# Publications by James Binney

## Trapped orbits and solar-neighbourhood kinematics

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY 495 (2020) 895-904

J Binney

## Angle-action variables for orbits trapped at a Lindblad resonance

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY 495 (2020) 886-894

J Binney

## Relaxation of spherical stellar systems

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY 490 (2019) 478-490

JY Lau, J Binney

## Action-based models for dwarf spheroidal galaxies and globular clusters

Monthly Notices of the Royal Astronomical Society Oxford University Press 488 (2019) 2423-2439

R Pascale, J Binney, C Nipoti, L Posti

A new family of self-consistent distribution function (DF)-based models of stellar systems is explored. The stellar component of the models is described by a DF depending on the action integrals, previously used to model the Fornax dwarf spheroidal galaxy (dSph). The stellar component may cohabit with either a dark halo, also described by a DF, or with a massive central black hole. In all cases we solve for the models self-consistent potential. Focussing on spherically symmetric models, we show how the stellar observables vary with the anisotropy prescribed by the DF, with the dominance and nature of the dark halo, and with the mass of the black hole. We show that precise fits to the observed surface brightness profiles of four globular clusters can be obtained for a wide range of prescribed velocity anisotropies. We also obtain precise fits to the observed projected densities of four dSphs. Finally, we present a three-component model of the Sculptor dSph with distinct DFs for the red and blue horizontal branch stars and the dark matter halo.

## The GALAH survey and Gaia DR2: dissecting the stellar disc's phase space by age, action, chemistry, and location

Monthly Notices of the Royal Astronomical Society Oxford University Press 486 (2019) 1167-1191

J Bland-Hawthorn, S Sharma, T Tepper-Garcia, J Binney, KC Freeman, J Kos, D De Silva, S Ellis, GF Lewis, M Asplund, S Buder, AR Casey, V D'Orazi, L Duong, S Khanna, J Lin, K Lind, SL Martell, MK Ness, JD Simpson, DB Zucker, T Zwitter, PR Kafle, AC Quillen

We use the second data releases of the European Space AgencyGaia astrometric survey and the high-resolution Galactic Archaeology with HERMES (GALAH) spectroscopic survey to analyse the structure of our Galaxy’s disc components. With GALAH, we separate the α-rich and α-poor discs (with respect to Fe), which are superposed in both position and velocity space, and examine their distributions in action space. We study the distribution of stars in the zVz phase plane, for both Vϕ and VR, and recover the remarkable ‘phase spiral’ discovered by Gaia. We identify the anticipated quadrupole signature in zVz of a tilted velocity ellipsoid for stars above and below the Galactic plane. By connecting our work with earlier studies, we show that the phase spiral is likely to extend well beyond the narrow solar neighbourhood cylinder in which it was found. The phase spiral is a signature of corrugated waves that propagate through the disc, and the associated non-equilibrium phase mixing. The radially asymmetric distribution of stars involved in the phase spiral reveals that the corrugation, which is mostly confined to the α-poor disc, grows in z-amplitude with increasing radius. We present new simulations of tidal disturbance of the Galactic disc by the Sagittarius (Sgr) dwarf. The effect on the zVz phase plane lasts ≳2Gyr⁠, but a subsequent disc crossing wipes out the coherent structure. We find that the phase spiral was excited ≲0.5Gyr ago by an object like Sgr with total mass ∼3 × 1010 M⊙ (stripped down from ∼5 × 1010 M⊙ when it first entered the halo) passing through the plane.

## The origin of the Gaia phase-plane spiral

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY 481 (2018) 1501-1506

J Binney, R Schonrich

## Models of rotating coronae

Monthly Notices of the Royal Astronomical Society Oxford University Press 481 (2018) 3370-3381

MC Sormani, E Sobacchi, G Pezzulli, J Binney, RS Klessen

Fitting equilibrium dynamical models to observational data is an essential step in understanding the structure of the gaseous hot haloes that surround our own and other galaxies. However, the two main categories of models that are used in the literature are poorly suited for this task: (i) simple barotropic models are analytic and can therefore be adjusted to match the observations, but are clearly unrealistic because the rotational velocity vϕ(R, z⁠) does not depend on the distance z from the galactic plane, while (ii) models obtained as a result of cosmological galaxy formation simulations are more realistic, but are impractical to fit to observations due to high computational cost. Here we bridge this gap by presenting a general method to construct axisymmetric baroclinic equilibrium models of rotating galactic coronae in arbitrary external potentials. We consider in particular a family of models whose equipressure surfaces in the (R, z⁠) plane are ellipses of varying axis ratio. These models are defined by two one-dimensional functions, the axial ratio of pressure qaxis(⁠z⁠) and the value of the pressure Paxis(⁠z⁠) along the galaxy’s symmetry axis. These models can have a rotation speed vϕ(R, z⁠) that realistically decreases as one moves away from the galactic plane, and can reproduce the angular momentum distribution found in cosmological simulations. The models are computationally cheap to construct and can thus be used in fitting algorithms. We provide a python code that given qaxis(⁠z⁠), Paxis(⁠z⁠), and Φ(R, z⁠) returns ρ(R, z⁠), T(R, z⁠), P(R, z⁠), vϕ(R, z⁠). We show a few examples of these models using the Milky Way as a case study.

## Revisiting relaxation in globular clusters

Monthly Notices of the Royal Astronomical Society Oxford University Press 481 (2018) 2041-2061

C Hamilton, J-B Fouvry, J Binney, C Pichon

The classical theory of cluster relaxation is unsatisfactory because it involves the Coulomb logarithm. The Balescu–Lenard (BL) equation provides a rigorous alternative that has no ill-defined parameter. Moreover, the BL equation, unlike classical theory, includes the cluster’s self-gravity. A heuristic argument is given that indicates that relaxation does not occur predominantly through two-particle scattering and is enhanced by self-gravity. The BL equation is adapted to a spherical system and used to estimate the flux through the action space of isochrone clusters with different velocity anisotropies. A range of fairly different secular behaviours is found depending on the fraction of radial orbits. Classical theory is also used to compute the corresponding classical fluxes. The BL and classical fluxes are very different because (a) the classical theory materially underestimates the impact of large-scale collectively amplified fluctuations and (b) only the leading terms in an infinite sum for the BL flux are computed. A complete theory of cluster relaxation likely requires that the sum in the BL equation be decomposed into a sum over a finite number of small wavenumbers complemented by an integral over large wavenumbers analogous to classical theory.

## Action-based dynamical models of dwarf spheroidal galaxies: application to Fornax

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY 480 (2018) 927-946

R Pascale, L Posti, C Nipoti, J Binney

## Improved distances and ages for stars common to TGAS and RAVE

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY 477 (2018) 5279-5300

PJ McMillan, G Kordopatis, A Kunder, J Binney, J Wojno, T Zwitter, M Steinmetz, J Bland-Hawthorn, BK Gibson, G Gilmore, EK Grebel, A Helmi, U Munari, JF Navarro, QA Parker, G Seabroke, F Watson, RFG Wyse

## Correlations between age, kinematics, and chemistry as seen by the RAVE survey

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY 477 (2018) 5612-5624

J Wojno, G Kordopatis, M Steinmetz, P McMillan, J Binney, B Famaey, G Monari, I Minchev, RFG Wyse, T Antoja, A Siebert, I Carrillo, J Bland-Hawthorn, EK Grebel, T Zwitter, O Bienayme, B Gibson, A Kunder, U Munari, J Navarro, Q Parker, W Reid, G Seabroke

## A theoretical explanation for the Central Molecular Zone asymmetry

Monthly Notices of the Royal Astronomical Society Oxford University Press 475 (2017) 2383-2402

MC Sormani, R Tress, M Ridley, SCO Glover, RS Klessen, J Binney, S Magorrian, R Smith

It has been known for more than thirty years that the distribution of molecular gas in the innermost 300 parsecs of the Milky Way, the Central Molecular Zone, is strongly asymmetric. Indeed, approximately three quarters of molecular emission comes from positive longitudes, and only one quarter from negative longitudes. However, despite much theoretical effort, the origin of this asymmetry has remained a mystery. Here we show that the asymmetry can be neatly explained by unsteady flow of gas in a barred potential. We use high-resolution 3D hydrodynamical simulations coupled to a state-of-the-art chemical network. Despite the initial conditions and the bar potential being point-symmetric with respect to the Galactic Centre, asymmetries develop spontaneously due to the combination of a hydrodynamical instability known as the “wiggle instability” and the thermal instability. The observed asymmetry must be transient: observations made tens of megayears in the past or in the future would often show an asymmetry in the opposite sense. Fluctuations of amplitude comparable to the observed asymmetry occur for a large fraction of the time in our simulations, and suggest that the present is not an exceptional moment in the life of our Galaxy.

## Is the Milky Way still breathing? RAVE-Gaia streaming motions

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY 475 (2018) 2679-2696

I Carrillo, I Minchev, G Kordopatis, M Steinmetz, J Binney, F Anders, O Bienayme, J Bland-Hawthorn, B Famaey, KC Freeman, G Gilmore, BK Gibson, EK Grebel, A Helmi, A Just, A Kunder, P McMillan, G Monari, U Munari, J Navarro, QA Parker, W Reid, G Seabroke, S Sharma, A Siebert, F Watson, J Wojno, RFG Wyse, T Zwitter

## Self-consistent modelling of our Galaxy with Gaia data

Proceedings of the International Astronomical Union Cambridge University Press 12 (2018) 111-118

J Binney

Galaxy models are fundamental to exploiting surveys of our Galaxy. There is now a significant body of work on axisymmetric models. A model can be defined by giving the DF of each major class of stars and of dark matter. Then the self-consistent gravitational potential is determined. Other modelling techniques are briefly considered before an overview of some early work on non-axisymmetric models.

## Distribution functions for resonantly trapped orbits in the Galactic disc

Monthly Notices of the Royal Astronomical Society Oxford University Press 471 (2017) 4314-4322

G Monari, B Famaey, J-B Fouvry, J Binney

The present-day response of a Galactic disc stellar population to a non-axisymmetric perturbation of the potential has previously been computed through perturbation theory within the phase-space coordinates of the unperturbed axisymmetric system. Such an Eulerian linearized treatment, however, leads to singularities at resonances, which prevent quantitative comparisons with data. Here, we manage to capture the behaviour of the distribution function (DF) at a resonance in a Lagrangian approach, by averaging the Hamiltonian over fast angle variables and re-expressing the DF in terms of a new set of canonical actions and angles variables valid in the resonant region. We then follow the prescription of Binney, assigning to the resonant DF the time average along the orbits of the axisymmetric DF expressed in the new set of actions and angles. This boils down to phase-mixing the DF in terms of the new angles, such that the DF for trapped orbits depends only on the new set of actions. This opens the way to quantitatively fitting the effects of the bar and spirals to Gaia data in terms of DFs in action space.

## Migration and kinematics in growing disc galaxies with thin and thick discs

Monthly Notices of the Royal Astronomical Society Oxford University Press 470 (2017) 3685-3706

M Aumer, J Binney, R Schoenrich

We analyse disc heating and radial migration in N-body models of growing disc galaxies with thick and thin discs. Similar to thin-disc-only models, galaxies with appropriate non-axisymmetric structures reproduce observational constraints on radial disc heating in and migration to the Solar Neighbourhood (Snhd). The presence of thick discs can suppress non-axisymmetries and thus higher baryonic-to-dark matter fractions are required than in models that only have a thin disc. Models that are baryon-dominated to roughly the Solar radius R0 are favoured, in agreement with data for the Milky Way. For inside-out growing discs, today’s thick-disc stars at R0 are dominated by outwards migrators. Whether outwards migrators are vertically hotter than non-migrators depends on the radial gradient of the thick disc vertical velocity dispersion. There is an effective upper boundary in angular momentum that thick disc stars born in the centre of a galaxy can reach by migration, which explains the fading of the high [α/Fe] sequence outside R0. Our models compare well to Snhd kinematics from RAVE-TGAS. For such comparisons it is important to take into account the azimuthal variation of kinematics at R ∼ R0 and biases from survey selection functions. The vertical heating of thin disc stars by giant molecular clouds is only mildly affected by the presence of thick discs. Our models predict higher vertical velocity dispersions for the oldest stars than found in the Snhd age velocity dispersion relation, possibly because of measurement uncertainties or an underestimation of the number of old cold stars in our models.

## The structural evolution of galaxies with both thin and thick discs

Monthly Notices of the Royal Astronomical Society Oxford University Press 470 (2017) 2113-2132

M Aumer, J Binney

We perform controlled N-body simulations of disc galaxies growing within live dark matter (DM) haloes to present-day galaxies that contain both thin and thick discs. We consider two types of models: a) thick disc initial conditions to which stars on near-circular orbits are continuously added over ∼ 10 Gyr, and b) models in which the birth velocity dispersion of stars decreases continuously over the same timescale. We show that both schemes produce double-exponential vertical profiles similar to that of the Milky Way (MW). We indicate how the spatial age structure of galaxies can be used to discriminate between scenarios. We show that the presence of a thick disc significantly alters and delays bar formation and thus makes possible models with a realistic bar and a high baryon-to-DM mass ratio in the central regions, as required by microlensing constraints. We examine how the radial mass distribution in stars and DM is affected by disc growth and non-axisymmetries. We discuss how bar buckling shapes the vertical age distribution of thin and thick disc stars in the bar region. The extent to which the combination of observationally motivated inside-out growth histories and cosmologically motivated dark halo properties leads to the spontaneous formation of non-axisymmetries which steer the models towards present-day MW-like galaxies is noteworthy.

## PLATO as it is : A legacy mission for Galactic archaeology

Astronomische Nachrichten Wiley 338 (2017) 644-661

A Miglio, C Chiappini, B Mosser, GR Davies, K Freeman, L Girardi, P Jofré, D Kawata, BM Rendle, M Valentini, L Casagrande, WJ Chaplin, G Gilmore, K Hawkins, B Holl, T Appourchaux, K Belkacem, D Bossini, K Brogaard, M-J Goupil, J Montalbán, A Noels, F Anders, T Rodrigues, G Piotto

Deciphering the assembly history of the Milky Way is a formidable task, which becomes possible only if one can produce high-resolution chrono-chemo-kinematical maps of the Galaxy. Data from large-scale astrometric and spectroscopic surveys will soon provide us with a well-defined view of the current chemo-kinematical structure of the Milky Way, but it will only enable a blurred view on the temporal sequence that led to the present-day Galaxy. As demonstrated by the (ongoing) exploitation of data from the pioneering photometric missions CoRoT, Kepler, and K2, asteroseismology provides the way forward: solar-like oscillating giants are excellent evolutionary clocks thanks to the availability of seismic constraints on their mass and to the tight age–initial mass relation they adhere to. In this paper we identify five key outstanding questions relating to the formation and evolution of the Milky Way that will need precise and accurate ages for large samples of stars to be addressed, and we identify the requirements in terms of number of targets and the precision on the stellar properties that are needed to tackle such questions. By quantifying the asteroseismic yields expected from PLATO for red giant stars, we demonstrate that these requirements are within the capabilities of the current instrument design, provided that observations are sufficiently long to identify the evolutionary state and allow robust and precise determination of acoustic-mode frequencies. This will allow us to harvest data of sufficient quality to reach a 10% precision in age. This is a fundamental prerequisite to then reach the more ambitious goal of a similar level of accuracy, which will be possible only if we have at hand a careful appraisal of systematic uncertainties on age deriving from our limited understanding of stellar physics, a goal that conveniently falls within the main aims of PLATO's core science. We therefore strongly endorse PLATO's current design and proposed observational strategy, and conclude that PLATO, as it is, will be a legacy mission for Galactic archaeology.

## The selection function of the RAVE survey

Monthly Notices of the Royal Astronomical Society Oxford University Press 468 (2017) 3368-3380

J Wojno, G Kordopatis, T Piffl, JJ Binney, M Steinmetz, G Matijevič, J Bland-Hawthorn, S Sharma, P McMillan, F Watson, W Reid, A Kunder, H Enke, EK Grebel, G Seabroke, RFG Wyse, T Zwitter, O Bienaymé, KC Freeman, BK Gibson, G Gilmore, A Helmi, U Munari, JF Navarro, QA Parker

We characterize the selection function of RAVE using 2MASS as our underlying population, which we assume represents all stars which could have potentially been observed. We evaluate the completeness fraction as a function of position, magnitude, and color in two ways: first, on a field-by-field basis, and second, in equal-size areas on the sky. Then, we consider the effect of the RAVE stellar parameter pipeline on the final resulting catalogue, which in principle limits the parameter space over which our selection function is valid. Our final selection function is the product of the completeness fraction and the selection function of the pipeline. We then test if the application of the selection function introduces biases in the derived parameters. To do this, we compare a parent mock catalogue generated using Galaxia with a mock-RAVE catalogue where the selection function of RAVE has been applied. We conclude that for stars brighter than I = 12, between $4000 \rm K &lt; T_{\rm eff} &lt; 8000 \rm K$ and $0.5 &lt; \rm{log}\,g &lt; 5.0$, RAVE is kinematically and chemically unbiased with respect to expectations from Galaxia.

## The Radial Velocity Experiment (RAVE): Fifth data release

Astronomical Journal Institute of Physics 153 (2017) 75-

P Jofre, T Antoja, G Gilmore, A Siebert, B Famaey, O Bienaymé, BK Gibson, KC Freeman, JF Navarro, U Munari, G Seabroke, B Anguiano, M Žerjal, I Minchev, W Reid, J Bland-Hawthorn, J Kos, S Sharma, F Watson, QA Parker, R-D Scholz, D Burton, P Cass, M Hartley, K Fiegert

<p>Data Release 5 (DR5) of the Radial Velocity Experiment (RAVE) is the fifth data release from a magnitude-limited (9 &lt; I &lt; 12) survey of stars randomly selected in the Southern Hemisphere. The RAVE medium-resolution spectra (R ~ 7500) covering the Ca-triplet region (8410–8795 Å) span the complete time frame from the start of RAVE observations in 2003 to their completion in 2013. Radial velocities from 520,781 spectra of 457,588 unique stars are presented, of which 255,922 stellar observations have parallaxes and proper motions from the Tycho-Gaia astrometric solution in Gaia DR1. For our main DR5 catalog, stellar parameters (effective temperature, surface gravity, and overall metallicity) are computed using the RAVE DR4 stellar pipeline, but calibrated using recent K2 Campaign 1 seismic gravities and Gaia benchmark stars, as well as results obtained from high-resolution studies. Also included are temperatures from the Infrared Flux Method, and we provide a catalog of red giant stars in the dereddened color - J Ks0 ( ) interval (0.50, 0.85) for which the gravities were calibrated based only on seismology. Further data products for subsamples of the RAVE stars include individual abundances for Mg, Al, Si, Ca, Ti, Fe, and Ni, and distances found using isochrones. Each RAVE spectrum is complemented by an error spectrum, which has been used to determine uncertainties on the parameters. The data can be accessed via the RAVE Web site or the VizieR database.</p>