arXiv subjects

Jorge Peñarrubia

Publications and source records attributed to Jorge Peñarrubia.

At least 19 recordsLinked to original sources

arXiv2026

Central stellar depletion in the Draco dwarf from Subaru photometry

Dark matter subhaloes are a fundamental prediction of the standard cosmological model, but their low-mass population remains difficult to constrain observationally. Recent work has shown that interactions between subhaloes and dwarf spheroidal galaxies can induce large-scale, out-of-equilibrium fluctuations in their stellar surface density fields, identifiable through Fourier-based statistics. We apply this formalism to deep Subaru photometry of the Draco dwarf, extending previous tests to $\gtrsim\mathcal{O}(10^{4})$ resolved stars. We use artificial-star tests to assign completeness weights to individual stars and incorporate them into a discrete likelihood-based framework. Relative to a cored axisymmetric Plummer model, Draco shows radial corrugations that appear in the filtered normalised residuals as a central stellar depletion surrounded by a ring-like excess. The same feature appears in Fourier space as a low-frequency peak with a signal-to-noise ratio ${\rm S/N}=6.0$. Independently, fitting the surface density $Σ$ with an $αβγ$ model yields ${\rm d}Σ/{\rm d}R>0$ at $>99.9\%$ confidence -- i.e., a profile that decreases towards the centre. Although these signatures cannot yet be regarded as robust evidence for dark subhaloes, they suggest that central stellar depletion in dwarf galaxies may reflect genuine physical structure rather than crowding alone.

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arXiv2026

Dynamical friction vs. subhalo heating in Cold Dark Matter haloes

The orbital evolution of massive stellar systems embedded in dark matter haloes is governed by competing processes. Dynamical friction removes orbital energy, whereas fluctuations in the gravitational field generated by dark matter subhaloes inject energy through stochastic heating. We investigate the balance between these two mechanisms using analytical arguments and numerical experiments. We show that, for a given host halo and subhalo population, there exists a critical mass $M_{\rm crit}$ at which heating and friction balance. Clusters with masses $M_{\rm cl}>M_{\rm crit}$ lose orbital energy and sink towards the centre of the halo, whereas those with $M_{\rm cl}<M_{\rm crit}$ gain energy and expand outwards. At $M_{\rm cl}\simeq M_{\rm crit}$, the two processes balance, leading to a cluster population that, on average, neither sinks nor expands within the host halo. In CDM haloes, the critical mass is primarily controlled by the upper end of the subhalo mass function. Since massive subhaloes are intrinsically rare, the balance between heating and friction shows substantial halo-to-halo scatter. For dark matter haloes in the mass range associated with dwarf spheroidal galaxies (dSphs), we find $M_{\rm crit}\gtrsim 10^5M_\odot$, comparable to the masses of globular clusters in the Fornax dSph. Stochastic heating by dark substructure may therefore significantly delay the orbital decay of globular clusters and help alleviate the Fornax timing problem.

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arXiv2026

$S^5$: Tidal Disruption in Crater 2 and Formation of Diffuse Dwarf Galaxies in the Local Group

We present results of a spectroscopic campaign around the diffuse dwarf galaxy Crater 2 (Cra2) and its tidal tails as part of the Southern Stellar Stream Spectroscopic Survey ($S^5$). Cra2 is a Milky Way dwarf spheroidal satellite with extremely cold kinematics, but a huge size similar to the Small Magellanic Cloud, which may be difficult to explain within collisionless cold dark matter. We identify 143 Cra2 members, of which 114 belong to the galaxy's main body and 29 are deemed part of its stellar stream. We confirm that Cra2 is dynamically cold (central velocity dispersion $2.51^{+0.33}_{-0.30}\,{\rm km \ s^{-1}}$) and also discover a $\approx$7$σ$ velocity gradient consistent with its tidal debris track. We separately estimate the stream's internal velocity dispersion to be $5.74^{+0.98}_{-0.83}\,{\rm km \ s^{-1}}$. We develop a suite of $N$-body simulations with both cuspy and cored density profiles on a realistic Cra2 orbit to compare with $S^5$ observations. We find that the velocity dispersion ratio between Cra2 stream and galaxy ($2.30^{+0.41}_{-0.35}$) is difficult to reconcile with a cuspy halo with fiducial concentration and an initial mass predicted by standard stellar mass--halo mass relationships. Instead, either a cored halo with relatively small core radius or a low-concentration cuspy model can reproduce this ratio. Despite tidal mass loss, Cra2 is metal-poor ($\langle \rm[Fe/H]\rangle=-2.16\pm0.04$) compared to the stellar mass--metallicity relation for its luminosity. Other diffuse dwarf galaxies similar to Cra2 in the Local Group (Antlia 2 and Andromeda 19) also challenge galaxy formation models. Finally, we discuss possible formation scenarios for Cra2, including ram-pressure stripping of a gas-rich progenitor combined with tides.

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arXiv2026

Collisional Dynamics of Stars and Dark Matter in Ultra-Faint Galaxies

We use controlled N-body simulations to study the collisional exchange of energy between stars and dark matter in ultra-faint galaxies. We find that dynamical friction between stars and subsolar-mass dark matter particles results in the depletion of dark matter from the galaxies' centers, thereby transforming dark matter cusps into constant-density cores. The process is particularly effective in tidally limited galaxies with low stellar velocity dispersion. As high-mass stars sink toward the center of the dark matter halo, the dynamical-to-stellar mass ratio within the stellar half-light radius decreases monotonically. The stellar population of a dark matter-dominated galaxy is thereby compacted into a dense, baryon-dominated cluster, surrounded by a dark matter halo. Such a cluster would share the chemical composition of an ultra-faint galaxy, yet would be virtually dark matter-free within its half-light radius. We moreover find that the collisional cooling with dark matter particles provides an efficient pathway for the formation of stellar binaries in the contracting cluster. The contraction is eventually slowed down due to the decreasing central dark matter densities and the formation of stellar binaries. Our models highlight that the dynamical processes governing the faintest galaxies give rise to a rich phenomenology, blurring the line between the dynamics of globular clusters and galaxies.

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arXiv2026

Structural Diversity Among the Milky Way's Dwarf Spheroidal Satellites

We fit a flexible double power-law (`$αβγ$') model to the stellar density fields observed for the Milky Way's known dwarf spheroidal satellite galaxies. We show that where standard criteria for model selection are decisive, the $αβγ$ model is favored over the special case of the Plummer model, and also over the \sersic\ model and its special case, the exponential. The Milky Way's dSph population exhibits a diverse range of stellar density profile shapes, as quantified by the values we infer for outer and inner power-law indices $β$ and $γ$. Several of the most massive dSphs (e.g., Eridanus II, Fornax, Leo I, Leo II) have steeply-declining outer profiles, with $β\gtrsim 8$; others (e.g., Sextans, Boötes I) fade slowly, with $β\lesssim 4$. The inner profiles of dSphs with stellar mass $\gtrsim 10^5 M_{\odot}$ are consistent with `cores' of uniform stellar density ($γ\approx 0$). At lower masses the slopes of inner density profiles are poorly constrained, except in a few ultrafaint dSphs (e.g., Hercules, Ursa Major II) where we infer steep stellar cusps, with $γ\gtrsim 1.5$. Owing to the $αβγ$ model's flexibility, the inferred halflight radii and total stellar masses are significantly more uncertain than previous estimates, with halflight radii larger by up to an order of magnitude in some cases. Finally, we demonstrate that allowing for flexibility in the shape of the stellar density profile is crucial for dSph mass modeling, where systematic errors associated with choice of stellar density profile can outweigh random errors in the observed velocity dispersions.

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arXiv2026

A dynamical attractor in the evolution of dwarf spheroidal galaxies

We use controlled $N$-body experiments to study the dynamical evolution of dwarf spheroidal galaxies (dSphs) embedded in dark-matter (DM) haloes containing a large population of dark subhaloes. We show that stellar orbits subject to stochastic force fluctuations irreversibly gain energy and expand toward a dynamical attractor characterized by a stellar half-light radius $r_{\rm half} \approx r_{\rm max}$ and a velocity dispersion $σ\approx 0.5\,v_{\rm max}$, where $v_{\rm max}$ is the peak circular velocity of the host halo at radius $r_{\rm max}$. This state is reached both in isolation and under tidal stripping, although tidal mass loss significantly accelerates the evolution. Assuming that the Milky Way (MW) dSphs have reached this state, we find that the inferred halo masses collapse onto narrow sequences as a function of $r_{\rm half}$. Under this assumption, MW satellites with $r_{\rm half} \lesssim 1\,\mathrm{kpc}$ follow the tidal tracks of cuspy haloes, while larger systems deviate in a manner consistent with cored DM profiles. Moreover, the mass--luminosity relation follows the slope expected from abundance matching, but with halo masses systematically lowered from their peak values at fixed luminosity. These results suggest that the structural diversity of dSphs is largely an evolutionary outcome driven by internal heating and tides, rather than by the conditions of star formation. This framework predicts that isolated, early-quenched dSphs should have systematically larger sizes than satellites, a prediction testable with upcoming surveys.

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arXiv2026

Constraining Dark Matter Density Profiles in UFDs with Wide Binaries: Forecast for the Chinese Space Station Survey Telescope

The internal structure of dark matter halos on sub-galactic scales remains a key open question, particularly in the context of the core-cusp problem. Ultra-faint dwarf galaxies (UFDs), owing to their extreme dark matter dominance, provide a promising laboratory to probe these density profiles through stellar tracers. In this work, we assess the capability of the Chinese Space Station Telescope (CSST) to detect and characterize wide binary stars in the nearby UFD Segue 1, using mock observations. We generate mock binary populations based on our existing $N$-body simulations and incorporate realistic CSST observational conditions, including the expected deep-field limiting magnitude ($g \sim 27.5$ mag) and a photometric completeness of approximately $90\%$. The two-point correlation function (2PCF) of stellar pairs is used as a statistical tool to recover the binary fraction under these assumptions. We find that CSST can robustly detect wide binaries at the $3σ$ level for binary fractions as low as $f_b \gtrsim 0.01$, provided a stellar sample size of $N_{\mathrm{star}} \gtrsim 2300$. However, distinguishing between cusped and cored dark matter profiles is significantly more demanding, requiring $N_{\mathrm{star}} \gtrsim 6000$ and $f_b \gtrsim 0.1$ within $\sim 40\mathrm{kpc}$.

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arXiv2026

Tailored mass estimators for Milky Way dwarf Spheroidals

Assuming spherical symmetry and dynamical equilibrium within a given gravitational potential, a dwarf spheroidal (dSph) galaxy's globally averaged stellar velocity dispersion depends entirely on the shape of its stellar density profile. Thus, the dynamical inference of a dSph's gravitational potential is necessarily sensitive to assumptions about that shape. Relaxing standard assumptions, we fit flexible stellar density models to observations of the Milky Way's known dSph satellites. Considering various choices for the density profile shape and spatial extent of a host dark matter halo, we use the virial theorem to propagate observational uncertainties about the shapes of the inferred dSph stellar density profiles to uncertainties in the inferred dynamical masses. We find that the observed structural diversity of the Milky Way dSph population implies a large range of potential systematic errors (up to factors of 10) associated with standard dynamical mass estimators. We show that accounting for these observational and systematic uncertainties can significantly alter the appearance and behavior of dSph dynamical scaling relations, including enclosed dynamical mass vs. stellar mass and the Radial Acceleration Relation.

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arXiv2026

HSTPROMO Internal Proper Motion Kinematics of Dwarf Spheroidal Galaxies: II. Velocity Anisotropy and Dark Matter Cusp Slope of Sculptor

We analyze three epochs of HST imaging over 20 years for the Sculptor dwarf spheroidal galaxy, measuring precise proper motions for 119 stars and combining them with 1760 existing line-of-sight velocities. This catalog yields the first radially-resolved 3D velocity dispersion profiles for Sculptor. We confirm mild oblate rotation, with major-axis velocities reaching $\sim 2$ km s$^{-1}$ beyond 20.0 arcmin. Using a methodology similar to that in the first paper in this series, we solve the Jeans equations in oblate axisymmetric geometry to infer the galaxy's mass profile. Our modeling reveals a significant degeneracy due to the unknown galaxy inclination, which is overlooked under spherical symmetry assumptions. This degeneracy allows acceptable fits across a range of dark matter profiles, from cuspy to cored. While we do not directly constrain the inclination with our Jeans models, higher-order line-of-sight velocity moments provide useful additional constraints: comparisons with scalefree models from de Bruijne et al. (1996) favor highly flattened (more face-on) configurations. Adopting an inclination well consistent with these comparisons ($i = 57.1$ degrees), we find, alongside radial velocity anisotropy, a dark matter density slope of $Γ_{\rm dark} = 0.29^{+0.31}_{-0.41}$ within the radial extent of the 3D velocity data, ruling out a cusp with $Γ_{\rm dark} \leq -1$ at 99.8% confidence. This confidence increases for lower inclinations and decreases drastically for nearly edge-on configurations. The results qualitatively agree with $Λ$CDM, SIDM, and Fuzzy DM scenarios that predict core formation, while our specific measurements provide quantitative constraints on the prescriptions of feedback, cross sections, or particle masses required by these models, respectively.

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arXiv2026

Signatures of dark subhalos in dwarf spheroidal galaxies: I. Fluctuations in surface density

Dark matter (DM) subhalos offer critical tests of cosmological models through their abundance and properties, yet most remain undetectable due to their lack of stars. We investigate whether their presence leaves measurable imprints on the projected stellar density fields of dwarf spheroidal galaxies (dSphs). Building on literature $N$-body experiments, we show that subhalo interactions induce subtle out-of-equilibrium fluctuations appearing as density corrugations. In a CDM framework, these fluctuations are dominated by the most massive subhalos in the host halo. We develop a Fourier-based framework to quantify these features, identifying characteristic peaks in the spatial frequency spectrum that are well described by Voigt profiles. The peak parameters are sensitive to both the subhalo mass function and the number of stellar tracers. For the configurations tested, $N_{\star} \sim 10^5$ stars suffice to detect subhalo populations with $M_{\rm subhalo} \lesssim 10^6~\mathrm{M}_{\odot}$, while larger masses produce stronger and more complex signatures. We assess the feasibility of this technique by analyzing Gaia and HST data: in this context, the Fornax dwarf shows residual low-frequency structures resembling those in our controlled subhalo experiments, making it an interesting case for follow-up. Prospectively, wide-field surveys such as Euclid, the Nancy Grace Roman Space Telescope, and the Vera C. Rubin Observatory are expected to deliver stellar samples of $N_{\star} \sim 10^5$ per dwarf, offering compelling prospects for probing subhalo imprints. Our results introduce a novel pathway to constrain the subhalo mass function in dSphs, and motivate follow-up work that incorporates alternative DM models and additional dynamical perturbations.

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arXiv2025

Stellar Mass Segregation in Dark Matter Halos

We study the effect of stellar mass segregation driven by collisional relaxation within the potential well of a smooth dark matter halo. This effect is of particular relevance for old stellar systems with short crossing times, where small collisional perturbations accumulate over many dynamical timescales. We run collisional $N$-body simulations tailored to the ambiguous stellar systems Ursa Major 3/Unions 1, Delve 1 and Eridanus 3, modelling their stellar populations as two-component systems of high- and low-mass stars, respectively. For Ursa Major 3/Unions 1 (Delve 1), assuming a dynamical-to-stellar mass ratio of 10, we find that after 10 Gyr of evolution, the radial extent of its low-mass stars will be twice as large as (40 per cent larger than) that of its high-mass stars. We show that weak tides do not alter this relative separation of half-light radii, whereas for the case of strong tidal fields, mass segregation facilitates the tidal stripping of low-mass stars. We further find that as the population of high-mass stars contracts and cools, the number of dynamically formed binaries within that population increases. Our results call for caution when using stellar mass segregation as a criterion to separate star clusters from dwarf galaxies, and suggest that mass segregation increases the abundance of massive binaries in the central regions of dark matter-dominated dwarf galaxies.

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arXiv2025

Gravothermal expansion of dwarf spheroidal galaxies heated by dark subhaloes

We use analytical and $N$-body methods to study the evolution of dwarf spheroidal galaxies (dSphs) embedded in dark matter (DM) haloes that host a sizeable subhalo population. Dark subhaloes generate a fluctuating gravitational field that injects energy into stellar orbits, driving a gradual expansion of dSphs. Despite the overall expansion, the stellar density profile preserves its initial shape, suggesting that the evolution proceeds in a self-similar manner. Meanwhile, the velocity dispersion profile, initially flat, evolves as the galaxy expands: the inner regions heat up, while the outer regions cool down. Kinematically, this resembles gravothermal collapse but with an inverted evolution, instead of collapsing the stellar system expands within a fluctuating halo potential. As the half-light radius $r_{\rm half}$ approaches the halo peak velocity radius $r_{\rm max}$, the expansion slows, and the velocity dispersion peaks at $σ_{\rm max} \simeq 0.54 v_{\rm max}$. The stellar heat capacity remains positive for deeply embedded stars but diverges near $r_{\rm max}$, turning negative beyond this threshold, which indicates a phase transition in the dynamical response to energy injection. The relaxation time scales as $t_{\rm rel} \sim r_{\rm half}^{3/2}$, showing that orbital diffusion slows as the galaxy expands. Ultra-faint dSphs, having the smallest sizes and shortest relaxation times, are particularly sensitive to the presence of dark subhaloes. Some of our dSph models expand beyond the detection of current photometric surveys, becoming `stealth' galaxies with half-light radii and velocity dispersions similar to ultra-diffuse galaxies (UDGs), but orders of magnitude lower luminosities, representing a distinct, yet currently undetected, population of DM-dominated satellites.

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arXiv2025

Impulsive mixing of stellar populations in dwarf spheroidal galaxies

We study the response of mono-energetic stellar populations with initially isotropic kinematics to impulsive and adiabatic changes to an underlying dark matter potential. Half-light radii expand and velocity dispersions decrease as enclosed dark matter is removed. The details of this expansion and cooling depend on the time scale on which the underlying potential changes. In the adiabatic regime, the product of half-light radius and average velocity dispersion is conserved. We show that the stellar populations maintain centrally isotropic kinematics throughout their adiabatic evolution, and their densities can be approximated by a family of analytical radial profiles. Metallicity gradients within the galaxy flatten as dark matter is slowly removed. In the case of strong impulsive perturbations, stellar populations develop power-law-like density tails with radially biased kinematics. We show that the distribution of stellar binding energies within the dark matter halo substantially widens after an impulsive perturbation, no matter the sign of the perturbation. This allows initially energetically separated stellar populations to mix, to the extent that previously chemo-dynamically distinct populations may masquerade as a single population with large metallicity and energy spread. Finally, we show that in response to an impulsive perturbation, stellar populations that are deeply embedded in cored dark matter halos undergo a series of damped oscillations before reaching a virialised equilibrium state, driven by inefficient phase mixing in the harmonic potentials of cored halos. This slow return to equilibrium adds substantial systematic uncertainty to dynamical masses estimated from Jeans modeling or the virial theorem.

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arXiv2025

Constraining the Milky Way dark matter halo with LMC-induced reflex motion

Modelling perturbations of the Milky Way (MW) halo induced by the infall of the Large Magellanic Cloud (LMC) offers new avenues to constrain the dark matter (DM) distribution in our Galaxy. A key observable is the reflex motion of the MW disc with respect to the halo induced by the LMC's infall, which imprints a velocity dipole on kinematics of halo stars. Here we investigate how the dipole varies with Galactocentric radius, and study the sensitivity of the reflex motion signal to different DM outer-halo profiles. Using a suite of basis function expansion (BFE) simulations with truncated NFW profiles ($ρ\propto r^{-β}$ beyond $r=50$ kpc), our $N$-body models show that (i) The reflex motion amplitude varies with Galactocentric radius but is largely insensitive to the outer DM slope, implying that the MW-LMC mass ratio alone does not set the dipole strength. (ii) In contrast, the direction of the disc motion is very sensitive to the density distribution of the outer DM halo. (iii) The contraction of the MW halo induced by the LMC's gravitational pull also depends strongly on the outer DM halo profile. (iv) We find a halo instability whose oscillation frequency increases with $β$ producing a potentially observable signature - a sinusoidal pattern of the mean radial velocity of halo stars. Finally, using BFE coefficients we find that steeper truncations produce smaller dipole distortions, while amplifying the quadrupole distortion. These results highlight the limited constraining power of the reflex motion amplitude alone for outer MW profile parameters.

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arXiv2025

The angular momentum spiral of the Milky Way disc in Gaia

Data from the Gaia mission shows prominent phase-space spirals that are the signatures of disequilibrium in the Milky Way (MW) disc. In this work, we present a novel perspective on the phase-space spiral in angular momentum (AM) space. Using Gaia DR3, we detect a prominent AM spiral in the solar neighbourhood. We demonstrate the relation of AM to the $z-v_z$ spiral and show that we can map to this space from angular momentum through simplifying assumptions. By modelling the orbit of stars in AM, we develop a generative model for the spiral where the disc is perturbed by a bulk tilt at an earlier time. Our model successfully describes the salient features of the AM spiral in the data. Modelling the phase spiral in AM is a promising method to constrain both perturbation and MW potential parameters. Our AM framework simplifies the interpretation of the spiral and offers a robust approach to modelling disequilibrium in the MW disc using all six dimensions of phase space simultaneously.

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arXiv2024

Capture of field stars by dark substructures

We use analytical and $N$-body methods to study the capture of field stars by gravitating substructures moving across a galactic environment. The majority of stars captured by a substructure move on temporarily-bound orbits that are lost to galactic tides after a few orbital revolutions. In numerical experiments where a substructure model is immersed into a sea of field particles on a circular orbit, we find a population of particles that remain bound to the substructure potential for indefinitely-long times. This population is absent from substructure models initially placed outside the galaxy on an eccentric orbit. We show that gravitational capture is most efficient in dwarf spheroidal galaxies (dSphs) on account of their low velocity dispersions and high stellar phase-space densities. In these galaxies `dark' sub-subhaloes which do not experience in-situ star formation may capture field stars and become visible as stellar overdensities with unusual properties: (i) they would have a large size for their luminosity, (ii) contain stellar populations indistinguishable from the host galaxy, and (iii) exhibit dark matter (DM)-dominated mass-to-light ratios. We discuss the nature of several `anomalous' stellar systems reported as star clusters in the Fornax and Eridanus II dSphs which exhibit some of these characteristics. DM sub-subhaloes with a mass function $d N/d M_\bullet\sim M_\bullet^{-α}$ are expected to generate stellar systems with a luminosity function, $d N/d M_\star\sim M_\star^{-β}$, where $β=(2α+1)/3=1.6$ for $α=1.9$. Detecting and characterizing these objects in dSphs would provide unprecedented constraints on the particle mass and cross section of a large range of DM particle candidates.

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arXiv2024

Micro galaxies in LCDM

A fundamental prediction of the Lambda Cold Dark Matter (LCDM) cosmology is the centrally divergent cuspy density profile of dark matter haloes. Density cusps render CDM haloes resilient to tides, and protect dwarf galaxies embedded in them from full tidal disruption. The hierarchical assembly history of the Milky Way may therefore give rise to a population of micro galaxies; i.e., heavily stripped remnants of early accreted satellites, which may reach arbitrarily low luminosity. Assuming that the progenitor systems are dark matter dominated, we use an empirical formalism for tidal stripping to predict the evolution of the luminosity, size, and velocity dispersion of such remnants, tracing their tidal evolution across multiple orders of magnitude in mass and size. The evolutionary tracks depend sensitively on the progenitor distribution of stellar binding energies. We explore three cases that likely bracket most realistic models of dwarf galaxies: one where the energy distribution of the most tightly bound stars follows that of the dark matter, and two where stars are defined by either an exponential density or surface brightness profile. The tidal evolution in the size-velocity dispersion plane is quite similar for these three models, although their remnants may differ widely in luminosity. Micro galaxies are therefore best distinguished from globular clusters by the presence of dark matter; either directly, by measuring their velocity dispersion, or indirectly, by examining their tidal resilience. Our work highlights the need for further theoretical and observational constraints on the stellar energy distribution in dwarf galaxies.

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arXiv2024

The radial variation of the LMC-induced reflex motion of the Milky Way disc observed in the stellar halo

We measure the kinematic signature arising from the Milky Way (MW) disc moving with respect to the outer stellar halo, which is observed as a dipole signal in the kinematics of stellar halo tracers. We quantify how the reflex motion varies as a function of Galactocentric distance, finding that (i) the amplitude of the dipole signal increases as a function of radius, and (ii) the direction moves across the sky. We compare the reflex motion signal against a compilation of published models that follow the MW--LMC interaction. These models show a similar trend of increasing amplitude of the reflex motion as a function of distance, but they do not reproduce the direction of the disc motion with respect to the stellar halo well. We also report mean motions for the stellar halo as a function of distance, finding radial compression in the outer halo and nonzero prograde rotation at all radii. The observed compression signal is also present in MW--LMC models, but the rotation is not, which suggests that the latter is not induced by the LMC. We extensively validate our technique to measure reflex motion against idealised tests. We discuss prospects for directly constraining the mass and orbital history of the LMC through the impact on the motion of the MW stellar disc, and how the modelling of the reflex motion can be improved as more and better data become available.

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