaia snail, but they excite fluctuations of $\sim 0.1-0.5 \ \rm{km} \ \rm{s^{-1}}$ in the mean vertical velocity of stars near the Galactic midplane that should persist to the present day. Subhalos also produce correlations between vertical frequency and orbital angle that could be mistaken as originating from a single past disturbance. Our results motivate investigation of the Milky Way's dark satellites by characterizing their kinematic signatures in phase-space spirals across the Galaxy.

astro-ph.GA↗

arXiv2024

The formation and survival of the Milky Way's oldest stellar disk

It remains a mystery when our Milky Way first formed a stellar disk component that survived and maintained its disk structure from subsequent galaxy mergers. We present a study of the age-dependent structure and star formation rate of the Milky Way's disk using high-alpha stars with significant orbital angular momentum that have precise age determinations. Our results show that the radial scale length is nearly independent of age, while the vertical scale height experienced dramatic evolution. A disk-like geometry presents even for populations older than 13 Gyr, with the scale height-to-length ratio dropping below 0.5 for populations younger than 12.5 Gyr. We dub the oldest population that has maintained a disk geometry - apparently formed over 13 Gyr ago - PanGu. With an estimated present-day stellar mass of $2 \times 10^9$ $M_\odot$, PanGu is presumed to be a major stellar component of our Galaxy in the earliest epoch. The total present-day stellar mass of the whole high-alpha disk is $2 \times 10^{10}$ $M_\odot$, mostly formed during a distinct star formation rate peak of 11 $M_\odot$ per year around 11 Gyrs ago. A comparison with Milky Way analogs in the TNG50 simulations implies that our Galaxy has experienced an exceptionally quiescent dynamical history, even before the Gaia-Enceladus merger.

astro-ph.GA↗

arXiv2024

The Age-Dependent Vertical Actions of Young Stars in the Galaxy

Stars in the Galactic disk are born on cold, nearly circular orbits with small vertical excursions. After their birth, their orbits evolve, driven by small- or large-scale perturbations in the Galactic disk's gravitational potential. Here, we study the vertical motions of young stars over their first few orbital periods, using a sample of OBA stars from \textit{Gaia} E/DR3, which includes radial velocities and ages $\tau$ from LAMOST. We constructed a parametric model for the time evolution of the stellar orbits' mean vertical actions $J_z$ as a function of Galactocentric radius, $R_{\mathrm{GC}}$. Accounting for data uncertainties, we use Markov Chain Monte Carlo (MCMC) analysis in annuli of Galactocentric radius to constrain the model parameters. Our best-fit model shows a remarkably linear increase of vertical actions with age across all Galactocentric radii examined. Orbital \textit{heating} by random scattering could offer a straightforward interpretation for this trend. However, various other dynamical aspects of the Galactic disk, such as stars being born in a warped disk, might offer alternative explanations that could be tested in the future.

astro-ph.GA↗

arXiv2024

Iron Snails: non-equilibrium dynamics and spiral abundance patterns

Galaxies are not in a dynamical steady state. They continually undergo perturbations, e.g., from infalling dwarf galaxies and dark-matter substructure. After a dynamical perturbation, stars phase mix towards a new steady state; in so doing they generally form spiral structures, such as spiral density waves in galaxy disks and the Gaia Snail observed in the vertical phase-space density in the solar neighborhood. Structures in phase-space density can be hard to measure accurately, because spatially varying selection effects imprint their own patterns on the density. However, stellar labels such as metallicity, or other element abundances, or stellar masses and ages, can be measured even in the face of complex or unknown spatial selection functions. We show that if the equilibrium galaxy has phase-space gradients in these labels, any perturbation that could raise a spiral wave in the phase-space density will raise a spiral wave in the distribution of labels as well. We work out the relationship between the spiral patterns in the density and in the labels. As an example, we analyze the Gaia Snail and show that its amplitude and dynamical age as derived from elemental abundances (mainly [Mg/Fe]) follow similar patterns to those derived from the phase-space density. Our best model dates the Snail's perturbation to about 400 Myr ago although we find significant variations with angular momentum in the best-fit age. Conceptually, the ideas presented here are related to Orbital Torus Imaging, chemical tagging, and other methods that use stellar labels to trace dynamics.

astro-ph.GA↗

arXiv2024

The Extremely Metal Rich Knot of Stars at the Heart of the Galaxy

We show with Gaia XP spectroscopy that extremely metal-rich stars in the Milky Way (EMR; $[M/H]_{XP} > 0.5$) - but only those - are largely confined to a tight "knot" at the center of the Galaxy. This EMR knot is round in projection, has a fairly abrupt edge near $\sim 1.5$kpc, and is a dynamically hot system. This central knot also contains very metal-rich (VMR; $+0.2\le [M/H]_{XP} \le +0.4$) stars. However, in contrast to EMR stars, the bulk of VMR stars form an extended, highly flattened distribution in the inner Galaxy ($R_{\mathrm{GC}}\lesssim 5$ kpc). We draw on TNG50 simulations of Milky Way analogs for context and find that compact, metal-rich knots confined to $<1.5$kpc are a universal feature. In typical simulated analogs, the top 5-10% most metal-rich stars are confined to a central knot; however, in our Milky Way data this fraction is only 0.1%. Dust-penetrating wide-area near-infrared spectroscopy, such as SDSS-V, will be needed for a rigorous estimate of the fraction of stars in the Galactic EMR knot. Why in our Milky Way only EMR giants are confined to such a central knot remains to be explained. Remarkably, the central few kiloparsecs of the Milky Way harbor both the highest concentration of metal-poor stars (the `poor old heart') and almost all EMR stars. This highlights the stellar population diversity at the bottom of galactic potential wells.

astro-ph.GA↗

arXiv2024

A path towards constraining the evolution of the interstellar medium and outflows in the Milky Way using APOGEE

In recent years, the study of the Milky Way has significantly advanced due to extensive spectroscopic surveys of its stars, complemented by astroseismic and astrometric data. However, it remains disjoint from recent advancements in understanding the physics of the Galactic interstellar medium (ISM). This paper introduces a new model for the chemical evolution of the Milky Way that can be constrained on stellar data, because it combines a state-of-the-art ISM model with a Milky Way stellar disc model. Utilizing a dataset of red clump stars from APOGEE, known for their precise ages and metallicities, we concentrate on the last 6 billion years -- a period marked by Milky Way's secular evolution. We examine the oxygen abundance in the low-$\alpha$ disc stars relative to their ages and birth radii, validating or constraining critical ISM parameters that remain largely unexplored in extragalactic observations. The models that successfully reproduce the radius -- metallicity distribution and the age -- metallicity distribution of stars without violating existing ISM observations indicate a need for modest differential oxygen enrichment in Galactic outflows, meaning that the oxygen abundance of outflows is higher than the local ISM abundance, irrespective of outflow mass loading. The models also suggest somewhat elevated ISM gas velocity dispersion levels over the past 6 billion years compared to galaxies of similar mass. The extra turbulence necessary could result from energy from gas accretion onto the Galaxy, supernovae clustering in the ISM, or increased star formation efficiency per freefall time. This work provides a novel approach to constraining the Galactic ISM and outflows, leveraging the detailed insights available from contemporary Milky Way surveys.

astro-ph.GA↗

arXiv2024

What Does the Large Magellanic Cloud Look Like? It Depends on [M/H] and Age

We offer a new way to look at the Large Magellanic Cloud through stellar mono-abundance and mono-age-mono-abundance maps. These maps are based on $\gtrsim 500\,000$ member stars with photo-spectroscopic [M/H] and age estimates from Gaia DR3 data, and they are the first area-complete, metallicity- and age-differentiated stellar maps of any disk galaxy. Azimuthally averaged, these maps reveal a surprisingly simple picture of the Milky Way's largest satellite galaxy. For any [M/H] below -0.1 dex, the LMC's radial profile is well described by a simple exponential, but with a scale length that steadily shrinks towards higher metallicities, from nearly 2.3~kpc at [M/H]$=-1.8$ to only 0.75~kpc at [M/H]$=-0.25$. The prominence of the bar decreases dramatically with [M/H], making it barely discernible at [M/H]$\lesssim -1.5$. Yet, even for metal-rich populations, the bar has little impact on the azimuthally averaged profile of the mono-abundance components. Including ages, we find that the scale length is a greater function of age than of metallicity, with younger populations far more centrally concentrated. At old ages, the scale length decreases with increasing metallicity; at young ages, the scale-length is independent of metallicity. These findings provide quantitative support for a scenario where the LMC built its stellar structure effectively outside in.

astro-ph.GA↗

arXiv2023

Decoding the age-chemical structure of the Milky Way disk: An application of Copulas and Elicitable Maps

In the Milky Way, the distribution of stars in the $[\alpha/\mathrm{Fe}]$ vs. $[\mathrm{Fe/H}]$ and $[\mathrm{Fe/H}]$ vs. age planes holds essential information about the history of star formation, accretion, and dynamical evolution of the Galactic disk. We investigate these planes by applying novel statistical methods called copulas and elicitable maps to the ages and abundances of red giants in the APOGEE survey. We find that the low- and high-$\alpha$ disk stars have a clean separation in copula space and use this to provide an automated separation of the $\alpha$ sequences using a purely statistical approach. This separation reveals that the high-$\alpha$ disk ends at the same [$\alpha$/Fe] and age at high $[\mathrm{Fe/H}]$ as the low-$[\mathrm{Fe/H}]$ start of the low-$\alpha$ disk, thus supporting a sequential formation scenario for the high- and low-$\alpha$ disks. We then combine copulas with elicitable maps to precisely obtain the correlation between stellar age $\tau$ and metallicity $[\mathrm{Fe/H}]$ conditional on Galactocentric radius $R$ and height $z$ in the range $0 < R < 20$ kpc and $|z| < 2$ kpc. The resulting trends in the age-metallicity correlation with radius, height, and [$\alpha$/Fe] demonstrate a $\approx 0$ correlation wherever kinematically-cold orbits dominate, while the naively-expected negative correlation is present where kinematically-hot orbits dominate. This is consistent with the effects of spiral-driven radial migration, which must be strong enough to completely flatten the age-metallicity structure of the low-$\alpha$ disk.

astro-ph.GA↗

arXiv2023

Disk flaring with TNG50: diversity across Milky Way and M31 analogs

We use the sample of 198 Milky Way (MW) and Andromeda (M31) analogs from TNG50 to quantify the level of disk flaring predicted by a modern, high-resolution cosmological hydrodynamical simulation. Disk flaring refers to the increase of vertical stellar disk height with galactocentric distance. The TNG50 galaxies are selected to have stellar disky morphology, a stellar mass in the range of $M_* = 10^{10.5 - 11.2}~\rm{M_{\odot}}$, and a MW-like Mpc-scale environment at $z=0$. The stellar disks of such TNG50 MW/M31 analogs exhibit a wide diversity of structural properties, including a number of galaxies with disk scalelength and thin and thick disk scaleheights that are comparable to those measured or inferred for the Galaxy and Andromeda. With one set of physical ingredients, TNG50 returns a large variety of flaring flavours and amounts, also for mono-age stellar populations. With this paper, we hence propose a non-parametric characterization of flaring. The typical MW/M31 analogs exhibit disk scaleheights that are $1.5-2$ times larger in the outer than in the inner regions of the disk for both old and young stellar populations, but with a large galaxy-to-galaxy variation. Which stellar population flares more, and by how much, also varies from galaxy to galaxy. TNG50 de facto brackets existing observational constraints for the Galaxy and all previous numerical findings. A link between the amount of flaring and the $z=0$ global galaxy structural properties or merger history is complex. However, a connection between the scaleheights and the local stellar vertical kinematics and gravitational potential is clearly in place.

astro-ph.GA↗

arXiv2023

The Origin of Stars in the Inner 500 Parsecs in TNG50 Galaxies

We investigate the origin of stars in the innermost $500\,\mathrm{pc}$ of galaxies spanning stellar masses of $5\times10^{8-12}\,\mathrm{M}_{\odot}$ at $\mathrm{z=0}$ using the cosmological magnetohydrodynamical TNG50 simulation. Three different origins of stars comprise galactic centers: 1) in-situ (born in the center), 2) migrated (born elsewhere in the galaxy and ultimately moved to the center), 3) ex-situ (accreted from other galaxies). In-situ and migrated stars dominate the central stellar mass budget on average with 73% and 23% respectively. The ex-situ fraction rises above 1% for galaxies $\gtrsim10^{11}\,\mathrm{M}_{\odot}$. Yet, only 9% of all galaxies exhibit no ex-situ stars in their centers and the scatter of ex-situ mass is significant ($4-6\,\mathrm{dex}$). Migrated stars predominantly originate closely from the center ($1-2\,\mathrm{kpc}$), but if they travelled together in clumps distances reach $\sim10\,\mathrm{kpc}$. Central and satellite galaxies possess similar amounts and origins of central stars. Star forming galaxies ($\gtrsim10^{10}\,\mathrm{M}_{\odot}$) have on average more ex-situ mass in their centers than quenched ones. We predict readily observable stellar population and dynamical properties: 1) migrated stars are distinctly young ($\sim2\,\mathrm{Gyr}$) and rotationally supported, especially for Milky Way mass galaxies, 2) in-situ stars are most metal-rich and older than migrated stars, 3) ex-situ stars are on random motion dominated orbits and typically the oldest, most metal-poor and $\alpha$-enhanced population. We demonstrate that the interaction history with other galaxies leads to diverse pathways of building up galaxy centers in a $\Lambda$CDM universe. Our work highlights the necessity for cosmological context in formation scenarios of central galactic components and the potential to use galaxy centers as tracers of overall galaxy assembly.

astro-ph.GA↗

arXiv2022

The origin and fate of the Gaia phase-space snail

The Gaia snail is a spiral feature in the distribution of solar-neighbourhood stars in position and velocity normal to the Galactic midplane. The snail probably arises from phase mixing of gravitational disturbances that perturbed the disc in the distant past. The most common hypothesis is that the strongest disturbance resulted from a passage of the Sagittarius dwarf galaxy close to the solar neighbourhood. In this paper we investigate the alternative hypothesis that the snail is created by many small disturbances rather than one large one, that is, by Gaussian noise in the gravitational potential. Probably most of this noise is due to substructures in the dark-matter halo. We show that this hypothesis naturally reproduces most of the properties of the snail. In particular it predicts correctly, with no free parameters, that the apparent age of the snail will be $ \sim 0.5$ Gyr. An important ingredient of this model is that any snail-like feature in the solar neighbourhood, whatever its cause, is erased by scattering from giant molecular clouds or other small-scale structure on a time-scale $\lesssim 1$ Gyr.

astro-ph.GA↗

arXiv2022

Vertical motion in the Galactic disc: unwinding the Snail

The distribution of stars in the Milky Way disc shows a spiral structure--the Snail--in the space of velocity and position normal to the Galactic mid-plane. The Snail appears as straight lines in the vertical frequency--vertical phase plane when effects from sample selection are removed. Their slope has the dimension of inverse time, with the simplest interpretation being the inverse age of the Snail. Here, we devise and fit a simple model in which the spiral starts as a lopsided perturbation from steady state, that winds up into the present-day morphology. The winding occurs because the vertical frequency decreases with vertical action. We use data from stars in Gaia EDR3 that have measured radial velocities, pruned by simple distance and photometric selection functions. We divide the data into boxels of dynamical invariants (radial action, angular momentum); our model fits the data well in many of the boxels. The model parameters have physical interpretations: one, $A$, is a perturbation amplitude, and one, $t$, is interpretable in the simplest models as the time since the event that caused the Snail. We find trends relating the strength and age to angular momentum: (i) the amplitude $A$ is small at low angular momentum ($<1\,600\mathrm{\,kpc\,km\,s}^{-1}$ or guiding-centre radius $< 7.3\,$kpc), and over a factor of three larger, with strong variations, in the outer disc; (ii) there is no single well-defined perturbation time, with $t$ varying between 0.2 and 0.6 Gyr. Residuals between the data and the model display systematic trends, implying that the data call for more complex models.

astro-ph.GA↗