Dr Jason Hunt

We have developed our original made-to-measure (M2M) algorithm, PRIMAL, with the aim of modelling the Galactic disc from upcoming Gaia data. From a Milky Way like N-body disc galaxy simulation, we have created mock Gaia data using M0III stars as tracers, taking into account extinction and the expected Gaia errors. In PRIMAL, observables calculated from the N-body model are compared with the target stars, at the position of the target stars. Using PRIMAL, the masses of the N-body model particles are changed to reproduce the target mock data, and the gravitational potential is automatically adjusted by the changing mass of the model particles. We have also adopted a new resampling scheme for the model particles to keep the mass resolution of the N-body model relatively constant. We have applied PRIMAL to this mock Gaia data and we show that PRIMAL can recover the structure and kinematics of a Milky Way like barred spiral disc, along with the apparent bar structure and pattern speed of the bar despite the galactic extinction and the observational errors.

We compare the stellar motion around a spiral arm created in two different scenarios, transient/co-rotating spiral arms and density-wave-like spiral arms. We generate Gaia mock data from snapshots of the simulations following these two scenarios using our stellar population code, SNAPDRAGONS, which takes into account dust extinction and the expected Gaia errors. We compare the observed rotation velocity around a spiral arm similar in position to the Perseus arm, and find that there is a clear difference in the velocity features around the spiral arm between the co-rotating spiral arm and the density-wave-like spiral arm. Our result demonstrates that the volume and accuracy of the Gaia data are sufficient to clearly distinguish these two scenarios of the spiral arms.

Under the assumption of a simple and time-invariant gravitational potential, many Galactic dynamics techniques infer the milky Way's mass and dark matter distributions from stellar kinematic observations. These methods typically rely on parameterized potential models of the Galaxy and must take into account nontrivial survey selection effects, because they make use of the density of stars in phase space. Large-scale spectroscopic surveys now supply information beyond kinematics in the form of precise stellar label measurements (especially element abundances). These element abundances are known to correlate with orbital actions or other dynamical invariants. Here, we use the Orbital Torus Imaging framework that uses abundance gradients in phase space to map orbits. In many cases these gradients can be measured without detailed knowledge of the selection function. We use stellar surface abundances from the Apache Point Observatory Galactic Evolution Experiment survey combined with kinematic data from the Gaia mission. Our method reveals the vertical (z-direction) orbital structure in the Galaxy and enables empirical measurements of the vertical acceleration field and orbital frequencies in the disk. From these measurements, we infer the total surface mass density, sigma, and midplane volume density, rho 0, as a function of Galactocentric radius and height. Around the Sun, we find sigma circle dot(z=1.1kpc)=72-9+6M circle dot pc-2 and rho circle dot(z=0)=0.081-0.009+0.015M circle dot pc-3 using the most constraining abundance ratio, [Mg/Fe]. This corresponds to a dark matter contribution in surface density of sigma circle dot,DM(z = 1.1 kpc) = 24 +/- 4 M circle dot pc-2, and in total volume mass density of rho circle dot,DM(z = 0) = 0.011 +/- 0.002 M circle dot pc-3. Moreover, using these mass density values we estimate the scale length of the low-alpha disk to be h R = 2.24 +/- 0.06 kpc.

A simple one-dimensional axisymmetric disc model is applied to the kinematics of O type and B type stars (OB stars) near the Sun obtained from Gaia Data Release 3 catalogue. The model determines the 'local centrifugal speed' V-c(R0) - defined as the circular velocity in the Galactocentric rest frame, where the star would move in a near-circular orbit if the potential is axisymmetric with the local potential of the Galaxy. We find that the V-c(R0) values and their gradient vary across the selected region of stars within the solar neighbourhood. By comparing with an N-body/hydrodynamic simulation of a Milky Way-like galaxy, we find that the kinematics of the young stars in the solar neighbourhood is affected by the Local arm, which makes it difficult to measure V-c(R-0). However, from the resemblance between the observational data and the simulation, we suggest that the known rotational velocity gap between the Coma Bernices and Hyades-Pleiades moving groups could be driven by the co-rotation resonance of the Local arm, which can be used to infer the azimuthally averaged circular velocity. We find that V-c(R) obtained from the D < 2 kpc sample is well matched with this gap at the position of the Local arm. Hence, we argue that our results from the D < 2 kpc sample, V-c(R0) = 234 +/- 2 km s(-1), are close to the azimuthally averaged circular velocity rather than the local centrifugal speed, which is influenced by the presence of the Local arm.

The stellar stream connected to the Sagittarius (Sgr) dwarf galaxy is the most massive tidal stream that has been mapped in the Galaxy, and is the dominant contributor to the outer stellar halo of the Milky Way (MW). We present metallicity maps of the Sgr stream, using 34,240 red giant branch stars with inferred metallicities from Gaia BP/RP spectra. This sample is larger than previous samples of Sgr stream members with chemical abundances by an order of magnitude. We measure metallicity gradients with respect to Sgr stream coordinates (Lambda, B), and highlight the gradient in metallicity with respect to stream latitude coordinate B, which has not been observed before. Including the core, we find del[M/H] = -2.48 +/- 0.08 x 10(-2) dex deg(-1) above the stream track (B > B-0, where B-0 = 1.5 degrees is the latitude of the Sgr remnant) and del[M/H] = -2.02 +/- 0.08 x 10(-2) dex deg(-1) below the stream track (B < B-0). By painting metallicity gradients onto a tailored N-body simulation of the Sgr stream, we find that the observed metallicities in the stream are consistent with an initial radial metallicity gradient in the Sgr dwarf galaxy of similar to-0.1 to -0.2 dex kpc(-1), well within the range of observed metallicity gradients in Local Group dwarf galaxies. Our results provide novel observational constraints for the internal structure of the dwarf galaxy progenitor of the Sgr stream. Leveraging new large data sets in conjunction with tailored simulations, we can connect the present-day properties of disrupted dwarfs in the MW to their initial conditions.

The second data release of ESA's Gaia mission revealed numerous signatures of disequilibrium in the Milky Way's disc. These signatures are seen in the planar kinematics of stars, which manifest as ridges and ripples in R-v(phi), and in vertical kinematics, where a prominent spiral is seen in the z-v(z) phase space. In this work, we show an equivalent Delta R-v(R) phase spiral forms following a perturbation to the disc. We demonstrate the behaviour of the Delta R-v(R) phase spirals in both a toy model and a high-resolution N-body simulation of a satellite interaction. We then confront these models with the data, where we find partial Delta R-v(R) phase spirals in the Solar neighbourhood using the most recent data from Gaia DR3. This structure indicates ongoing radial phase mixing in the Galactic disc, suggesting a history of recent perturbations, either through internal or external (e.g. satellite) processes. Future work modelling the z-v(z) and Delta R-v(R) phase spirals in tandem may help break degeneracy's between possible origins of the perturbation.

The Nancy Grace Roman Space Telescope is capable of delivering an unprecedented all-sky, high-spatial resolution, multi-epoch infrared map to the astronomical community. This opportunity arises in the midst of numerous ground- and space-based surveys that will provide extensive spectroscopy and imaging together covering the entire sky (such as Rubin/LSST, Euclid, UNIONS, SPHEREx, DESI, SDSS-V, GALAH, 4MOST, WEAVE, MOONS, PFS, UVEX, NEO Surveyor, etc.). Roman can uniquely provide uniform high-spatial-resolution (~0.1 arcsec) imaging over the entire sky, vastly expanding the science reach and precision of all of these near-term and future surveys. This imaging will not only enhance other surveys, but also facilitate completely new science. By imaging the full sky over two epochs, Roman can measure the proper motions for stars across the entire Milky Way, probing 100 times fainter than Gaia out to the very edge of the Galaxy. Here, we propose NANCY: a completely public, all-sky survey that will create a high-value legacy dataset benefiting innumerable ongoing and forthcoming studies of the universe. NANCY is a pure expression of Roman's potential: it images the entire sky, at high spatial resolution, in a broad infrared bandpass that collects as many photons as possible. The majority of all ongoing astronomical surveys would benefit from incorporating observations of NANCY into their analyses, whether these surveys focus on nearby stars, the Milky Way, near-field cosmology, or the broader universe.

The recent discovery of a spiral pattern in the vertical kinematic structure in the solar neighborhood provides a prime opportunity to study nonequilibrium dynamics in the Milky Way from local stellar kinematics. Furthermore, results from simulations indicate that even in a limited volume, differences in stellar orbital histories allow us to trace variations in the initial perturbation across large regions of the disk. We present ESCARGOT, a novel algorithm for studying these variations in both simulated and observed data sets. ESCARGOT automatically extracts key quantities from the structure of a given phase spiral, including the time since perturbation and the perturbation mode. We test ESCARGOT on simulated data and show that it is capable of accurately recovering information about the time since the perturbation occurred as well as subtle differences in phase spiral morphology due to stellar locations in the disk at the time of perturbation. We apply ESCARGOT to kinematic data from data release 3 of the Gaia mission in bins of guiding radius. We show that similar structural differences in morphology occur in the Gaia phase spirals as a function of stellar orbital history. These results indicate that the phase spirals are the product of a complex dynamical response in the disk with large-scale coupling between different regions of phase space.

The Galactic bulge is critical to our understanding of the Milky Way. However, due to the lack of reliable stellar distances, the structure and kinematics of the bulge/bar beyond the Galactic center have remained largely unexplored. Here, we present a method to measure distances of luminous red giants using a period–amplitude–luminosity relation anchored to the Large Magellanic Cloud, with random uncertainties of 10%–15% and systematic errors below 1%–2%. We apply this method to data from the Optical Gravitational Lensing Experiment to measure distances to 190,302 stars in the Galactic bulge and beyond out to 20 kpc. Using this sample, we measure a distance to the Galactic center of R0 = 8108 ± 106stat ± 93sys pc, consistent with direct measurements of stars orbiting Sgr A*. We cross-match our distance catalog with Gaia DR3 and use the subset of 39,566 overlapping stars to provide the first constraints on the Milky Way’s velocity field (VR, Vϕ, Vz) beyond the Galactic center. We show that the VR quadrupole from the bar’s near side is reflected with respect to the Galactic center, indicating that the bar is bisymmetric and aligned with the inner disk. We also find that the vertical height VZ map has no major structure in the region of the Galactic bulge, which is inconsistent with a current episode of bar buckling. Finally, we demonstrate with N-body simulations that distance uncertainty plays a factor in the alignment of the major and kinematic axes of the bar, necessitating caution when interpreting results for distant stars.

The Galactic bulge and bar are critical to our understanding of the Milky Way. However, due to the lack of reliable stellar distances, the structure and kinematics of the bulge/bar beyond the Galactic center have remained largely unexplored. Here, we present a method to measure distances of luminous red giants using a period-amplitude-luminosity relation anchored to the Large Magellanic Cloud, with random uncertainties of 10-15% and systematic errors below 1-2%. We apply this method to data from the Optical Gravitational Lensing Experiment (OGLE) to measure distances to $190,302$ stars in the Galactic bulge and beyond out to 20 kpc. Using this sample we measure a distance to the Galactic center of $R_0$ = $8108\pm106_{\rm stat}\pm93_{\rm sys}$ pc, consistent with astrometric monitoring of stars orbiting Sgr A*. We cross-match our distance catalog with Gaia DR3 and use the subset of $39,566$ overlapping stars to provide the first constraints on the Milky Way's velocity field ($V_R,V_\phi,V_z$) beyond the Galactic center. We show that the $V_R$ quadrupole from the bar's near side is reflected with respect to the Galactic center, indicating that the bar is both bi-symmetric and aligned with the inner disk, and therefore dynamically settled along its full extent. We also find that the vertical height $V_Z$ map has no major structure in the region of the Galactic bulge, which is inconsistent with a current episode of bar buckling. Finally, we demonstrate with N-body simulations that distance uncertainty plays a major factor in the alignment of the major and kinematic axes of the bar and distribution of velocities, necessitating caution when interpreting results for distant stars.

The fourth generation of the Sloan Digital Sky Survey (SDSS-IV) has been in operation since 2014 July. This paper describes the second data release from this phase, and the 14th from SDSS overall (making this Data Release Fourteen or DR14). This release makes the data taken by SDSS-IV in its first two years of operation (2014–2016 July) public. Like all previous SDSS releases, DR14 is cumulative, including the most recent reductions and calibrations of all data taken by SDSS since the first phase began operations in 2000. New in DR14 is the first public release of data from the extended Baryon Oscillation Spectroscopic Survey; the first data from the second phase of the Apache Point Observatory (APO) Galactic Evolution Experiment (APOGEE-2), including stellar parameter estimates from an innovative data-driven machine-learning algorithm known as "The Cannon"; and almost twice as many data cubes from the Mapping Nearby Galaxies at APO (MaNGA) survey as were in the previous release (N = 2812 in total). This paper describes the location and format of the publicly available data from the SDSS-IV surveys. We provide references to the important technical papers describing how these data have been taken (both targeting and observation details) and processed for scientific use. The SDSS web site (www.sdss.org) has been updated for this release and provides links to data downloads, as well as tutorials and examples of data use. SDSS-IV is planning to continue to collect astronomical data until 2020 and will be followed by SDSS-V.

Gaia DR2 has provided an unprecedented wealth of information about the positions and motions of stars in our Galaxy and has highlighted the degree of disequilibria in the disc. As we collect data over a wider area of the disc, it becomes increasingly appealing to start analysing stellar actions and angles, which specifically label orbit space, instead of their current phase space location. Conceptually, while (x) over bar and (v) over bar tell us about the potential and local interactions, grouping in action puts together stars that have similar frequencies and hence similar responses to dynamical effects occurring over several orbits. Grouping in actions and angles refines this further to isolate stars that are travelling together through space and hence have shared histories. Mixing these coordinate systems can confuse the interpretation. For example, it has been suggested that by moving stars to their guiding radius, the Milky Way spiral structure is visible as ridge-like overdensities in the Gaia data (Khoperskov et al. 2020). However, in this work, we show that these features are in fact the known kinematic moving groups, both in the L-z - phi and the v(R) - v(phi) planes. Using simulations, we show how this distinction will become even more important as we move to a global view of the MilkyWay. As an example, we show that the radial velocity wave seen in the Galactic disc in Gaia and APOGEE should become stronger in the action-angle frame, and that it can be reproduced by transient spiral structure.

We have discovered a clear sign of the disruption phase of the Perseus arm in the Milky Way using Cepheid variables, taking advantage of the accurately measured distances of Cepheids and the proper motions from Gaia Data Release 1. Both the Galactocentric radial and rotation velocities of 77 Cepheids within 1.5 kpc of the Perseus arm are correlated with their distances from the locus of the Perseus arm, as the trailing side is rotating faster and moving inward compared to the leading side. We also found a negative vertex deviation for the Cepheids on the trailing side, −27 6 2 4, in contrast to the positive vertex deviation in the solar neighborhood. This is, to our knowledge, the first direct evidence that the vertex deviation around the Perseus arm is affected by the spiral arm. We compared these observational trends with our N-body/hydrodynamics simulations based on a static density-wave spiral scenario and with those based on a transient dynamic spiral scenario. Although our comparisons are limited to qualitative trends, they strongly favor the conclusion that the Perseus arm is in the disruption phase of a transient arm.

A&A 663, A16 (2022) In this fourth article on weighing the Galactic disk using the shape of the phase-space spiral, we have tested our method on a billion particle three-dimensional N-body simulation, comprised of a Milky Way like host galaxy and a merging dwarf satellite. The main purpose of this work was to test the validity of our model's fundamental assumptions that the spiral inhabits a locally static and vertically separable gravitational potential. These assumptions might be compromised in the complex kinematic system of a disturbed three-dimensional disk galaxy; in fact, the statistical uncertainty and any potential biases related to these assumptions are expected to be amplified for this simulation, which differs from the Milky Way in that it is more strongly perturbed and has a phase-space spiral that inhabits higher vertical energies. We constructed 44 separate data samples from different spatial locations in the simulated host galaxy. Our method produced accurate results for the vertical gravitational potential of these 44 data samples, with an unbiased distribution of errors with a standard deviation of 7 %. We also tested our method under severe and unknown spatially dependent selection effects, also with robust results; this sets it apart from traditional dynamical mass measurements that are based on the assumption of a steady state and which are highly sensitive to unknown or poorly modelled incompleteness. Hence, we will be able to make localised mass measurements of distant regions in the Milky Way disk, which would otherwise be compromised by complex and poorly understood selection effects.

Context. Parallaxes for 331 classical Cepheids, 31 Type II Cepheids, and 364 RR Lyrae stars in common between Gaia and the Hipparcos and Tycho-2 catalogues are published in Gaia Data Release 1 (DR1) as part of the Tycho-Gaia Astrometric Solution (TGAS). Aims. In order to test these first parallax measurements of the primary standard candles of the cosmological distance ladder, which involve astrometry collected by Gaia during the initial 14 months of science operation, we compared them with literature estimates and derived new period-luminosity (PL), period-Wesenheit (PW) relations for classical and Type II Cepheids and infrared PL, PL-metallicity (PLZ), and optical luminosity-metallicity (MV-[Fe/H]) relations for the RR Lyrae stars, with zero points based on TGAS. Methods. Classical Cepheids were carefully selected in order to discard known or suspected binary systems. The final sample comprises 102 fundamental mode pulsators with periods ranging from 1.68 to 51.66 days (of which 33 with σϖ/ϖ< 0.5). The Type II Cepheids include a total of 26 W Virginis and BL Herculis stars spanning the period range from 1.16 to 30.00 days (of which only 7 with σϖ/ϖ< 0.5). The RR Lyrae stars include 200 sources with pulsation period ranging from 0.27 to 0.80 days (of which 112 with σϖ/ϖ< 0.5). The new relations were computed using multi-band (V,I,J,Ks) photometry and spectroscopic metal abundances available in the literature, and by applying three alternative approaches: (i) linear least-squares fitting of the absolute magnitudes inferred from direct transformation of the TGAS parallaxes; (ii) adopting astrometry-based luminosities; and (iii) using a Bayesian fitting approach. The last two methods work in parallax space where parallaxes are used directly, thus maintaining symmetrical errors and allowing negative parallaxes to be used. The TGAS-based PL,PW,PLZ, and MV− [Fe/H] relations are discussed by comparing the distance to the Large Magellanic Cloud provided by different types of pulsating stars and alternative fitting methods. Results. Good agreement is found from direct comparison of the parallaxes of RR Lyrae stars for which both TGAS and HST measurements are available. Similarly, very good agreement is found between the TGAS values and the parallaxes inferred from the absolute magnitudes of Cepheids and RR Lyrae stars analysed with the Baade-Wesselink method. TGAS values also compare favourably with the parallaxes inferred by theoretical model fitting of the multi-band light curves for two of the three classical Cepheids and one RR Lyrae star, which were analysed with this technique in our samples. The K-band PL relations show the significant improvement of the TGAS parallaxes for Cepheids and RR Lyrae stars with respect to the Hipparcos measurements. This is particularly true for the RR Lyrae stars for which improvement in quality and statistics is impressive. Conclusions. TGAS parallaxes bring a significant added value to the previous Hipparcos estimates. The relations presented in this paper represent the first Gaia-calibrated relations and form a work-in-progress milestone report in the wait for Gaia-only parallaxes of which a first solution will become available with Gaia Data Release 2 (DR2) in 2018.

We present a new theoretical population synthesis model (the Galaxy model) to examine and deal with large amounts of data from surveys of the Milky Way and to decipher the present and past structure and history of our own Galaxy. We assume the Galaxy to consist of a superposition of many composite stellar populations belonging to the thin and thick discs, the stellar halo and the bulge, and to be surrounded by a single dark matter halo component. A global model for the Milky Way's gravitational potential is built up self-consistently with the density profiles from the Poisson equation. In turn, these density profiles are used to generate synthetic probability distribution functions (PDFs) for the distribution of stars in colour-magnitude diagrams (CMDs). Finally, the gravitational potential is used to constrain the stellar kinematics by means of the moment method on a (perturbed)-distribution function. Spiral arms perturb the axisymmetric disc distribution functions in the linear response framework of density-wave theory where we present an analytical formula of the so-called 'reduction factor' using hypergeometric functions. Finally, we consider an analytical non-axisymmetric model of extinction and an algorithm based on the concept of probability distribution function to handle CMDs with a large number of stars. A genetic algorithm is presented to investigate both the photometric and kinematic parameter space. This galaxy model represents the natural framework to reconstruct the structure of the Milky Way from the heterogeneous data set of surveys such as Gaia-ESO, SEGUE, APOGEE2, RAVE and the Gaia mission.

Context. The first Gaia Data Release contains the Tycho - Gaia Astrometric Solution (TGAS). This is a subset of about 2 million stars for which, besides the position and photometry, the proper motion and parallax are calculated using H ipparcos and Tycho-2 positions in 1991.25 as prior information. Aims. We investigate the scientific potential and limitations of the TGAS component by means of the astrometric data for open clusters. Methods. Mean cluster parallax and proper motion values are derived taking into account the error correlations within the astrometric solutions for individual stars, an estimate of the internal velocity dispersion in the cluster, and, where relevant, the effects of the depth of the cluster along the line of sight. Internal consistency of the TGAS data is assessed. Results. Values given for standard uncertainties are still inaccurate and may lead to unrealistic unit-weight standard deviations of least squares solutions for cluster parameters. Reconstructed mean cluster parallax and proper motion values are generally in very good agreement with earlier H ipparcos -based determination, although the Gaia mean parallax for the Pleiades is a significant exception. We have no current explanation for that discrepancy. Most clusters are observed to extend to nearly 15 pc from the cluster centre, and it will be up to future Gaia releases to establish whether those potential cluster-member stars are still dynamically bound to the clusters. Conclusions. The Gaia DR1 provides the means to examine open clusters far beyond their more easily visible cores, and can provide membership assessments based on proper motions and parallaxes. A combined HR diagram shows the same features as observed before using the H ipparcos data, with clearly increased luminosities for older A and F dwarfs.

This paper describes a study of the value of in-vehicle travel time in Barcelona, Spain. In the study, values of time were established by considering the behaviour of drivers making a tradeoff between money and time when selecting a route for a trip by car. Disaggregate revealed preference observations were collected and used to estimate the coefficients in a logit model representing this behaviour. The variation in the value of time was considered for several dimensions, such as length of journey and driver income. It was found to be most appropriate to split the value according to whether the trip is made on a weekday or during the weekend, with values of 40.0 and 67.1 pesetas-1989/minute per vehicle, respectively, for these two categories.

I summarize two recent projects involving the Gaia-TGAS data. Firstly, I discuss a detection of a lack of disc stars in the Solar neighbourhood with velocities close to zero angular momentum. We use predictions of this effect to make a measurement of the Solar rotation velocity around the Galactic centre, and also of R 0. Secondly, I discuss a detection of a group of stars with systematically high Galactic rotation velocity. We propose that it may be caused by the Perseus arm and compare the data with simulations.

Action space synthesizes the orbital information of stars and is well suited to analyse the rich kinematic substructure of the disc in the second Gaia data release's radial velocity sample. We revisit the strong perturbation induced in the Milky Way disc by an m = 2 bar, using test particle simulations and the actions (J(R), L-z, J(z)) estimated in an axisymmetric potential. These make three useful diagnostics cleanly visible. (1) We use the well-known characteristic flip from outward to inward motion at the outer Lindblad resonance (OLR; l = +1, m = 2), which occurs along the axisymmetric resonance line (ARL) in (L-z, J(R)), to identify in the Gaia action data three candidates for the bar's OLR and pattern speed Omega(bar): 1.85 Omega(0), 1.20 Omega(0), and 1.63 Omega(0) (with similar to 0.1 Omega(0) systematic uncertainty). The Gaia data is therefore consistent with both slow and fast bar models in the literature, but disagrees with recent measurements of similar to 1.45 Omega(0). (2) For the first time, we demonstrate that bar resonances - especially the OLR - cause a gradient in vertical action < J(z)> with L-z around the ARL via 'J(z)-sorting' of stars. This could contribute to the observed coupling of < v(R)> and in the Galactic disc. (3) We confirm prior results that the behaviour of resonant orbits is well approximated by scattering and oscillation in (L-z, J(R)) along a slope Delta J(R)/Delta L-z = l/m centred on the l:m ARL. Overall, we demonstrate that axisymmetrically estimated actions are a powerful diagnostic tool even in non-axisymmetric systems.

We have developed the initial version of a new particle-by-particle adaptation of the made-to-measure (M2M) method, aiming to model the Galactic disc from upcoming Galactic stellar survey data. In our new particle-by-particle M2M, the observables of the target system are compared with those of the model galaxy at the position of the target stars (i.e. particles). The weights of the model particles are changed to reproduce the observables of the target system, and the gravitational potential is automatically adjusted by the changing weights of the particles. This paper demonstrates, as the initial work, that the particle-by-particle M2M can recreate a target disc system created by an N-body simulation in a known dark matter potential, with no error in the observables. The radial profiles of the surface density, velocity dispersion in the radial and perpendicular directions, and the rotational velocity of the target disc are all well reproduced from the initial disc model, whose scalelength is different from that of the target disc. We also demonstrate that our M2M can be applied to an incomplete data set and recreate the target disc reasonably well when the observables are restricted to a part of the disc. We discuss our calibration of the model parameters and the importance of regularization.

We have modified our particle-by-particle adaptation of the made-to-measure (M2M) method, with the aim of modelling the Galactic disc from upcoming Galactic stellar survey data. In our new particle-by-particle M2M algorithm, primal, the observables of the target system are compared with those of the model galaxy at the position of the target stars, i.e. particles. The mass of the model particles are adjusted to reproduce the observables of the target system, and the gravitational potential is automatically adjusted by the changing mass of the particles. This paper builds upon our previous work, introducing likelihood-based velocity constraints in primal. In this paper, we apply primal to barred disc galaxies created by an N-body simulation in a known dark matter potential, with no error in the observables. This paper demonstrates that primal can recover the radial profiles of the surface density, velocity dispersion in the radial and perpendicular directions, and the rotational velocity of the target discs, along with the apparent bar structure and pattern speed of the bar, especially when the reference frame is adjusted so that the bar angle of the target galaxy is aligned to that of the model galaxy at every timestep.

The ongoing merger of the Sagittarius (Sgr) dwarf galaxy with the Milky Way is believed to strongly affect the dynamics of the Milky Way's disk. We present a suite of 13 N-body simulations, with 500 million-1 billion particles, modeling the interaction between the Sgr dwarf galaxy and the Galactic disk. To quantify the perturbation to the disk's structure and dynamics in the simulation, we compute the number count asymmetry and the mean vertical velocity in a solar-neighborhood-like volume. We find that, overall, the trends in the simulations match those seen in a simple one-dimensional model of the interaction. We explore the effects of changing the mass model of Sgr, the orbital kinematics of Sgr, and the mass of the Milky Way halo. We find that none of the simulations match the observations of the vertical perturbation using Gaia Data Release 2. In the simulation that is the most similar, we find that the final mass of Sgr far exceeds the observed mass of the Sgr remnant, the asymmetry wavelength is too large, and the shape of the asymmetry does not match past z approximate to 0.7 kpc. We therefore conclude that our simulations support the conclusion that Sgr alone could not have caused the observed perturbation to the solar neighborhood.

Gaia DR2 has provided an unprecedented wealth of information about the kinematics of stars in the Solar neighbourhood, and has highlighted the degree of features in the Galactic disc. We confront the data with a range of bar and spiral models in both action-angle space, and the R-G-v(phi) plane. We find that the phase mixing induced by transient spiral structure creates ridges and arches in the local kinematics which are consistent with the Gaia data. We are able to produce a qualitatively good match to the data when combined with a bar with a variety of pattern speeds, and show that it is non-trivial to decouple the effects of the bar and the spiral structure.

We have observed an N-body/smoothed particle hydrodynamics simulation of a Milky Way-like barred spiral galaxy. We present a simple method that samples N-body model particles into mock Gaia stellar observations and takes into account stellar populations, dust extinction and Gaia's science performance estimates. We examine the kinematics of stars with V

Gaia Data Release 2 revealed that the Milky Way contains significant indications of departures from equilibrium in the form of asymmetric features in the phase space density of stars in the Solar neighbourhood. One such feature is the z-v(z) phase spiral, interpreted as the response of the disc to the influence of a perturbation perpendicular to the disc plane, which could be external (e.g. a satellite) or internal (e.g. the bar or spiral arms). In this work, we use Gaia Data Release 3 to dissect the phase spiral by dividing the local data set into groups with similar azimuthal actions, Jf, and conjugate angles, theta(phi) which selects stars on similar orbits and at similar orbital phases, thus having experienced similar perturbations in the past. These divisions allow us to explore areas of the Galactic disc larger than the surveyed region. The separation improves the clarity of the z- v(z) phase spiral and exposes changes to its morphology across the different action-angle groups. In particular, we discover a transition to two armed `breathing spirals' in the inner Milky Way. We conclude that the local data contain signatures of not one, but multiple perturbations with the prospect to use their distinct properties to infer the properties of the interactions that caused them.

Discoveries of gaps in data have been important in astrophysics. For example, there are kinematic gaps opened by resonances in dynamical systems, or exoplanets of a certain radius that are empirically rare. A gap in a data set is a kind of anomaly, but in an unusual sense: instead of being a single outlier data point, situated far from other data points, it is a region of the space, or a set of points, that is anomalous compared to its surroundings. Gaps are both interesting and hard to find and characterize, especially when they have nontrivial shapes. We present in this paper a statistic that can be used to estimate the (local) "gappiness" of a point in the data space. It uses the gradient and Hessian of the density estimate (and thus requires a twice-differentiable density estimator). This statistic can be computed at (almost) any point in the space and does not rely on optimization; it allows us to highlight underdense regions of any dimensionality and shape in a general and efficient way. We illustrate our method on the velocity distribution of nearby stars in the Milky Way disk plane, which exhibits gaps that could originate from different processes. Identifying and characterizing those gaps could help determine their origins. We provide in an appendix implementation notes and additional considerations for finding underdensities in data, using critical points and the properties of the Hessian of the density.

We investigate the kinematic signatures induced by spiral and bar structure in a set of simulations of Milky Way-sized spiral disc galaxies. The set includes test particle simulations that follow a quasi-stationary density wave-like scenario with rigidly rotating spiral arms, and N-body simulations that host a bar and transient, corotating spiral arms. From a location similar to that of the Sun, we calculate the radial, tangential and line-of-sight peculiar velocity fields of a patch of the disc and quantify the fluctuations by computing the power spectrum from a two-dimensional Fourier transform. We find that the peculiar velocity power spectrum of the simulation with a bar and transient, corotating spiral arms fits very well to that of APOGEE red clump star data, while the quasi-stationary density wave spiral model without a bar does not. We determine that the power spectrum is sensitive to the number of spiral arms, spiral arm pitch angle and position with respect to the spiral arm. However, it is necessary to go beyond the line-of-sight velocity field in order to distinguish fully between the various spiral models with this method. We compute the power spectrum for different regions of the spiral discs, and discuss the application of this analysis technique to external galaxies.

Studies of the ages, abundances, and motions of individual stars in the Milky Way provide one of the best ways to study the evolution of disc galaxies over cosmic time. The formation of the Milky Way's barred inner region in particular is a crucial piece of the puzzle of disc galaxy evolution. Using data from APOGEE and Gaia, we present maps of the kinematics, elemental abundances, and age of the Milky Way bulge and disc that show the barred structure of the inner Milky Way in unprecedented detail. The kinematic maps allow a direct, purely kinematic determination of the bar's pattern speed of 41 +/- 3 km s(-1) kpc(-1) and of its shape and radial profile. We find the bar's age, metallicity, and abundance ratios to be the same as those of the oldest stars in the disc that are formed in its turbulent beginnings, while stars in the bulge outside of the bar are younger and more metal-rich. This implies that the bar likely formed approximate to 8 Gyr ago, when the decrease in turbulence in the gas disc allowed a thin disc to form that quickly became bar-unstable. The bar's formation therefore stands as a crucial epoch in the evolution of the Milky Way, a picture that is in line with the evolutionary path that emerges from observations of the gas kinematics in external disc galaxies over the last approximate to 10 Gyr.

In this work, we present two new similar to 10(9) particle self-consistent simulations of the merger of a Sagittarius-like dwarf galaxy with a Milky Way (MW)-like disc galaxy. One model is a violent merger creating a thick disc, and a Gaia-Enceladus/Sausage-like remnant. The other is a highly stable disc which we use to illustrate how the improved phase space resolution allows us to better examine the formation and evolution of structures that have been observed in small, local volumes in the MW, such as the z-v(z) phase spiral and clustering in the v(R)-v(phi) plane when compared to previous works. The local z-v(z) phase spirals are clearly linked to the global asymmetry across the disc: we find both 2-armed and 1-armed phase spirals, which are related to breathing and bending behaviours, respectively. Hercules-like moving groups are common, clustered in v(R)-v(phi) in local data samples in the simulation. These groups migrate outwards from the inner galaxy, matching observed metallicity trends even in the absence of a galactic bar. We currently release the best-fitting 'present-day' merger snapshots along with the unperturbed galaxies for comparison.

Amongst dynamical modelling techniques, the made-to-measure (M2M) method for modelling steady-state systems is amongst the most flexible, allowing non-parametric distribution functions in complex gravitational potentials to be modelled efficiently using N-body particles. Here, we propose and test various improvements to the standard M2M method for modelling observed data, illustrated using the simple set-up of a one-dimensional harmonic oscillator. We demonstrate that nuisance parameters describing the modelled system's orientation with respect to the observer - e.g. an external galaxy's inclination or the Sun's position in the Milky Way-as well as the parameters of an external gravitational field can be optimized simultaneously with the particle weights. We develop a method for sampling from the high-dimensional uncertainty distribution of the particle weights. We combine this in a Gibbs sampler with samplers for the nuisance and potential parameters to explore the uncertainty distribution of the full set of parameters. We illustrate our M2M improvements by modelling the vertical density and kinematics of F-type stars in Gaia DR1. The novel M2M method proposed here allows full probabilistic modelling of steady-state dynamical systems, allowing uncertainties on the non-parametric distribution function and on nuisance parameters to be taken into account when constraining the dark and baryonic masses of stellar systems.

We have developed a novel Markov Chain Monte Carlo chemical 'painting' technique to explore possible radial and vertical metallicity gradients for the thick disc progenitor. In our analysis, we match an N-body simulation to the data from the Apache Point Observatory Galactic Evolution Experiment survey. We assume that the thick disc has a constant scaleheight and has completed its formation at an early epoch, after which time radial mixing of its stars has taken place. Under these assumptions, we find that the initial radial metallicity gradient of the thick disc progenitor should not be negative, but either flat or even positive, to explain the current negative vertical metallicity gradient of the thick disc. Our study suggests that the thick disc was built-up in an inside-out and upside-down fashion, and older, smaller and thicker populations are more metal poor. In this case, star-forming discs at different epochs of the thick disc formation are allowed to have different radial metallicity gradients, including a negative one, which helps to explain a variety of slopes observed in high-redshift disc galaxies. This scenario helps to explain the positive slope of the metallicity-rotation velocity relation observed for the Galactic thick disc. On the other hand, radial mixing flattens the slope of an existing gradient.

The second data release from ESA's Gaia mission has revealed many ridge-like structures in the velocity distribution of the Milky Way. We show that these can arise naturally from winding transient spiral structure that is commonly seen in N-body simulations of disc galaxies. We construct test particle models of the winding spiral structure, and compare the resulting distribution of orbits with the observed two-dimensional velocity distribution in the extended solar neighbourhood and with the distribution of rotational velocities over 8 kpc along the Sun-Galactic-centre-Galactic anticentre line. We show that the ridges in these observations are well reproduced by the winding spiral model. Additionally, we demonstrate that the transient winding spiral potential can create a Hercules-like feature in the kinematics of the solar neighbourhood, either alone, or in combination with a long-slow bar potential.

This paper documents the 16th data release (DR16) from the Sloan Digital Sky Surveys (SDSS), the fourth and penultimate from the fourth phase (SDSS-IV). This is the first release of data from the Southern Hemisphere survey of the Apache Point Observatory Galactic Evolution Experiment 2 (APOGEE-2); new data from APOGEE-2 North are also included. DR16 is also notable as the final data release for the main cosmological program of the Extended Baryon Oscillation Spectroscopic Survey (eBOSS), and all raw and reduced spectra from that project are released here. DR16 also includes all the data from the Time Domain Spectroscopic Survey and new data from the SPectroscopic IDentification of ERosita Survey programs, both of which were co-observed on eBOSS plates. DR16 has no new data from the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey (or the MaNGA Stellar Library "MaStar"). We also preview future SDSS-V operations (due to start in 2020), and summarize plans for the final SDSS-IV data release (DR17).

Signatures of vertical disequilibrium have been observed across the Milky Way's (MW's) disk. These signatures manifest locally as unmixed phase spirals in z-v ( z ) space ("snails-in-phase"), and globally as nonzero mean z and v ( z ), wrapping around the disk into physical spirals in the x-y plane ("snails-in-space"). We explore the connection between these local and global spirals through the example of a satellite perturbing a test-particle MW-like disk. We anticipate our results to broadly apply to any vertical perturbation. Using a z-v ( z ) asymmetry metric, we demonstrate that in test-particle simulations: (a) multiple local phase-spiral morphologies appear when stars are binned by azimuthal action J ( phi ), excited by a single event (in our case, a satellite disk crossing); (b) these distinct phase spirals are traced back to distinct disk locations; and (c) they are excited at distinct times. Thus, local phase spirals offer a global view of the MW's perturbation history from multiple perspectives. Using a toy model for a Sagittarius (Sgr)-like satellite crossing the disk, we show that the full interaction takes place on timescales comparable to orbital periods of disk stars within R less than or similar to 10 kpc. Hence such perturbations have widespread influence, which peaks in distinct regions of the disk at different times. This leads us to examine the ongoing MW-Sgr interaction. While Sgr has not yet crossed the disk (currently, z (Sgr) approximate to -6 kpc, v ( z,Sgr) approximate to 210 km s(-1)), we demonstrate that the peak of the impact has already passed. Sgr's pull over the past 150 Myr creates a global v ( z ) signature with amplitude proportional to M (Sgr), which might be detectable in future spectroscopic surveys.

Abstract The Hercules stream is a group of comoving stars in the solar neighbourhood, which can potentially be explained as a signature of either the outer Lindblad resonance (OLR) of a fast Galactic bar or the corotation resonance (CR) of a slower bar. In either case, the feature should be present over a large area of the disc. With the recent commissioning of the APOGEE-2 Southern spectrograph we can search for the Hercules stream at (l, b) = (270°, 0), a direction in which the Hercules stream, if caused by the bar's OLR, would be strong enough to be detected using only the line-of-sight velocities. We clearly detect a narrow, Hercules-like feature in the data that can be traced from the solar neighbourhood to a distance of about 4 kpc. The detected feature matches well the line-of-sight velocity distribution from the fast-bar (OLR) model. Confronting the data with a model where the Hercules stream is caused by the CR of a slower bar leads to a poorer match, as the corotation model does not predict clearly separated modes, possibly because the slow-bar model is too hot.

In the coming decade, thousands of stellar streams will be observed in the halos of external galaxies. What fundamental discoveries will we make about dark matter from these streams? As a first attempt to look at these questions, we model Magellan/Megacam imaging of the Centaurus A (Cen A) disrupting dwarf companion Dwarf 3 (Dw3) and its associated stellar stream, to find out what can be learned about the Cen A dark matter halo. We develop a novel external galaxy stream-fitting technique and generate model stellar streams that reproduce the stream morphology visible in the imaging. We find that there are many viable stream models that fit the data well, with reasonable parameters, provided that Cen A has a halo mass larger than M (200) > 4.70 x 10(12) M (circle dot). There is a second stream in Cen A's halo that is also reproduced within the context of this same dynamical model. However, stream morphology in the imaging alone does not uniquely determine the mass or mass distribution for the Cen A halo. In particular, the stream models with high likelihood show covariances between the inferred Cen A mass distribution, the inferred Dw3 progenitor mass, the Dw3 velocity, and the Dw3 line-of-sight position. We show that these degeneracies can be broken with radial-velocity measurements along the stream, and that a single radial velocity measurement puts a substantial lower limit on the halo mass. These results suggest that targeted radial-velocity measurements will be critical if we want to learn about dark matter from extragalactic stellar streams.

The length and pattern speed of the Milky Way bar are still controversial. Photometric and spectroscopic surveys of the inner Galaxy, as well as gas kinematics, favour a long and slowly rotating bar, with corotation around a Galactocentric radius of 6 kpc. On the other hand, the existence of the Hercules stream in local velocity space favours a short and fast bar with corotation around 4 kpc. This follows from the fact that the Hercules stream looks like a typical signature of the outer Lindblad resonance of the bar. As we showed recently, reconciling this local stream with a slow bar would need to find a yet unknown alternative explanation, based, for instance, on the effect of spiral arms. Here, by combining the TGAS catalogue of the Gaia DR1 with LAMOST radial velocities, we show that the position of Hercules in velocity space as a function of radius in the outer Galaxy indeed varies exactly as predicted by fast bar models with a pattern speed no less than 1.8 times the circular frequency at the Sun's position.

We have observed a snapshot of our N-body/smoothed particle hydrodynamics simulation of a Milky Way-sized barred spiral galaxy in a similar way to how we can observe the Milky Way. The simulated galaxy shows a corotating spiral arm, i.e. the spiral arm rotates with the same speed as the circular speed. We observed the rotation and radial velocities of the gas and stars as a function of the distance from our assumed location of the observer at the three lines of sight on the disc plane, (l, b) = (90, 0), (120, 0) and (150, 0) deg. We find that the stars tend to rotate slower (faster) behind (at the front of) the spiral arm and move outwards (inwards), because of the radial migration. However, because of their epicycle motion, we see a variation of rotation and radial velocities around the spiral arm. On the other hand, the cold gas component shows a clearer trend of rotating slower (faster) and moving outwards (inwards) behind (at the front of) the spiral arm, because of the radial migration. We have compared the results with the velocity of the maser sources from Reid et al., and find that the observational data show a similar trend in the rotation velocity around the expected position of the spiral arm at l = 120 deg. We also compared the distribution of the radial velocity from the local standard of the rest, V-LSR, with the Apache Point Observatory Galactic Evolution Experiment (APOGEE) data at l = 90 deg as an example.

Using idealized N-body simulations of a Milky Way-sized disc galaxy, we qualitatively study how the metallicity distributions of the thin disc star particles are modified by the formation of the bar and spiral arm structures. The thin disc in our numerical experiments initially has a tight negative radial metallicity gradient and a constant vertical scaleheight. We show that the radial mixing of stars drives a positive vertical metallicity gradient in the thin disc. On the other hand, if the initial thin disc is flared, with vertical scaleheight increasing with galactocentric radius, the metal-poor stars, originally in the outer disc, become dominant in regions above the disc plane at every radii. This process can drive a negative vertical metallicity gradient, which is consistent with the current observed trend. This model mimics a scenario where the star-forming thin disc was flared in the outer region at earlier epochs. Our numerical experiment with an initial flared disc predicts that the negative vertical metallicity gradient of the mono-age relatively young thin disc population should be steeper in the inner disc, and the radial metallicity gradient of the mono-age population should be shallower at greater heights above the disc plane. We also predict that the metallicity distribution function of mono-age young thin disc populations above the disc plane would be more positively skewed in the inner disc compared to the outer disc.

We make use of APOGEE and Gaia data to identify stars that are consistent with being born in the same association or star cluster as the Sun. We limit our analysis to stars that match solar abundances within their uncertainties, as they could have formed from the same giant molecular cloud (GMC) as the Sun. We constrain the range of orbital actions that solar siblings can have with a suite of simulations of solar birth clusters evolved in static and time-dependent tidal fields. The static components of each galaxy model are the bulge, disc, and halo, while the various time-dependent components include a bar, spiral arms, and GMCs. In galaxy models without GMCs, simulated solar siblings all have J(R) < 122 km s(-1) kpc, 990 < L-z < 1986 km s(-1) kpc, and 0.15 < J(z) < 0.58 km s(-1) kpc. Given the actions of stars in APOGEE and Gaia , we find 104 stars that fall within this range. One candidate in particular, Solar Sibling 1, has both chemistry and actions similar enough to the solar values that strong interactions with the bar or spiral arms are not required for it to be dynamically associated with the Sun. Adding GMCs to the potential can eject solar siblings out of the plane of the disc and increase their J(z), resulting in a final candidate list of 296 stars. The entire suite of simulations indicate that solar siblings should have J(R) < 122 km s(-1) kpc, 353 < L-z < 2110 km s(-1) kpc, and J(z) < 0.8 km s(-1) kpc. Given these criteria, it is most likely that the association or cluster that the Sun was born in has reached dissolution and is not the commonly cited open cluster M67.

Using a numerical simulation of an isolated barred disc galaxy, we first demonstrate that the resonances of the inner bar structure induce more prominent features in the action space distribution for the kinematically hotter stars, which are less sensitive to the local perturbation, such as the transient spiral arms. Then, we analyse the action distribution for the kinematically hotter stars selected from the Gaia EDR3 data as the stars with higher values of radial and vertical actions. We find several resonance features, including two new features, in the angular momentum distribution similar to what are seen in our numerical simulations. We show that the bar pattern speeds of about Omega(bar) similar to 34 and 42 km s(-1) kpc(-1) explain all these features equally well. The resonance features we find correspond to the inner 4:1, co-rotation (CR), outer 4:1, outer Lindblad, and outer 4:3 (CR, outer 4:1, outer Lindblad, outer 4:3, and outer 1:1) resonances, when Omega(bar )similar to 34 (42) km s(-1) kpc(-1) is assumed.

We report on the detection of a small overdensity of stars in velocity space with systematically higher Galactocentric rotation velocity than the Sun by about 20 km s(-1) in the Gaia Data Release 1 Tycho-Gaia astrometric solution data. We find these fast Galactic rotators more clearly outside of the Solar radius, compared to inside of the Solar radius. In addition, the velocity of the fast Galactic rotators is independent of the Galactocentric distance up to R - R0 similar to 0.6 kpc. Comparing with numerical models, we qualitatively discuss that a possible cause of this feature is the co-rotation resonance of the Perseus spiral arm, where the stars in the peri-centre phase in the trailing side of the Perseus spiral arm experience an extended period of acceleration owing to the torque from the Perseus arm.

We present and analyse mock stellar catalogues that match the selection criteria and observ-ables (including uncertainties) of the Gaia satellite data release 2 (DR2). The source are six cosmological high-resolution magneto-hydrodynamic ACDM zoom simulations of the formation of Milky Way analogues from the AURIGA project. Mock data are provided for stars with V < 16 mag and V < 20 mag at vertical bar b vertical bar > 20 deg. The mock catalogues are made using two different methods: the public SNAPDRAGONS code, and a method based on that of Lowing et al. (2015) that preserves the phase-space distribution of the model stars. These publicly available catalogues contain five-parameter astrometry, radial velocities, multiband photometry, stellar parameters, dust extinction values, and uncertainties in all these quantities. In addition, we provide the gravitational potential and information on the origin of each star. By way of demonstration, we apply the mock catalogues to analyses of the young stellar disc and the stellar halo. We show that (i) the young outer stellar disc exhibits a flared distribution that is detectable in the height and vertical velocity distribution of A- and B-dwarf stars up to radii of similar to 15 kpc, and (ii) the spin of the stellar halo out to 100 kpc can be accurately measured with Gala DR2 RR Lyrae stars. These catalogues are well suited for comparisons with observations and should help to (i) develop and test analysis methods for the Gaia DR2 data, (ii) gauge the limitations and biases of the data, and (iii) interpret the data in the light of theoretical predictions from realistic ab initio simulations of galaxy formation in the ACDM cosmological model.

The mean Galactocentric radial velocities of luminous red giant stars within the midplane of the Milky Way reveal a spiral signature, which could plausibly reflect the response to a nonaxisymmetric perturbation of the gravitational potential in the Galactic disk. We apply a simple steady-state toy model of a logarithmic spiral to interpret these observations, and find a good qualitative and quantitative match. Presuming that the amplitude of the gravitational potential perturbation is proportionate to that in the disk's surface mass density, we estimate the surface mass density amplitude to be at the solar radius when choosing a fixed pattern speed of . Combined with the local disk density, this implies a surface mass density contrast between the arm and inter-arm regions of approximately 10% at the solar radius, with an increase toward larger radii. Our model constrains the pitch angle of the dynamical spiral arms to be approximately 12°.

ABSTRACT We report on the detection in the combined Gaia-DR1/RAVE data of a lack of disk stars in the solar neighborhood with velocities close to zero angular momentum. We propose that this may be caused by the scattering of stars with very low angular momentum onto chaotic, halo-type orbits when they pass through the Galactic nucleus. We model the effect in a Milky Way-like potential and fit the resulting model directly to the data, finding a likelihood ( ) of a dip in the distribution. Using this effect, we can make a dynamical measurement of the solar rotation velocity around the Galactic center: . Combined with the measured proper motion of Sgr A*, this measurement gives a measurement of the distance to the Galactic center: .

By taking advantage of the superbmeasurements of position and velocity for an unprecedented large number of stars provided in Gaia DR2, we have generated the first maps of the rotation velocity, V-rot, and vertical velocity, V-z, distributions as a function of the Galactocentric radius, R-gal, across a radial range of 5 < R-gal < 12 kpc. In the R - V-rot map, we have identified many diagonal ridge features, which are compared with the location of the spiral arms and the expected outer Lindblad resonance of the Galactic bar. We have detected also radial wave-like oscillations of the peak of the vertical velocity distribution.

We have adapted our made-to-measure (M2M) algorithm PRIMAL to use mock Milky Way like data constructed from an N-body barred galaxy with a boxy bulge in a known dark matter potential. We use M0 giant stars as tracers, with the expected error of the ESA (European Space Agency) space astrometry mission Gaia. We demonstrate the process of constructing mock Gaia data from an N-body model, including the conversion of a galactocentric Cartesian coordinate N-body model into equatorial coordinates and how to add error to it for a single stellar type. We then describe the modifications made to PRIMAL to work with observational error. This paper demonstrates that PRIMAL can recover the radial profiles of the surface density, radial velocity dispersion, vertical velocity dispersion and mean rotational velocity of the target disc, along with the pattern speed of the bar, to a reasonable degree of accuracy despite the lack of accurate target data. We also construct mock data which take into account dust extinction and show that PRIMAL recovers the structure and kinematics of the disc reasonably well. In other words, the expected accuracy of the Gaia data is good enough for PRIMAL to recover these global properties of the disc, at least in a simplified condition, as used in this paper.